Real Value Valuation for Real Estate Investments

Real Value Valuation for Real Estate Investments (Jefferies, 2017)

Real Value Valuation for Real Estate Investments A concise explanatory text of the complete All-Risks Real Yield (ARRY) Investment Property Valuation and Analysis Model in theory, practice and applications .

By

Rodney Lynn Jefferies BCA Vict., GradDipProp Auck., DipUrbVal Auck., FNZIV(Life), LPNZ

October, 2017 Contact: [email protected]


Abstract A generic real value valuation model presented for property investment analysis and valuation. The model uses a new ‘real value’ all-risks real yield (ARRY) methodology for analysing sales of commercially leased properties and their valuation where current sales prices / market value represents the capitalised present value of future expected net (real) rental receipts. The ARRY real valuation is distinguished from historical property analysis and their conventional valuation models. ARRY real valuation and property return analysis re-invents real value valuation models from those developed over the last four decades. Conventional valuation and return analysis models have serious limitations, particularly discounted cash flow models, and adoption by the real estate valuation/appraisal profession of previous real value models failed due to their complexity. The ARRY is a ‘real’ discount rate, calculated annually in arrears, that explicitly excludes expected monetary inflation and real rental growth. The ARRY reflects all other property risks. The generic ARRY valuation model utilises universal economic and financial principles, in short-cut discounted cash flow algorithms, and expressed in mathematical formulae, and applictions using MS Excel™ ARRY valuation spreadsheet templates. The ARRY model calculates present real values (PRVs) of leased real estate/property by capitalising expected future real cash flows in a term and reversion format, using ‘real value’ capitalisation rates. Each forecast future periodic tranche of real income and expense is capitalised, with reversionary real values discounted at the ARRY to calculate their PRVs both summed to the current market value. The model is based on mathematical algorithms, expressed in mathematical formulae and equations, illustrated in manually calculated examples, and confirmed using the MS Excel™ ARRY valuation spreadsheet templates. The generic ARRY model and spreadsheet templates are progressively adapted for a range of retail, commercial and industrial properties’ lease terms and conditions based on practical case studies in New Zealand (NZ) but adaptable for and equally applicable in any international real estate market. Keywords: all-risks real yield, discounted cash flow, market sales analysis, property interests, property investment, property returns, property valuation models, investment yield analysis, real value, term and reversion, practical valuation case studies.

ii


Contents

Page

List of Tables ...............................................................................................................................vii List of Figures and Charts ............................................................................................................viii Chapter 1 — All-Risks Real Yield valuation - What is it?................................................................ 11 1.1

The basic aim and objective............................................................................................... 11

1.2

Benefits anticipated from using the ARRY valuation model in practice................................ 11

1.3

Historic real value valuation models .................................................................................. 12

1.4

An overview of investment property valuation models ...................................................... 12

1.5

The problem of monetary inflation .................................................................................... 13

1.6

Basic real value valuation theory ....................................................................................... 15

1.7

The all-risks real yield (ARRY) investment property valuation model .................................. 17

1.8

Professional application and significance ........................................................................... 19

1.9

Policy implications ............................................................................................................ 20

1.10 Case studies ...................................................................................................................... 20 Chapter 2 — Developing the theoretical all-risks real yield (ARRY) model ..................................... 21 2.1

Introduction...................................................................................................................... 21

2.2

Methodological concerns with DCFs .................................................................................. 21

2.3

Summary of concerns about DCFs ...................................................................................... 23

2.4

The quest for an improved investment valuation model..................................................... 23

2.5

Real value valuation for the 21st Century........................................................................... 24

2.6

Conventional nominal value versus real value concepts ..................................................... 24

2.7

Implementing the development of real valuation models................................................... 25

2.8

Stage A: Direct capitalisation and conventional DCFs ......................................................... 29

2.9

Explanation by way of a progressive valuation problem ..................................................... 30

2.10 Comparable sale and its analysis ....................................................................................... 31 2.11 Calculation of the “correct” capitalisation rate ................................................................... 31 2.12 Extracting the expected overall yield YO from the sale analysis ........................................... 32 2.13 Conventional term and reversion application in valuing Example 1..................................... 34 2.14 Conventional DCF application in valuing Example 1 ............................................................ 34 2.15 Stage B: Real yield DCFs..................................................................................................... 35 2.16 Stage C: Net of growth (or hybrid real value short-cut) DCFs............................................... 37 2.16.1 Firstly, based on the nominal value model in stage A .................................................... 37 2.16.2 Secondly, compared to the “real value” models in stage B ............................................ 39 2.16.3 Thirdly, net of growth explicit term and reversion DCF valuation model ...................... 40 2.17 Chapter Summary ............................................................................................................. 41 Chapter 3 — Building the all-risks real yield (ARRY) valuation model ............................................ 42 3.1

Introduction...................................................................................................................... 42 iii

Real Value Valuation for Real Estate Investments (Jefferies, 2017) 3.2

3.3

3.4

3.5

Stage D: Building the generic all-risks real yield (ARRY) valuation model ............................. 42 3.2.1

Expected inflation Ie ........................................................................................................ 42

3.2.2

The structure and approach of the all-risks real yield (ARRY) valuation ........................ 44

3.2.3

PRV of the term to run .................................................................................................... 44

3.2.4

PRV of the reversion ....................................................................................................... 45

3.2.5

Total PRV represents the current market value (CMV) .................................................. 45

3.2.6

A note re reversionary assumption................................................................................. 45

Derivation of the basic all-risks real yield ARRY (YA) ........................................................... 46 3.3.1

The seminal all-risks real yield (ARRY, YA) definition and concept.................................. 46

3.3.2

Explanation of ARRY concept .......................................................................................... 46

3.3.3

The ARRY model’s distinguishing features and advantages ........................................... 47

3.3.4

Formulary for Stage D ..................................................................................................... 48

The all-risks real yield capitalisation rates .......................................................................... 49 3.4.1

Term to run capitalisation rate ....................................................................................... 50

3.4.2

Reversionary capitalisation rate ..................................................................................... 50

The basic ARRY valuation model ........................................................................................ 52 3.5.1

3.6

Specifying the ARRY YA valuation model ......................................................................... 52

Applying the ARRY real valuation model to sales analysis ................................................... 55 3.6.1

Initial yield analysis ......................................................................................................... 55

3.6.2

Analysis of YA from a sale ................................................................................................ 56

3.7

Applying the ARRY real valuation model to value a property .............................................. 57

3.8

Comparison of real valuation models ................................................................................. 59 3.8.1

3.9

Illustrative charts of ARRY valuation methodology application to Example 1d ............. 60

Further advantages of the ARRY model .............................................................................. 60

3.10 Chapter summary.............................................................................................................. 61 Chapter 4 — Generic adaptations to the all-risks real yield (ARRY) model .................................... 62 4.1

Introduction...................................................................................................................... 62

4.2

Adaptations to the ARRY valuation model ......................................................................... 62

4.3

Generic adaptations .......................................................................................................... 63

4.4

Specific lease variation adaptations ................................................................................... 63

4.5

Specialised market adaptations ......................................................................................... 63

4.6

Multi-tenanted and mixed use adaptations ....................................................................... 65

4.7

Specialised leasehold valuation adaptations ...................................................................... 65

4.8

Adaptations for investment analysis .................................................................................. 65

4.9

The Excel™ spreadsheet format of the basic ARRY model ................................................... 66

4.10 The inputs and calculations ............................................................................................... 67 4.11 Sales analysis use .............................................................................................................. 68 iv

Real Value Valuation for Real Estate Investments (Jefferies, 2017) 4.12 Valuation use .................................................................................................................... 70 4.13 Sales analyses and valuation printouts............................................................................... 70 4.14 Formulary tables for adaptations ....................................................................................... 71 4.15 The required generic adaptations to the basic ARRY model ................................................ 71 4.15.1 Adaptation (i) ― Timing: cash flow payments in advance or in arrears ......................... 71 4.15.2 Adaptation (ii) ― Payment frequencies: monthly, quarterly, or other payment periods ............................................................................................................................ 74 4.16 ARRY valuation as a sales comparison approach ................................................................ 81 4.17 Failures in traditional valuations to correctly allow for timing and frequency...................... 82 4.18 Specific lease variation adaptations ................................................................................... 84 4.18.1 Adaptation (iii) ― Terminating investments................................................................... 84 4.18.2 Adaptation (iv) ― Expiry of a current lease, and re-leasing on different market rent review terms ................................................................................................................... 89 4.18.3 Adaptation (v) ― OPEX allowances with gross leases .................................................... 94 4.18.4 Re-leasing a net lease as a gross lease .......................................................................... 101 4.18.5 Adaptation (vi) ― Prescribed or Specified rental formulas .......................................... 101 4.19 Adaptation (vi) Scenario 1. ― Prescribed rental escalation = expected inflation for gross lease ................................................................................................................................104 4.20 Adaptation (vi) Scenario 2 ― Specified nominal escalation rate > expected inflation for net lease ..........................................................................................................................107 4.22 Adaptation (vi) Scenario 3 ― Specified rent formula for net lease .....................................111 4.23 Chapter summary.............................................................................................................114 Chapter 5 — Special adaptations to the ARRY valuation model ...................................................115 5.1

Introduction.....................................................................................................................115

5.2

Advanced ARRY valuation template model .......................................................................115

5.3

Property or tenancy worksheets .......................................................................................118

5.4

Formulary tables for adaptations ......................................................................................122

5.5

Special adaptations ..........................................................................................................122

5.6

5.5.1

Adaptation (vii) — Renewals of the current lease, and re-leasing with different terms and/or rent review periods................................................................................. 123

5.5.2

Adaptation (viii) — Under-developed properties with redevelopment potential........ 133

Adaption to the basic ARRY algorithm for an alternative redevelopment use on lease expiry ..............................................................................................................................134 5.6.1

Adaptation (ix) — Vacancies, rent-free periods, leasing incentives, and leasing costs 139

5.7

Capital outlay incentives ..................................................................................................141

5.8

Rent-free period algorithms, formulas and equation with explanations .............................142 5.8.1

5.9

Formulary for Adaptation (ix) ....................................................................................... 142

Adaptions to the basic ARRY algorithm for vacancies, rent-free periods, leasing incentives, and leasing costs ..............................................................................................................144 v

Real Value Valuation for Real Estate Investments (Jefferies, 2017) 5.10 Adaptation (x) — Allowance for costs of purchase (including due diligence) and costs of sale ..................................................................................................................................151 5.10.1 Adaptation (x) Scenario 1: Due diligence and purchase costs ...................................... 154 5.10.2 Adaptation (x) Scenario 2: Disposal costs ..................................................................... 156 5.10.3 Adaptation (x) Scenario 3: Due diligence, purchase costs and future disposal costs ... 158 5.11 Adaptation (xi) — CAPEX (expectations of capital expenditure), refurbishment, and deferred maintenance liabilities .......................................................................................160 5.12 Adaptation (xii) — Partial gross leases with fixed and/or variable OPEX recoveries ............163 5.12.1 Introduction and content .............................................................................................. 163 5.12.2 Formulary for OPEX adaptations................................................................................... 164 5.12.3 Amendments to ARRY valuation model for Adaptation (xii) ........................................ 166 5.13 Adaptation (xii) Scenarios.................................................................................................168 5.14 Partial gross lease ARRY valuation and gross re-leasing option algorithm adaptations .......168 5.15 Adaptation (xii) Scenario examples ...................................................................................171 5.15.1 Adaptation (xii) Scenario 1: Gross lease, perpetual renewals, and base date OPEX .... 171 5.15.2 Adaptation (xii) Scenario 2: Gross lease with no RoR, current partial OPEX, No releasing ........................................................................................................................... 175 5.15.3 Adaptation (xii) Scenario 3: Gross lease with 1 x RoR, base date OPEX, re-leasing as a gross lease .................................................................................................................. 178 5.15.4 Adaptation (xii) Scenario 4: Gross lease with no RoR, current partial OPEX, releasing as a gross lease ................................................................................................. 182 5.15.5 Adaptation (xii) Scenario 5: Gross lease with no RoR, nil initial partial OPEX, releasing as a gross lease ................................................................................................. 185 5.16 Adaptation (xiii) Ratchet clauses in leases affecting rental reviews ....................................189 5.17 Adaptation (xiii) Ratchet clause scenarios .........................................................................189 5.18 Effect of ratchet clauses where rights of renewal expected to be exercised .......................190 5.19 Adaptation (xiii) Ratchet scenarios examples ....................................................................191 5.19.1 Adaptation (xiii) Scenario 1 PartOpex, with gross re-leasing and Nil ratchet ............... 191 5.19.2 Adaptation (xiii) Scenario 2 PartOpex, with gross re-leasing and Hard ratchet ........... 194 5.19.3 Adaptation (xiii) Scenario 3 PartOpex, with Gross Re-leasing and Soft Ratchet........... 196 5.20 The complete ARRY real value valuation algorithm ...........................................................198 5.21 Chapter summary.............................................................................................................199 Appendix A — Formulary ...........................................................................................................201 Appendix B ................................................................................................................................209 B.1 ARRY Valuation template property or tenancy worksheet – complete ...............................210 B.2

An explanation of ARRY Valuation template property or tenancy worksheet .....................212

B.3

Partial OPEX inputs in the MS Excel™ ARRY valuation template .........................................214

B.4

APPENDIX ― ADLS 6th Edition 2012 standard commercial deed of lease.............................218

B.5

APPENDIX ― Copy of Unrecoverable OPEX Excel™ template matrix with formula shown ...221 vi

Real Value Valuation for Real Estate Investments (Jefferies, 2017) References ................................................................................................................................223

List of Tables Table: Chapter—No. Label Page Table 1 Conventional nominal versus real value concepts .................................................................... 25 Table 2 Formulary for Stage A, B, and C ................................................................................................. 26 Table 3 Formulary for Stage D................................................................................................................ 49 Table 4 Formulary for payment frequencies.......................................................................................... 74 Table 5 Formulary for terminating investment model adaptation ........................................................ 84 Table 6 Formulary for re-leasing on different market rent review terms ............................................. 89 Table 7 Formulary for OPEX allowances with gross leases .................................................................... 96 Table 8 Formulary for prescribed rental formulas ............................................................................... 102 Table 9 Formulary for different rent reviews and lease renewal periods ........................................... 124 Table 10 Formulary for under-developed properties with redevelopment potential ......................... 134 Table 11 Formulary for vacancies, rent-free periods, leasing incentives, and leasing costs ............... 143 Table 12 Formulary for partial gross leases with fixed and/or variable OPEX recoveries ................... 164

vii


List of Figures and Charts Figure or Chart No. Label Page Chart 1 Example 1: Forecast cash flows and term and reversion structure .......................................... 30 Figure 2 Extracting the expected overall yield YO from the sale analysis .............................................. 33 Chart 3 Sale 1: Forecast cash flows and term and reversion structure ................................................. 33 Figure 4 Example 1a: Traditional fully explicit nominal DCF valuation .................................................. 34 Figure 5 Example 1b(1): Net of inflation – Real yield Yr explicit DCF Valuation ..................................... 35 Figure 6 Example 1b(2): True real yield Yr explicit DCF valuation .......................................................... 37 Figure 7 Example 1c(1): Net of growth YN explicit DCF valuation .......................................................... 38 Figure 8 Example 1c(2): Net of growth YN explicit DCF valuation .......................................................... 40 Figure 9 Example 1c(3): Net of growth YN explicit DCF valuation term and reversion format .............. 41 Chart 10 The basic structure and approach of the all-risks real yield (ARRY) valuation ........................ 44 Chart 11 ARRY investment valuation flow chart .................................................................................... 48 Chart 12 All-risks real yield (ARRY) basic valuation with formula .......................................................... 54 Chart 13 All-risks Real Value (ARRY) concepts ....................................................................................... 55 Figure 14 Analysis of Sale 1 .................................................................................................................... 56 Figure 15 Valuation application in re-valuing Example 1d ..................................................................... 57 Figure 16 ARRY Real Value explicit DCF revaluation of Example 1d ...................................................... 58 Figure 17 Comparison of nominal and real value valuation models...................................................... 59 Chart 18 Term to run and reversionary present and future real value cash flows ................................ 60 Chart 19 ARRY Term and reversionary real value cash flows ................................................................ 61 Chart 20 Adaptation (ix) methodology for allowing for initial or re-leasing vacancies and costs ......... 64 Figure 21: Blank ARRY Valuation spreadsheet template model ............................................................ 66 Figure 22: Excel’s Goal Seek dialog box.................................................................................................. 68 Figure 23: Completed ARRY valuation template for a sales analysis ..................................................... 68 Figure 24: ARRY basic valuation template in formula view with row and column headers .................. 69 Figure 25: Completed ARRY valuation template print area for a sales analysis .................................... 70 Figure 26 Time value of money function Excel ™ dialog box ................................................................. 71 Figure 27 ARRY valuation template for Adaptation (i) for timing .......................................................... 73 Figure 28 ARRY valuation template printout section for Adaptation (i) for timing ............................... 74 Figure 29 ARRY valuation template for Adaptation (ii) for monthly BOP payments ............................. 79 Figure 30 ARRY valuation template print-out section for Adaptation (ii) for frequency ....................... 80 Chart 31 ARRY model as a sales comparison approach ......................................................................... 81 Figure 32 ARRY valuation template for Adaptation (iii) for terminating lease ...................................... 87 Figure 33 ARRY valuation template printout for Adaptation (iii) terminating lease ............................. 88 Chart 34 Adaptation (iv) lease expiry and releasing .............................................................................. 91 viii

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Figure 35 ARRY valuation template for Adaptation (iv) Re-leasing on lease expiry .............................. 93 Figure 36 ARRY valuation template printout for Adaptation (iv) Re-leasing on lease expiry ................ 94 Figure 37 ARRY valuation template Adaptation (v) for Gross lease allowing for OPEX ......................... 99 Figure 38 ARRY valuation template printout Adaptation (v) for Gross lease allowing for OPEX......... 100 Figure 39 ARRY valuation Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease .... 106 Figure 40 ARRY valuation printout Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease ................................................................................................................................. 107 Figure 41 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease 109 Figure 42 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease — Valuation template printout ....................................................................................... 110 Figure 43 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease ................................................................................................................................. 112 Figure 44 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease — Valuation printout section ................................................................................. 113 Figure 45 Format and layout of MS Excel ARRY valuation templates .................................................. 116 Figure 46 Copy of template summary sheet for the Chapter 7 Adaptations ....................................... 117 Figure 47 Enlarged individual property template sheet showing input cells....................................... 119 Figure 48 Enlarged individual property template sheet showing calculated valuation outputs ......... 120 Figure 49 Enlarged individual property template sheet showing vacancy allowance outputs ........... 120 Figure 50 Individual property template sheet valuation printout ....................................................... 121 Figure 51 examples of message box and drop-down lists for Gross/Net lease input and for Releasing or not on lease expiry .......................................................................................... 122 Chart 52 Chart of different renewal and re-leasing rental review terms ............................................ 123 Figure 53 Adaptation (vii) valuation template inputs section.............................................................. 130 Figure 54 Adaptation (vii) valuation calculations section .................................................................... 131 Figure 55 Copy of capitalisation rate calculations ............................................................................... 131 Figure 56 Adaptation (vii) valuation printout section .......................................................................... 132 Chart 57 Real rental flows and PRVs for alternative use redevelopment at final expiry..................... 135 Figure 58 Adaptation (viii) Redevelopment on final lease expiry – template inputs section .............. 137 Figure 59 Adaptation (viii) Redevelopment on final lease expiry – valuation printout ....................... 138 Chart 60 Adaptation for initial vacancies and re-leasing on lease expiry ............................................ 139 Chart 61 Adaptation for vacancies and rent-free periods ................................................................... 141 Figure 62 Adaptation (ix) Expected vacancy and rent-free periods - time-line ................................... 145 Figure 63 Cap rates for Adaptation (ix) Vacancies, and rent-free periods example ............................ 147 Figure 64 Adaptation (ix) Inputs for vacancies, rent-free periods, leasing incentives, and leasing costs ................................................................................................................................. 148 Figure 65 Adaptation (ix) Valuation output for vacancies, rent-free periods, leasing incentives, and leasing costs ..................................................................................................................... 149 Figure 66 Adaptation (ix) Details of outputs for vacancies, rent-free periods, leasing incentives, and leasing costs .............................................................................................................. 149 ix

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Figure 67 Adaptation (ix) valuation printout for vacancies, rent-free periods, leasing incentives, and leasing costs .............................................................................................................. 150 Figure 68 Adaptation (x) Scenario 1: Valuation printout for due diligence and purchase transaction costs ................................................................................................................................. 155 Figure 69 Adaptation (x) Scenario 2: Valuation printout for disposal transaction costs ..................... 157 Figure 70 Adaptation (x) Scenario 3: Valuation printout for due diligence, purchase costs and future disposal costs ........................................................................................................ 159 Figure 71 Adaptation (xi) Scenario: CAPEX (expectation of deferred maintenance liability) .............. 162 Chart 72 Generic expected income cash flows OPEX cash flows and OPEX PRVs ............................... 166 Chart 73 Perpetually renewable gross lease with BPOpex, expected cash flows and OPEX PRVs ...... 172 Figure 74 Scenario 1: Gross lease, perpetual renewals, and base date OPEX – valuation printout .... 174 Chart 75 Adaptation (xii) Scenario 2 — Gross lease with no RoR, current partial OPEX, No releasing .............................................................................................................................. 175 Figure 76 Adaptation (xii) Scenario 2 — Gross lease with no RoR, current partial OPEX, with redevelopment on expiry valuation printout .................................................................. 177 Chart 77 Adaptation (xii) Scenario 3 — Gross lease with base date OPEX, re-leasing as a gross lease178 Figure 78 Adaptation (xii) Scenario 3 — Gross lease with 1 x RoR, base date OPEX, re-leasing as a gross lease valuation printout ......................................................................................... 181 Chart 79 Adaptation (xii) Scenario 4 — Gross lease with no RoR, current partial OPEX, re-leasing as a gross lease..................................................................................................................... 182 Figure 80 Adaptation (xii) Scenario 4 — Gross lease with no RoR, current partial OPEX, re-leasing as a gross lease valuation printout .................................................................................. 184 Chart 81 Adaptation (xii) Scenario 5 — Gross lease with only increase in OPEX as recoverable from tenant .............................................................................................................................. 186 Figure 82 Adaptation (xii) Scenario 5 — Gross lease with no RoR, increase in OPEX only recovered, re-leasing as a gross lease valuation printout ................................................................. 188 Figure 83 Adaptation (xiii) Scenario 1 — GRL Nil Ratchet valuation printout ..................................... 193 Figure 84 Adaptation (xiii) Scenario 2 — GRL Hard Ratchet valuation printout .................................. 195 Figure 85 Adaptation (xiii) Scenario 3 — GRL with soft ratchet valuation printout ............................ 197 Figure 86 ARRY Valuation template property or tenancy worksheet – complete (Top half) .............. 210 Figure 87 ARRY Valuation template property or tenancy worksheet – complete (Bottom half) ........ 211 Figure 88 ARRY Valuation Template — OPEX inputs and results for BDOpex ..................................... 214 Figure 89 ARRY Valuation Template — OPEX inputs and results for CPOpex...................................... 214 Figure 90 ARRY Valuation Template — Re-leasing inputs showing GRL cell input message and drop-down list.................................................................................................................. 214 Figure 91 ARRY Valuation Template — Net partial OPEX deduction — BDOpex ................................ 214 Figure 92 ARRY Valuation Template — Net partial OPEX deduction — CPOpex ................................. 215 Figure 93 ARRY Valuation Template — Copy of matrix for calculating unrecoverable OPEX.............. 215 Figure 94 ARRY Valuation Template — Unrecoverable OPEX variations/combinations ― with 0 or 1 RORs, variations in BDOpex or CPOpex and GRL giving different PRVs of Net OPEX ... 217

x


Chapter 1 — All-Risks Real Yield valuation - What is it? 1.1 The basic aim and objective The All-Risks Real Yield (ARRY) valuation is as a generic "real value" investment property valuation model being an advance on older real value models, but of inherent simplicity. The primary objective was to build a comprehensive and practical valuation model of general application to real property with a high degree of accuracy (compared to conventional valuation models). The model was designed for use where present real (and nominal) values of real estate/property investment reflect expected future cash flows. The model is original, its genesis was in “net of growth” YN valuation models (Jefferies, 1997a) then proposed as a generic real net of growth valuation model, described in Jefferies (2016, pp. 61 - 76, Chapter 3). The ‘term and reversion’ structure of that model’s basic algorithm and capitalisation methodology therein was, however, a part nominal value (term) and part real value (reversion) model, which is developed further into a fully real value model as described in this text. The all-risks real yield (ARRY) model was first introduced as an embryonic concept in a conference paper, Jefferies (2010b) and given a notation of YR, Y representing yield and the subscript R, representing real, defined there as the net of inflation and real growth rate on an investment. This was developed into the ARRY model with a less confusing and a distinctive notation of YA, Y representing yield and the subscript A, representing all-risks real. The name of the model and its notation was deliberately adopted to distinguish it in many important ways from the traditional UK all-risks yield (ARY), and is fully distinguished in Subsection 3.3.3 at page 47. Primarily, the ARRY is a real yield (real discount rate) not a capitalisation rate as is the ARY, except under tightly defined parameters, explained under Subsection 3.4.2 in applying Equation 18 at page 50. The new ARRY model was first presented publicly at the start of a series of ARRY Valuation Seminars held in Havelock, Nelson / Marlborough in NZ, in November 2010 (Jefferies, 2010a), with the first publication (Jefferies, 2010c) being a fully developed basic generic model.

1.2 Benefits anticipated from using the ARRY valuation model in practice The expected benefits of the model's adoption expressed as potential benefits are:

1. 2. 3.

ARRY valuation model producing more accurate valuations than conventional property valuation models. ARRY valuations completed more efficiently, quicker and easier to use compared to conventional valuation models. Valuation differences using the ARRY model reducing valuation variances between valuers valuing the same properties compared to differences using conventional models.

One key reason for the practical benefits benefit Nos. 1 and 3 above, is that the ARRY valuation model contributes to improved accuracy. Sales analyes produces a tighter range of possible yield rates from the extraction process, thereby minimizing the size and number of subjective valuer adjustments in the valuation process. Capitalisation rates are calculated on explicit expected inflation (Ie) rates and real growth rates (Gr) that combine with the terms of lease rent reviews, payment timing, and payment bases in the lease terms and conditions for each future tranche of expected real cash flows. The main valuation professions' expected policy benefits anticipated explained in Jefferies (2016, p. 75, Section 4.6) are seen as hereunder: 11


4.

The new ARRY valuation model promoted in a technical information paper (TIP) for use in income property valuations under International (and local) Valuation Standards that provides guidance for the model’s adoption, use and application.

The technical and application benefits will depend on further research leading to potential applications of the model as discussed in Jefferies (2016, Section 12.16), in particular the development of well-designed and customised valuation spreadsheet templates for computers and application programs (Apps) for use on mobile electronic devices.

1.3 Historic real value valuation models UK real value valuation models originated with Wood’s (1967, 1972, 1973) inflation risk free yield (IRFY) model and built upon by his protégé in Crosby’s (1983, 1985, 1986a) hybrid real value / equated yield valuation model. These models have been criticised for being too complex for the valuation/appraisal profession to understand or accept – let alone adopt them (Trott, 1980, 1986b). These UK real value models are discussed and summarised in Jefferies (2016, Sections 2.9 & 2.10) The only USA fully developed real value real estate investment appraisal model, Blackadar’s (1984, 1986, 1989) “dynamic capitalization (sic)” model, was more complex and developed using actuarial theory, symbols and notations which North American appraisers largely ignored. A later independent generic net of growth real value model (Jefferies, 1997a, 1997b) was similar to Crosby’s model (a hybrid of nominal and real value discounting) and is now superseded by the ARRY model. This ‘new’ ARRY valuation model is a simpler ‘fully real value’ generic model. Whilst having its genesis in the earlier net of growth model, the ARRY is in a new format and basic algorithms that distinguishes this model from all previous real value and conventional valuation models (yield capitalisation, DCF, or traditional term and reversion models).

1.4 An overview of investment property valuation models Current valuation models in use by property and real estate professions internationally come in various forms but are all based on nominal currency, and when explicitly forecasting future incomes are almost universally DCF based with nominal discount rates used, i.e. including allowing for anticipated nominal growth in future income and values. For example, the future rental income, property owner’s expenses, and resulting net cash flows together with terminal (reversionary) values where applicable (in DCF or term and reversion models) are forecast in future nominal values and explicitly allow for growth in future nominal currency. Conceptually, and in theory, the discount rate used is comprised of a nominal required investor’s rate of return ‘built-up’ from: • • • • •

a risk-free real rate; plus a premium (for expected and unexpected) inflation risk; plus a property risk premium; less a (constant or stabilised) market income and expense growth rate adjustment (anticipating an increase in long-term nominal rentals and future values); plus an offsetting building depreciation rate (where the asset reduces in income earning capacity compared to an equivalent new property).

Income property pricing models described by Hoesli & MacGregor (2000) explicitly allow for depreciation as also advocated by Baum (1988, 1991) and by Crosby et al. (2009). Most valuers do not, in the author’s experience, realise these components are all “packed” into the discount rate required to be applied, and even more so “packed into” the market capitalisation rate. With the DCF technique, i.e. where a typical 10-year holding period is used, the valuation is substantially dependent on both nominal income forecasts and a terminal capitalisation rate to calculate the 12

Real Value Valuation for Real Estate Investments (Jefferies, 2017) nominal terminal or exit value. All future nominal cash flows are discounted at a nominal discount (or yield) rate to give the present value (PV) as the investment value or current market value (CMV). The practical problem with the traditional ‘direct’ or ‘yield’ income capitalisation property pricing (valuation) models is the number of assumptions required or the complex (market based) analyses of sales to derive the necessary model inputs – primarily the required return. Whipple (1995, 2006) explains how an assumption of growth and offsetting depreciation rate is required to derive the implied discount rate, and Brown (1991) describes how in deriving the implied growth rate, an assumption of the discount and depreciation rates are required, i.e. inter-reliant circularity. Over the last two decades, development and promotion of proprietary DCF software packages – such as Cougar, Argus (previously Dyna) and EstateMaster, have complicated the process by requiring (as an industry expected standard) nominal cash flow forecasts of 10 years. 1 The effect of this is that it takes away reliance on current values of rentals and sales evidence in real terms and relies on uncertain future nominal forecasts, most of which is time consuming and burdensome to do. The software has allowed the mechanisation of inputting the lease data and assumptions underlying those cash flow forecasts and providing the electronic valuation calculation. In the process, transparency of the effects of these underlying inputs on the resulting estimated current market value is lost, with all component cash flows discounted into a single PV. In multi-tenanted properties, there will be a mix of differently dated lease commencements, rental reviews, lease renewals, termination dates, and rental levels. Each tenancy will exhibit different characteristics contributing different value weightings, along with the forecast timing of rental changes affecting the future uncertain cash flows, reflected in the sale price and/or valuation. However, there will be offsetting effects smoothing the analysed over-all property combined tenancy risks reflected in the initial return and analysed nominal yield. The new ARRY valuation model explicitly allows for the variations resulting from these dynamics when the ARRY or YA is analysed from comparable sales, simplifying the application to another property with different lease weightings and leasing risk profiles. This should logically lead to improved valuation accuracy. None of the previous real value model theses empirically tested their models (Crosby, 1985; Wood, 1972), nor did the USA ‘dynamic capitalization (sic)’ model (Blackadar, 1984, 1986, 1989) or the net of growth models (Jefferies, 1997a, 1997b) though all gave examples applying their models based on hypothetical data. No other recent attempt to use real value methodology has been found (Jefferies, 2009a) in on-going research and up to current date (2017). A short history of all income property valuation models is contained in Jefferies (2009b, Section 2.2); and the historic development of real value models in particular is fully described in Jefferies (2009a) and in Jefferies (2016, Section 2.8).

1.5 The problem of monetary inflation The terms ‘inflation’ rate and ‘growth’ rate are frequently confused and often treated as synonymous in valuation and appraisal literature, especially prior to the 1990’s but is still misunderstood. Sullivan (2013) in advocating practical risk mitigation by linking evidence to the (valuation) answer, questions valuers (inter alia) “If you used discounted cash flow, how did you choose the internal rate of return, discount rates and rationale for varying levels of inflation adjustment over the period?” Not only does he confuse IRR for the discount rate but also assumes “inflation” is the same thing as nominal growth in cash flows. This is a common error, with risk mitigation not assisted when fundamental methodology and terminology are confused, by the the valuation profession's ‘watchdogs’. 2 1

Created and marketed respectively by (Cougar, 2013) founded in Sydney Australia in 1992;(Argus, 2013) out of Houston, TX (Acquired Dyna in 1991); (EstateMaster IA, 2013) founded in Sydney, Australia in 1991.

2

Sullivan is the Valuer-General and Chair of the Valuers Registration Board (NZ).

13

Real Value Valuation for Real Estate Investments (Jefferies, 2017) The greater issue is whether accuracy in valuations is ultimately more important and dependent on proper methodology, rather than process. It is more important in mitigating risk to use improved methodology that is more accurate than using erroneous methodology and false concepts that will lead to error. However, ‘stink thinking’ in valuation permeates the profession in NZ, and the ‘inflation equals growth’ mythology is being perpetuated (Jefferies, 2012, p. 33). Monetary inflation is a sub-set of nominal growth in both future income and values that includes real growth (nominal growth adjusted for inflation). Few property valuation or appraisal writers have successfully disentangled these two factors, especially in terms of property investment expectations and valuation models. Wood (1972) and Crosby (1985) tried but failed to do this. Blackadar (1984) achieved it, but in an actuarial model that Parker (1996, p. 28) disparaged as far too difficult and "foreign" for valuers to understand, follow or use as couched in a single complex unfriendly equation, refer to Jefferies (2016, Subsection 2.11.1. ). The ARRY valuation model explicitly deals with future inflation and real rental growth as separate future expectations. Monetary expected inflation (Ie) is exogenously obtained from reliable and reputable economic forecasters and expected real income growth (Gr) is extracted from property sales analyses by the valuer, both combining as expected overall nominal growth (GO). These inputs then combine with the expected property investment all-risks yield (YA), also extracted from sales analyses. The ARRY valuation model computes capitalisation rates using mathematically "correct" formulae, applying the model’s algorithms calculating the present real values (PRVs) of the future tranches of expected real income (expected rentals from each separate tenant), real expense cash flows, and reversionary future real values (FRVs). The total PRVs for each future real tenancy income and (negative) expense component total to the current market value. In multi-tenant property, each tenancy’s real value as a contribution to the overall value is transparently calculated, and their PRVs and of any unrecovered operating expenses (OPEX) or capital expenditure (CAPEX) are summed to the total PRV of the property, being the estimated total current market value (CMV). These components are the essential strengths of this new model that distinguishes the ARRY model from all other valuation models. Prior to the recognition that monetary inflation was an epidemic post World War II economic problem, valuation models did not consider the effect of monetary inflation, generally based on a ‘steady state’ assumption. Problems caused by inflation became a concern in the UK in the 1970’s with Wood (1972, 1973) developing his real value valuation model to deal with it. It also prompted Sykes (1981, 1984) to develop rational models that were explicit about growth assumptions. The RICS formally favoured and endorsed Marshall’s (1975, 1976) equated yield (EY) model that allows for growth in nominal terms, as a recommendation from its Property Valuation Methods: Research Reports (interim and final), Chaired by Trott (1980, 1986b). The difficulty faced by UK valuers in understanding and using the superior real value and rational valuation models lead Crosby (1985, 1986b, 1987) to develop and promote a hybrid real value/rational/short-cut-DCF model combining the officially adopted EY model and Wood’s real value models. Notwithstanding extensive publications including textbooks (Baum & Crosby, 1988, 1995) teaching and promoting the method, UK valuers did not adopt it. One of the problems not addressed by the property valuation profession, while accepting income growth as an investor’s expectation, is the fact that the monetary inflationary element is often the dominant driver of nominal growth. This was not recognised, inflation being regarded as synonymous with growth and not separated from real growth. Even though Wood (1972) recognised this, in part, his model confused monetary inflation with growth, while at that time the economic theory and statistics available on expected inflation was yet to be developed. In the USA concerns about allowing for future growth lead to the explicit allowance for growth in yield capitalisation models, e.g. Ellwood’s (1959) mortgage-equity model. However, Ellwood’s model only allowed for growth (or decline) in nominal terms and combined this with growth in equity from mortgage repayments using an equity-yield discount rate. Initially his model was based on capitalising a uniform (stabilised over the holding period) net operating income (NOI) with growth only recognised by way of a percentage of capital value increase realisable by a presumed sale at the 14

Real Value Valuation for Real Estate Investments (Jefferies, 2017) end of a fixed holding period (of 5 or 10 years). Ellwood’s tables gave capitalization rates based on either a 66-⅔% or a 75% long term fixed interest for 15, 20, 25, or 30 year table mortgages. See an expanded treatment of Ellwood’s method in Jefferies (2016, p. 39, Section 2.5: Ellwood’s mortgageequity model). Ramsland (1971) opined that "The reliance on past information could result in substantial equityyield on paper, but after discounting for inflation, or the gradual decline in purchasing power of the dollar, the effective yield measured in terms of purchasing power could be considerably less." Singer (1971) observed that "due to inflation, increasing emphasis is being placed on evaluating the future stream of benefits in light of likely purchasing power as well as the anticipated level of dollar receipts." However, neither of these practitioners offered any way of adjusting appraisals for this loss of purchasing power due to monetary inflation. Forecasting in nominal terms masks the effect of monetary inflation, as growth in nominal terms may not be growth at all in real terms, i.e. where inflation equals or exceeds nominal growth, the latter resulting in loss (decline) in purchasing terms, i.e. decline in real terms. The ARRY valuation model allows for all the above scenarios, real growth, real decline depending on the rate of assumed expected general monetary inflation in the economy. The ARRY valuation model takes advantage of the availability of the late 20th Century economic development of expected (anticipated or ex-ante) inflation forecasting by experts as distinct from historic or ex-post inflation as measured by consumer price index (CPI) or other price increase statistics. Today, the issue of expected inflation relying on independent available statistical forecasting services used by investors is available to real estate valuers/appraisers for this component of expected rental growth as a reliable extrinsic factor. In the ARRY model, expected inflation (Ie), is an explicit input exogenously derived from independent reliable econometric forecasts and/or surveys. This leaves only the need for the valuer's estimated forecast real growth (Gr) as appropriate for the investment property's physical, location and economic characteristics, based on evidence of similar properties' rental growth trends and real value growth analyses. Together, expected inflation (Ie) together with a forecast real growth (Gr) combine to represent expected annual nominal growth (GO) = (Ie) + (Gr).

1.6 Basic real value valuation theory The fundamental and underlying simplification of income property valuation under a real value concept is that the current market value of an investment property is the current or present real value (PRV) of all future ownership benefits. As familiar as this basic land economics' doctrine is — it is also axiomatic. In real terms, the market price of an asset at the date of sale or valuation represents what willing buyers and sellers agree to exchange those property asset interests for in current dollar terms. In real terms, the current market value of a property investment asset at the date of valuation represents the PRV of future real net cash flows. Thus, real value valuation is discounting expected future real values (FRVs) of rents and reversionary real values at the required property market based real yield. This yield is, as defined and derived to follow, is the all-risks real yield (ARRY). Real value exists only where buyers perceive real benefits in both real income and the maintenance and growth (or decline) in real values flowing from the future use of property. In theory this real value exists for both owner-occupiers, to owners in terms of notional income (annual use value), or non-owners in possession as tenants (as lessees) paying rental – as income to the owners (as lessors). The latter real occupational use values, subject to the terms of tenure and contractual lease rights and obligations determines the real rental value as at the commencement of the lease or when assessed on rent review or at renewal of the lease.

15

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Market rental is defined by the International Valuation Standards Council (IVSC) as: The estimated amount for which an interest in real property should be leased on the valuation date between a willing lessor and a willing lessee on appropriate lease terms in an arm’s length transaction, after proper marketing and where the parties had each acted knowledgeably, prudently and without compulsion. (IVSC, 2011 ― IVS 230 Real Property Interests, p. 4, Clause C9) (IVSC, 2016- IVS 104: Bases of Value - Exposure Draft, 7 April ) p.10 Section 40. IVSDefined Basis of Value – Market Rent In the ARRY valuation model current market rent (CMV) as defined above, as discussed later in Subsection 4.18.2 at page 89, is given the symbol (Cm), and more fully defined as: The rental normally paid for typical market lease terms and conditions as at the commencement, sale, or valuation date. If currently at a review or renewal date, that rental adjusted for both inflation and any real rental growth (offset by any real rental depreciation) due to both market and physical property changes. All value derives from rational expectations, i.e. forecasts of the future based on current market trends following past experiences and without bias due to personal circumstances or non-market factors, to comply with the willing lessor-willing lessee and arm’s length transactions criteria in the IVS rental definition above. No real value exists in the past with current capital value measured by discounting to present real values all real future benefits (real rentals and/or future real values) at the market’s required real discount rate relative to expectations of risk and return. Current market rentals represent in real terms what the periodic occupancy benefits are worth reflecting future real growth expectations during the rental term. Similarly, expected current and future operating expenses (OPEX) and capital expenditure (CAPEX), as well as any future net resale value, if applicable, are expressed in (current) present real values. This simplifies the real value valuation process, in that it is not necessary, as in conventional and DCF techniques, to escalate (inflate or deflate) future rents, costs and values in nominal terms allowing implicitly for a monetary (currency) inflation component. Those future nominal values discounted back to present value at a nominal discount rate implicitly necessitates incorporating the same expectations of nominal growth including inflation. One needs only to discount the forecast future real cash flows using real required rates of returns, allowing for any real growth/depreciation components relative to their risks. This is one of the inherent simplifications of the ARRY model. This does not mean ignoring monetary inflation, in the ARRY model, as expected inflation is specifically taken out of the nominal monetary discount rate. Nor does it mean that one ignores real growth (or decline) providing any forecast is in expected real terms and by applying net of expected inflation and real growth discounting at a real rate of return that includes all other property investment risk. Only when there is a real prospect of real growth in future rentals and future real values resulting therefrom — will the forecasts require adjustment for that expectation, and viceversa for real value decline (such as that due to expected depreciation and/or obsolescence, demographic shifts or effects of changes in demand/supply). In terms of the building rental value component, any real depreciation is allowed due to age and obsolescence, arising from the reduced ability to command rental(s) in the market in competition with new or more modern space. Further, these separate components of growth in the ARRY valuation model provide the derivation and justification for the capitalisation rates applied to the various tranches of expected net real income to determine current market values. Overriding these components, to achieve valuation accuracy, the assumptions made and data inputs must be market based evidence, i.e. expected inflation, and expected real growth in income as well as risk/return reflected in the real yield expectation derived from sales analyses. The ARRY valuation model seeks to be transparent in 16

Real Value Valuation for Real Estate Investments (Jefferies, 2017) respect of all these components, based on factual data to which the valuer applies nouse and experience in making consistent assumptions.

1.7 The all-risks real yield (ARRY) investment property valuation model This real value valuation model is a departure from and an advance on previous attempts to produce a practical and fully workable ‘real value’ ‘income property’ valuation model. Its emphases simplicity despite some complex economics and mathematical theory underlying it. Previous models proposed by Wood (1972), Crosby (1985), and Blackadar (1984, 1986, 1989) have used non-market critical assumptions in deriving the “real” discount rate, not based on the analyses of comparable sales. 3 Application was by hand calculations or using precomputed valuation tables; some complicated and not easily applied to multi-tenanted properties. They were not user-friendly. The theoretical development of the ARRY valuation model arose primarily out of methodological concerns with DCF valuations that lead to inaccuracies as detailed in Section 2.2 commencing at page 21. The relevancy of real value models as an answer to the quest for an improved investment valuation model is set within a framework of real value versus conventional valuation models. The detailed development of the ARRY valuation model through its nascent stages starts with a conventional nominal DCF model explained and illustrated. This is converted to a real value DCF and then into a net of growth model using the same progressive simple spreadsheet valuation example. The new all-risks real yield (ARRY) or YA model, as up till now described in Jefferies (2010c, 2011), is expanded on in detail in Chapter 3. This explains its theory and structure, new inputs required and their definitions, a full description and definition of the all-risks real yield is introduced and the basic ARRY valuation Algorithm 19 at page 52. This is a simplistic term and reversion form of a short-cut DCF that gives the present real value (PRV) of the contractual tranche of real income over the lease term to run plus the PRV of the reversionary value of capitalised future real rentals. The previous illustrative example carries over into the ARRY model using an expanded spreadsheet template, allowing comparison to conventional direct capitalisation models and to other earlier real value models. The ARRY real value valuation model is distinctly different from both Wood’s and Crosby’s models. The ARRY valuation model is ‘objective’ and less dependent on the valuer’s ‘subjective’ assumptions in analysing sales, and in application to valuing property. Some element of ‘judgement’ still exists ― as it should ― valuation is an art as well as a science (Gilbertson, 2002; Klaasen, 1989) particularly in terms of ‘adjustment for risk’ as between non-comparable sales being analysed and the property being valued. The adoption, in any particular application of the ARRY (YA) model requires inputs based on analysing sales – using the model as an analysis tool – assembling the evidence as to the resulting range of applicable ARRYs. The valuer should only then apply judgement in selecting an appropriate ARRY or YA to apply in using the model in valuing a specific property. Essentially, all future unknowns and uncertain value influencing factors have already been priced into (discounted to) current present values as evidenced by the expectations of market players in determining current prices paid for comparable properties. This data is analysed by the relationship of those sales to the current and forecast future real cash flows from the properties sold. The most important data being the current contract rental actually being paid (if any) and an assessment of current market rental value for the property which can be determined by comparative analysis of comparable current market rentals. It is the relationship of the sale price to these two market data, coupled with the known factual data on the lease terms (primarily the next rental review date, and rental review frequency and any 3

Though Blackadar in Part 3 of his series does show how some inputs could be derived from market data, both sales evidence and other economic data. However, critical assumptions are still required in his model.

17

Real Value Valuation for Real Estate Investments (Jefferies, 2017) renewal terms) which “drives” the market value. Using these market data the all-risks real yield ARRY, or YA, is analysed from the sale(s). The definition of the ARRY (YA) is: The real value annually in arrears yield – the real internal rate of return that discounts the real values of the term to run and the real reversionary value(s) to the present real value (PRV), being the sale price or current market value. The key difference in this ARRY valuation model, compared to existing and traditional models, as well as earlier ‘real value’ models, is the derivation of and reliance on the all-risks real rate of return or required yield (ARRY) YA in both sales analyses and in valuation of income property. In the ARRY real value valuation model, the YA reflects the risk profile of the property being valued, and in reverse procedure from analysing sales, the model derives the appropriate ARRY capitalisation rates to apply to reflect the terms of the lease. The YA is combined with expected inflation, Ie, and expected real rental growth, Gr, together with the rent review frequency to determine an accurate capitalisation rate. Different rental review frequencies may apply to the contractual term to run, the next review term or as will apply on renewal or on expiry with a new market leasing. Calculating the PRVs of these different tranches of real rentals is by adapting the basic ARRY Algorithm 19, to give algorithms that give effect also to specific lease terms and conditions. Adaptations of the ARRY generic valuation model are required to enable progressive application allowing for different lease terms — in a continuation of the systematic explanations. These adaptations of the basic ARRY model’s algorithm, formulae, and equations are required firstly to allow for the timing and frequency of payments, and secondly to allow for lease termination, or releasing on expiry. Allowance for operating expenses (OPEX), prescribed or pre-determined rent review formula concludes the completed generic model. These steps are proven by mathematical examples and confirmed using an updated user-friendly Excel™ valuation template. The latter is the technological advance on previous real value models that simplifies the practical use of the model in the hands of valuers, investors, and analysts. Testing the ARRY valuation model on actual property sales analyses and valuations in conformity with commonly found variations in lease terms and market conditions in NZ, requires further adaptations of the ARRY valuation model as included in the balance of this model's descriptive development. These adaptations to the ARRY model’s algorithms, formulae, and equations allow for renewals of leases with changed terms, under-developed properties, vacancies, re-leasing costs, and rent-free periods. Allowances for costs of purchase and/or sale, capital expenditure (CAPEX), and for partial gross leases with variable OPEX recoveries concludes the generic model. User-friendly Excel™ ARRY valuation templates are developed which are used to illustrate the fully worked mathematical examples, confirming the results. This advanced development of the ARRY valuation model concludes its development in preparation for the empirical testing of the model by application in real world sales analyses and valuations for market transactions involving single-tenant properties. To apply the ARRY valuation model to single multi-tenanted properties or to portfolios of separate properties does not require major adaptations to the ARRY valuation algorithms, but is achieved by separate calculations for each separate tenancy, income and expense item, in each separate property, and the summation of those PRVs to the total value of each property. A special multitenant Excel™ ARRY valuation user-friendly spreadsheet template is used. Where the valuation involves the analyses of sales, or valuation of portfolios of different properties, a different property portfolio Excel™ ARRY valuation user-friendly spreadsheet template is used, see Section 5.2 Advanced ARRY valuation template model at page 115. The development of these templates as introduced and explained have demonstrations presented in case studies (Jefferies, 2017a).

18


1.8 Professional application and significance This ARRY model's design, founded and developed principally for income property (rented real estate) valuation, based on economic and financial theory/principles has robustness in its simplicity and effectiveness. Developed theoretically, illustrated by examples, and empirically tested as demonstrated by case studies, it shows the ARRY model to be user-friendly in comparison to existing valuation models. The expectation is that its use will prove to be superior in efficiency; more transparent; achieving equal or better accuracy by comparison to synchronous sales prices; being reliant on fewer uncertain and/or unreliable forecasts of future property performance assumptions. ‘Competition’ comes from a long history and use of simple ‘direct’ and ‘yield’ capitalisation models. Since the mid 1990’s these traditional models have been superseded by increased use and reliance on explicit discounted cash flow (DCF) techniques – especially since the availability of proprietary ‘off-the-shelf’ computer software packages and customised Excel based templates (Jefferies, 1995; Parker, 2001a, 2003, 2004c; Parker & Robinson, 2002). All these DCF valuation models use nominal value theory, rely on forecasting growth (or decline) in nominal values, and then discount these forecasts using ‘risk adjusted’ nominal required rates of return. These, in effect, have a large offsetting element (nominal growth inclusive of inflation) built into the cash flow forecasts and into the nominal discount rates - that allow (or are increased for) expected inflation and any real growth included implicitly in the over-all nominal growth rate used in the models. Thus in offsetting those uncertain forecasts, these models are illusionary in their presentation of ‘forecasting accuracy’ and result in complexity requiring detailed, often unfounded explicit dollar future forecasts. Such forecasts give false representation of accuracy due to specifying future nominal cash flows that are inherently uncertain. The European Mortgage Federation (EMF) called for improved transparency, accuracy and acceptance of methodology, reliability and usability of valuations especially for cross-border valuations and updating (EMF, 2009). The ARRY model aims to address these types of objectives. Notwithstanding the aim is to build and test the new ARRY model, part of its testing necessarily includes applying the model alongside conventional methods of actual completed valuations carried out by valuers in their practices, allowing observations, and feedback on: •

Ease of application (in an Excel™ user-friendly format) by busy practitioners.

•

Difficulty or ease of establishing the inputs required.

•

Difference in the model’s results compared to completed valuations using conventional methodology.

•

Accuracy measured by the model’s resulting valuation(s) compared to any actual subsequent sale(s) where applicable. This allows measurement of the relative accuracy of the ARRY valuations against the valuations using the models currently used by professional valuers.

•

Differences in application and accuracy with use in valuations of different types of investment properties, number of tenants, location, and expertise of practitioner, etc.

•

Problems encountered in use and suggested improvements.

The purpose of the case studies, empirically testing the above, and the interim results achieved leads to the conclusions that the ARRY real valuation model has potential benefits to the valuation profession, subject to further testing and any necessary further adaptations.

19


1.9 Policy implications The policy implications for the real estate and property valuation industry include promotion of real value valuation model(s) for use in income property valuations. The international and local valuation standards should provide for and set standards around their adoption and develop appropriate International Professional Standards (IPSs) that govern the competency of valuation professionals, through codes and benchmarks for their conduct, capability, and competency. These include International Valuation Standards (IVSs) and supporting technical guidance — published by the International Valuation Standards Council (IVSC) for their use and application. 4 The ARRY model must comply with and satisfy the objective test of compliance with such standards (or the standards need updating to allow its use). Valuation standards and IVS Applications (previously Technical Information papers (TIPs) need to be universal in nature and not modelspecific. Other real value models may be developed and promoted as also satisfying such objective valuation standards and criteria.

1.10 Case studies Case studies are widely used in property research, both as a primarily research methodology with the aim of showing not only how the model is applied in practice, but also to test its accuracy, effectiveness and flexibility compared to conventional valuation methods. Readers are referred to a full description of the use of six ARRY case studies and their results in (Jefferies, 2017a). Variations of the fully developed ARRY valuation Excel™ spreadsheet templates are used as in the case studies, applied variously to single tenancy properties or multi-tenancy properties as discussed in detail in Section 4.6. These case studies demonstrate the flexibility of the model, especially in the use of the user-friendly Excel™ spreadsheet templates to adapt to a wide variety of tenancy lease terms and conditions, with minimal data and assumption inputs. Additional Excel™ spreadsheet templates developed for portfolios of separate properties are described in Section 5.2 Advanced ARRY valuation template model. See an application and use in (Jefferies, 2017a, Section 6. CASE STUDY 6 ― Portfolio sales analysis ― Farm supply depots saleleasebacks p. 119). Four of these case studies give comparisons with conventional valuation methods where subsequent sales did not occur, a typical scenario in valuation practice – especially where undertaking asset valuations i.e. for financial reporting purposes. Two of the case studies compare the ARRY valuations to DCF valuations, where synchronous sales had not taken place, so could not be tested for valuation accuracy and are limited to measuring valuation differences.

4

It is noted that under the IVSC April 2016 Exposure draft of IVS 104: Bases of Value "The IVSC definition of Fair Value contained in IVS 2013 has had its nomenclature changed to Equitable Value to avoid confusion with IFRS 13 and other definitions of “Fair Value” currently used in the market place."

20


Chapter 2 — Developing the theoretical all-risks real yield (ARRY) model 2.1 Introduction This Chapter firstly outlines the methodological and practical concerns raised about the use of DCFs, focusing on the need for market based required yields and the limitations of DCFs. The valuation profession’s response to these concerns follows, detailing the attempts to improve DCFs. Secondly, a case stated for ‘real value’ property valuation models follows, developing a focus on comparing conventional versus real value concepts, that is resolved over the rest of the Chapter. Thirdly, the relevancy of real value valuation models follows, describing the objectives of the quest for an improved valuation method, i.e. the relevancy of real value models in achieving that aim and its potential as a 21st Century valuation model. A comparison of conventional valuation versus real valuation concepts sets the scene for development of a generic real value valuation ARRY model. Fourthly, a detailed staged development process follows, leading to introducing the all-risks real yield (ARRY) valuation model. The theory behind the new model, using a descriptive valuation problem, is progressively compared against direct capitalisation and conventional DCFs, real yield DCFs and net of growth DCFs. The purpose of the Chapter is to set the scene for the pedagogy of the detailed all-risks real yield (ARRY) model in the following Chapters 3 to 5.

2.2 Methodological concerns with DCFs Over the years, a number of concerns have been raised about the assumptions behind and inaccuracy inherent in traditional DCF valuation methodology in major respects, as follows: 1.

There is a perceived need for consistency in obtaining the data inputs, especially the required overall yield or discount rate from analysis of comparable sales transactions. The IVSC Guidance Note No. 9 (2003, Section 5.0) introduced the requirement to reflect market data. Data should be sourced, analysed and applied in a consistent process to achieve accuracy in resulting valuations. Gunnelin et al. (2004) researched DCF valuations for the Swedish SFI/IPD property index and found inconsistencies in the key input variables, discount rate, expected growth rate and exit capitalisation rate. Criticisms also include too much reliance is placed on opinion, client surveys or utilising a capital asset pricing model relying on finance theory. The practical difficulty is in obtaining sufficient data on the sales and from their analyses to produce defensible marketbased yields. These criticisms add to the multiplicity of other assumptions and forecasts that the model requires, rendering the explicit DCF valuation both challenging to execute properly and resulting in dubious valuation reliability. Hordijk & van de Ridder (2005) researching DCFs in the Netherlands for the ROZ/IPD Dutch property index also found little consistency. They suggested improvements particularly the need for high accuracy, consistency, integrity, and uniformity of input variables in DCF valuations, especially for valuations used in establishing market benchmarks such as for property performance indices.

2.

Lack of transparency due to reliance on proprietary DCF valuation software with concealed calculations i.e. in hidden cells and pivot tables, etc. This gives rise to criticism of valuers relying on calculations they are unable to explain or duplicate by hand. This is reflected in the IVSC Guidance Note No. 9 (2003, Sections 5.8 and 5.9). Section 5.8 recommends the valuer who supervised the construction of the DCF model or the selection of a proprietary model to be responsible for the integrity, theoretical, mathematical correctness, magnitude of the cash flows, and appropriateness of all inputs to allow replication of the results by users of the valuations. Section 5.9 requires the valuer to disclose the assumptions so that users of the valuation can replicate the results, and identify the proprietary DCF model, if used. This onerous 21

Real Value Valuation for Real Estate Investments (Jefferies, 2017) requirement was maintained in the later 2007 revision (IVSC, 2008) but not included in the latest and more generic Technical Information Paper 1 (TIP1) (IVSC, 2012) that replaces the previous IVSC Guidance Notes. 3.

DCFs have been criticised as being obsolete (Jefferies, 1996). Parker (1993, 1994, 1996, 2001b, 2004a, 2005) a long-time critic of the Australian valuation efforts to standardise valuation methods in that country has written extensively on the problems with DCFs, especially its use in depressed markets and the impact of unjustified capitalisation rates on terminal values. Parker (2002, 2004b) also criticised the proposed Australian DCF Guidance Notes and researched the influence and use of DCF software packages by valuers, investors and fund managers in Australia (Parker, 2001a, 2003, 2004c; Parker & Robinson, 2002). He attacked the influence of fund managers on valuer’s inputs and assumptions and the dichotomy between theory and practice. The efforts at introducing Valuation Guidance Notes for DCFs was more successful with New Zealand leading the way (NZIV, 1995) with much of the content being incorporated into the first International DCF Guidance Notes (IVSC, 2003).

4.

Other criticisms relate to differing assumptions used and the techniques applied. Boyd (1995) focussed on inconsistencies in model construction and data accuracy; Hanford (1973; and later in 1991) reveals how DCFs changed in the US over the intervening years but retain a set of potential flaws and concluded that DCFs must be rational if the results are to be credible. Kishore (1996) criticised the use of DCFs arguing they should reflect investors’ decision making, and be based on property market evidence. Mackmin (1995) was concerned at the use of DCFs in over-rented property, especially with determining market target discount rates, the inappropriateness of assuming long-term rental growth rates when conducted during critical short-term market phases, and the acceptance of intuition in DCF assumptions as a basis for market valuations. Martin (1993) was concerned with multi-year DCFs that rely on value determining variables such as the ‘heroic’ assumption concerning reversion value, and that the target yield should reflect rates currently anticipated by typical investors not a subjective assessment, i.e. must be market-extracted. A growing concern by investors relying on valuations quoted in financial reports and prospectuses over the inaccuracy of valuers’ inputs 5 lead to valuers being sued (Dey, 1998) for avoidable errors that drove the forecasts of cash flows, terminal values and how both discount rates and terminal capitalisation rates were being determined.

5.

Recent research includes Wyatt (2011) who addresses the issue of comparative analysis to determine the relevant discount rates using the same rate throughout. His concern is that this implicit approach fails to recognise the difference in risk between the early term income and the riskier reversion. A uniform discount rate ignores the risk of a highly illiquid reversionary property interest resulting in over-valuation by using too low a rate to discount the terminal value.

6.

In Australia, Boyd (2003) conducted a study on the variation in valuations due to inconsistencies in DCF model construction and data collection finding these cause bias as a major concern. Lusht and Squirrell (1997) focussed a study on two key DCF’s relationships 1) between income and value change; and 2) holding period and discount rate. They found that the credibility of the resulting value is a function of the quality of assumptions about rents, vacancies, expenses and the reversionary value and these cannot be made in a vacuum. In respect of the terminal value, they stated:

5

“The Newmarket Property Trust …told the stock exchange yesterday that the $72.5 million valuation of its Rialto property by Ernst & Young on 30 June 1997, should have read $69.5 million. Two errors were found in the valuer’s input into their discounted cash flow model for the 1997 assessment during a review of the valuation for the June 1998 balance date. Mr Keys said the errors’ combined effect was to overstate certain present and future rents.” Bob Dey, New Zealand Herald, 3 June 1998, p. E12. In May the 1997 books were corrected with a $3 million deduction. In August the trust said revised valuations had shaved 11% off its Rialto property's worth.

22

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Forecasting 5-10 years is difficult. Beyond that it is truly heroic, though there is comfort in the thought that the task is equally difficult for the market, and it is the market’s expectations the valuer is attempting to simulate. 7.

Examination of DCF valuations invariably show considerable variation between ex-post cash flow performances and ex-ante forecasts. Questions raised also highlighted valuation difference and error arising from assumptions in valuations.

2.3 Summary of concerns about DCFs The discounted cash flow valuation method is well established in NZ, Australia, parts of Europe & throughout North America for market valuations, but is not used in the UK for market valuations, but for assessments of “worth”. Other than for prime, multi-tenant “investment grade” property, DCFs are still not widely used in NZ, especially outside the three main metropolitan centres of Auckland, Wellington and Christchurch. The major limitations of conventional explicit period-by-period DCF valuations are that: i. ii. iii. iv. v. vi. vii. viii. ix.

Calculations being in nominal currency – requires forecasting of future rents, expenses and terminal values. Nominal growth rates mask expected monetary inflation and real growth. An assumed holding period and sale date (usually in exactly 10 years). Adopting a subjective terminal capitalisation rate applied to then forecast net rentals. A nominal discount rate (normally pre-tax, 100% equity). Overall yields used, implicitly includes monetary inflation and real growth. Potential bias due to client influence in specifying data inputs, discount rates and software. Many valuers use proprietary software with limited knowledge of the calculations actually done, whilst being held liable for their accuracy. A reluctance by valuers to use DCFs even when requested as this requires making future explicit forecasts, as found in the feedback from presentations in NZ of the ARRY valuation model, see Jefferies (2016, Subsection 10.3.1).

Section 2.4 begins a discussion of a new alternative that would overcome most of the above methodology related criticisms of DCFs applied to valuing income producing property.

2.4 The quest for an improved investment valuation model Against this background of the limitations of DCFs, the need for a better market place based ‘expectations’ valuation model became evident. Klaasen (1989) opined, “appraisal is an art (not a science) and cannot be made into a science” and further that “appraisers are human” and “... not omniscient ... cannot meet impossible expectations”. However, the foregoing historical perspective in Chapter 1 and the limitations of conventional DCF valuations above sets the scene for the quest for a ‘better way’ to conduct investment property valuations. The objectives of a better valuation model, compared to conventional DCFs is to offer the following benefits: 1. Relies primarily on current property market evidence. 2. Involves a simpler and more efficient method of analysing sales data to determine yields. 3. Eliminates suspicious explicit period-by-period forecasts as to timing and forecasting of future cash flows. 4. Removes arbitrary conventional holding period constraints. 5. Simplifies and saves time avoiding the mechanics of explicit period-by-period DCF forecasting, with their complex calculations. 6. Limits valuers’ exposure to ex-post scrutiny and liability for forecasting and valuation errors. 7. Avoids errors due to assumptions and formula hidden in spreadsheet cells or black box custom software, macros and pivot tables, etc. 23

Real Value Valuation for Real Estate Investments (Jefferies, 2017) 8. Achieves transparency in presentation of assumptions and calculations for manual checking, even if incorporated into a spreadsheet model. 9. Provides a model that relies on a minimum of the valuer’s assumptions, which are related to observable market evidence and its analysis. 10. Relies on valid extrinsic data that is verifiable, available to, and relied on by the investment market players at the date of valuation and inherent in their decisions, e.g. expected inflation. 11. Focuses on current values as the present real value of all future expectations, i.e. in real terms, as indicated by the current market not unsubstantiated prediction, or conjecture. 12. Able to be expressed without too much difficulty, in conventional nominal currency terms and replicated in more familiar explicit DCF methods as a check on its validity for confidence building in the process of adopting of the new model. 13. Provides a defensible alternative valuation approach where valuers resist (or refuse) to provide DCF valuations due to the uncertainty of the forecasts required, easily understandable to clients. The above list provides specific and tangible criteria for objectively assessing the aims and objectives more generally expressed in Section 1.1 at page 11.

2.5 Real value valuation for the 21st Century To transform the ‘old’ real valuation models, as referred to in Sections 1.3 to 1.5 and covered in Section 3.2 Stage D: Building the generic all-risks real yield (ARRY) valuation model, into a ‘new’ model, and to have any hope of its adoption by the valuation profession, requires re-mastering the concepts simply in terms of presentation and ease of use. Ideally, it needs minimal formulary, coupled with a paradigm shift from a ‘nominal’ valuation construct to a ‘real’ valuation construct. The ARRY valuation model is described from its nascency through to its fully developed model in the balance of this and following Chapters 3 to 5. The model is described narratively, shown in basic algorithms (logical computational procedure for solving problems), then expressed in formulae and equations, mathematically calculated following a common but progressively adapted example that is duplicated in user-friendly spreadsheet templates.

2.6 Conventional nominal value versus real value concepts The term conventional here refers to the common or traditional valuation methodologies used by valuers and appraisers that rely on models that calculate present values based on nominal forecast monetary future rents, costs and values. These future nominal cash flows are discounted at an overall required nominal rate of return or yield that includes an (unspecified) inflation assumption. Current and future values utilise capitalisation rates that implicitly include or an allowance for any nominal growth. The financial use of the term real value is where rentals and capitalised values are expressed in present currency with expected future rentals and values that are deflated (i.e. after allowing for future expected inflation) but allowing for a ‘real’ growth assumption. The two paradigms underlying the nominal value versus real value models’ concepts are shown in Table 1 following at page 25. This table sets out the fundamental comparisons between the two basic concepts in terms of the two types of valuation models. It notes commonality in concept and details the differences between conventional (or traditional) valuation models that compute values in accordance with a nominal currency paradigm compared to real value valuation models that compute values within a real terms paradigm.

24

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Based on these contrasting features of the two types of valuation models the next Chapter 3 develops the real value model concept and compares it to the nominal value equivalent, after introducing the basic real value theory and capitalisation concepts, algorithms and formulae.

Table 1 Conventional nominal versus real value concepts The fundamental point of commonality is that: i. The present or current value of a property when expressed in nominal terms is also its value in current real terms. The simple difference between models are: Conventional nominal models Real value models ii. Future income is forecast in nominal terms, iii. Future income is forecast in current real terms; allowing for real growth in rentals and allowing for nominal growth in rentals and future real values. future nominal values. Capitalisation rates allow explicitly for iv. Capitalisation rates allow implicitly or v. expected monetary inflation and growth in explicitly for growth in nominal terms real terms. (including unspecified inflation). vi. In DCF valuations, future nominal income and vii. In DCF valuations, explicit future expected reversionary values are discounted to present real growth in real income and reversionary value at a required nominal yield rate values are discounted to present value at a (including implicit expected inflation). required real yield rate (excluding expected inflation). In terms of operating expense (OPEX): viii. Unrecovered OPEX is allowed for by Unrecovered OPEX are allowed for by ix. capitalising their current costs at a nominal capitalising the current real costs at a real overall capitalisation rate that implies future capitalisation rate that implies no future real nominal increases at the rental growth rate. (but only expected inflation) or explicit OPEX cost indexed increases. In terms of capital expenditure (CAPEX): x. Future forecast nominal CAPEX is discounted xi. Future forecast real CAPEX is discounted at a at a nominal discount rate that implies future real discount rate that implies no real (only nominal increases at the implied rental CPI inflation or an explicit expected growth rate. construction cost index) future increases.

2.7 Implementing the development of real valuation models The all-risks real yield ARRY (YA) valuation model needs to be placed in its progressive developmental context. The following description of the ARRY model’s development is illustrated by a simple common valuation example, in the progressive expansion of each of the following four nascent stages A, B, C and D of its development. A formulary is shown in the following Table 2 defining the symbols, abbreviations, definitions, explanations, and formulae used in the next three stages. These are combined into an overall Formulary shown in Appendix A at page 201.

25

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Table 2 Formulary for Stage A, B, and C Symbol or abbreviation C Cc

CMV Co F GO Gr

Ie

RO

ROF

ROT

RrF

Definition Cash flow Current market contract review rental

The periodic rental (as a receipt). Assuming the rental was reviewed at the sale or valuation date in accordance with the lease. The lower case subscript c denotes current. The sum of the present values of the contract term(s) Current market value to run and the reversionary value(s) The rental actually paid under an existing lease. The Contract rental lower case subscript o denotes contract. Frequency of rent reviews In years, specified in the lease contract Nominal (overall) annual Growth in market rentals on an annual basis. The (p.a.) rental growth rate subscript O is a capital letter, not 0 (zero) = overall. Real annual (p.a.) rental Growth in rentals excluding inflation on an annual growth rate basis. The subscript r = real. Expected (e) monetary inflation rate, p.a. Growth in monetary value only: Note I = inflation a capital Ie = (GO−Gr) p.a. or compounding basis i (I) not 1 or L, and the Ie = [(1+GO)/(1+Gr)]−1; excludes real growth, similar lower case e denotes to Wood's (1973) “d” = inflation risk. expected Where R = rate, the subscript O is a capital letter: Over-all capitalisation Co not 0 (zero) = overall. RO ⇐ CMV rate Nominal annual (p.a.) rental cap rate where F years rent review frequency Nominal annual (p.a.) rental cap rate where T years term to run Nominal annual (p.a.) real yield rental cap rate where F years rent review frequency

T

Term to run

YN

Net of growth yield

YO

Over-all yield

YO

Yr

Explanation and formula (if any)

Required annual overall yield rate, or nominal rate of return on investment; where O is a subscript capital letter O, not a zero 0 Real yield

Based on nominal annual rental p.a in arrears: RO F ⇐ YO �1 −

(1+GO )F − 1 � (1+YO )F − 1

Based on nominal annual rental p.a. in arrears: RO F ⇐ YO �1 −

(1+GO )T − 1 � (1+YO )T − 1

Based on nominal annual rental p.a in arrears: Rr F ⇐ (Yr +Ie ) �1 −

(1+Ie +Gr )F − 1 � (1+Yr +Ie )F − 1

T = Term to next rent review or renewal, whichever is the lesser, in years The Y = yield, the N is a subscript capital letter N = net of growth. The Y = yield, the subscript O is a capital letter, not 0 (zero) = overall (See redefined below). Considers all expected property benefits and risks, without financing or tax similar to IRR where: NPV = 0; in nominal terms Yo = Ro+Go; also Yo = Ro+Ie+Gr

Where Y = yield; and r (subscript, lower case) = real

26


Stage A: Direct capitalisation and conventional DCFs The direct (over-all) capitalisation and nominal explicit DCF valuation models, in which all forecasts are in nominal cash flows, are based on discounting future receipts and /or payments at an over-all required yield rate YO. Direct capitalisation applies an over-all capitalisation rate RO to the contract rental (or a stabilised net operating income (NOI). The conventional explicit forecast period-by-period DCF can be simplified and expressed in a term and reversion method, i.e. a short-cut DCF format. This format discounts the contract rental Co payable over the term to run to the next rent review in T payment periods as an annuity due, to give the present value (PV) of the ‘term’. Then the direct capitalisation of the current market review contract rental Cc forecast at the nominal growth rate GO to the beginning of the next rent review, also in T payment periods, is capitalised at the over-all capitalisation rate RO and discounted at the overall required nominal yield rate YO to give the PV of the ‘reversion’. The sum of the PVs of the ‘term’ plus the ‘reversion’ is the total PV of the investment or the CMV. Both direct capitalisation and nominal explicit DCF valuation models assume that after expiry of the term to run, the lease will be renewed on the same review periods with the implied (or explicit) nominal compounding growth GO as a continuum in perpetuity.

Stage B: Real yield DCFs This re-expresses the above conventional term and reversion model as a real yield model explicit DCF valuation, i.e. converting cash flows into real terms. This is done by discounting all nominal forecast rentals and terminal (reversionary) values for expected inflation Ie, to express them in current real terms. Then these future real cash flows are discounted at a (net of expected inflation) real yield compounding rate Yr.

Stage C: Net of growth (or hybrid real value short-cut) DCFs The real value DCF model in Stage B is re-expressed by converting it into a generic net of growth yield real value valuation model (equivalent to Crosby’s hybrid real value - equated yield model). This splits the treatment of the (i) term and (ii) reversion elements, respectively applying nominal and real value approaches: (i) The term is valued based on the nominal contract rental Co during the term to run to the next rent review in T periods, discounted at a nominal discount or overall yield rate YO to calculate its present value (PV). This is calculated as the PV of a terminating annuity due. (ii) The reversion is valued based on the current market contract review rental Cc capitalised at the over-all capitalisation rate RO, but discounted at a net of growth discount or real yield rate YN to calculate its present real value (PRV). Note: no growth is forecast to the review date. The PV of the (i) term to run is added to the PRV of the (ii) reversion to give the total present (and real) value or current market value (CMV).

Stage D: An introduction to the generic all-risks real yield (ARRY) valuation model Following the above three stages is a description of the advancement to develop the all-risks real value ARRY (YA) model. It requires the introduction of a new concept of real growth Gr that together with expected inflation Ie, is used with YA to calculate the basic all-risks real yield capitalisation rates RAT and RAF. These are respectively used for capitalising the contract rent Co based on T = the term to run review frequency rental; and for capitalising the current market contract review rental Cc based on F = the contract rent review frequency for calculating the reversionary value. [See definitions in Subsection 3.3.4 Table 3 Formulary for Stage D at page 49, and full explanation in Section 3.4 at page 49.]

27

Real Value Valuation for Real Estate Investments (Jefferies, 2017) The all-risks real yield, ARRY (YA) is now introduced and defined as: The real value annually in arrears yield is the real internal rate of return that discounts the real values of the term to run and the real reversionary value(s) to the present real value (PRV), being the sale price or current market value. The YA is determined from sales analyses, and on an annual non-compounding basis its relationship to YO, Yr and YN is: YA = YO – (Ie +Gr); = Yr - Gr; = YN – Gr where Ie is the expected inflation rate; and Gr is the expected real growth rate. The model’s formulation is a special and new format of a term and reversion model that also allows for modifications for additional non-annual incomes or expenses. Each of the preceding stages A, B, and C are described in detail in the balance of this Chapter as to their development, algorithms, formulae, calculation and with examples under the following subsections. Critiques discuss the advantages, limitations, and disadvantages of these models. Stage D is describes in detail the ARRY real value valuation theory and methodology with algorithms, formulae, and illustrative examples in Chapter 3.

28


2.8 Stage A: Direct capitalisation and conventional DCFs The basic nominal conventional direct capitalisation and explicit DCF valuation model, forecasts nominal cash flows that are discounted at the over-all yield rate YO. Direct capitalisation simply capitalises the contract rental or a stabilised net operating income (NOI) applying an over-all market capitalisation rate RM. Where a sale is analysed the contract rental ÷ sale price = the initial yield R1 = RM. Where the valuation/sale date coincides with a lease commencement or rental review date RM = RO the over-all capitalisation rate. RO is correctly determined by market factors of: the over-all yield rate YO, the frequency F of the rent reviews, and the expected rental growth rate GO, and redefined more correctly and explicitly as ROF as detailed under Section 2.11 following at page 31 and defined previously in the Formulary in Table 2 at page 26. When the valuation date is between the commencement date and the next rent review date coupled with positive market rental growth i.e. GO >0, the initial yield R1 will reduce due to the fixed rental until approximately mid-way in the term to run. Then it will rise to the next review date, R1 ≤ RM, but correctly determining R1 when a valuation is required (other than coinciding with a rent review date) is problematic and very difficult to do subjectively. Technically, it is a time-weighted average of the basic all-risks real yield capitalisation rates RAT and RAF as is described in detail following in Section 2.12 using Algorithm 3 at page 32. For example, see analysis of Sale 1 as introduced in Section 2.10 at page 31 and as analysed in Section 2.12 in Equation 7 and confirmed using a nominal DCF analysis in Figure 2 at page 33, where the initial yield R1 = 7.0175% p.a. However the market cap rate is RM = RO3 = 7.2141% p.a. for three year reviews, based on GO = 3.0000% p.a. and YO = 10.0151% p.a. Inaccuracies regularly occur in direct capitalisation valuation usage by valuers who simply arrive at capitalisation rates subjectively, based on ‘comparable’ initial yields, using unsophisticated adjustments based solely on experience or nouse. The conventional explicit DCF model takes the contract rent Co (less any unrecovered outgoings) as the net cash inflows (outflows) over the term to run T, i.e. until the next rent review. Then a forecast, in nominal value terms, is made of the rental as from the next review in T years, based on the current market contract review rental at the date of sale or valuation in terms of the lease review and other terms and conditions, etc. This is grown at the nominal growth rate GO% p.a. This forecast calculates a future reviewed rental at Cc(1+GO)T. The following rent review then forecast to increase to Cc(1+GO)T+F. The rental growth is repeated at the following rent review, i.e. at Cc(1+GO)T+(2xF) and so on, until the selected termination date at the end of the holding period. However, the termination date is rarely synchronous with the then next review date(s) at the end of a conventional DCF’s 10-year holding period. Unless the terminal value is based on another forecast term and reversion valuation, this mismatch of dates causes an error especially where the 11th year’s forecast rentals are capitalised at the over-all capitalisation rate RO. The error in the terminal value is discounted to the PV. As the PV of the terminal value varies between 40% to 60% of the CMV (Bottum, 1993; Jefferies, 2012) it can be a material error. Where unrecovered OPEX and non-annual capital expenditure (CAPEX) or other expenses occur, such as costs of refurbishment or releasing, these are not necessarily forecast at the same growth rate as the rental growth. These are often based on a forecast CPI (Ie) or other inflation growth in nominal terms. The forecast net cash flow for each year (or period, such as monthly) in the holding period is calculated. Sometimes the 10th year’s net cash flow is capitalised at the terminal capitalisation rate adopted to determine the terminal value (TV) and added to the 10th year’s net cash flow from income less expenses. More correctly, the forecast 11th year’s net cash flow is used to represent the first year’s income that a hypothetical new purchaser would receive by purchasing the property at the end of the 10th year. 29

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Practice varies as to whether purchase costs are deducted at the beginning of the investment period (i.e. at period 0), or deducted from the resulting PV or gross value to arrive at a net value as at the date of valuation. Similarly, practice varies as to whether sale costs are deducted at the end of the investment period (i.e. at end of period 10) resulting in a reduced TV. The net cash flows, including the TV added to the 10th year’s net income cash flow is discounted at the required yield YO to give the PV as at the date of valuation, being the current market value (CMV) on a DCF valuation basis.

2.9 Explanation by way of a progressive valuation problem To compare the conventional nominal value term and reversion model with the ARRY real value model in Stage D, a simple Example 1 is used as a basis to illustrate the three progressive explicit DCF valuation models in Stages A, B and C. The Example 1 property being valued has F = 5 year rent reviews, the lease has T = 4 years to run to the next review at the existing contract rent Co= $39,500 p.a., payable annually in arrears. The current market contract review rental assuming it was reviewed at the valuation date is Cc = $40,685 p.a. It is in a location where growth in market rental, is supported by recent reviews and new leasings, indicates an approximate GO = 3% p.a. nominal growth in rentals is sustainable, and an overall nominal yield of YO = 10% p.a. is assumed, based on recent sales analyses (see following Section 2.10). A chart of the assumed annual cash flows annually in arrears for the term to run and assumed

perpetually renewable lease terms to infinity ∞ (though shown for 11 years) follows in Chart 1 below. Chart 1 Example 1: Forecast cash flows and term and reversion structure Example 1: Forecast Nominal Cash Flows and "Term & Reversion" Structure PV of Reversion PV of Term to Run

$55,000 $52,500 $50,000 $47,500 $45,000 $42,500 $40,000 $37,500 $35,000 $32,500 $30,000 $27,500 $25,000 $22,500 $20,000 $17,500 $15,000 $12,500 $10,000 $7,500 $5,000 $2,500 $-

1

2

3

FV of Reversionary Incomes

4

Nominal Contract Rental p.a. (EOP): Present Value of Forecast Rentals @ 10% p.a.:

Reversion

Nominal Cash Flow Income P.a.

Total PV of Future Cash Flows

Period Ended 5 6

7

8

∞

9

10

→∞

11

Nominal Market Rentals @ Go = 3% p.a. Expon. (Nominal Market Rentals @ Go = 3% p.a.)

The columns in the chart represent the contract rental Co = $39,500 p.a. for the four years to run and then five yearly rent reviews thereafter. The forecast current market contract review rental increases over four years at GO = 3% p.a. compounding nominal growth forecast to the next review at Cc = $40,685(1.03)4 = $45,791 p.a. from the end of the fifth year. Thereafter Cc increases from every additional fifth year’s review. This series of tranches of income carries on in perpetuity in this simple shaded columns show the annually increasing example, with five-year reviews. Similarly, the market contract rentals at the GO = 3% p.a. growth per annum. The columns with the thick black outline show the present values of each contract rental received, discounted at the YO = 10% p.a. to the beginning of period 1 (i.e. = end of period 0), being the sale or valuation date. 30


2.10 Comparable sale and its analysis It is assumed there is good comparable recent market evidence, the most comparable being Sale 1 of a similar property type, characteristics, location, asset class and investment risk profile as Example 1. This Sale 1 property sold recently for $570,000 and has a lease with F = 3 year rent reviews and sold (to make the calculation simpler) on an anniversary of a rent review date with T = 2 years to run until the next rental review. The existing contract rental Co = $40,000 p.a., the current contract market review rental (if reviewed at sale date) Cc = $41,200 showing $1,200/$40,000 = GO = +3% p.a. nominal growth in one year and in line with the general market evidence of growth rates. In a conventional direct capitalisation approach the sale analyses to derive an initial yield R1 or capitalisation rate (but not a RO or ARY as the date of sale is between rent reviews) is: R1 = $40,000 p.a. ÷ $570,000 ⇒ 0.070175 or 7.0175% p.a. Intuitively the valuer will know this initial yield is lower than it would be if recently let, i.e. R1 < RO or ARY shown later in Equation 6 at page 32 as RO3 = 7.2137% p.a., as the rent is low compared to the current market. This reflects the pending rental review in two years’ time. It is not indicative of the capitalisation rate to apply to Example 1, due to quite a different term to run T = 4 years and review term F = 5 years. It requires the calculation of a capitalisation rate that adjusts for these differences. If it was applied without an (upward) adjustment, it would result in an over-valuation (of $39,500/0.070175 = $562,870, $14,512 or 2.65% higher than the correct valuation of $548,367 in Equation 8 at page 34, but it is impossible to make that capitalisation rate adjustment intuitively.

2.11 Calculation of the “correct” capitalisation rate To analyse the sale to derive the implied overall market yield, given evidence of the rental growth rate – for a more accurate valuation, the valuer might apply a term and reversion technique. This short-cut discounted cash flow (DCF) technique requires the three inputs of YO, GO, and F to calculate the market contract review rental capitalisation rate ROF. Whipple (2006, p. 232) gives the nominal capitalisation rate formula as the present value factor applied to an annual in arrears annuity of $1 p. a. that increases at a constant growth rate at regular frequency of time intervals = F, in perpetuity. Whipple attributes his formula to Rose (1979) but this source only postulated this formula in that paper and in Rose’s Valuation Tables (Rose, 1976). Whipple also refers to a derivation and proof provided by Worthington (1979, pp. 368-369) later published in Worthington’s text (1990, p. 42), and independent proof 6 in Jefferies (2016, p. 381). Where: ⇐ indicates ‘results from’, not an equality (=), the capitalisation rate formula is: (1+G )F −1

RO F ⇐ YO − YO � (1+Y O)F −1 � O

The second term in Equation

(1+G )F −1 1, YO � (1+Y O)F � adjusts O −1

Equation 1 the overall required yield rate YO for the

deferred timing of the growth GO over the rent review frequency F, to derive the capitalisation rate. Where there is no growth, i.e. GO = 0; then the capitalisation rate equals the discount rate, proved by simplifying Equation 1 and recalculating it so that ROF = YO. This is the result of a ‘steady state’ assumption where current nominal and real values are assumed to be fixed in perpetuity, i.e. never going to change, which has never been a reality in property markets. Equation 1 above is also simplified to: (1+G )F −1

RO F ⇐ YO �1 − YO (1+Y O)F −1 � O

6

Equation 1

Kindly provided by Assoc. Prof. Dr Amal Sanyal, Lincoln University.

31

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Note: At this stage of the model’s development, it is assumed rentals are received annually in arrears or at end of period (EOP) and reversions at the end of the rental term to run. This is a simplification of reality as rents in NZ are normally received monthly in advance or at beginning of period (BOP). However, later when developing the ARRY valuation model in Section 4.3 beginning at page 63, the basic generic adaptation is introduced to allow for the contractual frequency of rental payments paid in advance (BOP) or in arrears (EOP).

2.12 Extracting the expected overall yield YO from the sale analysis In a conventional nominal term and reversion valuation model, analysing Sale 1, given the market evidence of GO = 3.0% p.a., where F = 3 yearly, and T = 2 years to run, the valuer solves by ‘trial and error’ for YO and this will also simultaneously calculate RO3. The term and reversion short-cut DCF calculation is where: CMV ⇐ [PV of term T to run to next review] + [PV of forecast market value as at period T] Algorithm 2

CMV ⇐ [PV of Co as an annuity in arrears discounted @ YO over T periods] +[PV of forecast Cc capitalised in T periods @ ROF, disc. @ YO over T periods] CMV ⇐ Co

1−(1+YO )−T + �Cc (1+GO )T ÷ YO �1 YO

(1+G )F −1

− (1+Y O)F � ×(1+YO )−T � −1 O

Algorithm 3 Equation 4

Substituting the known data in Equation 4, the valuer solves by trial and error for YO: (1.030)3 − 1 1 − (1+YO )−2 $570,000 ⇐ $40,000 + � $41,200(1.03)2 ÷ YO �1 − � ×(1+YO )−2 � (1+YO )3 − 1 YO Equation 5 Which results in YO = 10.0151% p.a. and thus ROF = RO3 = 7.2141% p.a: (1.030)3 −1

0.092727

RO3 = 0.100151 �1 − (1.100151)3−1� = 0.100151 �1 − � = 0.072141, or 7.2141% p.a. 0.331548

Equation 6

This is difficult to do manually, so has been carried out in a spreadsheet using a ‘Goal Seek’ utility. The mathematical formula and abbreviated confirming calculation follows in Equation 7:

(1.030)3 − 1 1 − (1.100151)−2 + � $41,200(1.03)2 ÷0.100151 �1 − � × (1.100151)−2 � (1.100151)3 − 1 0.100151 0.092727 0.173781 +$43,709 ÷ �0.100151 �1 − � × 0.826219� $570,000 ⇐ $40,000 0.331548 0.100151 0.173781 +$43,709 ÷ 0.072141 × 0.826219 $570,000 ⇐ $40,000 0.100151 $570,000 ⇐ $69,407+$605,884 × 0.826219 $570,000 ⇐ $40,000

$570,000 ⇐ $69,407+$500,593

Equation 7

The full step-by-step mathematical solution is shown below: $570,000 ⇐ $40,000

(1.030)3 − 1 1 − (1.100151)−2 + � $41,200(1.03)2 ÷0.100151 �1 − � ×(1.100151)−2 � (1.100151)3 − 1 0.100151

1 − 0.826219 1.092727 − 1 +($41,200 × 1.0609)÷ �0.100151 �1 − � × 0.826219� 0.100151 1.331548 − 1 0.173781 0.092727 $570,000 ⇐ $40,000 +$43,709 ÷ �0.100151 �1 − � × 0.826219� 0.100151 0.331548 $570,000 ⇐ $40,000

$570,000 ⇐ ($40,000 × 1.735186)+$43,709 ÷{0.100151[1 − 0.279679] × 0.826219}

32

Real Value Valuation for Real Estate Investments (Jefferies, 2017) $570,000 ⇐ $69,407+$43,709 ÷(0.100151 × 0.720321) × 0.826219 $570,000 ⇐ $69,407+$43,709 ÷0.072141 × 0.826219 $570,000 ⇐ $69,407+$605,884 × 0.826219 $570,000 ⇐ $69,407+$500,593

This Sale 1 analysis, solved to find the correct market indicated over-all yield YO, is also set out in the following fully explicit period-by-period nominal value DCF over the period from the sale date to the reversion to a full market review rental commencing in three years, confirming the above calculations shown in Figure 2 as follows: Sale analysis : Traditional fully explicit nominal DCF valuation Nom. growth: GO = 3.0000% p.a. Over-all yield: YO = 10.0151% p.a. Period from sale date - Year Ended: 0 1 2 3 Market rental grown @ GO: $ 40,000 $ 41,200 $ 42,436 $ 43,709 F = 3.00 Yr Reviews Contract rental, 2 Yrs to run: $ 40,000 $ 40,000 Discounted @ overall required yield YO 10.0151% p.a. $ 36,359 $ 33,049 PV of Term to run: Total period discounted rents : Reversionary nominal value: forecast rental $43,709 p.a. capitalised at RO3: 7.2141 % p.a. PV of Reversionary value in 2 Yrs: Discounted @ overall yield YO 10.0151% p.a.

$ $ $

69,407 605,884 O/all cap rate: RO3 = 7.2141% p.a. 500,593

Total Present Value = Sale price:

$

570,000

Initial yield: R1= 7.0175% p.a.

Figure 2 Extracting the expected overall yield YO from the sale analysis

Similar to Chart 1, a chart of Sale 1 assumed annual cash flows annually in arrears for the term to run

and assumed perpetually renewable lease terms to infinity ∞ (though shown for 11 years) follows below that shows the different rentals and their PVs: Chart 3 Sale 1: Forecast cash flows and term and reversion structure

Sale 1: Forecast Nominal Cash Flows and "Term & Reversion" Structure

$55,000 $52,500 $50,000 $47,500 $45,000 $42,500 $40,000 $37,500 $35,000 $32,500 $30,000 $27,500 $25,000 $22,500 $20,000 $17,500 $15,000 $12,500 $10,000 $7,500 $5,000 $2,500 $-

FV of Reversionary Incomes

PV of Term to Run

∞

Reversion

Nominal Cash Flow Income P.a.

Total PV of Future Cash Flows

PV of Reversion

1

2

3

4

Period Ended 5 6

7

8

9

10

Nominal Contract Rental p.a. (EOP):

Nominal Market Rentals @ Go = 3% p.a.

Present Value of Forecast Rentals @ 10.0151% p.a.:

Expon. (Nominal Market Rentals @ Go = 3% p.a.)

33

→∞

11


2.13 Conventional term and reversion application in valuing Example 1 The Example 1 property is valued using a conventional term and reversion short-cut DCF model using the analysed market overall yield rate YO together with other similar sales analyses and judgement that YO = 10.0% p.a. together with market evidence of GO = 3.0% p.a. is applicable to this property. Applying Equation 4 to Example 1, where T = 4, F = 5, Co = $39,500 p.a., Cc = $40,685 p.a.: CMV ⇐ $39,500

(1.03)5 − 1 1 − (1.10)−4 + �$40,685(1.03)4 ÷ 0.10 �1 − � ×(1.10)−4 � (1.10)5 − 1 0.10

CMV ⇐ $39,500×3.169865+{$40,685×1.125509÷0.073911×0.683013} CMV ⇐ $125,210+($45,791÷0.073911)×0.683013 CMV ⇐ $125,210+($619,545×0.683013) $548,367 ⇐ $125,210+$423,157

Equation 8

2.14 Conventional DCF application in valuing Example 1 These definitions and formulae are applied in Example 1a which forecasts cash flows in a conventional DCF format until the next rent review, when the reversion is treated as a terminal value, in contrast to the conventional 10-year holding period as explained earlier. The capitalisation rate for the Example 1a property at the date of lease commencement or at a rent review is RO5 applying Equation 1 where: YO is 10% p.a.; GO is 3% p.a. and F = 5 fully calculated as follows: RO 5 = 0.10 �1 −

(1.03)5 − 1 � (1.10)5 − 1

1.159274 − 1 � 1.610510 − 1 0.159274 = 0.10 �1 − � 0.610510 = 0.10[1 − 0.260887] = 0.10×0.739113= 0.073911 or 7.3911% p.a. = 0.10 �1 −

Equation 9

Assuming the contract rental Co was a market rental fixed a year ago at $39,500 p.a. and growth since is consistent with future over-all growth forecasts of GO = 3% p.a.; the nominal value spreadsheet explicit DCF model valuation follows in Figure 4: Example 1a : Traditional fully explicit nominal DCF valuation Nom. growth: GO = 3.0000% p.a. Over-all yield: YO = 10.0000% p.a. Period from valuation date - Year Ended: 0 1 2 3 4 5 Market rental grown @ GO: $ 39,500 $ 40,685 $ 41,906 $ 43,163 $ 44,458 $ 45,791 F = 5.00 Yr Reviews Contract rental, 4 Yrs to run: $ 39,500 $ 39,500 $ 39,500 $ 39,500 5 $ 619,544 O/all cap rate: RO5 = 7.3911% p.a. Reversionary nominal value: forecast rental $45,791 p.a. capitalised at Ro : 7.3911 % p.a. Total periodic nominal future cash flows: $ 39,500 $ 39,500 $ 39,500 $ 659,044 PVs Discounted @ overall overall yield YO 10% p.a. $ 35,909 $ 32,645 $ 29,677 $ 450,136 Total Present Value :

$

548,367

Initial yield: R1= 7.2032% p.a.

Figure 4 Example 1a: Traditional fully explicit nominal DCF valuation

34


2.15 Stage B: Real yield DCFs This staged development of the model re-expresses the above conventional nominal value DCF model as a real yield model explicit DCF valuation, by converting it to real terms. This is done by discounting all nominal forecasted rentals and terminal (reversionary) values firstly for expected inflation Ie to express them in current real terms; and then secondly discounting at a compounding real yield (net of expected inflation) rate Yr where: Yr =(1+YO)/(1+Ie) –1. The expected monetary inflation Ie is obtained exogenously from independent economic forecasts, (sources are explained later under Stage D, in Subsection 3.2.1 at page 42. The following assumption is made for expected inflation at Ie = 2% p.a. and real growth is therefore Gr where Gr = GO – Ie = 3% p.a. – 2% p.a. = 1% p.a. The nominal conventional explicit DCF valuation model forecast cash flows is amended by discounting firstly for inflation Ie = 2% p.a.; and then secondly the resulting forecast real cash flows are discounted at the real yield (net of inflation) discount rate. On an annual non-compounding nominal basis the real yield Yr is derived as: Yr = YO − Ie = 0.10 − 0.02 = 0.08 or 8.00% p.a.

The compounding real yield is: Yr = (1+YO )/(1+Ie ) − 1 = (1.10)/(1.02) − 1 = 0.078431 or 7.8431% p.a.

The reversionary capitalisation rate Rr5 remains ≅ RO5 as in Equation 9 at page 34, also used in Example 1a at 7.3911% p.a. See real yield capitalisation rate formula in Equation 10 at page 36 and recalculation in Equation 11 at page 36. The real value spreadsheet explicit DCF valuation of Example 1b(1) follows in Figure 5: Example 1b(1) : Net of inflation - real yield Yr explicit DCF valuation Expected inflation: Ie= 2.0000% p.a. Period from valuation date - Year Ended: 0 $ 39,500 Market rental grown @ GO: Contract rental, 4 Yrs to run: Discounted for expected inflation @ Ie: 2% p.a.

Nom. growth: GO = 1 $ 40,685 $ 39,500 $ 38,725

Discounted @ net of inflation real yield Yr: 7.8431% p.a $

3.0000% p.a. 2 $ 41,906 $ 39,500 $ 37,966

35,909 $

Over-all yield: YO = 3 $ 43,163 $ 39,500 $ 37,222

32,645 $

5

Reversionary nominal value: forecast rental $45,791 p.a. capitalised at RO : 7.3911 % p.a. Discounted for expected inflation @ Ie: 2% p.a. Discounted @ net of inflation real yield Yr: 7.8431% p.a. Sum of discounted real cash flows: $ Total Present Value : $ 548,367

35,909 $

32,645 $

10.0000% p.a. Comp. Real yield: Yr = 7.8431% p.a. 4 5 $ 44,458 $ 45,791 F = 5.00 Yr Reviews $ 39,500 $ 36,492

29,677 $

26,979

$

619,544

$

572,363

$ 29,677 $

423,157 450,136

5 O/all cap rate: RO = 7.3911% p.a.

Initial yield: R1 = 7.2032% p.a.

Figure 5 Example 1b(1): Net of inflation – Real yield Yr explicit DCF Valuation This DCF net of inflation or real yield model format separates out the effect of inflation on the fixed and inflation prone rental cash flows in periods 1, 2, 3, and 4. The real value of the future contract rental to run is discounted first for expected inflation Ie = 2% p.a. and gives the current real value that reduces as at the end of each future period from $38,725 to $37,966 to $37,222 to $36,492 respectively. These expected real cash flows are then discounted at the real yield Yr = 7.8431% p.a. to give the PRVs reducing from $35,909 to $32,645 to $29,677 to $26,979 respectively for periods 1, 2, 3, and 4. Additional rows show separately the period 4 reversionary values, which results in a nominal future reversionary value of $619,544. This is similarly discounted for inflation to a current real value of $572,363, which is then discounted for time at the real yield Yr = 7.8431% p.a. to give a PRV of $423,157, and added to the PRV of the rentals gives the total PRV of $548,367, shown in Figure 5. The valuation in Figure 5 is not a true real value DCF, as the cash flow forecasts are calculated first in nominal terms; hence, it is more properly described as “excluding inflation”. It gives the same total PRVs as the PVs and CMV in the conventional explicit DCF valuation model. However, it does explicitly separate out the effect of expected inflation, which is informative.

35

Real Value Valuation for Real Estate Investments (Jefferies, 2017) A true real value yield DCF requires all the future cash flows, both contract rental and reversion to be forecast in current real terms and a real discount rate is applied to those future real values to derive the CMV. An error will result (causing an over-valuation) if current nominal values are used and discounted at the real discount rate. The steps required are: i. Each inflation prone cash flow is forecast with real growth (if any). ii. These inflation prone cash flows are discounted for the effect of inflation to bring them to current price levels or true current ‘real values’ at the valuation date. iii. Those ‘real values’ are discounted for time by the required real rate of return Yr to give their PRVs. A true real value yield explicit DCF is shown in Figure 6 at page 37. The PRV of the term to run is based on the nominal contract rental cash flows that are discounted separately for inflation, to give the current real cash flows. These are discounted over the term to run at the compounding real yield discount rate to give their PRVs. The total of these gives the total PRV of the term to run. The PRV of the reversion is based on the current market contract rental capitalised at the real yield capitalisation rate RrF that equates to the overall capitalisation rate ≅ ROF as in Equation 1. To calculate RrF requires it being based on the total nominal yield YO being the real yield Yr plus expected inflation Ie, shown as YO = (Yr + Ie) in the standard capitalisation formula. The real growth Gr plus the expected inflation Ie, i.e. GO = (Ie + Gr) is used in the real yield capitalisation formula:

(1+Ie +Gr )F − 1 Rr ⇐ (Yr +Ie ) �1 − � (1+Yr +Ie )F − 1 F

Equation 10

The real yield capitalisation rate RrF for this property at the date of commencement or at a rent review applying Equation 10 where F = 5 years and where the Yr is the annual (non-compounding) Yr = YO – Ie = 10% – 2% = 8% p.a. is: (1+0.02+0.01)5 − 1 � Rr 5 = (0.08+0.02) − (0.08+0.02) � (1+0.08+0.02)5 − 1 (1.03)5 − 1 � = 0.073911 or 7.3911% p.a. = 0.10 − 0.10 � (1.10)5 − 1

Equation 11

RO5

This is the same reversionary capitalisation rate as ≅ in Equation 9 at page 34 and used in Example 1a and Example 1b(1) at 7.3911% p.a. This is applied to the current real contract market rental to give the current real reversionary value. The real (not nominal) compounding growth rate is: Gr = (1+GO )/(1+Ie ) − 1 = (1.03/1.02) − 1 = 0.009804 or 0.9804 % p.a.

This is used to forecast the future real reversionary value (FRV).

FRV = �$40,685×1.0098044 �/0.073911= ($40,685×1.039796)/0.073911= $42,304/0.073911 = $572,363 Alternatively: first calculating the current reversionary value (CRV) and secondly growing this at the real growth rate Gr to derive the FRV at reversion:

CRV = ($40,685/0.073911) = $550,457 FRV = ($550,457×1.039796) = $572,363 Applying the above inputs in Example 1b(2) calculates the true yield DCF valuation shown in two steps in the DCF spreadsheet in Figure 6 following:

36

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Example 1b(2) : True real yield Yr explicit DCF valuation Expected inflation: Ie= 2.0000% p.a. Period from valuation date - Year Ended: 0 Market rental grown @ GO: $ 39,500 Contract rental, 4 Yrs to run: Real rental cash flows: discounted for inflation @ Ie: 2% p.a.

Nom. growth: GO = 3.0000% p.a. Over-all yield: YO = 10.0000% p.a. Comp. real yield: Yr = 1 2 3 4 5 $ 40,685 Not Required as current real rental capitalised at reversion @: Rr5 $ 39,500 $ 39,500 $ 39,500 $ 39,500 Annual real yield = 38,725 $ 37,966 $ $ 37,222 $ 36,492 Annual real growth =

PRVs: rentals discounted @ real yield Yr: 7.8431% p.a. $ 35,909 $ 32,645 $ 29,677 $ Total PRVs of 4 Yr. term to run: $ 125,210 $ Current reversionary real value: contract market review rental $40,685 p.a. capitalised at Rr5: 7.3911 % p.a. $ FRV current real reversionary value grown @ compounding real growth rate: 0.9804% p.a. over 4 years = PRV of FRV reversion @ Yr 7.8431% p.a. $ 423,157 Total PRV of term and reversion :

$

548,367

7.8431% p.a. F = 5.00 Yr Reviews 8.0000% p.a. 1.0000% p.a.

26,979 Comp. real growth = 0.9804% p.a. 550,457 572,363

O/all cap rate: Rr5 = 7.3911% p.a.


Figure 6 Example 1b(2): True real yield Yr explicit DCF valuation

This calculates the future real values (FRVs) firstly of the contract rentals over the term to run that are then discounted to their total PRVs of $125,210. Secondly, the reversion is separately calculated, the future FRV is calculated in real terms directly by capitalising the current contract review rental at the real capitalisation rate RrF to give the CRV of $550,457. The FRV of the CRV is forecast to grow at the real growth rate of 0.0984% p.a. over the 4 years to run to give the FRV of $572,373. This is then discounted at the real discount rate Yr = 7.8431% p.a. to give its PRV of $423,157. This is added to the PRV of the contract rentals of $125,210 to total the PRV of $548,367.

2.16 Stage C: Net of growth (or hybrid real value short-cut) DCFs This staged development of the model re-expresses the above models by converting them into a generic net of growth yield real value valuation model that is similar to Crosby’s real-value/short-cut DCF hybrid model, as described in Baum and Crosby’s text (2008, p. 138). However, the ARRY model is different in many respects and was independently developed; see (Jefferies, 2016, p. 222). The real valuation model quest commenced with a positive problem analysis and value definition following the approach suggested by Whipple (2006, pp. Ch 4: 78-117) to avoid the normative implication of the widely held view that explicit DCF valuations are a superior valuation technique that gives the ‘right’ answers. This required a new approach, a generic net of growth yield YN real value valuation model was formulated initially, by Jefferies (1997b) in a term and reversion model format, but with later modifications, and improvements to develop it into a fully real value model. To maintain the model’s development in conformity to the foregoing stages, it is expressed in a net of growth explicit DCF valuation model adapting the explicit DCF approaches in two formats so that comparisons can be made with the above explicit DCF valuation models in Stages A and B in Subsections 2.16.1 and 2.16.2 respectively that follow. A third net of growth explicit DCF valuation model re-expresses the term and reversion model format in an explicit DCF format as included in the summary referred to above, is found later in Subsection 2.16.3 at page 40.

2.16.1 Firstly, based on the nominal value model in stage A The term is treated as a normal nominal currency annuity due, and the reversion is treated also in nominal terms capitalising the forecast nominal market contract rental, as if it was reviewed at the valuation date based on the rent review frequency capitalisation rate, added to the cash flow at the end of the term to run. The resulting nominal cash flows are then discounted in a two-step calculation, first discounting them for growth at the nominal growth rate RO to express them in future real values. Then those future values are discounted at a net of growth discount rate, YN. This rate is equivalent to the overall yield YO excluding (or deducting) the over-all growth rate GO on a compounding basis where: YN = (1+YO)/(1+GO) –1. This gives the present real values that are summed to give the total present real value, or current market value. In effect, the PV of the term to run and the PRV (present real value) of the reversion are added to give the total current market value (CMV). 37

Real Value Valuation for Real Estate Investments (Jefferies, 2017) This involves the reconstruction of the DCF model in terms of real values that explicitly discounts all growth out of the explicitly forecast nominal value rental and reversionary values (not just inflationary growth) to give the current real values. It then calculates the total PVs of these periodby-period real value future cash flows using a net of growth discount rate YN, as the expected growth GO has already been allowed for. The YN rate is equivalent to the overall yield YO excluding (or deducting) the over-all growth rate GO on an annual compounding basis. Expected inflation, Ie, is not separated out nor specified in this model, only the over-all nominal growth GO is used. The net of growth compounding discount rate YN in this example is: YN = (1+YO )/(1+GO ) − 1 = (1.10/1.03) − 1 = 0.067961 or 6.7961 % p.a.

The reversionary capitalisation rate remains the nominal capitalisation rate RO5 as in Equation 9 in Example 1a at 7.3911% p.a. Applied as Example 1c(1): Net of growth YN explicit DCF valuation model spreadsheet follows in Figure 7: Example 1c(1) :Net of growth YN explicit DCF valuation Nom. growth: GO = 3.0000% p.a. O/all yield: YO = 10.0000% p.a. Net of Growth: YN = Period from valuation date - Year Ended: 0 1 2 3 4 5 $ 39,500 $ 40,685 $ 41,906 $ 43,163 $ 44,458 $ 45,791 Market rental grown @ GO: Contract rental, 4 Yrs to run: $ 39,500 $ 39,500 $ 39,500 $ 39,500 5 619,544 O/all cap rate: RO5 = Reversionary nominal value: Forecast market rental with growth $45,791 p.a. capitalised at RO : 7.3911 $ Total forecast per period nominal future cash flows: $ 39,500 $ 39,500 $ 39,500 $ 659,044 Forecast real values: discounted for growth @ GO 3% $ 38,350 $ 37,233 $ 36,148 $ 585,552 PRVs: discounted @ net of growth yield YN: 6.7961% $ 35,909 $ 32,645 $ 29,677 $ 450,136 Total Present Value :

$ 548,367


Figure 7 Example 1c(1): Net of growth YN explicit DCF valuation

38

6.7961% p.a. F = 5.00 Yr Reviews 7.3911% p.a. = in "real terms"


2.16.2 Secondly, compared to the “real value” models in stage B For complete comparative purposes, the above example is re-expressed alternatively as an explicit net of growth DCF valuation below: Firstly, the PRV of the term to run is based on the nominal contract rentals discounted for over-all growth GO (including inflation) to give the current real cash flows. Secondly, the PRVs of the current real cash flows are then discounted over the term to run at the net of growth discount rate YN to give their PRVs. Thirdly, the PRV of the future reversion is based on the real current market contract rental, capitalised at the net of growth capitalisation rate RNF that equates to the overall capitalisation rate ≅ ROF as in Equation 1. To calculate ROF requires it to be based on the total yield as the sum of the net of growth nominal yield YN plus the expected nominal growth GO, shown as (YN +GO) replacing the overall required yield YO in the standard capitalisation formula; and based on the nominal growth GO giving the capitalisation formula. The net of growth capitalisation rate for this property at the date of commencement or at a rent review date is RN5 where: (1+GO )F − 1 � RN F = (YN +GO ) − (YN +GO ) � (1+YN +GO)F − 1

Equation 12

Applying this to Example 1c(1) above, follows:

(1.03)5 − 1 � RN 5 = (0.07+0.03) − (0.07+0.03) � (1+0.07+0.03)5 − 1 (1.03)5 − 1 RN 5 = 0.10 − 0.10 � � (1.10)5 − 1 RN 5 = 0.10 − 0.10 �

0.159274 � = 0.10 − (0.10 × 0.260887) 0.610510

RN 5 = 0.10 − 0.0260887 = 0.073911 or 7.3911% p.a.

Equation 13

It is noted that this gives the same reversionary capitalisation rate as ≅ RO5 in Equation 9 at page 34 and used in Example 1c(1) at 7.3911% p.a. This is important to emphasise, as the correct capitalisation rate should result from any methodology where the terms of lease are the same. This point will be returned to later when dealing with the ARRY model capitalisation rates, because it relies on the overall yield rate, YO that can be made up of different components, in the above case the sum of YN +GO. The reversionary real value is based on the current (not forecast) real contract market rental which is capitalised at RN5 and is added to the forecast real income term cash flow at the next rent review period. The total per period forecast net of growth cash flows are discounted to their PRVs at the net of growth yield required yield rate YN and summed to the total PRV, i.e. the CMV. Applied as Example 1c(2) net of growth YN explicit DCF valuation model spreadsheet follows in in Figure 8: (next page)

39

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Example 1c(2) :Net of growth YN explicit DCF valuation Nom. growth: GO = Period from valuation date - Year Ended: 0 1 Market rental grown @ GO: $ 39,500 $ 40,685 Contract rental, 4 Yrs to run: 39,500 $ Discounted for expected growth @ GO 3% p.a. 38,350 $

3.0000% p.a. O/all yield: YO = 10.0000% p.a. Net of Growth: YN = 6.7961% p.a. 2 3 4 5 Not Required as current real rental capitalised at reversion @ RO5: F = 5.00 Yr Reviews $ 39,500 $ 39,500 $ 39,500 $ 37,233 $ 36,148 $ 35,095 550,457 $ Reversionary Value: Current market real rental $40,685 p.a. capitalised at RO5: 7.3911 % p.a. O/all cap rate: RO5 = 7.3911% p.a. Total forecast net of growth real value cash flows: $ 38,350 $ 37,233 $ 36,148 $ 585,552 Discounted @ net of growth yield YN: 6.7961% p.a. 35,909 $ 32,645 $ $ 29,677 $ 450,136 Total Present Value :


$ 548,367

Figure 8 Example 1c(2): Net of growth YN explicit DCF valuation

The purpose is to contrast this model format with and to provide an alternative explicit DCF calculation to the real value model explicit DCF valuation in Stage A earlier. The above simple DCF example format shows the generic (net of growth) real value model's advantage of not having to explicitly forecast nominal cash flows, the only input being the actual rental and the current contract market rental, if renewed as at the valuation date, and an overall nominal growth rate GO.

2.16.3 Thirdly, net of growth explicit term and reversion DCF valuation model Similar to the net of growth spreadsheet DCF model format in Example 1c(2), a net of growth explicit DCF valuation model re-expresses the generic (net of growth) real value model in a term and reversion model format. It replicates, in an explicit DCF format the Jefferies’ (1997a) generic (net of growth) real value model and Crosby’s (1985, 1986a) real value equated yield hybrid model as these are normally calculated in a short-cut DCF (term & reversion) format. A summarised net of growth valuation model in a term and reversion format is shown in Algorithm 14 and formula in Equation 15 with explanation follows: CMV ⇐ [PV of the contract rental for the term to run to next review in T periods, discounted at the nominal discount rate YO] + [PRV of the real market contract rental capitalised at the net of growth capitalisation rate RNF, deferred to the date of next review in T periods, discounted at the net of growth discount rate YN] Algorithm 14 Where: Co is the current contract rental Cc is the current market contract rental – if reviewed at valuation date RNF is the net of growth capitalisation rate YO is the over-all required yield and overall discount rate YN is the net of growth discount rate

CMV ⇐ Co

1−(1+YO )−T YO

C

+ R cF (1+YN )−T N

Equation 15

Applying Equation 15 to Example 1c follows:

CMV ⇐ $39,500

1−(1.10)−4 0.10

$40,685

+ 0.073911 (1.067961)−4

CMV ⇐ ($39,500×3.169865)+($550,457×0.768738) CMV ⇐ $125,210+$423,157 = $548,367

Note in this model the real value application is only applied to the reversionary value (to avoid explicit forecasts) – but still relies on an overall growth input. The valuation is immaterially different to that in the following table due to rounding in the calculations of the cap rate and PV factors.

40

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Applied as Example 1c(3) the net of growth explicit DCF valuation model re-expresses the above generic (net of growth) real value term and reversion model format in a spreadsheet DCF valuation model follows in Figure 9: Example 1c(3) :Net of growth YN explicit DCF valuation — re-expressing the Term and Reversion format Nom. growth: GO = 3.0000% p.a. O/all yield: YO = 10.0000% p.a. Net of Growth: YN = 6.7961% p.a. Period from valuation date - Year Ended: 0 1 2 3 4 5 Market rental grown @ GO: $ 39,500 $ 40,685 Not Required as current real rental capitalised at reversion @ RO5: F = 5.00 Yr Reviews Contract rental, 4 Yrs to run: $ 39,500 $ 39,500 $ 39,500 $ 39,500 Discounted @ Over-all rate incl. growth @ YO 10% p.a $ 35,909 $ 32,645 $ 29,677 $ 26,979 Total PV of term to run: $ 125,210 5 $ 550,457 O/all cap rate: RO5 = 7.3911% p.a. Reversionary real value: Current market real rental $40,685 p.a. capitalised at RO : 7.3911 % p.a. PRV of reversion @ YN 6.7961% p.a.

$ 423,157

Total Present Value :

$ 548,367

$

423,157


Figure 9 Example 1c(3): Net of growth YN explicit DCF valuation term and reversion format The term element is treated in nominal terms as in a conventional model, whereby the actual i.e. existing contract rental, is discounted over the term to run at an over-all required nominal yield rate YO, as in stage A. It is similar to the conventional UK equivalent yield (EY) model and Crosby’s hybrid real value/equated yield model. This treatment allows implicitly for the lack of growth, both real and nominal in the inflation prone fixed income over the term to run, i.e. the depreciating effect of inflation in real terms, as reflected in the annual required over-all nominal yield as YO = YN +GO, and in the overall growth rate GO (but not distinguished or separated out). The reversion element is treated differently to the traditional and conventional term and reversion models. A two-step calculation is made in real terms by: Firstly, taking the current real market contract rental, as if it was reviewed at the valuation date, not grown to the reversionary date and capitalising this at the “net of growth” capitalisation rate at RNF for the review term = F, as formulated in Equation 12 and calculated in Equation 13 at page 39. Secondly, by deferring the resulting “real reversionary value” in current real terms and discounting it to period T, at the required net of growth discount rate YN. This modification is claimed to be an improvement compared to other models (and is the real value element). This gives the present real value (PRV) of the reversion. The PV of the term to run and the PRV of the reversion are added to give the total current market value (CMV) subject to the lease, i.e. the lessor’s interest in the investment property. Hence, the “hybrid” description, given by Crosby (1986a) to his real value model as being a Real Value/Equated Yield Hybrid Model, later re-named Real Value/Short-Cut DCF Hybrid Model.

2.17 Chapter Summary This Chapter has carefully traced the theoretical and practical modelling involved by the use of a progressively developed valuation example to show how the real value models have grown out of conventional term and reversion models. It has duplicated this in terms of converting conventional DCF models into a full generic real value DCF model that gives the same results where assumptions do not change. This Chapter has set the foundation for building the real value valuation models that progress into the development of the all-risks real yield (ARRY) model as described in the next Chapter 3.

41


Chapter 3 — Building the all-risks real yield (ARRY) valuation model 3.1 Introduction This Chapter expands on the introduction of the all-risks real yield (ARRY or YA) valuation model, in Chapter 2. The foregoing valuation models described in Stages A, B and C in — Developing the theoretical all-risks real yield (ARRY) model set the foundations on which to build the ARRY (YA) model. This Chapter explains the Stage D – Development of the generic all-risks real yield (ARRY) valuation model that was briefly introduced in Chapter 2. It explains the importance of separating out and sourcing the expected inflation Ie that distinguishes this model from prior real value models discussed in Chapter 2. An outline of the ARRY valuation structure and approach explains how the sum of the present real values (PRVs) of the term to run and the reversion, i.e. the total PRV equals the current market value (CMV). The derivation and definition of the ARRY with an explanation of the concept of its source from market sales evidence precedes a discussion of its distinguishing features and advantages. A diagrammatic illustration and discussion shows how the ARRY sales analysis and valuation process works. The balance of the Chapter details how the correctly formulated ARRY capitalisation rates are required to reflect the different lease term to run, and rent review periods. New algorithms using ARRYs and capitalisation rates summarise how these apply to the future tranches of real cash flows within the term and reversion format. A basic algorithm is described that calculates the PRVs of the real cash flows of the term to run and the PRV of the real capitalised value at the reversion. Reversionary values assume a renewal from the expiry of the current lease terms. Totalling these PRVs gives the total PRV or CMV of the property. At this primary Stage D, the ARRY valuation model presumes a single lease with a term to run in whole years, which is less than the rent review periods, and continues on in similar perpetually renewable lease terms. The Chapter completes the development of a generic ARRY YA model. Examples are provided that continue the progression of the examples in Stages A, B and C. This generic ARRY model is a simplistic and basic structure upon which progressive additions and adaptations are made in the following Section 3.2 — Building the all-risks real yield (ARRY) valuation model. Then in Chapter 4 — Generic adaptations to the all-risks real yield (ARRY) model are progressively introduced to reflect real world property markets, lease types, terms and conditions.

3.2 Stage D: Building the generic all-risks real yield (ARRY) valuation model 3.2.1 Expected inflation Ie The ARRY (YA) valuation model is distinguished by its treatment of expected inflation (Ie) as necessarily separated from the real value growth (Gr) as both elements combine to produce overall growth (GO). Both components are present in expectations of future rental increases deriving overall long-term annual growth in rentals, i.e. Ie+Gr = GO. Given Ie can be exogenously forecast, Gr can be derived from the market and implied from overall growth GO from sales analyses i.e. GO – Ie = Gr. Expected inflation (Ie) is an independent variable sourced from sound economic forecasting data, such as (in NZ) the Reserve Bank of New Zealand (RBNZ) and the New Zealand Treasury forecasts as well as independent economic forecasting providers, such as the New Zealand Institute of Economic

42

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Research (NZIER), Business and Economic Research Limited (BERL) and others. 7 In Australia, sources of reputable inflation forecasts are obtainable from the Reserve Bank of Australia, Australian Bureau of Statistics, and also State governments’ departments as well as other private agencies. Other countries and states have equivalent government or private sources of forecasts as well as independent international sources including the International Monetary Fund (IMF), Organisation for Economic Co-operation and Development (OECD) and World Bank forecasts. Expected inflation (Ie) allowed for as a separate data input in the ARRY valuation model relies on external data sources. This treatment as an exogenous input makes this important factor more transparent. It takes the reliance on this aspect of forecasting out of the valuers’ responsibility as generally having limited econometric forecasting skills. Valuers have a professional responsibility for sourcing reliable data, updating these as appropriate. In NZ, Ie has been stable, averaging at approximately 2.5% p.a. for a number of years (New Zealand Treasury, 2010, 2012, 2014) and is the current long-term forecast relied on by investors and their advisers generally. This Ie = 2.5% p.a. input is used in the case study examples in Jefferies (2017a). A real growth forecast is still required as a valuer’s input responsibility, based on property market analysis, and is relevant where rentals and consequentially values are normally expected to grow in monetary terms at a greater rate than expected inflation. At this stage of the model’s development, no explicit account is made of the offsetting effect of real rental depreciation, Gr being inclusive of any rental depreciation. See definition of current market rental (CMR) as Cm at page 16. In the ARRY model, separating out the expected inflationary element of growth is a significant advancement on previous real value models. The prospect of market rental growth and thus capital value growth is a major component contributing to the attractiveness of property investment, i.e. to have an inflation prone cash flow hedged by explicit inflation proofing compared to fixed securities. In property investment, the prospect of expected real growth makes property important as an asset class. This will depend on the overall growth, which investors expect in ex-post performance measures to exceed the rate of expected and unexpected inflation. Real growth Gr occurs where the rental in nominal terms GO increases by a greater amount than is necessary to compensate for monetary inflation Ie or more than offsets the inflation proneness of nominal rental growth. This provides inflation proofing, i.e. where GO is at least ≥ Ie and GO – Ie = Gr >0; and if not, a real loss will occur where GO < Ie and GO – Ie = Gr –(+Ie); when Gr = –(+Ie) there will be no growth, either nominal or real. When expected Gr is negative and in absolute terms is greater than positive inflation, negative nominal growth in values will be forecast, resulting in falling nominal values, i.e. –Gr M) a marginally lower or reduced PRV will result, or vice versa where (M>F). At this stage of the ARRY valuation model development, the re-leasing on expiry adaptation (iv) assumes that a new tenant is found before the expiry of the contract lease and commences one day after the existing lease expires, with the new rental paid from that expiry date. The current market rental (Cm) is assessed in current real terms as the real growth rate expected is allowed for in the ARRY capitalisation rate that is based on the M years rent reviews and deferred at the ARRY YA discount rate to its assumed commencement on releasing in EX years’ time. No allowance is made, at this stage of the models’ development, for any expected vacancy costs after expiry and until re-leasing as these are dealt with under Subsection 5.6.1 Adaptation (ix) — Vacancies, rent-free periods, leasing incentives, and leasing costs at page 139. Nor are re-leasing costs or expenditure to upgrade or fitout the premises or for any incentives to obtain a new tenant dealt with as these are CAPEX items under Section 5.11 Adaptation (xi) at page 160. Cm requires a new input as assessed by the valuer based on current market evidence allowing for the new rental payment basis and review frequency, and RAm requires applying the new capitalisation formula and RAM is calculated as in the Table 6 Formulary for re-leasing on different market rent review terms, at page 89. The generic ARRY terminating valuation model in Algorithm 51, is adapted for re-leasing at expiry, and re-expressed mathematically based on Equation 55, i.e. calculated monthly BOP. It is adapted by adding back the PRV of the capitalised real value of the FRV of the re-leasing at expiry, with this added fourth term as in the Algorithm 59 with re-leasing below and mathematically in Equation 60 following: CMV ⇐ PRV of term + PRV of reversion – PRV at expiry + PRV of new leasing at expiry: CMV ⇐

Cc Cc Cm Co (1 − (1+YA )−T )+ F (1+YA )−T − F (1+YA )−EX + M (1+YA )−EX T RA RA RA RA

Algorithm 59

Equation 60

The above model is used in the Excel ™ template to separate out the above components of the current market value. This Adaptation (iv) is diagrammatically shown in Chart 34 following.

90

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Chart 34 Adaptation (iv) lease expiry and releasing CM PRV = Present Real Value (1 + YA )−EX RA M

(

CC (1 + YA )−T − (1 + YA )−EX RA F

(

CO 1 − (1 + YA )− T RA T

)

)

Each tranche of real cash flow is capitalised and discounted at the ARRY YA to Present Real Value (PRV) @ valuation or sale date

8

This adaptation is applied to revalue the property in Example 1d by applying the above BOP monthly payments scenario in Equation 60 assuming the current contract lease is terminating in nine (9) years, EX = 9 which would coincide with the lease expiry after one further renewal term of the lease. A further assumption is that on re-leasing an ADLS current net lease based market rental is based on a three (3) year rental review frequency, i.e. M = 3 and m= 3 x 12 = 36 monthly periods; and that the current real market rental (Cm) on a three year review basis is $40,250 p.a. paid monthly BOP. The ARRY re-leasing capitalisation rate RAm on a BOP payment basis is shown in the Formulary in Table 6 above and is calculated as in Equation 44 but replacing f with m as follows: (1+ie+gr)m –1 ya+ie+gr RA m = � � �1– � �� (1+ya+ie+gr)m –1 1+ya Equation 61 Using the figures already calculated in Equation 45 except inserting m = 36 as above:

(1.0024811)36 − 1 0.0081353 0.0933099 RA = � � �1 − � �� = 0.0080895 �1 − � (1.0081353)36 − 1 1.0056541 0.3386808 RA m = 0.0080895(1 − 0.2755098)= 0.0080895 × 0.7244902 = 0.0058608 m

Therefore: RA M = 12 × RA m = 12 × 0.0058608 = 0.0703294 or 7.03294% p.a.

Equation 62 Equation 63

Applying the RA M in Equation 63 as used in Equation 60, also based on the previous calculations in Equation 57, i.e. adding back the above reversion to a re-leasing at the current real market rental Cm in the fourth term in the equation below gives the CMV of the revalued Example 1(d) as follows: CMV ⇐

$40,685 $40,250 $39,500 $40,685 (1–(1.07)–4 )+ (1.07)–4 – (1.07)–9 + (1.07)–9 0.0722169 0.0703294 0.0712813 0.0722169 Equation 64

CMV ⇐ ($554,143×0.2371048)+($563,372×0.7628952) − ($563,372×0.5439337) +($572,307×0.543934) CMV ⇐$566,044 ⇐ $131,390+$429,794 − $306,437+$311,297 ⇒ Say $566,000 91

Equation 65

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Note that as M is less than F, the RAM is less than RAF and hence the PRV of the current market real value on reversion at expiry of the current lease is higher (at $311,297) than the contract rental reversionary value deducted (at $306,437). The overall value increases of $5,860 to $566,044 compared to a perpetually renewable lease as in Equation 50 of $561,184. Though the differences in this foregoing example are relatively small, with a greater difference between the contract rental Co and the current market rental Cm coupled with greater variation between F and M, as well as in the time to run to expiry EX, the differences can be greater and more significant. The same theoretical approach is used in the Excel™ template as defined in Equation 60 to Equation 64. The template is adapted to allow for an additional input specifying M, Cm defining these variables, calculating m, RAm, RAM and providing the additional output for calculating and allowing for the market rental reversion at expiry of the contract lease, both in the model workings, and the valuation printout sections. A copy of the Excel ™ template model with the new required inputs and outputs is shown in Figure 35 ARRY valuation template for Adaptation (iv) Re-leasing on lease expiry, (see following page 93). The valuation printout section is shown in Figure 36 ARRY valuation template printout for Adaptation (iv) Re-leasing on lease expiry, (see page 94).

92

Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY Valuation spreadsheet template (Version Oct 2011)

Adaptation (iv) Valuation of Example 1(d) Re-Letting on Lease Expiry Model

Instructions

Cell Definitions

2.00% Insert a number, i.e. 3.00 for 3.00%

Expected (Nominal) Inflation rate: Ie


Real Growth rate: Gr

Adaptations

Calculation

Ie

p.p. i_e = (1+Ie )^(1/P)-1

0.165158% p.p.

Gr

p.p. g_r = (1+Gr)^(1/P)-1

0.082954% p.p.

Nominal Value Growth rate: GO = Ie + Gr

3.00000% Will calculate automatically

Go

p.p. g_o = (1+GO)^(1/P)-1

0.246627% p.p.

All-risks Real Yield rate: YA

7.00000% Solve for sale analysis; or Insert for valuation

YA

p.p. y_a = (1+YA)^(1/P)-1

0.565415% p.p.

Yo

p.p. y_o = (1+YO)^(1/P)-1

0.797414% p.p.

Over-all Required Nominal Yield (Disc. Rate): YO = (YA + Ie + Gr)


Contract Review Term Frequency in yrs: F

5.00 years Insert a number, i.e. 3 for 3 years

F

p.p. f_ = P × F

60


M

p.p. m_ = P × M

36


T

p.p. t_ = P × T

48

9.00 years Leave blank or Insert yrs as decimal, i.e. 9.50 for 9 yrs 6 mths

EX

p.p. e_x = P × T

108

Current Market Term Frequency in yrs: M Term to Run in yrs: T

Adaptation (iv): New input cell for specifying the current market review frequency M

Contract Lease Expiring in yrs: EX

Y

Re-letting on contract lease expiry: RL Y = Yes, N = No

Enter Y for Yes or N for No (e.g. if redeveloping or a terminating investment)

All-risks Contract Real Yield Capitalisation rate = RA5


Adaptation (iv): New output cell for Contract Rent Co : the ARRY cap rate Contract Market Rent C C : for the current Current Market Rent (on normal terms and conditions) C m : market review frequency M Rental payments: In advance (BOP) =1; In arrears (EOP) =0


All-risks Current Market Real Yield Capitalisation rate = RA3

Adaptation (iv): New input cell for specifying whether lease expires or is assumed perpetually renewable

$

39,500 Insert rental, i.e. 40,000 for $40,000

$

40,685 Insert estimate, i.e. 41,500 for $41,500

$

40,250 Insert current market rental valuation, i.e. 40,250 for $40,250

Number of rental payments per annum P:

1

Enter number "1" for BOP; or zero "0" for EOP

12

Enter number of payments p.a., i.e. 12 for monthly

Term & Reversion: i.e. Valuation not at Review or Commencement 7.12813%

All-Risks Real Yield Term Capitalisation rate = RA4 $

554,143

Deferred Real Reversion for 4 yrs @ YA: 7 % p.a.

$

422,753

PRV of 4 years term to run (by deduction):

$

131,390

$

563,372

PRV of Deferred Real Reversion for 4 yrs @ YA: 7 % p.a.

$

429,794

LESS - PRV of Deferred Value at Termination or Expiry in 9 years @ YA: 7 % p.a.:

-$

306,437

$

123,357

Current Market Value = Market Rental $40250 capitalised @ RA3: 7.03294% p.a.

$

572,307

PRV of Market Value at Lease Expiry in 9 years @ YA: 7 % p.a.:

$

311,297

Total PRV: Term + Reversions =

$

566,044

Current Market Value (Rounded)

$

566,000 Valuation: or Solve for ARRY to = Sale Price

Reversion - Contract Lease Real Value:

Reversion - Current Market Real Value:

Initial Yield or over-all capitalisation rate RO:

RAM

p.a. RAM = P × RAm_

7.221687% p.a. 7.032939% p.a.

Co

p.p. c_O = CO/P

$

3,291.67

Cc

p.p. c_c = CC/P

$

3,390.42

CMV

p.p. c_m = Cm/P

$

3,390.42

pay P

RAT

Contract Rental $39500 Capitalised @ RA4: 7.12813% p.a.

PRV of reversionary renewals until Termination or Expiry in 9 years:

p.a. RAF = P × RAf_

p_ = 1/P on annual basis

0.083333333

p.a. RAT = P × RAt_

7.128126% p.a.

Note ALL cells are locked except input cells

Term - Real Value:

Contract Market Rental $40685 capitalised @ RA5: 7.22169% p.a.

RL RAF

Cells will calculate automatically

Adaptation (iv): New output cell for the capitalised normal current market rental value. Note this part of spreadsheet will not print as excluded from print area Adaptation (iv): New output cell for the deferred added-value of the reversion to market value on expiry.

6.97880% p.a.

Figure 35 ARRY valuation template for Adaptation (iv) Re-leasing on lease expiry

93

CMV


Adaptation (iv) Valuation of Example 1(d) Re-Letting on Lease Expiry Model

All Risks Real Yield - Real Value - Investment approach valuation: Rental, lease and data assumptions:

Current Contract Rent to run until next rent review: Contract Market Rent - if reviewed at valuation date : Rental payments 12 times per year In Advance Review Term Frequency in yrs: Term to Run in yrs: Expected (Nominal) Inflation rate: Real Growth rate: Nominal Value Growth rate: All-Risks Real Yield rate: Over-all Required Nominal Yield: Term to Run - Real Value: All-risks Real Yield Capitalisation rate for 4 year rent reviews: Contract Rental $39500 p.a. Capitalised @: 7.12813% p.a. Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. Present Real Value of 4 years term to run (by deduction): Reversion - Contract Lease Real Value: All-risks Real Yield Capitalisation rate for 5 year rent reviews: Contract Market Rental $40685 capitalised @ 7.22169% p.a. : Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. LESS - PRV of Deferred Value at Termination or Expiry in 9 years @: 7 % p.a.: PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: All-risks Real Yield Capitalisation rate for 3 year rent reviews: Current Market Value = Current Market Rental $40250 capitalised @ 7.03294% p.a. PRV of Market Value at Lease Expiry in 9 years @ All-Risks Real Yield: 7 % p.a.:

$ $

$ $

7.12813% p.a. 554,143 422,753

$ $ -$

7.22169% p.a. 563,372 429,794 306,437

$

7.03294% p.a. 572,307

$

$

$

$ $

Total PRV: Term + Reversions = Current Real Market Value - CMV: (Rounded) Initial Yield (over-all capitalisation rate): Current Contract Rental ÷ CMV:

39,500 p.a. 40,685 p.a. 12 times p.a. BOP 5.00 years 4.00 years 2.00000% p.a. 1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a.

131,390

123,357

311,297

566,044 566,000 6.97880% p.a.

Figure 36 ARRY valuation template printout for Adaptation (iv) Re-leasing on lease expiry

4.18.3 Adaptation (v) ― OPEX allowances with gross leases Office, retail and industrial leases are typically net leases, which means that the tenant is obligated to pay a fixed rent paid monthly in advance, plus the monthly operating expenses (OPEX) of the building or a proportionate share on a lettable area basis where multi-tenanted. Rental comparisons between spaces are normally made on a total occupancy cost (TOC) basis, including OPEX. Typically, the components of the OPEX are specified in the lease contract. These normally include all common area energy costs, cleaning, common area and parking area maintenance, insurance premiums, local authority rates (property taxes). Goods and Services Tax (GST) in NZ is paid on both rents and OPEX, but not included in valuation calculations as this is both an input and output tax paid/claimed by both the landlord and the tenant, similar to Value Added Tax (VAT) in other countries. In NZ, sale prices of commercial fully tenanted properties are transacted on a GST zero-rated basis, treating the property as a “going concern” for GST purposes. NZ Valuation Standards require valuation of commercial property to be based on GST (if any) exclusive prices and/or values. Parking spaces are normally leased separately, often on a weekly or monthly basis per car space tenancy, or specifically included in the lease and reviewable along with the retail, office or factory space. If car parks are separately leased or on different terms or expected rental growth rates to the primary tenancy lettable area then the rental is treated as a separate tenancy and the multi-tenanted ARRY valuation model as in Adaptation (xii) is applicable as dealt with in Chapter 5. 94

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Where net leases apply there is no need to adapt the ARRY Valuation model for OPEX as an outgoing20 in the ARRY valuation model. Cash flows consist of net rents, except where vacancies occur (see Adaptation (ix) — Vacancies, rent-free periods, leasing incentives, and leasing costs at page 139), as owners will incur the expenses of non-recoverable OPEX and other vacancy or related leasing costs. Structural maintenance is excluded from the OPEX charge and is taken into account under a CAPEX adaptation, as an occasional expense as detailed under Adaptation (xi) — CAPEX (expectations of capital expenditure), refurbishment, and deferred maintenance liabilities at page 160. In the less common commercial gross lease, where the tenant pays no separate OPEX charges for building operating expenses, (except direct utility charges such as power, gas or internal cleaning costs not paid by the building owner) an adaptation of the generic ARRY valuation model is required. In this case, the landlord will pay all OPEX costs out of the gross rental received and that will result in the net cash flow. It is unlikely that the escalation in OPEX will match the rental increases and additionally OPEX will increase continually as utility charges and local body rates usually increase annually with varying increases over time, frequently at a greater rate of increase than expected inflation. Consequently, the landlord’s cash flow will consist of two tranches of cash flow streams, the gross rental inflow and the OPEX outflows, but on different reviewable frequencies and growth rates. The gross rental inflow will be constant until the next rent review and thereafter increase only at future rent reviews. However, the OPEX outflows will increase annually. 21 Therefore, each cash flow stream needs to be capitalised separately. The ARRY valuation model needs to be adapted by deducting the capitalised forecast OPEX expenses at a capitalisation rate that reflects the most likely forecast escalation rate in those expenses. This would normally be at the expected inflation rate Ie but utility escalation costs in recent years have been rising at an annual rate greater than inflation, and greater than nominal rental growth GO. For example, recent and prospective insurance premiums are affected by the Christchurch and Kaikoura major earthquakes. It is necessary to introduce additional symbols, abbreviations, definitions, explanations, and formulae used to define and allow for OPEX costs. These are shown in Table 7 Formulary for OPEX allowances with gross leases at page 96, and are combined into an overall Formulary shown in Appendix A at page. 201.

20

DCFs often treat OPEX differently to be more transparent. Some show the recovered OPEX as an additional income item and the total OPEX as an expense item, the result being a net unrecovered OPEX reducing the landlord’s net cash flow. Alternative some show only the unrecovered OPEX and their sources, being more transparent. This approach is adopted in the ARRY valuation method as applied to the terms of each tenancy. 21

The timing of these OPEX increase dates are likely to be different from the rental increase dates and paid at different frequencies to rental receipts, adding to the mismatch of income/expense timing.

95


OP op (lower case) OPEX

RAop

RAOP

Table 7 Formulary for OPEX allowances with gross leases OPEX annual escalation The annual expected nominal increase in the OPEX (as rate distinct from a rental growth rate). The per OPEX payment period escalation rate. OPEX p.p. escalation rate P op =(1+OP)1/P − 1, or = �(1+OP) − 1 The operating expenses of the building as defined in Operating expenses the lease, which in the case of a gross lease will all be As a negative (–$) cash paid by the landlord; whereas under a net lease the flow defined recoverable operating expenses are charged to and paid by the tenant. Based on monthly BOP OPEX payments p.p. (1+op)P –1 ya+ie+gr ARRY OPEX per payment RA op = � � �1– � �� (1+ya+ie+gr)P –1 1+ya period (p.p.) cap rate for p months payment period where EOP payments ×(1+ya) reviews N.B. (1+op) replaces (1+ie+gr) as growth rate in the second term of above cap rate formula. ARRY annual (p.a.) OPEX nominal OP escalating Based on nominal annual OPEX p.a.; where cap rate for P = 12 p = 1×P = 1×12 = 12 BOP payments p.p.: payments p.a. i.e. RAOP = P×RAop ; where EOP ×(1+ya) monthly and p payment periods OPEX increases

The OPEX annual escalation rate (as distinct from a rental growth rate) is defined as OP and is likely to be a minimum of the expected inflation rate Ie, as a default assumption. The landlord’s forecast liability for OPEX can be simply allowed for by capitalising the current OPEX annual costs at a suitably adapted annual ARRY capitalisation rate, RAOP. This is calculated using the per payment period OPEX nominal escalation rate defined as [op p.p.] in place of the [ie +gr p.p.] as the expected nominal growth rate in the OPEX. The OPEX forecast annualised budgeted cost, in the basic ARRY model assumes perpetual renewals on expiry, and is simply capitalised in perpetuity at RAOp, as calculated on a per payment period basis. The capitalised OPEX cost is deducted from the term and reversion value of the rentals on a gross lease basis. As OPEX costs are subject to annual escalations, commencing from the sale or valuation date, there is no (negative) OPEX reversionary value. At this stage of the model’s development, it is assumed that on expiry of the current lease or final expiry if subject to lease renewal, the property will be re-leased immediately on a normal gross lease with normal growth and current prevailing rent reviews, and perpetually renewed on that basis. Where it is assumed that on lease expiry, or final expiry if subject to lease renewal, the property will be re-leased on a market net lease basis, the reversionary negative PRV of the FRV of the OPEX cost will be added back, as from re-leasing OPEX will be recouped from future lessees. This is dealt with under Adaptation (vii) — Renewals of the current lease, and re-leasing with different terms and/or rent review periods at page 123. If redevelopment is expected on lease expiry, or at final expiry if subject to lease renewal, then similarly an adjustment is made for the reversionary PRV of the FRV of the OPEX saved. As well an estimated real redevelopment reversionary value of the property will apply, that is separately allowed for under Adaptation (viii) — Under-developed properties with redevelopment potential at page 133. The combination of the RAOP being normally greater than YA, and OP usually being lower than GO, but not higher than Ie, coupled with an annual review frequency, means that the resulting adjusted ARRY RAOP capitalisation rate is higher than RAM and the capitalised OPEX cost is decreased (as a negative figure). The resulting deduction accurately adjusts for the difference between the OPEX escalation 96

Real Value Valuation for Real Estate Investments (Jefferies, 2017) rate and the rental growth rate. This is then reflected in lowering the PRV of the future net cash flows and reversions, hence reducing the CMV, subject to the gross lease terms and conditions. If the physical leased premise, in the examples, is the same, one would expect the current market rental on a gross basis would be higher by the absolute amount of the OPEX ‒$3,200 p.a. assumed. How the resulting CMV compares to that of a net lease is problematic. Usually a building with gross leases would be expected to be less valuable than an otherwise comparable one on net leases, if only because all OPEX and its annual cost increases are not recoverable from tenants. However, in theory rents are set on a total occupancy basis (TOC) that would anticipate increases in OPEX affecting the net rental set, after allowing for expected OPEX, and in an efficient market would largely iron out the differences. Note: In the examples that follow, for simplicity and consistency of calculation and illustration, the same levels of rental on a gross lease basis is assumed as on a net lease basis. This avoids the need for a new set of rental input assessments and assumptions. Alternatively, an assumption could be made that the gross lease example involved smaller premises to compensate for the OPEX differential – but for calculation purposes to illustrate the principles being enunciated, no rental reassessment is made. No adjustment for any differential risk between a net and gross lease is made in the ARRY, YA, though if considered relevant a subjective assessment can be made in the assumptions. In a market dominated by gross leases, such as in Wellington, NZ, the analyses of sales would all reflect that market factor and be reflected in the ARRYs forming the database relied on by the valuer. The generic ARRY valuation re-leasing at expiry model in Algorithm 59 and based on adapting the methodology in Equation 60, calculated on a BOP basis, is further adapted for a gross lease by adding an additional deduction for the capitalised unrecovered OPEX as shown as the fifth term in the following Algorithm 66 and Equation 67: CMV ⇐ PRV of term + PRV of reversion – PRV at expiry + PRV of new leasing at expiry – PRV of OPEX: Algorithm 66 CMV ⇐ OP

Cc Cm OPEX Co Cc (1 − (1+YA )−T )+ F (1+YA )−T − F (1+YA )−EX + Q (1+YA )−EX − OP T RA RA RA RA RA

Equation 67

op

RA is P × RA and is calculated having regard to the assumption that the OPEX payments occur on the same payment basis as the rental is received, e.g. monthly in advance, similar to Equation 47 but in the nominator in the second term of the cap rate formula replacing t with p = P x F = 12 x 1 = 12 as annually reviewable, and replacing the growth rate [ie +gr] with op,. Hence, the ARRY OPEX capitalisation rate RAop per payment period BOP formula is as follows: (1+op)p − 1 ya+ie+gr � �1 − � �� RA op = � (1+ya+ie+gr)p − 1 1+ya

Equation 68

This adaptation is applied to revalue the property in Example 1d based on the previous adaptation with the further assumption that the lease is a gross lease and that the landlord is responsible for all OPEX. The OPEX is forecast to escalate annually at the minimum default rate of 2% p.a. in this scenario, i.e. equivalent to the expected inflation rate OP ≅ Ie = 2% p.a. The case studies in Jefferies (2017a) show situations where these are different, as the OP may be greater or less than Ie. Where; P = 12; F = 1; f = P x F = 12 x 1 = 12; 12

ya = �(1+0.07) − 1 = 0.0056541 (as before); 12

op = �(1+0.02) − 1 = 0.0016516 (as before, for this example’s assumption); ya+ie+gr

= 0.00081353 (as before).

The ARRY OPEX annual capitalisation rate formula RAop is calculated as follows: 97


RA

op

(1.0016516)12 − 1 0.0081353 0.0200000 =� � �1 − � �� = 0.0080895 �1 − � 12 (1.0081353) − 1 1.0056541 0.102118

RA op = 0.0080895(1 − 0.1958636)= 0.0080815 × 0.8041364 = 0.0065051

Therefore: RA OP = 12 × RA op = 12 × 0.0065051 = 0.0780610 or 7.80610% p.a.


This adaptation is applied to revalue the property in Example 1d in the previous Subsection on the further assumption that the lease is a gross lease and that the landlord is responsible for all OPEX currently of –$3,200 p.a. OPEX RA

Op

=

–$3,200 = − $40,994 0.0780610

Equation 71

Therefore making this deduction as in Equation 67, adopting the other previous calculations as in the previous example in Equation 65, i.e. deducting the capitalised OPEX cost of –$40,994 as the fifth term as follows: CMV ⇐ $525,050 ⇐ $131,390+$429,794 − $306,437+$311,297 − $40,994 ⇒ Say $525,000 Equation 72

The Excel™ ARRY valuation template is further adapted to allow for an additional input specifying OPEX and the OPEX escalation rate (default rate is OP = Ie but another forecast future escalation manual rate input can override this), defining these variables, calculating and applying RAOP with the additional output for the capitalised OPEX deduction. A copy of the Excel ™ valuation template is shown in Figure 37 ARRY valuation template Adaptation (v) for Gross lease allowing for OPEX, at page 99.

The valuation printout section is shown in Figure 38 ARRY valuation template printout Adaptation (v) for Gross lease allowing for OPEX, at page 100. In some properties, such as multi-level office buildings and shopping centres, the expected OPEX escalation rate is likely to differ – at least in the short to medium term, from the CPI for the country. It may be more influenced by prospective energy costs (oil, electricity or gas) as well as insurance premiums and local authority rating (property taxes), which may escalate at a forecast rate greater (or less than) expected inflation. The property owner controls the real option to re-lease or not, at final lease expiry, on either a gross or a net lease basis. In theory, this should not materially affect the valuation. Differential market rentals should reflect a gross or net lease assumption assessed having regard to a total occupancy cost (TOC) basis. The differential should be approximately equal to the annual total OPEX, though some adjustment would be appropriate for the length of the rental review term as in a net lease the landlord does not suffer the cost of the annual escalation in the OPEX. However, the market is unlikely to be sophisticated enough to correctly factor this differential into negotiated leases. Where net leases predominate there will be a lack of evidence for rentals on a gross basis to empirically analyse the differences compared to net leases. However, it is more complicated where partial or variable recovery of OPEX lease terms exit.

98

Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY Valuation spreadsheet template (Version Oct 2011)

Adaptation (v) Valuation of Example 1(d) Gross Lease allowing for OPEX

Instructions




Real Growth rate: Gr Nominal Value Growth rate: GO = Ie + Gr All-risks Real Yield rate: YA

Cell Definitions Ie

Adaptations

Calculation

p.p. i_e = (1+Ie )^(1/P)-1

0.165158% p.p.

Gr

p.p. g_r = (1+Gr)^(1/P)-1

0.082954% p.p.


Go

p.p. g_o = (1+GO)^(1/P)-1

0.246627% p.p.


YA

p.p. y_a = (1+YA)^(1/P)-1

0.565415% p.p.

Yo

p.p. y_o = (1+YO)^(1/P)-1

0.797414% p.p.





F

p.p. f_ = P × F

60

Current Market Term Frequency in yrs: M


M

p.p. m_ = P × M

36

Term to Run in yrs: T


T

p.p. t_ = P × T

48

Contract Lease Expiring in yrs: EX


EX

p.p. e_x = P × T

108

Y



RL

All-risks Contract Real Yield Capitalisation rate = RA5


RAF




RAM


7.221687% p.a. 7.032939% p.a.

Contract Rent Co :

$


Co

p.p. c_O = CO/P

$

3,291.67

Contract Market Rent C C :

$


Cc

p.p. c_c = CC/P

$

3,390.42

CMV

p.p. c_m = Cm/P

$

3,390.42

Current Market Rent (on normal terms and conditions) C m :

Adaptation (v):

$

annual OPEX cost.

IF Gross lease - Current OPEX –$p.a.

40,250 Insert current market rental valuation, i.e. 40,250 for $40,250 1

Rental payments: In advance (BOP) =1; In arrears (EOP) =0New input cell for Number of rental payments per annum P: the current real


12 -$

Enter number of payments p.a., i.e. 12 for monthly 3,200 If Gross lease Enter Estimated current OPEX budget, i.e. –3,000 for –$3,000 2.00% If Gross lease - Leave as default or Insert a number, i.e. 2.00 for 2.00%

If Gross lease: Annual escalation rate for OPEX (Default = expected inflation Ie ) Term & Reversion: i.e. Valuation not at Review or Commencement

pay P


0.083333333

OP

p.p. O_p = (1+OP)^(1/P)-1

0.165158% p.p.

RAT


7.128126% p.a.

OPEX


Term - Real Value: 7.12813%

All-Risks Real Yield Term Capitalisation rate = RA4 Contract Rental $39500 Capitalised @ RA4: 7.12813% p.a.

$

554,143

Deferred Real Reversion for 4 yrs @ YA: 7 % p.a.

$

422,753


$

131,390

Contract Market Rental $40685 capitalised @ RA5: 7.22169% p.a.

$

563,372


$

429,794


-$

306,437

$

123,357

Current Market Value = Market Rental $40250 capitalised @ RA3: 7.03294% p.a.

$

572,307


$

311,297

Adaptation (v): New cell for automatically the annual Cellsinput will calculate OPEX escalation rate


PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value:

Other Adjustments: IF Gross lease: All-Risks Real Yield OPEX Capitalisation rate = RAOp p.a.

7.80610%

-$

40,994

Total PRV: Term + Reversions ± Other Adjustments

$

525,050


$

IF Gross lease: OPEX $-3200 p.a. Capitalised @ RAOp : 7.8061% p.a.


Note this part of spreadsheet will not print as excluded from print area

Adaptation (v): New output cell for the ARRY OPEX capitalisation rate. Adaptation (v): New output cell for the capitalised OPEX cost as a deduction or negative value.


RAO_p

p.p. RAO_p

RAOp

p.a. RAOP = P × RAO_p

CMV

7.52381% p.a.

Figure 37 ARRY valuation template Adaptation (v) for Gross lease allowing for OPEX

99

0.6505082% p.p. 7.806098% p.a.

Real Value Valuation for Real Estate Investments (Jefferies, 2017) There may be short-term higher OPEX escalation (and also growth rates or inflation as well) than is forecasted in the longer term. It is possible to adapt the ARRY model to allow for changes in these forecast rates, but it complicates the model’s application. It is one advantage of a fully explicit DCF model where each cash flow period and line item can be explicitly structured to reflect a change in the growth/escalation assumptions in each payment period or periods (months, quarterly, halfyearly, yearly etc.). These adaptations are rarely done or carried out in valuation practice, as they increase the valuer’s professional liability risk in making these forecasts. For the foregoing reasons such adaptations to the ARRY valuation model are not pursued further in this work, though it is an area of potential future research.

Adaptation (v) Valuation of Example 1(d) Gross Lease allowing for OPEX

All Risks Real Yield - Real Value - Investment approach valuation: Rental, lease and data assumptions:

Current Contract Rent to run until next rent review: Current Contract Rent - if reviewed at valuation date : Current Market Rent (on normal terms and conditions): Rental payments 12 times per year In Advance Review Term Frequency in yrs: Term to Run in yrs: Expected (Nominal) Inflation rate: Real Growth rate: Nominal Value Growth rate: All-Risks Real Yield rate: Over-all Required Nominal Yield: Term to Run - Real Value: All-risks Real Yield Capitalisation rate for 4 year rent reviews: Contract Rental $39500 p.a. Capitalised @: 7.12813% p.a. Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. Present Real Value of 4 years term to run (by deduction): Reversion - Contract Lease Real Value: All-risks Real Yield Capitalisation rate for 5 year rent reviews: Contract Market Rental $40685 capitalised @ 7.22169% p.a. : Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. LESS - PRV of Deferred Value at Termination or Expiry in 9 years @: 7 % p.a.: PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: All-risks Real Yield Capitalisation rate for 3 year rent reviews: Current Market Value = Current Market Rental $40250 capitalised @ 7.03294% p.a. PRV of Market Value at Lease Expiry in 9 years @ All-Risks Real Yield: 7 % p.a.: Other Adjustments: IF Gross lease: All-Risks Real Yield OPEX Annual Capitalisation rate = IF Gross lease: OPEX $-3200 p.a. Capitalised @: 7.8061% p.a.

$ $ $

$ $

7.12813% p.a. 554,143 422,753

$ $ -$

7.22169% p.a. 563,372 429,794 306,437

$

7.03294% p.a. 572,307

$

$

$

-$

$ $

Total PRV: Term + Reversions ± Other Adjustments Current Real Market Value - CMV: (Rounded) Initial Yield (over-all capitalisation rate): Current Contract Rental ÷ CMV:

39,500 p.a. 40,685 p.a. 40,250 p.a. 12 times p.a. BOP 5.00 years 4.00 years 2.00000% p.a. 1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a.

131,390

123,357

311,297

7.80610% p.a.

40,994

525,050 525,000 7.52381% p.a.

Figure 38 ARRY valuation template printout Adaptation (v) for Gross lease allowing for OPEX

100


4.18.4 Re-leasing a net lease as a gross lease The ARRY valuation model does not envisage the need, with an existing net lease, for a real option to change to a gross lease on re-leasing in the NZ context. However, if such an assumption is required, then a manual adjustment would be necessary. This would involve: •

Assessing the current market rental (CM) on a gross lease basis; and

•

Calculating the PRV of the gross lease rental capitalised at the market rental cap rate (RAM) deferred to the final lease expiry.

The PRV of the OPEX would be capitalised at the RAOP rate and deferred to the final expiry and deducted as a future on-going cost (of its non-recovery). This foregoing adaptation of the ARRY valuation model is not developed here as it is not likely to produce a materially different CMV from the default net lease re-leasing assumption, particularly if assessing the rental on a properly adjusted gross rental market basis.

4.18.5 Adaptation (vi) ― Prescribed or Specified rental formulas Prescribed or Specified rental formulas in commercial occupational leases in NZ are not common, with examples being in some shopping centre leases. In other countries a prescribed or indexed rental escalation rate (as being distinguished from a market rental growth rate) is common, e.g. in Australia, parts of Europe, particularly Germany, North America as described in international valuation texts, for example Europe in Adair et al. (1995) and other countries covered in Gelbtuch et al. (1997; 2011). This section develops the required adaptations to the foregoing ARRY valuation model to deal with leases in which rental increases on review are determined by a prescribed index or a fixed increase at each rent review. Other examples include being based on the CPI increase over the review term, or on a proportion thereof as is sometimes found in the USA. Where rent reviews are pre-set at a fixed nominal increase at each rent review or an overall increase as a percentage of the existing rental, these can be converted into a compounding rental escalation rate to be effectively dealt with. Compared to the valuation of a comparable investment property with non-prescribed rental growth, there will be a difference between the contract rental and the normal market rental. When appropriately capitalised, this will generate a difference in the CMV, subject to the lease, i.e. the lessor’s interest or leased fee (USA) compared to being a fully let property at normal market rental Cm based CMV. To calculate a technically correct valuation, a special adaptation to ARRY model is made for the most common of these prescribed rental scenarios. This requires a preliminary calculation of the required compensatory adjustment to the ARRY capitalisation rate to reflect the overall forecast growth in rentals until final expiry. This is similar to the treatment under the previous Subsection 4.18.3 Adaptation (v) ― OPEX allowances with gross leases, at page 94. An offsetting simplification is that for any prescribed rental review rate (if it is not linked to a % p.a. of normal market value (CMV) or % p.a. of a normal market rental Rm) the inclusion of a normal market rental is superfluous with a perpetually renewable lease assumption. 22 However, if the current contract lease is a terminating one, it will be re-leased on different normal market rent review terms on expiry as under Adaptation 4.18.2 at page 89. This is because, subject to 22

A proviso to this is that the resulting escalated (prescribed) rental at each renewal is expected to result in a less than normal market rental. If not, and a higher than market rental is expected, a prudent lessee would not renew the lease unless due to the desire to exercise the renewals of the lease for a non-financial consideration, such as a locational advantage or special building suitability for continued business use.

101

Real Value Valuation for Real Estate Investments (Jefferies, 2017) the above provisos, the future rental paid until the expiry of the lease will be calculated only in relation to the existing contract rental Co and its prescribed nominal escalation at each review date. An adjustment is required for a prescribed rental escalation rate Esc that is below normal expected growth rate GO, resulting in less than expected market real growth Gr (or vice versa giving an above expected market rental growth rate). Due to the contract terms, this is necessary in calculating the ARRY capitalisation rates for the term to run and for the contract reversion. The mathematical treatment is similar to the adaptation for OPEX as under Adaptation (v). This escalated contract rental at a level less than (or greater than) normal growth expectation would endure until the lease expires and the property would be re-leased on normal terms, conditions, and reversion to normal expectations of inflation and real growth. This requires splitting the reversionary values by deducting the PRV of deferred FRV of the contractual rental reversions at the expiry of the lease, and its replacement by the PRV of the deferred FRV of the real market rental reversions on releasing on a normal market basis. The prescribed rental annual escalation rate is defined as Esc and allowed for by adjusting for any difference compared to the normal expected growth GO in the ARRY capitalisation rates. The current contract rental, CO, will need escalating in accordance with the prescribed escalation rate Esc to give the current contract rental Cc. This is defined as CEsc, on the assumption that the rent was due for review at the sale or valuation date. The current market rental Cm will still need assessing for the market reversion at expiry of the lease unless the lease is perpetually renewable on a prescribed basis (subject to previous provisos and a comment later regarding sustainability where onerous rent review terms from a prudent lessees perspective apply). The ARRY capitalisation rate REscT is calculated and applied to capitalise the escalating contract rental CO, over the term to run, and REscF to capitalise the forecast escalated rental CEsc on reversion from the next rent review at F yearly periods until lease expiry, or if renewals are assumed until final expiry. These are calculated using the per payment period escalation rate [esc p.p.] in place of the expected inflation rate [ie p.p.] and the real growth rate [gr p.p.] in the capitalisation rate formula. It is necessary, however, to introduce symbols, abbreviations, definitions, explanations, and formulae used to define and allow for prescribed rentals. These are shown in Table 8 Formulary for prescribed rental formulas, and similarly to previous additions, are combined into an overall Formulary shown in Appendix A at page 201. CEsc

Esc esc (lowercase) Rescf

Table 8 Formulary for prescribed rental formulas Current prescribed Assuming the rent was due for review at the sale or contract escalated rental valuation date. at the sale or valuation NB the Esc rent is indicated by the subscript Esc. date Prescribed rental A pre-set contractual annual or periodic nominal rent escalation rate p.a. increase as a % p.a. at each rental review Prescribed rental P esc =(1+Esc)(1/P) − 1 or esc =�(1+Esc) − 1 escalation rate p.p. Based on rental BOP payments p.p. ARRY per period (p.p.) (1+esc)f − 1 ya+ie+gr prescribed nominal Resc f = � � �1 − � �� (1+ya+ie+gr)f − 1 escalation cap rate for f 1+ya payment period reviews where EOP payments ×(1+ya)

102


ARRY annual (p.a.) prescribed nominal escalation cap rate for F year reviews p.a. ARRY per period (p.p.) prescribed nominal escalation cap rate for t payment period reviews ARRY annual (p.a.) prescribed nominal escalation cap rate for T year reviews

F

REsc

Resct

REsc

T

Based on nominal annual rental p.a.; where 1/P BOP payments p.p.: REscF = P×Rescf ; where EOP ×(1+ya) Based on rental BOP payments p.p.

(1+esc)t − 1 ya+ie+gr Resc t = � � �1 − � �� (1+ya+ie+gr)t − 1 1+ya

where EOP payments ×(1+ya)

Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: REscT = P×Resct ; where EOP ×(1+ya)

Note: (as defined above),CEsc is calculated in the Excel ™ valuation template once the Co and the Esc rate inputs are made. Esc is sourced from the lease contract and input into the model, the esc p.p. is calculated by the template once the Esc input is made and then Rescf and Resct p.p. cap rates and REscF and REscT annual cap rates are calculated by the template using the above formulae, explained below. The generic ARRY valuation terminating and re-leasing model in Algorithm 59 is applied based on Equation 60, being a net lease calculated on a BOP basis, assuming a new leasing on market terms and conditions at expiry, adapted for a prescribed contract rental review formula lease (until that expiry). This involves replacing Cc with CEsc, RAT with REscT, and RAF with REscF as below: CMV ⇐

CEsc Cm Co CEsc (1 − (1+YA )−T )+ (1+YA )−T − (1+YA )−EX + M (1+YA )−EX T F F REsc REsc REsc RA

Equation 73

REscT is P × Resct, REscF is P × Rescf and on the same payment basis as the rental is received, e.g. monthly in advance, similarly as in Equation 68, the expected OPEX rate op p.p. is replaced with the nominal prescribed growth rate esc p.p.; in the nominator in the second term of the capitalisation rate formula. Hence, the ARRY prescribed rental lease capitalisation rates Resct and Rescf BOP formula are as follows: (1+esc)t − 1 ya+ie+gr Resc t = � � �1 − � �� (1+ya+ie +gr)t − 1 1+ya Equation 74 (1+esc)f − 1 ya+ie+gr Resc f = � � �1 − � �� (1+ya+ie+gr)t − 1 1+ya

Equation 75

Three different scenarios are applied to revalue the previous Example 1(d) Monthly BOP to illustrate some of the various combinations of lease terms that may apply in practice: 1 Prescribed rental escalation = expected inflation for gross lease allowing for OPEX 2 Specified nominal escalation rate > expected inflation for net lease 3 Specified rent formula for net lease

103


4.19 Adaptation (vi) Scenario 1. ― Prescribed rental escalation = expected inflation for gross lease This scenario assumes the escalation rate is linked to expected inflation only i.e. Esc = Ie = 2% p.a. (no real growth). This compares, in this scenario, to the market expectation of an overall rental growth rate GO of 3.00% p.a. This gives a lower negative real growth rate of Esc –GO = 2% –3% = –1.00% p.a., or when the expected inflation is deducted gives the real escalation rate of Esc –Ie = 2% –2.00% = 0% p.a., or no real growth. Assuming the contract rental Co at $39,500 p.a. was fixed under the gross lease at the last review, 1 year ago, and that the escalated rental CEsc if reviewed at the valuation date would be the existing contract rental Co rental escalated at the escalation rate Esc = 2% p.a., i.e. CEsc = Co(1+Esc)F–T being $39,500 x (1.02)1 = $40,290 p.a. The current market rental Cm is maintained at $40,250 p.a., being on a 3 year market rent review frequency basis, without an escalation clause. As per the earlier Note, in Adaptation (v), similarly the resulting CEsc rental is immaterially different from the market rental due to the escalation rate in the lease adopted. In reality these could be materially different. The ARRY prescribed rental escalation capitalisation rate formula for the term to run, Resct is calculated applying Equation 74 using the previously calculated growth rate for 12 ie = esc = �(1.02) –1 = 0.0016516, T = 4 years to run, and t = P x T = 12 x 4 = 48 periods, affecting the pre-computed components in Equation 62, and adapted as follows:

(1.0016516)48 − 1 0.0824322 � �1 − � �� = 0.0080895 �1 − � 48 (1.0081353) − 1 1.0056541 0.4753760 0.0081353

Resc t = �

Resc t = 0.0080895(1 − 0.1734041)= 0.0080895× 0.8265959 Resc t = 0.0066868 or 0.66868% p.p. T

t

∴ REsc = 12 × Resc = 12 × 0.0066868 = 0.0802412 or 8.02412% p.a.


Similarly, the ARRY prescribed rental escalation capitalisation rate formula Rescf is calculated applying Equation 75 with F = 5 years or f = P x F = 12 x 5 = 60 periods as follows: (1.0016516)60 − 1 0.0081353 0.1040808 f Resc = � � �1 − � �� = 0.0080895 �1 − � (1.0081353)60 − 1 1.0056541 0.6260294

Resc f = 0.0080895(1 − 0.1662554)= 0.0080895 × 0.8337446 Resc f = 0.0067446 or 0.67446 % p.p.

∴ REsc F = 12 × Resc f = 12 × 0.0067446 = 0.0809352 or 8.09352% p.a.


The adaptation for the Scenario 1 CMV formula is based on the earlier current market valuation in Equation 73 but adding for the gross lease OPEX allowance adaptation as for the fifth term in Equation 67. It is adapted for the escalating lease with re-leasing on a similar gross lease but without the prescribed escalation clause on expiry, the RAM being as per the earlier market rental review Adaptation (iv) example in Equation 61 and using the pre-computed component calculations in Equation 62 and Equation 63 at page 91.

104

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Using the above capitalisation rates, and previously calculated components, the prescribed rental escalation algorithm as applied to the Scenario 1 CMV formula and calculations follow: CMV ⇐ PRV of term + PRV of reversion – PRV at expiry + PRV of new leasing at expiry – PRV of OPEX: Algorithm 80 CMV ⇐

CEsc Cm OPEX Co CEsc (1 − (1+YA )−T )+ (1+YA )−T − (1+YA )−EX + M (1+YA )−EX − Op T F F REsc REsc REsc RA RA

Equation 81

For additional clarity, as an intermediary step, the rentals, OPEX, timing inputs are shown before the full calculations: CMV ⇐

$40,290 $39,500 $40,290 $40,250 $3,200 −4 −4 −9 −9 − + − 4 (1 − (1+YA ) ) + 5 (1+YA ) 5 (1+YA ) M (1+YA ) REsc REsc REsc RA RA Op

Equation 82

CMV ⇐

$40,290 $40,290 $39,500 $40,250 $3,200 (1 – (1.07)–4 )+ (1.07)–4 – (1.07)–9 + (1.07)–9 – 0.0809352 0.0809352 0.0802412 0.0703294 0.0768661

CMV ⇐ ($492,266 × 0.237105)+($497,806 × 0.762895) − ($497,806 × 0.543934)+($572,307 × 0.543934) − $40,994

$496,023 ⇐ $116,719+$379,774 − $270,773+$311,297 − $40,994 ⇒ Say $496,000

Equation 83

The Scenario 1 Excel™ ARRY valuation template for the gross lease ARRY valuation model further adapted for the prescribed rental formula and inputs as above, is shown in Figure 39 ARRY valuation Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease, a page 106.

The Scenario 1 valuation printout is shown, in Figure 40 ARRY valuation printout Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease, at page 107.

105

Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY Valuation Model© - Copyright R L Jefferies, Oct 2010

Adaptation (vi) Valuation of Example 1(d) Scenario 1: Precribed Rental + Gross lease

Instructions

Cell Definitions

Adaptations

Calculation





Gr

p.p. g_r = (1+Gr)^(1/P)-1

0.082954% p.p.



Go

p.p. g_o = (1+GO)^(1/P)-1

0.246627% p.p.



Ie

p.p. i_e = (1+Ie )^(1/P)-1

0.165158% p.p.

YA

p.p. y_a = (1+YA)^(1/P)-1

0.565415% p.p.



Yo

p.p. y_o = (1+YO)^(1/P)-1

0.797414% p.p.



F

p.p. f_ = P × F

Adaptation (vi): Adapted description and Term to Run in yrs: T cell formula to allow for Contract Lease Expiring in yrs: EX escalation rate if a Re-letting on contract lease expiry: RL Y = Yes, N = Noprescribed lease


M

p.p. m_ = P × M

36


T

p.p. t_ = P × T

48


EX

p.p. e_x = P × T

108

Current Market Term Frequency in yrs: M

Y


All-risks Contract Real Yield Capitalisation rate = Resc5




Adaptation (vi): New input for prescribed rental escalation rate

Contract Rent Co :

$



$



$


Rental payments: In advance (BOP) =1; In arrears (EOP) =0

1



12

Enter number of payments p.a., i.e. 12 for monthly

IF Gross lease - Current OPEX –$p.a.

-$

3,200 If Gross lease Enter Estimated current OPEX budget, i.e. –3,000 for –$3,000

60

RL RAF


RAM


7.22169% 7.032939% p.a.

Co

p.p. c_O = CO/P

$

Cc

p.p. c_c = CC/P

$

3,390.42

CMV

p.p. c_m = Cm/P

$

3,390.42

3,291.67

pay P


0.083333333 0.165158% p.p.

OPEX

IF Gross lease: Annual escalation rate for OPEX (Default = expected inflation Ie )

2.00000% If Gross lease - Leave as default or Insert a number, i.e. 2.00 for 2.00%

OP

p.p. i_e = (1+Ie )^(1/P)-1

IF Precribed Rental - Annual escalation rate for rental Esc (Default = Ie ):

2.00000% If Precribed Rental - Insert a number, e.g. 3.00 for 3.00%; or Insert a Formula

Esc

p.p. e_sc = (1+Esc)^(1/P)-1

40,290 Will calculate automatically based on Co , Esc rate and expired term to date

CEsc

p.p. ce_sc = CEsc/P

RAT


7.128126% p.a.

REscT

p.a. REscT= P × Re_sct

8.024122% p.a.

REscF

p.a. REscF= P × Re_scf

8.093517% p.a.

RAOp


7.806098% p.a.

IF Prescribed Rental - Current Escalated Rental if reviewed $p.a. : CEsc

$

Term & Reversion: i.e. Valuation not at Review or Commencement 8.02412%

All-Risks Real Yield Term Capitalisation rate = REsc4


$

492,266

$

375,547

$

116,719

$

497,806

Adaptation (vi): Adapted description and cell formula for Cells will calculate automatically capitalisation rate to allow for escalation rate if a prescribed lease

Reversion - Contract Lease Real Value: Current Contract Rental $40290 capitalised @ REsc5: 8.09352% p.a. PRV of Deferred Real Reversion for 4 yrs @ YA: 7 % p.a.

$

379,774


-$

270,773

$

109,000

PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: Current Market Value = Market Rental $40250 capitalised @ RA3: 7.03294% p.a.

$

572,307


$

311,297

Other Adjustments: Gross lease: All-Risks Real Yield OPEX Capitalisation rate = RAOp p.a.

7.80610%

-$

40,994


$

496,022


$

IF Gross lease: OPEX $-3200 p.a. Capitalised @ RAOp : 7.8061% p.a.


3,357.50


Term - Real Value:

Adaptation (vi): New output cell for Escalate rental as at Contract Rental $39500 Capitalised @ REsc4: 8.02412% p.a. sale or valuation date Deferred Real Reversion for 4 yrs @ YA: 7 % p.a. (if reviewed)

0.165158% p.p. $

Adaptation (vi): Adapted description and cell formula for capitalisation rate to allow for escalation rate and based on escalated rental - if a prescribed Note this part of spreadsheet will not print lease as excluded from print area

Adaptation (vi): Adjusted concatenation formula to allow for Gross or Net lease


CMV

7.96371% p.a.

Figure 39 ARRY valuation Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease 106

Real Value Valuation & Analysis for Real Estate Investments (Jefferies, 2017)

Adaptation (vi) Valuation of Example 1(d) Scenario 1: Precribed Rental + Gross lease

All Risks Real Yield - Real Value - Investment approach valuation: Rental, lease and data assumptions: Contract Rent to run until next rent review: Current Contract Rent - if reviewed at valuation date : IF Precribed Rental - Nominal Annual escalation rate for rental : Current Market Rent (on normal terms and conditions): Rental payments 12 times per year In Advance Review Term Frequency in yrs: Term to Run in yrs: Expected (Nominal) Inflation rate: Real Growth rate: Nominal Value Growth rate: All-Risks Real Yield rate: Over-all Required Nominal Yield: Term to Run - Real Value: All-risks Real Yield Capitalisation rate for 4 year rent reviews: Contract Rental $39500 p.a. Capitalised @: 8.02412% p.a. Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. Present Real Value of 4 years term to run (by deduction): Reversion - Contract Lease Real Value: All-risks Real Yield Capitalisation rate for 5 year rent reviews: Current Contract Rental $40290 capitalised @ 8.09352% p.a. : Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. LESS - PRV of Deferred Value at Termination or Expiry in 9 years @: 7 % p.a.: PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: All-risks Real Yield Capitalisation rate for 3 year rent reviews: Current Market Value = Current Market Rental $40250 capitalised @ 7.03294% p.a. PRV of Market Value at Lease Expiry in 9 years @ All-Risks Real Yield: 7 % p.a.: Other Adjustments: IF Gross lease: All-Risks Real Yield OPEX Annual Capitalisation rate = IF Gross lease: OPEX $-3200 p.a. Capitalised @: 7.8061% p.a.

39,500 p.a. 40,290 p.a. 2.00000% p.a. 40,250 p.a. $ 12 times p.a. BOP 5.00 years 4.00 years 2.00000% p.a. 1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a.

$ $

$ $

8.02412% p.a. 492,266 375,547

$ $ -$

8.09352% p.a. 497,806 379,774 270,773

$

7.03294% p.a. 572,307

$

$

$

-$

$ $


116,719

109,000

311,297

7.80610% p.a.

40,994

496,022 496,000 7.96371% p.a.

Figure 40 ARRY valuation printout Adaptation (vi) Scenario 1: Prescribed escalated rental for gross lease

4.20 Adaptation (vi) Scenario 2 ― Specified nominal escalation rate > expected inflation for net lease This scenario assumes a different overall nominal escalation rate specified in the lease, greater than expected inflation, being 3.5% p.a., and also assumes a net lease. Compared to the market expectation overall rental growth rate GO = 3% p.a., the Esc = 3.50% p.a. scenario gives an increased positive real growth rate of Gr = +0.50% p.a.; or when the expected inflation is deducted gives the real escalation rate of Gr = Esc –Ie = 3.5% –2.00% = 1.5% p.a. during the term of the lease only. To allow for the escalated growth rate the capitalisation rates are similarly calculated on a monthly basis, where the monthly escalation rate esc = (1.035)1/12 –1 = 0.0028709) = 0. 28709% p.p.

107

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Assuming the contract rental CO = $39,500 p.a. was fixed under the lease at the last review, 1 year ago, and that the CEsc if reviewed at the valuation date would be that CO rental escalated at the Esc = 3.5% p.a., i.e. CEsc = Co(1+Esc)F–T = $39,500 x (1.035)1 = $40,883 p.a. The Cm is $40,250 p.a., as before, similarly assumed from expiry on a new non-prescribed market net lease rental with 3 year rent reviews. The ARRY prescribed rental capitalisation rate formula Resct applying Equation 74 as follows:

Resc t = �

0.0081353

� �1 − �

1.0056541

(1.0028709)48 − 1 0.1475230 �� = 0.0080895 � 1 − � (1.0081353)48 − 1 0.4753760

Resc t = 0.0080895 (1 − 0.3103291)= 0.0080895 × 0.6896709 Resc t = 0.0055791 or 0.55791% p.p.

Equation 84

∴REsc T = 12 × Resc t = 12 × 0.0055791 = 0.0669493 or 6.69493% p.a.

Equation 85

∴ REsc F = 12 × Resc f = 12 × 0.0056643 = 0.0679710 or 6.79710% p.a.

Equation 87

f

The ARRY prescribed rental capitalisation rate formula Resc applying Equation 75 as follows: (1.0028709)60 − 1 0.0081353 0.1876863 f Resc = � � �1 − � �� =0.0080895 � 1 − � (1.0081353)60 − 1 1.0056541 0.6260294 Resc f = 0.0080895(1 − 0.2998043)= 0.0080895 × 0.7001957 Resc f = 0056643 or 0.56643 % p.p. Equation 86 The Scenario 2 CMV formula is adapted based on the earlier prescribed rental formula market valuation in Equation 73 for the net lease with new leasing on expiry for the prescribed escalating rental with re-leasing on a current market rental on expiry. Using the above capitalisation rates, inputs and previously calculated components the Scenario 2 CMV algorithm and mathematical equations and calculations follows: CMV ⇐ PRV of term + PRV of reversion – PRV at expiry + PRV of New Leasing at expiry: CMV ⇐

CMV ⇐

CEsc Cm Co CEsc (1 − (1+YA )−T )+ (1+YA )−T − (1+YA )−EX + M (1+YA )−EX T F F REsc REsc REsc RA

Algorithm 88

Equation 89

$40,883 $39,500 $40,883 $40,250 (1 – (1.07)–4 ) + (1.07)–4 − (1.07)–9 + (1.07)–9 0.0679710 0.0669493 0.0679710 0.0703294

Equation 90

CMV ⇐ ($589,998× 0.237105)+($601,477 × 0.762895) – ($$601,477 × 0.543934)+($572,307 × 0.543934)

$582,888 ⇐ $139,891+$458,864 − $327,164+$311,297 ⇒ Say $583,000

Equation 91

The Scenario 2 valuation is shown in Figure 41 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease (see next page) The valuation printout is shown in Figure 42 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease — Valuation template printout at page 110.

108

Real Value Valuation & Analysis for Real Estate Investments (Jefferies, 2017) ARRY Valuation spreadsheet template (Version Oct 2011)

Adaptation (vi) Valuation Scenario 2: Precribed Rental > Expected inflation + Net Lease

Instructions

Cell Definitions

Adaptations

Calculation



Ie

p.p. i_e = (1+Ie)^(1/P)-1

0.16516% p.p.



Gr

p.p. g_r = (1+Gr)^(1/P)-1

0.08295% p.p.



Go

p.p. g_o = (1+GO)^(1/P)-1

0.24663% p.p.



YA

p.p. y_a = (1+YA)^(1/P)-1

0.56541% p.p.


Yo

p.p. y_o = (1+YO)^(1/P)-1

0.79741% p.p.


F

p.p. f_ = P × F

60


M

p.p. m_ = P × M

36


T

p.p. t_ = P × T

48


EX

p.p. e_x = P × T

108


Adaptation (vi) Adapted description and cell formula to allow for effect of specified escalation rate increasing cap rate

Contract Review Term Frequency in yrs: F Current Market Term Frequency in yrs: M Term to Run in yrs: T Contract Lease Expiring in yrs: EX

Y







Adaptation (vi): New input for prescribed rental escalation rate

Contract Rent Co :

$



$



$


Rental payments: In advance (BOP) =1; In arrears (EOP) =0 Adaptation (1): Additional input Cell Number of rental payments per annum P: for EOP or BOP option. IF Gross lease - Current OPEX –$p.a.


12

Enter number of payments p.a., i.e. 12 for monthly If Gross lease Enter Estimated current OPEX budget, i.e. –3,000 for –$3,000

Not Applicable

IF Gross lease: Annual escalation rate for OPEX (Default = expected inflation Ie) IF Precribed Rental - Annual escalation rate for rental Esc (Default = Ie): IF Precribed Rental - Current escalated rental if reviewed $p.a. Cesc

1

p.p. c_O = CO/P

$

3,291.67

Cc

p.p. c_c = CC/P

$

3,390.42

CMV

p.p. c_m = Cm/P

$

3,390.42

pay P


0.0833333

OPEX p.p. i_e = (1+Ie)^(1/P)-1

#VALUE! 0.28709% p.p.


CEsc

p.p. ce_sc = CEsc/P

RAT

p.a. RA = P × RA

6.69493% $

589,998

$

450,107

$

139,891

Current Contract Rental $40883 capitalised @ REsc5: 6.7971% p.a.

$

601,477


$

458,864


-$

327,164

$

131,700

Reversion - Current Market Real Value: Current Market Value = Market Rental $40250 capitalised @ RA3: 7.03294% p.a.

$

572,307


$

311,297

Other Adjustments: Not Applicable

Net Lease Not Applicable

$


$


$


7.032939% p.a.

Co

p.p. e_sc = (1+Esc)^(1/P)-1

Adaptation (vi) Adapted description and cell formula for Cells will calculate automatically capitalisation rate to allow for escalation rate if a prescribed lease



7.221687% p.a.

m_

$

3,406.92




p.a. RAM = P × RA

OP

Term - Real Value:


RAM

Esc

Term & Reversion: i.e. Valuation not at Review or Commencement

Rodney: New output cell for Contract Rental $39500 Capitalised @ REsc4: 6.69493% p.a. Escalated rental as at sale or valuation Deferred Real Reversion for 4 yrs @ YA: 7 % p.a. date (if reviewed)

f_

p.a. RAF = P × RA

3.50000% If Precribed Rental - Insert a number, e.g. 3.00 for 3.00%; or Insert a Formula $

If Gross lease - Leave as default or Insert a number, i.e. 2.00 for 2.00%

RL RAF

-

T

t_

7.128126% p.a.

T

t

6.694933% p.a.

F

f

6.797101% p.a.

REscT

p.a. REsc = P × Re_sc

REscF

p.a. REsc = P × Re_sc

Adaptation (vi) Adapted description and cell formula for capitalisation rate to allow for escalation rate Note this part of spreadsheet will not print and based on escalated rental - ifprint a area as excluded from prescribed lease

Rodney: Adjusted concatenation formula to allow for Gross or Net lease

RAO_p RAOp

582,889 583,000 Valuation: or Solve for ARRY to = Sale Price

CMV

6.77530% p.a.

Figure 41 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease 109

OP

p.a. RA

O_p

= P × RA

#VALUE!

Real Value Valuation & Analysis for Real Estate Investments (Jefferies, 2017)

Adaptation (vi) Valuation Scenario 2: Precribed Rental > Expected inflation + Net Lease

All Risks Real Yield - Real Value - Investment approach valuation: Rental, lease and data assumptions: Contract Rent to run until next rent review: Current Contract Rent - if reviewed at valuation date : IF Precribed Rental - Nominal Annual escalation rate for rental : Current Market Rent (on normal terms and conditions): Rental payments 12 times per year In Advance Review Term Frequency in yrs: Term to Run in yrs: Expected (Nominal) Inflation rate: Real Growth rate: Nominal Value Growth rate: All-Risks Real Yield rate: Over-all Required Nominal Yield: Term to Run - Real Value: All-risks Real Yield Capitalisation rate for 4 year rent reviews: Contract Rental $39500 p.a. Capitalised @: 6.69493% p.a. Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. Present Real Value of 4 years term to run (by deduction): Reversion - Contract Lease Real Value: All-risks Real Yield Capitalisation rate for 5 year rent reviews: Current Contract Rental $40883 capitalised @ 6.7971% p.a. : Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. LESS - PRV of Deferred Value at Termination or Expiry in 9 years @: 7 % p.a.: PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: All-risks Real Yield Capitalisation rate for 3 year rent reviews: Current Market Value = Current Market Rental $40250 capitalised @ 7.03294% p.a. PRV of Market Value at Lease Expiry in 9 years @ All-Risks Real Yield: 7 % p.a.: Other Adjustments: Net Lease - Not Applicable Net Lease - Not Applicable

39,500 p.a. 40,883 p.a. 3.50000% p.a. 40,250 p.a. $ 12 times p.a. BOP 5.00 years 4.00 years 2.00000% p.a. 1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a. $ $

$ $

6.69493% p.a. 589,998 450,107

$ $ -$

6.79710% p.a. 601,477 458,864 327,164

$

7.03294% p.a. 572,307

$

$

$

139,891

131,700

311,297

Not Applicable

$

$ $


-

582,889 583,000 6.77530% p.a.

Figure 42 Adaptation (vi) Valuation Scenario 2: Prescribed rental > expected inflation for net lease — Valuation template printout

110


4.22 Adaptation (vi) Scenario 3 ― Specified rent formula for net lease This scenario assumes an overall nominal escalation rate of 20% per five years rental review is specified (or a non-compounding or straight-line increase of 4% p.a. per year). This calculates to an effective compounding overall nominal escalation rate of Esc = (1.20)(1/5) –1 = 0.0371373 or 3.71373% p.a. This compares to the market expectation overall of GO = 3.00% p.a. gives an added positive real growth rate of + 0.71373% p.a.; or when the expected inflation is deducted gives the real escalation rate of Gr = Esc – Ie = 3.71373% –2.00% = 1.71373% p.a. until expiry of the lease. It will then revert to a normal market rental expectation. Assuming the contract rental Co = $39,500 p.a. was fixed under the lease at the last review, 1 year ago, and that the escalated rental CEsc if reviewed at the valuation date would be that rental escalated at the Esc = 3.71373% p.a. ., i.e. CEsc = Cc (1+Esc)F–T = $39,500 x (1.0371373)1 = $40,967 p.a. The ARRY prescribed rental capitalisation rate formula Resct applying Equation 74 is calculated as: Where esc = 1.03713731/12 – 1 = 0.0030433

(1.0030433)48 − 1 0.1570310 �� = 0.0080895 �1 � 48 (1.0081353) − 1 1.0056541 0.4753760 Resc t = 0.0080895(1 − 0.3303301)= 0.0080895 × 0.6696699 Resc t = 0.0054173 or 0.54173% p.p. Resc t = �

0.0081353

� �1 − �

∴ REsc T = 12 × Resct = 12 × 0.0054173 = 0.0650077 or 6.50077% p.a.

Equation 92

Equation 93 The ARRY prescribed rental capitalisation rate formula Resc applying Equation 92 is calculated as: (1.0030433)60 − 1 0.0081353 0.2000000 f Resc = � � �1 − � �� = 0.0080895 � 1 − � (1.0081353)60 − 1 1.0056541 0.6260294 Resc f = 0.0080895(1 − 0.3194738)= 0.0080895× 0.6805262 Resc f = 0.0055051 or 0.55051% p.p. Equation 94 ∴REsc F = 12 × Rescf = 12 × 0.0055051 = 0.066016 or 6.6016% p.a. Equation 95 Applying the Scenario 3 CMV formula based on Equation 73 using the above capitalisation rates , but with no change to the re-leasing on expiry market capitalisation rate RAM follows: f

CEsc Cm Co CEsc (1 − (1+YA )−T )+ (1+YA )−T − (1+YA )−EX + M (1+YA )−EX T F F REsc REsc REsc RA $40,967 $40,250 $39,500 $40,967 (1 – (1.07)–4 )+ (1.07)–4 – (1.07)–9 + (1.07)–9 CMV ⇐ 0.0660616 0.0703294 0.0650077 0.0660616 Equation 96

CMV ⇐

CMV ⇐ ($607620×0.237105)+($620,133 × 0.762895) – ($620,133 × 0.543934)+($572,307 × 0.543934) $591,152⇐ $144,070+$473,097 − $337,311+$311,297 ⇒ Say $591,000 Equation 97

The Scenario 3 Excel spreadsheet valuation template Figure 43 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease is shown on page 112 following:

111

Real Value Valuation & Analysis for Real Estate Investments (Jefferies, 2017) ARRY Valuation spreadsheet template (Version Oct 2011)

Instructions

Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified Rent Formula + Net Lease

Cell Definitions

Calculation

Adaptations



Ie

p.p. i_e = (1+Ie )^(1/P)-1

0.16516% p.p.



Gr

p.p. g_r = (1+Gr)^(1/P)-1

0.08295% p.p.



Go

p.p. g_o = (1+GO)^(1/P)-1

0.24663% p.p.



YA

p.p. y_a = (1+YA)^(1/P)-1

0.56541% p.p. 0.79741% p.p.



Yo

p.p. y_o = (1+YO)^(1/P)-1



F

p.p. f_ = P × F


M

p.p. q_ = P × M

36


T

p.p. t_ = P × T

48


EX

p.p. e_x = P × T

108

Current Market Term Frequency in yrs: M Term to Run in yrs: T Contract Lease Expiring in yrs: EX Re-letting on contract lease expiry: RL Y = Yes, N = No

Adaptation (vi) Adapted description and cell formula to allow for escalation rate if a prescribed lease

Y






Adaptation (vi): New input for specified rental escalation rate formula

Contract Rent Co :

$



$



$


Rental payments: In advance (BOP) =1; In arrears (EOP) =0

1


12

Enter number "1" for BOP; or zero "0" for EOP Enter number of payments p.a., i.e. 12 for monthly If Gross lease Enter Estimated current OPEX budget, i.e. –3,000 for –$3,000

IF Gross lease - Current OPEX –$p.a. IF Gross lease: Annual escalation rate for OPEX (Default = expected inflation Ie )

Not Applicable

IF Precribed Rental - Annual rental escalation rate Esc (Default = Ie ): IF Precribed Rental - Current escalated rental if reviewed $p.a. Cesc

$

p.p. c_O = CO/P

$

3,291.67

Cc

p.p. c_c = CC/P

$

3,390.42

CMV

p.p. c_m = Cm/P

$

3,390.42

pay P

0.083333333


OPEX


CEsc

p.p. ce_sc = CEsc/P

RAT


7.128126% p.a.

REscT

p.a. REscT= P × Re_sct

6.500774% p.a.

REscF

p.a. REscF= P × Re_scf

6.606161% p.a.

6.50077% $

607,620

$

463,550

$

144,070


$

473,097


-$

337,311

$

135,785

Reversion - Current Market Real Value: Current Market Value = Market Rental $40250 capitalised @ RA3: 7.03294% p.a.

$

572,307


$

311,297

Adaptation (vi) Adapted description and cell formula for Cells will calculate automatically capitalisation rate to allow for escalation rate if a prescribed lease

#VALUE! 0.30433% p.p. $

3,413.92

Not Applicable

$

Adaptation (vi) Adapted description and cell formula for capitalisation rate to allow for escalation rate and based escalated rental - if awill prescribed Noteon this part of spreadsheet not print lease as excluded from print area

Adaptation (vi) Adjusted concatenation formula to allow for Gross or Net lease

Other Adjustments:

RAO_p RAOp


-


$

591,152


$



Co

p.p. i_e = (1+Ie )^(1/P)-1

620,133


7.22169% 7.032939% p.a.

p.p. e_sc = (1+Esc)^(1/P)-1

$


p.a. RAM = P × RAq_

OP






Current Contract Rental $40967 capitalised @ REsc5: 6.60616% p.a.

RAF RAM

Esc

If Gross lease - Leave as default or Insert a number, i.e. 2.00 for 2.00%

Term - Real Value:


RL

3.71373% If Precribed Rental - Insert a number, e.g. 3.00 for 3.00%; or Insert a Formula

Term & Reversion: i.e. Valuation not at Review or Commencement

Rodney: New output cell for Escalated rental as at Contract Rental $39500 Capitalised @ REsc4: 6.50077% p.a. sale or valuation date Deferred Real Reversion for 4 yrs @ YA: 7 % p.a. (if reviewed)

60

CMV

6.68359% p.a.

Figure 43 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease

112

#VALUE!

Real Value Valuation for Real Estate Investments (Jefferies, 2017) The Scenario 3 valuation is shown in Figure 44 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease — Valuation printout section below:

Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified Rent Formula + Net Lease

All Risks Real Yield - Real Value - Investment approach valuation: Rental, lease and data assumptions: Contract Rent to run until next rent review: Current Contract Rent - if reviewed at valuation date : IF Precribed Rental - Nominal Annual escalation rate for rental : Current Market Rent (on normal terms and conditions): Rental payments 12 times per year In Advance Review Term Frequency in yrs: Term to Run in yrs: Expected (Nominal) Inflation rate: Real Growth rate: Nominal Value Growth rate: All-Risks Real Yield rate: Over-all Required Nominal Yield: Term to Run - Real Value: All-risks Real Yield Capitalisation rate for 4 year rent reviews: Contract Rental $39500 p.a. Capitalised @: 6.50077% p.a. Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. Present Real Value of 4 years term to run (by deduction): Reversion - Contract Lease Real Value: All-risks Real Yield Capitalisation rate for 5 year rent reviews: Current Contract Rental $40967 capitalised @ 6.60616% p.a. : Deferred Real Reversion for 4 years @ All-Risks Real Yield: 7 % p.a. LESS - PRV of Deferred Value at Termination or Expiry in 9 years @: 7 % p.a.: PRV of reversionary renewals until Termination or Expiry in 9 years: Reversion - Current Market Real Value: All-risks Real Yield Capitalisation rate for 3 year rent reviews: Current Market Value = Current Market Rental $40250 capitalised @ 7.03294% p.a. PRV of Market Value at Lease Expiry in 9 years @ All-Risks Real Yield: 7 % p.a.: Other Adjustments: IF Gross lease: All-Risks Real Yield OPEX Annual Capitalisation rate = Net Lease - Not Applicable

$ $

39,500 p.a. 40,967 p.a. 3.71373% p.a. $ 40,250 p.a. 12 times p.a. BOP 5.00 years 4.00 years 2.00000% p.a. 1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a.

$ $

6.50077% p.a. 607,620 463,550

$ $ -$

6.60616% p.a. 620,133 473,097 337,311

$

7.03294% p.a. 572,307

$

$

$

Current Real Market Value - CMV: (Rounded) Initial Yield (over-all capitalisation rate): Current Contract Rental ÷ CMV:

135,785

311,297

Not Applicable

$

$ $


144,070

-

591,152 591,000 6.68359% p.a.

Figure 44 Adaptation (vi) Valuation of Example 1(d) Scenario 3: Specified rent formula for net lease — Valuation printout section A Proviso: The difference in values arising will depend on how long into the future the renewals under the existing leases can be exercised by the lessee. The lease, which provides renewable advantages, would rationally be renewed by the lessee for as long as possible. Where the lease provided for an increasing rental resulting in a greater than normal market rental it would rationally not be renewed the lessee at the next renewal date.

113


4.23 Chapter summary This chapter, whilst technically challenging is the key to showing the various required adaptations both mathematically, by worked examples and in the template versions of the ARRY valuation model. It demonstrates how and why the ARRY real valuation model is adapted for the most commonly found variations in lease terms and conditions. It also shows how market based evidence for the assumptions, inherent in the model are included, and their impacts. The progressive developments of the model illustrates how variations in the lease terms, in combination with market conditions, are factored into the model and affect the valuation results. Further, it shows the effect of each different adaptation and quantifies these with examples. The progressive examples show that using a consistent set of algorithms and formulae incorporated into a basic Excel™ spreadsheet template this can be used efficiently in practice both for analysing sales, and for undertaking valuations. Though the mathematics behind the models’ valuations is set out in detail, the practical application by valuers using the ARRY valuation template takes the painstaking math out of this real valuation method. Its use assures calculation accuracy of the otherwise laborious multiple manual calculations required that are prone to human error due to their complexity. Compared to previous real value valuation methods, the ARRY real value valuation model is shown by example to be mathematically sound. The use of the Excel™ ARRY valuation templates developed are efficient, compared to manually completing the calculations or competing explicit DCFs, even using modern computerised programs. Period-by-period assumptions and calculations are avoided and less prone to forecasting errors and the ARRY model is adaptable to a wide range of commonly found leases for all types of commercial and industrial income producing property valuations. This chapter leads into the development of more required adaptations, as built into the latest ARRY valuation templates, to enable the model to be used for specialist valuation adaptations in Chapter 5.

114


Chapter 5 — Special adaptations to the ARRY valuation model 5.1 Introduction This chapter adapts the ARRY valuation model for lease variations associated with different types and uses of properties, their development, or marketing resulting in special lease terms and conditions. It sets out the following required adaptations: Adaptation (vii) Renewals of the current lease, and re-leasing with different terms and/or rent review periods. Adaptation (viii) Under-developed properties with redevelopment potential. Adaptation (ix) Vacancies, rent-free periods, leasing incentives, and leasing costs. Adaptation (x)

Allowance for costs of purchase (including due diligence) and costs of sale.

Adaptation (xi) CAPEX (expectations of capital expenditure), refurbishment, and deferred maintenance liabilities. Adaptation (xii) Partial gross leases with fixed and/or variable OPEX recoveries. Adaptation (xiii) Ratchet clauses in leases affecting rental review increases. The above adaptations consecutively build upon the generic adaptations in Chapter 4 by worked examples and using an advanced spreadsheet template version of the ARRY valuation model.

5.2 Advanced ARRY valuation template model To apply these special adaptations in practice, advanced MS Excel™ ARRY valuation templates incorporate new inputs, calculations, and outputs, including a new valuation printout section, presented here as progressively amended for each new adaptation. A diagrammatic overview of the format and layout of the valuation templates in Figure 45 at page 116 shows ten different tenancy or separate property sheets linked (shown by arrows) to the summary sheet. It is not intended that the details in the sheets are readable ― just the structure. The enlarged summary sheet in Figure 46 at page 117 shows the Adaptations (vii) to (xii)3 displaying these as ten properties to fit across a computer screen. The template shows only ten tenancies or properties at a time depending on the screen size, resolution, and viewing scale, printing them in sets of ten on A4 landscape orientated sheets.

115


Inputs (Yellow), Instructions and outputs area

Key data from each individual property or tenancy sheet is shown on a Summary Sheet

Structure of ARRY Valuation Templates

Property 1 or Tenancy 1







Property 8 or Property 8

SUMMARY Sheet Summary (Blue) print area

Summary of PRVs of rental cash flows and reversionary values Figure 45 Format and layout of MS Excel ARRY valuation templates

116



Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY Valuation - Separate Single Tenant Properties (Up to 10 Properties) - Version May 2013 Key common data: Expected (nominal) inflation rate (Ie): 2.00000% p.a. Adaptation (vii) Adaptation (viii) PROPERTY: Lease data, rental, and assumptions: Valuation (or sale) date: Real growth rate assumed (Gr): All-risks real yield (ARRY) rate adopted (Yᴀ):

Commencement date: Expiry date: Term in years: Rental commencement date or last rent review date (as appropriate): Initial vacancy to lease commencement (if applicable and unexpired): N.B. The summary Final expiry date, i.e. termination (if applicable): figures from Contract rent to run until next rent review: individual property Rental & OPEX payments frequency (EOP = in arrears; BOP = in advance) sheets will appear Rental review frequency during current contract lease term - in years: when the commencement date IF prescribed rental - nominal annual escalation rate for rental: Comm is entered on If prescribed rental - current escalated rental, if reviewed: each individual sheet. Ratchet clause?; i.e. on review rental cannot fall below base rental. [This box will not If soft ratchet clause above - minimum rental: print] Next rent review date (If applicable): Current rental term to run, i.e. to next review (or expiry if no further review): Contract lease expiring in years:

Lease renewal data - assuming rights of renewal (If any) are exercised:

-$

Current contract rent - if reviewed at valuation date: Current market rent (on normal market and ADLS lease terms and conditions): Current market rental review frequency (in years): Agency new leasing fee or commission rate as % of contract rental: Rent-free fitting out period and/or rent free incentive = number of months: Pre-leasing refurbishment, free lessee's fitout or other incentive cost:

$ $

ASSUMPTIONS on lease expiry (if not perpetually renewable):

Re-leasing on contract lease expiry: If vacancy expected (on re-leasing) = number of months vacant until re-let: If redeveloping at lease termination - current real redevelopment value: If above - forecast real redevelopment value growth rate p.a.:

SUMMARY of term & reversion valuations: components of present real value (PRV):

20/03/2012

20/03/2012

20/03/2012

20/03/2012

20/03/2012

20/03/2012

20/03/2012

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.0000% p.a. 7.0000% p.a.

1.00 Renewals 6.00 years 2.00 years 15.00 years 19/03/2027

3,200 p.a.


Not Applicable -$

40,883 p.a. $ 40,883 p.a. $ 40,250 p.a. Not Applicable $ 3.00 years Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable -$ Yes No Not Applicable Not Applicable Not Applicable $ 500,000 Not Applicable 4.0000% p.a.

PRV of current contract rental over term to run to next rent review: PRV of contract rental(s) from next rent review to current lease expiry: PRV of contract rental(s) from lease expiry to final expiry of renewals: PRV at rent review (if perpetually renewable); or re-leasing at final expiry: PRV of real redevelopment value at lease termination: PRV of unrecovered OPEX: if applicable - see individual property sheets for details PRV of initial vacancies and/or vacancies on re-leasing: PRV of CAPEX, added-value (e.g. vacant land) or other adjustments TOTAL PRESENT REAL VALUES of terms and reversions ± other adjustments

$ $ $ $ $ $ $ $ $

Current real market value - CMV: (rounded)

$

Net initial yield - after any initial vacancies (if applicable) ÷ CMV:

Adaptation (xii) 1 Adaptation (xii) 2 Adaptation (xii) 3

20/03/2012


Full or partially unrecovered net OPEX - after any initial vacancy leasing (if applicable):

Current market data:

Adaptation (x) 1 Adaptation (x) 2 Adaptation (x) 3 Adaptation (xi)

20/03/2012

20/03/2011 20/03/2011 20/06/2012 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 19/03/2021 19/03/2021 19/06/2018 19/03/2021 19/03/2021 19/03/2021 19/03/2021 19/03/2021 19/03/2021 19/03/2021 10.00 years 10.00 years 6.00 years 10.00 years 10.00 years 10.00 years 10.00 years 10.00 years 10.00 years 10.00 years 20/03/2011 20/03/2011 20/09/2012 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 20/03/2011 Not applicable Not applicable 3.00 months Not applicable Not applicable Not applicable Not applicable Not applicable Not applicable Not applicable 19/03/2033 19/03/2027 19/06/2021 19/03/2027 19/03/2027 19/03/2021 19/03/2027 Perp. Renewable Perp. Renewable 19/03/2027 $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. $ 39,500 p.a. Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP Monthly BOP 2.00 years 5.00 years 5.00 years 5.00 years 5.00 years 5.00 years 5.00 years 5.00 years 5.00 years 5.00 years 3.5000% p.a. 3.5000% p.a. 0.0000% p.a. 3.5000% p.a. 3.5000% p.a. 3.5000% p.a. 3.5000% p.a. 3.5000% p.a. 3.5000% p.a. 3.5000% p.a. $ 40,883 p.a. $ 40,883 p.a. Not applicable $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet No Ratchet Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable 20/03/2016 20/03/2016 20/06/2014 20/03/2016 20/03/2016 20/03/2016 20/03/2016 20/03/2016 20/03/2016 20/03/2016 4.00 years 4.00 years 2.25 years 4.00 years 4.00 years 4.00 years 4.00 years 4.00 years 4.00 years 4.00 years 9.00 years 6.25 years 9.00 years 9.00 years 9.00 years 9.00 years 9.00 years 9.00 years 9.00 years 9.00 years

Perpetually renewable or number of rights of renewal (If any) assumed: Length of contract lease renewal terms (if any): Contract renewal rental review frequency (if applicable): Contract lease with assumed renewals - terminating in: Final expiry date, i.e. termination at end of assumed renewals (if applicable):

OPEX (operating expenses): for details see individual property sheets:

Adaptation (ix)

20/03/2012

139,891 131,700 186,497 138,220 596,309

$ $ $ $ $ $ $ $ $

596,000 $ 6.6275% p.a.

139,891 131,700 111,920 326,372 709,884

3,200 p.a. -$


3,200 p.a. -$


3,200 p.a. -$


3,200 p.a. -$

Perp. Renewable 10.00 years 5.00 years Perp. renewable Perp. Renewable

3,200 p.a. -$

$ $ $ $ $ $ -$ $ $

Perp. Renewable 10.00 years 5.00 years Perp. renewable Perp. Renewable

1,964 p.a. -$


1,964 p.a. -$

1,964 p.a.

39,500 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. $ 40,883 p.a. 41,000 p.a. Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable $ 41,000 p.a. 3.00 years Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable 3.00 years 12.00% Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable 12.00% 3.00 months Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable 3.00 months 50,000 Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable Yes No No No No 3.00 months Not Applicable Not Applicable Not Applicable Not Applicable Not Applicable $ 500,000 $ 500,000 $ 500,000 500,000 $ Not Applicable 4.0000% p.a. 4.0000% p.a. 4.0000% p.a. 4.0000% p.a.

710,000 $ 5.5634% p.a.


61,473 115,958 70,164 301,408 83,806 465,198

$ $ $ $ $ $ $ -$ $

465,000 $ 8.4946% p.a.

139,891 131,700 111,920 326,372 92,747 617,137

$ $ $ $ $ $ $ -$ $

617,000 $ 6.4019% p.a.

139,891 131,700 111,920 326,372 42,593 667,291

$ $ $ $ $ $ $ -$ $

667,000 $ 5.9220% p.a.

139,891 131,700 387,094 114,693 543,992

$ $ $ $ $ $ $ -$ $

544,000 $ 7.2610% p.a.

Figure 46 Copy of template summary sheet for the Chapter 7 Adaptations

117

139,891 131,700 111,920 326,372 168,566 541,318

Not Applicable Not Applicable Not Applicable Not Applicable

$ $ $ $ $ -$ $ -$ $

541,000 $ 7.3013% p.a.

139,891 458,864 28,649 75,819 494,287

Not Applicable Not Applicable Not Applicable Not Applicable

$ $ $ $ $ -$ $ -$ $

494,000 $ 7.5984% p.a.

139,891 458,864 28,649 75,819 494,287

Yes 6.00 months Not Applicable Not Applicable

$ $ $ $ $ -$ -$ -$ $

494,000 $ 7.5984% p.a.

139,891 131,700 111,920 200,841 35,184 2,011 75,819 471,339

471,000 7.9694% p.a.

Real Value Valuation for Real Estate Investments (Jefferies, 2017) There is no practical limit in principle to the number of properties or multiple-tenancies that can be added (limited only by the number of columns in the Excel sheet). Slightly different structures are necessary for other templates, such as those designed for a greater number of properties, portfolios of properties, or multi-tenanted properties. For example, a portfolio valuation of different separate properties will have limited common data, e.g. a common valuation date and expected inflation rate. The growth rates may differ as well as the ARRYs reflecting different locations and specific property risk. The importance of this template structure is to enable sales analyses and/or valuations of any number of different properties and/or tenancies to be handled efficiently in a single spreadsheet model utilising common inputs and data. At this stage of the development of the model, the template version becomes more critical as the practical means of doing the ARRY sales analyses and valuations, and is the effective ARRY valuation methodology tool used and becomes the practical working ARRY valuation model. To undertake ARRY valuations requires an understanding of the templates, how they are structured, and the different inputs required for different types of valuation assignments. The summary sheet collates the key common inputs and valuation data from individual property or tenancy sheets in a separate column. With portfolios of properties and multi-tenanted properties a totals column is inserted at the left-hand side showing the totals of all key figures that contribute to the total value of the portfolio or multi-tenancy property (see variously used in the case studies in Jefferies (2017a).

5.3 Property or tenancy worksheets Appendix B.1 ARRY Valuation template property or tenancy worksheet – complete, at page 210, shows an A3 sized copy of a whole property worksheet with highlighted comments boxes of the main features and changes from the earlier 2010 versions of the template used in Chapter 4. An explanation of this template, its features and its key inputs, yield data and output areas are fully detailed in Appendix B.2 An explanation of ARRY Valuation template property or tenancy worksheet, commencing at page 212. Enlargements of this template are shown in Figure 47, to Figure 51 following, that show various sections of this template using the Adaption (vi) Scenario 2 data. This advanced ARRY valuation template is used to illustrate the progressive Adaptations (vii) to (xiii) by detailing the examples to follow in the subsequent sections of this chapter.

118

Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY Valuation - Separate Single Tenant Properties (Up to 10 Properties) - Version May 2013 Model example: vacancies, rent-free periods, and leasing costs; plus GRL; CAPEX

New input cell: For valuation or sale date, from which term to run is calculated.

Key Inputs & Yield data:

Valuation (or Sale) date: VDate Expected (nominal ) inflation rate: I e [from summary sheet] Real growth rate: G r Nominal value growth rate: G o = I e + G r All-risks real rield (ARRY) rate: Y A

YELLOW highlighted data input

20/03/2012 2.00000% p.a.

cells are unlocked and have validation boxes with data entry message. If invalid data is entered an Error Alert is shown.

1.00000% p.a. 3.00000% p.a. 7.00000% p.a.

Tab  to next input cell.

Over-all required nominal yield (disc. rate): (Y A + I e + G r ) = Y o Lease commencement date: Comm

10.00000% p.a.

New input cell: Lease commenecement date from which the Term is calculated.

CONTRACT LEASE DATES (Existing contract lease or assumed leasing terms if initial vacancy allowed).

20/06/2012

New input cell: For lease expiry date, from which the time to lease expiry is calculated.

Lease expiry date: ExpDate Term in years: Term

19/06/2018 6.00 years 20/09/2012

Rental commencement date, (i.e. last rent review date if not Comm above), or after initial rent-free period if any: RentComm Initial rent-free payment periods (If any): IRF Pre initial leasing refurbishment, free lessee's fit out or other incentive cost -$ : Contr Initial vacancy, in whole rental payment periods, to lease commencement (if applicable and unexpired): V i

New input cell: Rental commencement date, from which the term to run (T), next rent review (ReviewDate) and years to expiry (EX) is calculated.

3 months -$

50,000 3 months

CONTRACT RENTAL DATA (Existing contract lease or assumed leasing terms if initial vacancy allowed). Premises annual rental: PRent Car parks annual rental: CpRent Total annual contract rental: Co Monthly contract rental: Co_pcm Rental and OPEX payments frequency per annum: P

For clearest viewing and for data inputting select Columns A:B; on menu View Tab, Click on "Zoom to Selection"

$ New input cell: For any separate car parking rental.

38,000

$

1,500

$

39,500 $3,292 p.c.m. 12

Rental payments: in advance (BOP) = 1; in arrears (EOP) = 0: pay

1

Rental review frequency, or fixed rental term, during contract lease term - in years: F

2.00 years

IF prescribed rental - nominal annual escalation rate for rental: Esc

New input cell: For ratchet options Hard or Soft choice from drop-down list.

IF prescribed rental - current escalated rental if reviewed $p.a. : CEsc Ratchet clause?: Rcht If soft ratchet clause above - minimum rental: Min

New Input Cell: For minimum rent if Soft ratchet

Next rental review date (If applicable): ReviewDate

4.00000% p.a. $

39,115 Hard

$

38,000 20/06/2014

Period to run in years, to next rental review, or to expiry if fixed term or no further review, incl. any unexpired vacancy & rent-free: T

2.25 years

Current contract lease expires in years: EX

6.25 years

New input cell: For number of lease renewals allowed and assumed to be taken up.

LEASE RENEWAL DATA - assuming rights of renewal (If any) are exercised: Perpetually renewable or number of rights of renewal (If any) assumed: RoRs

1

New input cell: For length of renewal terms.

Length of contract lease renewal terms (if any) in years: RT Contract renewal rental review frequency or fixed rental term during renewal term (in years): RR

3.00 years 3.00 years

New input cell: For rent review frequency during renewals.

Contract lease with assumed renewals - if applicable - terminating in years: To_Exp Final expiry date, - if applicable - i.e. termination at end of assumed renewals: FinalExp

OPEX (operating expenses) - default is an ADLS net lease with 100% of outgoings recovered from tenant: IF gross lease - (nil, or partial i.e. CO), CF is adopted as at the next rental review and capitalised at the review of frequency capitalisation rate RAF. This is the normal market basis and the basis for comparison with the two following ratchet scenarios. 2. Where there is a "hard" ratchet clause and the current contract rent if reviewed is lower than the contract rent (CF < CO), CO is adopted at the next rental review and capitalised at the review of frequency capitalisation rate RAF. 3. Where there is a "soft" ratchet clause and the current contract rent if reviewed is lower than the minimum rent (CF < Min), Min is adopted at the next rental review and capitalised at the review of frequency capitalisation rate RAF. Under Scenario 3 above, a soft ratchet the minimum rent (Min) needs to be calculated if the rent review clause provides a formula for it; or if not, then the rental applying at the commencement of 189

Real Value Valuation for Real Estate Investments (Jefferies, 2017) the lease will need to be determined from the lease document and input for this purpose. If the valuation date is before the first rent review date in a lease, it is likely to be the same as the contract rent (CO), i.e. becomes effectively a hard ratchet, preventing the rental from falling at the first review. Where the valuer assumes future lease renewals will be exercised and no special ratchet adaptation of the model is required, only a realistic estimate of the current renewal rental (CRR) is required for the right of renewal rental review terms RR. This may be different from the rent review terms during the first term of the lease (F). This adaption also requires different renewal rental capitalisation rate to be applied (RARR) that reflects the expected real growth (Gr) over the renewal rent (RR) periods during the lease renewal terms. The ARRY model assumes that a ratchet clause operates to limit the rent falling on rent review, where the market review rental is lower than the contract rent, either to a minimum rent or with a “soft” ratchet to the rental at lease commencement. However, the model does not test for, nor adjust for, the estimated time it will take for the normal market review rental to grow to or exceed the existing contract rent, so that a rental increase would be expected to take place during the remaining review terms of the lease (if any). The model assumes that at the next rent review (if the lease does not expire) the current market review rental will increase at the real rental growth rate and assumed to apply. Making any other assumption would be too problematic and uncertain as to any future outcome as the basis of future expectations. This problem does not occur where there are escalated rentals as such provisions override the market growth in any case. In the case of properties where a highly over-rented situation occurs, the application of the ARRY valuation model may not be appropriate. If encountered it would be better to assume that no further renewals will be exercised and that all leases will revert to normal market rentals at the next lease expiry. Also subject to the earlier proviso as previously pointed out in Footnote 22 at page 101 discussed relative to this situation in Section 5.18 following:

5.18 Effect of ratchet clauses where rights of renewal expected to be exercised As noted earlier under Section 5.17 where the current lease renewal provisions provides for ratchet clauses to be carried forward into renewals. This causes problems where the current rental CO is in excess of a normal rent review (CF) level and it would be imprudent for a valuer to assume the tenant will exercise the renewal option. It would be imprudent for a valuer to assume the tenant will exercise the renewal option, where the current rental CO is in excess of a normal rent review (CF) level. This is particularly so where the effects of the rental escalation/ratchet clauses causes an unfair or burdensome rental on the tenant (that could lead to default and loss of the otherwise good tenant). Assuming renewals may be unadvisable it is better to assume the lease will cease at the next lease expiry date. In effect, this replaces the lease renewals by allowing for re-leasing at a current market rent (CM) on normal ADLS the lease terms and conditions including a typical market rent review frequency (M). The effect of this is that it negates the otherwise hard ratchet clause with the rental falling back to a current market rental with normal real growth following as allowed for in the market capitalisation rate (RAM). Note that where the normal contract review rental is less than the existing contract rental level, CF< CO, i.e. CO >CF, there may be little or no growth expected in contract rental as at the next rent review or even beyond this until the real growth in CF brings that rental up to equal or exceeds Co. This will depend upon the difference between CF and CO, and the real growth rate assumed. However, the ARRY model capitalises the renewal rental CRR at the renewal rental capitalisation rate RARR that allows the normal expected real growth. 190

Real Value Valuation for Real Estate Investments (Jefferies, 2017) It should be noted that the ARRY valuation model does not allow for an option for re-leasing on an escalated rental basis, as this is not typical type of lease terms in NZ. A different adaption to the model would be required if this were the case but is not pursued in this work. To date in NZ where the existing contract has a prescribed rental escalation at rent reviews, it is unusual to have a ratchet clause as well. However, the latest ADLS 2012 lease form now allows this, preventing a falling CPI-based rental under a hard ratchet provision. This would only come into effect with future deflation whereby nominal rentals fell over a rent review period, and a new lease negotiated after November 2012 where the tenant accepted the new ADLS CPI based rental provisions without amendment. The ARRY valuation model provides for an estimate of the nominal rental growth rate for prescribed escalation rentals, where the nominal rental will increase at a greater (or lesser) rate than expected inflation, as previously explained. The model will also work where a negative expected inflation or deflation is expected. However, this an unlikely expectation in the long-term, but may apply for short-term economic forecasts. It is uncommon, however, in NZ to find rental adjusted to CPI on an annual basis, and will typically be on a normal review period basis i.e. three yearly. However, if a hard or soft ratchet clause is included then this would provide a minimum rental effectively negating any downward rental adjustment due to the CPI having fallen over the rental review period.

5.19 Adaptation (xiii) Ratchet scenarios examples Examples illustrating the three scenarios in Section 5.17 are based on Adaptation (xii) as in Scenario 4, being a gross leases with a normal market rental review basis (not prescribed escalating), with PartOpex recovery, retaining deferred CAPEX maintenance liability, with gross re-leasing (GRL = Y). The OPEX and PartOpex figures remaining the same, and the OPEX escalation rate, OP = 3% p.a. The current market rental (CM), if re-leasing assumed as a gross lease with M = 3 year rental review period (but otherwise ADLS terms and conditions) is assessed at $35,000 p.a. It is assumed there would be a vacancy period of 6 months before re-leasing, and a 3-month rent-free period before the rental commenced. These are applied to the three scenarios: with Nil, Hard, and Soft Ratchet options assuming an overrented scenario to illustrate the effect of the ratchet variations.

5.19.1 Adaptation (xiii) Scenario 1 PartOpex, with gross re-leasing and Nil ratchet The nil ratchet option: where contract rent is CO = $39,500 p.a. but the current Contract rental (CF) if reviewed at valuation or sale date, applicable if due a rent review before expiry, on F = 5 year rental review period, is assessed at $36,000 p.a. This reflects a current over-rented situation and the expected rent will fall in current real terms at the next rent review. The PRV of Contract Rental to Run to next Rent Review in 4 years time, would not change, remaining at CO = $39,500 for 4 years. The PRV of Rental Term from Rental Review in 4 years to Lease Expiry in 9 years will reduce reflecting the effect of the current real market rental falling from the next rent review. The lower CF = $36,000 p.a. is capitalised at RAF, with the two-step calculation deducting the PRV deferred to lease expiry in 9 years from the PRV deferred to the next review in 4 years. The PRV on re-leasing in 9.5 years time will reduce due to the capitalisation of the current market rental of the lower CM = $38,000 p.a. capitalised at RAM and the PRV deferred to rental commencing after the 3 month rent-free period after the re-leasing date in 9.5 years, i.e. in 9.75 years time. This requires recalculation of the altered amounts based on Adaptation (vii) Algorithm 98, replacing the rental abbreviations Cc with CF, Cm with CM. The market capitalisation rate RAQ is replaced with RAM (as explained earlier in this chapter) adopting the previously calculated components; recalculating the required non-escalating rental capitalisation rates and using the lower rentals highlighted, as follows: 191

Real Value Valuation for Real Estate Investments (Jefferies, 2017) PRV of terms to run and re-leasing: PRV ⇐ PRV ⇐

Vr RF CO CF CF CM (1 − (1+YA )−T )+ � F (1+YA )−T − F (1+YA )−EX � + M (1+YA )−�Ex+12+12� T RA RA RA RA

$36,000 $36,000 $35,000 $39,500 (1 − (1.07)−4 )+ � (1.07)−4 − (1.07)−9 � + (1.07)−9.75 0.0722169 0.0722169 0.0703294 0.0712813

PRV ⇐ ($554,143×0.2371048) +($498,498×0.7628952) − ($498,498×0.5439337)+($497,658×0.5170210)

PRV ⇐ 131,390+($380,302 − $271,150)+$257,300 PRV ⇐ 131,390+$109,152+$257,300 =

$497,842

The PRV of re-leasing commission requires recalculating to allow for rental growth to the re-leasing date and is the current market rental CM = $35,000 p.a. @ 12% with real rental growth at Gr = 1% p.a. discounted @ ARRY: 7 % p.a.to re-leasing in RL = 9.5 years, adapting the PRV of value dependent costs in Algorithm 117 applying Equation 121 highlighted, as follows: PRV PRV PRV PRV

= −[(Value dependant costs)(1 + Gr )RL ](1 + YA )−RL = −[($35,000 × 0.12)(1.01)−9.5 ] = −($4,200 × 1.0991401) × 0.5258406 = −$4,616 × 0.5258406 =

‒$2,427 Equation 155

The PRV of net partial OPEX and the PRV of future CAPEX to replace the roof remain unchanged at ‒ $38,456 and ‒$75,819, respectively. The CMV adopting the previously calculated components of the valuation with the recalculated PRVs of the terms to run and re-leasing as a gross lease; and the PRV of re-leasing agency commission is highlighted, as follows: CMV = PRV of terms to run: PRV of contract rental to run to next rent review in 4 years:

$131,390

+PRV of rental term from rental review in 4 years to lease expiry in 9 years:

$109,152

+PRV of gross re-leasing in 9.75 years time:

$257,300 $497,842

+Other adjustments: (if applicable) ‒PRV of commission @ 12% of current market rental $35,000 with real rental growth at 1% p.a. to re-leasing in 9.5 years @ ARRY: 7 % p.a.:

‒$ 2,427

‒PRV of net partial OPEX ‒$1,964 p.a. escalating @ 3% p.a. over period until final lease expiry in 15 years and re-leasing as a gross lease:

‒$ 38,456

‒PRV of future CAPEX to replace roof at current cost of $85,000, expected to escalate @ 3% p.a. to replacement in 3 years time discounted @ Yᴀ: 7 % p.a.

‒$ 75,819 –$116,702

CMV $381,000 rounded ⇐ Total PRV

= $381,140 Equation 156

The selection of the “Nil” ratchet option (or leaving it blank in the ARRY valuation template) means the CMV is calculated in the normal manner, using the contract review rental and current market rental calculations, as above. See the valuation printout in Figure 83 Adaptation (xiii) Scenario 1 — GRL Nil Ratchet valuation printout following:

192

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Adaptation (xiii) Scenario 1: GRL Nil Ratchet All-risks real yield (ARRY) - Yᴀ based - present real value (PRV) - investment approach valuation: SUMMARY of lease data, rental basis, current market data & assumptions as to renewals, re-leasing etc. as at valuation or sale date:

20/03/2012

Partial gross lease, term: 10 years, ex 20/3/2011 with 5 year rent reviews, expiring in 9 years on 19/3/2021, assuming re-leasing as gross lease at current market rental with 3 year rent reviews after assumed vacancy of 6 months and associated releasing costs with a rent-free period of 3 months. Contract rental to run from valuation date 20/3/2012 until next rental review as at: 20/3/2016

$

39,500 p.a.

Current contract rental - if reviewed as at valuation or sale date: 20/3/2012

$

36,000 p.a.

For prescribed rental only - not applicable Current market rental for re-letting (on 3 year rental reviews ADLS terms and conditions) as at valuation or sale date: 20/3/2012

$

Rental frequency and payments basis (EOP = in arrears; BOP = in advance):

35,000 p.a. Monthly BOP

Contract rental review frequency in years:

5.00 years

Current rental term to run from valuation or sale date to next rental review as at: 20/3/2016 in years:

4.00 years

Expected (nominal) annual expected inflation rate:

2.00000% p.a.

Forecast real annual growth rate:

1.00000% p.a.

Nominal value annual growth rate: (sum of above two rates):

3.00000% p.a.

Required all-risks real yield annual (ARRY) rate Yᴀ :

7.00000% p.a.

Required nominal annual over-all yield (sum of above two rates):

10.00000% p.a.

PRV of term to run to next rental review (if any) or to lease expiry; or PRV of first review term after initial vacancy (if allowed): Contract rental: $39500 p.a. with expected real growth over 4 years term to run, capitalised in perpetuity @: 7.12813% p.a. :

$

554,143

No vacancy allowed and/or no unexpired rent-free period - capitalised contract rental in perpetuity - as above:

$

554,143

LESS PRV of capitalised contract rental in 4 years time discounted @ Yᴀ: 7 % p.a.

-$

$

PRV of contract rental to run to next rent review in 4 years time:

422,753

131,390

PRV of contract rental(s) from next rent review (If applicable) to current lease expiry: Current review Rental $36000 p.a. with real growth over 5 years rent reviews capitalised in perpetuity @ 7.22169% p.a. :

$

PRV of capitalised current review rental real value above, deferred to next rent review in 4 years time discounted @ Yᴀ: 7 % p.a. :

$

380,302

LESS - PRV of capitalised current review rental real value above, deferred to lease expiry in 9 years time discounted @ Yᴀ: 7 % p.a. :

-$

271,150

PRV of rental term from rental review in 4 years to lease expiry in 9 years (by deduction):

$

498,498

109,152

PRV of contract rental(s) - renewals from lease expiry to final expiry of renewals (If applicable): No rights of renewal - lease expires in 9 years - not applicable

$

-

No rights of renewal - lease expires in 9 years - not applicable

$

-


$

No rights of renewal - lease expiry in 9 years - not applicable

$

-

-

PRV at next rental review (if perpetually renewable); or on re-leasing (at final expiry); or at termination (as applicable): Current market rental $35000 p.a. with expected real growth over 3 years rent reviews, capitalised in perpetuity @: 7.03294% p.a.

$

PRV of Capitalised CMR above, deferred to rental commencement in 9.75 years time including vacancy & rent-free period @ Yᴀ: 7 % p.a. :

$ $ $

No redevelopment on termination - Not applicable.

Total PRV at next rental review; or on re-leasing; or at termination - (as applicable):

497,658

257,300 257,300

OTHER ADJUSTMENTS: (if applicable) $

-

PRV of re-leasing vacancy costs, leasing commissions, unrecoverable OPEX (if net lease), leasing incentives (other than rent-free period), as applicable:

-$

2,427

PRV of net partial OPEX $-1964 p.a. escalating @ 3% p.a. over period until lease expiry in 9 years, then re-leasing as a gross lease

-$

38,456

PRV of expected CAPEX; other liabilities; non-income based added-value (e.g. vacant land); or other adjustments (see notes below):

-$

75,819

No PRV of initial vacancy costs allowed - as currently tenanted.

Total other adjustments (if applicable):

*OPEX = Operating Expense; *CAPEX = Capital Expenditure

TOTAL PRV: term & reversions ± other adjustments = CMV Current real market value - CMV: (rounded) Net initial yield after unrecverable net OPEX (if any) - or overall capitalisation rate - after any initial vacancy (if applicable) ÷ CMV: Ro Notes: Based on scenario in Adaptation (xii) PartOpex, retaining deferred maintenance allowance, with Gross Re-Leasing and Nil Ratchet. PRV of future CAPEX to replace roof at cost of $85,000, expected to escalate @ 3% p.a. to replacement in 3 years = -$75819 (As Above) Current Market rental < Contract, assessed on Gross Lease Basis at $35,000 p.a. NO Ratchet, Current Review Rental $36,000 p.a..

Figure 83 Adaptation (xiii) Scenario 1 — GRL Nil Ratchet valuation printout

193

-$ $ $

116,702 381,139 381,000 9.8520% p.a.


5.19.2 Adaptation (xiii) Scenario 2 PartOpex, with gross re-leasing and Hard ratchet The hard ratchet option: where the contract review rental is prevented from falling at the next review, otherwise expected as above. The expected rental will be maintained at the current contract real rental of CO = $39,500 p.a. The hard ratchet has the effect of continuing the current contract rent (CO) $39,500 p.a. and not reducing to the current review rental CF of $36,000 p.a. as in Scenario 1. Assumes CF unlikely to exceed CF during lease term to expiry. The consequential effects are to only alter the calculation of the PRV of the rental review term from the review in 4 years to lease expiry in 9 years, and shown highlighted as follows: PRV ⇐ PRV ⇐

CO RA

T

Vr RF CO CM CO (1 − (1+YA )−T )+ � F (1+YA )−T − F (1+YA )−EX � + M (1+YA )�Ex+12+12� RA RA RA

$39,500 $39,500 $39,500 $35,000 (1 − (1.07)−4 )+ � (1.07)−4 − (1.07)−9 � + (1.07)−9.75 0.0722169 0.0712813 0.0722169 0.0703294

PRV ⇐ $554,143×0.2371048+[($546,963×0.7628952) − ($546,963×0.5439337)]+($497,658×0.5170210)

PRV ⇐ 131,390+[ $417,276 − $297,512]+$257,300 PRV ⇐ 131,390+$119,764+$257,300 =

$508,454

+Other adjustments: (if applicable)

‒PRV of commission @ 12% of current market rental $35,000 with real rental growth at 1% p.a. to re-leasing in 9.5 years @ ARRY: 7 % p.a.:

‒$ 2,427

‒PRV of net partial OPEX ‒$1,964 p.a. escalating @ 3% p.a. over the period until final lease expiry in 15 years and re-leasing as a gross lease:

‒$ 38,456


‒$ 75,819 –$116,702


= $391,752 Equation 157

The effect of the "hard" ratchet is to increase the value, compared to Scenario 1, of the PRV of the rental review term by $10,612 ($119,764 ‒ $109,152).This similarly increases the PRV of Contract Rental(s) from Next Rent Review (if applicable) to current Lease Expiry section, and the CMV by $10,612 from $381,139 to $391,751. See the valuation printout in Figure 84 Adaptation (xiii) Scenario 2 — GRL Hard Ratchet valuation printout following:

194

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Adaptation (xiii) Scenario 2: GRL Hard Ratchet All-risks real yield (ARRY) - Yᴀ based - present real value (PRV) - investment approach valuation: SUMMARY of lease data, rental basis, current market data & assumptions as to renewals, re-leasing etc. as at valuation or sale date:

20/03/2012


$

39,500 p.a.


$

36,000 p.a.


$




5.00 years


4.00 years


2.00000% p.a.


1.00000% p.a.


3.00000% p.a.


7.00000% p.a.


10.00000% p.a.


$

554,143


$

554,143


-$

$


422,753

131,390

PRV of contract rental(s) from next rent review (If applicable) to current lease expiry: Ratcheted current contract Rental $39500 p.a. with real growth over 5 years rent reviews capitalised in perpetuity @ 7.22169% p.a. :

$


$

417,276


-$

297,512


$

546,964

119,764


$

-


$

-


$


$

-

-


$


$ $ $



497,658

257,300 257,300


-


-$

2,427


-$

38,456


-$

75,819




TOTAL PRV: term & reversions ± other adjustments = CMV Current real market value - CMV: (rounded)

-$ $ $

Net initial yield after unrecverable net OPEX (if any) - or overall capitalisation rate - after any initial vacancy (if applicable) ÷ CMV: Ro Notes: Based on scenario in Adaptation (xii) PartOpex, retaining deferred maintenance allowance, with Gross Re-Leasing and Hard Ratchet. PRV of future CAPEX to replace roof at cost of $85,000, expected to escalate @ 3% p.a. to replacement in 3 years = -$75819 (As Above) Current Market rental < Contract, assessed on Gross Lease Basis at $35,000 p.a. Hard Ratchet Current contract Rental $39,500 p.a.

Figure 84 Adaptation (xiii) Scenario 2 — GRL Hard Ratchet valuation printout

195

116,702 391,751 392,000 9.5755% p.a.


5.19.3 Adaptation (xiii) Scenario 3 PartOpex, with Gross Re-leasing and Soft Ratchet The soft ratchet option: has a minimum rental (Min), being the commencement rental of CM = $38,000 p.a. The expected rental will fall at the next rental review but only to this minimum as current real review rental. The soft ratchet has the effect of reducing the current review rental to the minimum base rental (Min) of $38,000 p.a., compared to the current review rental of $36,000 p.a. as in Scenario 1. The consequential effects are to only alter the calculation of the PRV of rental review term from the review in 4 years to lease expiry in 9 years, and shown highlighted as follows: PRV ⇐

$38,000 $38,000 $39,500 $35,000 (1 − (1.07)−4 )+ � (1.07)−4 − (1.07)−9 � + (1.07)−9.75 0.0722169 0.0722169 0.0712813 0.0703294

PRV ⇐ ($554,143×0.2371048)+[ ($526,193×0.7628952) − ($526,193×0.5439337)]+($497,658×0.5170210)

PRV ⇐ 131,390+[ $401,430 − $286,214]+$257,300 PRV ⇐ 131,390+$115,216+$257,300 =

$503,906

+Other adjustments: (if applicable)

‒PRV of commission @ 12% of current market rental $35,000 with real rental growth at 1% p.a. to re-leasing in 9.5 years @ ARRY: 7 % p.a.:

‒$ 2,427

‒PRV of net partial OPEX ‒$1,964 p.a. escalating @ 3% p.a. over period until final lease expiry in 15 years and re-leasing as a gross lease:

‒$ 38,456


‒$ 75,819 –$116,702


= $387,204 Equation 158

The effect of the Soft ratchet compared to Scenario 1 (No ratchet) is to increase the value of the PRV of rental review term by $6,064 ($115,216 ‒ $109,152) and the increase the CMV by $6,064 ($381,139 to $387,203). The effect of the Soft ratchet compared to Scenario 2 (Hard ratchet) is to decrease the value of the PRV of rental review term by $4,548 ($119,764 ‒ $115,216) and decrease the CMV by ‒$4,548 ($391,751 to $387,203). Where there is a greater difference between the contract rental (CO) compared to the minimum rental (Min) or to the current review rental (CF), or to the current contract rental if renewed (CRR) where there are RORs, then the differences could be very material, especially where coupled with a long term to run or a number of RoRs until final lease expiry. See the valuation printout in Figure 85 Adaptation (xiii) Scenario 3 — GRL with soft ratchet valuation printout following:

196

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Adaptation (xiii) 3 Scenario: GRL Soft Ratchet All-risks real yield (ARRY) - Yᴀ based - present real value (PRV) - investment approach valuation: SUMMARY of lease data, rental basis, current market data & assumptions as to renewals, re-leasing etc. as at valuation or sale date:

20/03/2012


$

39,500 p.a.


$

36,000 p.a.


$




5.00 years


4.00 years


2.00000% p.a.


1.00000% p.a.


3.00000% p.a.


7.00000% p.a.


10.00000% p.a.


$

554,143


$

554,143


-$

422,753

$


131,390

PRV of contract rental(s) from next rent review (If applicable) to current lease expiry: Ratcheted minimum base Rental $38000 p.a. with real growth over 5 years rent reviews capitalised in perpetuity @ 7.22169% p.a. :

$

526,193


$

401,430


-$

286,214


$

115,216


$

-


$

-


$

-


$

-


$


$ $ $



497,658

257,300 257,300


-


-$

2,427


-$

38,456


-$




TOTAL PRV: term & reversions ± other adjustments = CMV Current real market value - CMV: (rounded)

-$ $ $

Net initial yield after unrecverable net OPEX (if any) - or overall capitalisation rate - after any initial vacancy (if applicable) ÷ CMV: Ro Notes: Based on scenario in Adaptation (xii) PartOpex, retaining deferred maintenance allowance, with Gross Re-Leasing and Soft Ratchet. PRV of future CAPEX to replace roof at cost of $85,000, expected to escalate @ 3% p.a. to replacement in 3 years = -$75819 (As Above) Current Market rental < Contract, assessed on Gross Lease Basis at $35,000 p.a. Soft Ratchet, minimum commencement rental of $38,000 p.a.

Figure 85 Adaptation (xiii) Scenario 3 — GRL with soft ratchet valuation printout

197

75,819

116,702 387,203 387,000 9.6992% p.a.


5.20 The complete ARRY real value valuation algorithm The following complete ARRY valuation model is expressed as a composite Algorithm 159, in a logical timing sequence from a lease commencement to its final expiry or perpetual renewals. Not all of the component algorithms will apply in all cases, but will depend on the date of valuation, terms of lease and its renewals expiry and/or redevelopment or termination.

198


Algorithm 159

5.21 Chapter summary This chapter completes the full and substantive development of the ARRY valuation model’s theory and methodology. Chapters 3 to 5 contain the academic theory, with algorithms, model adaptations, illustrated by progressive valuation examples. The Excel™ user-friendly ARRY valuation template carries out practical investment valuations to demonstrate its applications in “real” real estate market situations. The adaptations are essential to provide a flexible and practical investment valuation model to challenge traditional valuation methods, especially DCFs. However, for a new model to achieve acceptance by the valuation profession requires more than good theory or models, but needs to demonstrate flexibility in application to real world property markets, lease terms, and conditions. Facilitating the means of achieving this aim is the wide range of adaptations examined and detailed to extend the basic ARRY valuation model in Chapter 3 as covered in Chapters 4 to allow for:

199

Real Value Valuation for Real Estate Investments (Jefferies, 2017) •

Renewals of the current lease, and re-leasing with different terms and conditions.

•

Under-developed properties with redevelopment potential at expiry.

•

Vacancies, rent-free periods, leasing incentives, and leasing costs.

•

Allowance for costs of purchase (including due diligence) and costs of sale.

•

Expectations of capital expenditure for refurbishment, or deferred maintenance liabilities.

And in this Chapter 5 to allow for: •

Partial gross leases with fixed and/or variable OPEX recoveries.

•

Ratchet clauses in leases affecting rental review increases.

Each of these adaptations allow for variations commonly found in real estate leases in NZ and in other countries. As the ARRY valuation model is developed, examples given and the user-friendly Excel™ ARRY valuation template used to check the model, confirm the manual calculations, and show how the model is flexible and can be efficiently used in valuation practice. The complete ARRY real value valuation model is compiled that is a composite algorithm in a logical timing sequence from a lease commencement to its final expiry or perpetual renewals or redevelopment. This chapter completes all the adaptations required to cover most practical investment valuation situations. Further adaptations and modifications will be needed to apply the model in specialist valuations and investment analysis – not pursued further in this work. Discussions of some of these potential applications are discussed in Jefferies (2016) as matters for future research. This ARRY valuation model is tested by way of case studies involving actual properties that have sold for sales analyses, and then the model is used for valuation purposes as found in Jefferies (2017a). How the ARRY valuation model fits into the historical development of investment valuation models is described in Jefferies (2017b)

200


Appendix A— Formulary The following formulary defines the symbols, abbreviations, definitions, explanations, and formulae used — combining all the separate formulary tables as follows: * The replacement/redefinition of the cash flows, i.e. changing the subscripts added to the C (cash flow) for the rentals was to rationalise all text, symbols, abbreviations, and cell references to display them consistently as in the new MS Excel ™ ARRY valuation template as used in Chapter 5. FORMULARY In alphabetical order by symbol or abbreviation

Symbol or abbreviation

Definition

AltUseGr

Forecast redevelopment value real growth rate

BDOpex

Base date OPEX –$p.a.

BOP

Beginning of period

C Cc

Cash flow Current market contract review rental

CEsc

Current prescribed contract escalated rental at the sale or valuation date Current prescribed contract escalated rental at the sale or valuation date Current contract lease review rental for F (years) if reviewed at valuation or sale date Current market rent

CEsc

CF Cm

CM

CMV Co

Explanation and formula (if any) May be more or less than the real rental growth rate Gr, (could be ‒ve, e.g. if poor demand or other negative factors, i.e. contamination or remediation liability). Where the tenant pays OPEX increases over a base date amount per annum, stated in the lease. The total OPEX will escalate at the OP% annual growth rate, from which the escalated BDOpex is deducted to arrive at the NetOpex (see below). Rental paid in advance. The periodic rental (as a receipt). Assuming the rental was reviewed at the sale or valuation date in accordance with the lease. The lower case subscript c denotes current. Assuming the rent was due for review at the sale or valuation date. NB the Esc rent is indicated by the subscript Esc. (See below fpr updated definition) Replaces CEsc in earlier model & template.* Assuming the rent was due for review at the sale or valuation date. NB the Esc rent is indicated by the normal case not the previous subscript Esc. Replaces Cc in earlier model & template.* Now redefined as what the premises (including car parks) would currently lease for on the contractual lease terms, i.e. F (years) rental review terms, etc. If leased on normal market terms and conditions.

Replaces Cm in earlier model & template*. Now Current market rental for redefined as what the premises (including car parks) M (years) reviews if rewould currently lease for on the market lease terms leased at valuation or sale on normal ADLS 2012 net lease terms and M (years) date rent review terms, etc. The sum of the present values of the contract term(s) Current market value to run and the reversionary value(s) The rental actually paid under an existing lease. The Contract rental lower case subscript o denotes contract.

201

Real Value Valuation for Real Estate Investments (Jefferies, 2017) Co

Total actual annual contract rental

Co_pcm

Monthly contract rental

Comm

Lease commencement date

Contr

Contribution by landlord as an initial leasing incentive to secure a tenant e.g. a material incentive or cost (where not already paid)

CPOpex

Current partial OPEX – $p.a.

CpRent

Car parks annual rental

CRR EOP Esc esc (lowercase)

Esc

RR

EX

Current contract renewal rental for RR (years) if renewed at valuation or sale date End of period Prescribed rental escalation rate p.a. Prescribed rental escalation rate p.p. ARRY annual (p.a.) prescribed nominal escalation cap rate for P x RR = r_r payment period rent reviews

Years to current contract lease expiry

EX (in years)

Period to expiry or termination in years

Exp (as a date)

Expiry or termination date of lease

Redefines earlier Co, now redefined* as the sum of annual premises and car parks rental: Co = PRent+CpRent. To reconcile with that shown in the lease schedule: = Co/12. Date contract lease commenced, or date it was last renewed, not the last rent review date, input in dd/mm/yyyy format. This requires the calculation of the PRV of any incentive, other than a rent-free period, calculated as a current monetary input (i.e. in real terms). This might be a contribution to a fitout; or a refurbishment; or assuming a liability for the lessee's rental payable for prior premises, or other ex-gratia inducement payments. A fixed partial OPEX annually payable by the tenant – the amount stated in the lease. The total OPEX will increase at the OP% annual growth rate, from which the fixed CPOpex is deducted to arrive at the NetOpex (see below). Where separate rental shown in the lease schedule. Otherwise total contract rental, Co entered as PRent (see below). What premises (incl. car parks) would currently lease for on the contract renewal rental review RR (years) frequency terms. Rental paid in arrears. A pre-set contractual annual or periodic nominal rent increase as a % p.a. at each rental review. P

esc =(1+Esc)(1/P) − 1 or esc =�(1+Esc) − 1

Based on nominal annual rental p.a.; where 1/P BOP payments p.p.: REscRR = P × Rescr_r ; where EOP rental payments ×(1+ya)

Template calculates this in decimals (displayed rounded up to 2 decimal places), of years to run to expiry (excluding any renewal terms). Template calculates on number of days, on a 365.25 days per years basis to allow for leap years): EX = (ExpDate-VDate)/365.25 (See below for updated). Days from valuation or sale date to the expiry date of the current lease, excluding any rights of renewal, in decimals of a year, (displayed to two decimal points in template input). See above for updated description. Date at which the current lease term ends, excluding any rights of renewal.

202


ExpDate F f (lower case) FinalExp GO Gr

Date current lease term expires. Excludes any intermediate rent review dates. If renewed, should be Lease expiry date one day before next renewal date, input in: dd/mm/yyyy format. Frequency of rent reviews In years, specified in the lease contract Number of rental payment periods in rental review term Final expiry date, i.e. termination date at end of assumed renewals (if any) Nominal (overall) annual (p.a.) rental growth rate Real annual (p.a.) rental growth rate

gr (lower case)

Real growth rate, p.p.

GRL

Gross re-leasing

Ie

Expected (e) monetary inflation rate, p.a. Note I = inflation a capital i (I) not 1 or L, and the lower case e denotes expected

ie (lower case)

IRF

LFee M

M

Expected monetary inflation rate, p.p. Initial rent-free fitting out period and/or rent-free incentive period in months Actual or expected agent’s leasing fee as a percentage of contract rent negotiated. Number of years in current market rent review terms Current market rental review period in years

f = P × F, normally truncated to an integer, used as a superscript "f" in p.p. capitalisation rate formula: e.g. RAf Template calculates this automatically (if applicable) and should be as in the lease schedule. Growth in market rentals on an annual basis. The subscript O is a capital letter, not 0 (zero) = overall. Growth in rentals excluding inflation on an annual basis. The subscript r = real. Growth excluding inflation, per payment period basis in real terms: 1/P P gr =(1+Gr ) − 1, or gr =�(1+Gr ) − 1 gr = (go−ie) p.p. or compounding basis gr = [(1+go)/(1+ie)] – 1 Where re-leasing (RL = Y) applies, but on an assumed gross lease (not a net lease which is default assumption). Template has drop-down list for selecting "Y" for "Yes" in input cell, or selecting "N" for "No" or by leaving it blank where not applicable. Growth in monetary value only: Ie = (GO−Gr) p.a. or compounding basis Ie = [(1+GO)/(1+Gr)]−1; excludes real growth, similar to Wood's (1973) “d” = inflation risk. Growth in monetary value only, per payment period basis: P ie =(1+Ie )1/P − 1, or �(1+Ie ) − 1 ie = (go−gr) p.p. or compounding basis ie = [(1+go)/(1+gr)] – 1 Where already negotiated, or is expected on initial leasing the ARRY valuation model delays the PRVs of the subsequent rental receipts by these periods. Based upon the current real estate agency practice, or specified in an agreement to lease. The ARRY valuation model assumes that this fee is paid in the same month as the lease commences. Distinct from the existing contract lease term F. Used as a superscript "M" in annual capitalisation rate formula, i.e. RAM (see updated definition below). Replaces Q in earlier model and template. Now assumes re-leasing (on ADLS net lease terms and conditions). 203

Real Value Valuation for Real Estate Investments (Jefferies, 2017) m (lower case) m (lower-case) m_ (lower case)

Market (distinguished from mortgage ratio M) Number of payment periods in current market review terms Current market rental review frequency (in payment periods)

NetOpex

Unrecoverable net OPEX (if applicable) –$p.a.

OP

OPEX annual escalation rate

op (lower case)

OPEX p.p. escalation rate

OPComm

OPEX base date (if applicable)

OPEX

Operating expenses As a negative (–$) cash flow

p (lower-case)

Payments frequency per year Payments on p.p. frequency

PartOpex

Current part OPEX –$p.a.

p.p.

Per period

PRent

Premises annual rental

P

r_r (lower case) RA F

RA f

Contract renewal rental review frequency (in payment periods) ARRY annual (p.a.) EOP rental payment cap rate where F years rent review frequency ARRY per period (p.p.) cap rate for f payment period reviews

Used as a suffix “m” denoting the type, e.g. Cm (See updated definition below). m = P × M, normally truncated to an integer, used as a superscript "m" in p.p. capitalisation rate formula: i.e. RAm Number of rental payments in re-leasing rent review periods: m_ = P × M The amount of OPEX not recoverable under a gross or partial gross lease at valuation or sale date, resulting from the escalated excess over CPOpex or PartOpex recoverable from the tenant. The annual expected nominal increase in the OPEX (as distinct from a rental growth rate). The per OPEX payment period escalation rate: P op =(1+OP)1/P − 1, or = �(1+OP) − 1 The date from which BDOpex increases, usually the lease commencement date (Comm) and not later than the valuation date (VDate). The operating expenses of the building as defined in the lease, which in the case of a gross lease will all be paid by the landlord; whereas under a net lease the defined recoverable operating expenses are charged to and paid by the tenant. e.g. Monthly P = 12 p.a. p = 1/P p.p., e.g. P=12 p.a., p =1/12 p.p. Is the annual amount of OPEX at valuation or sale date, recoverable from the tenant under a BDOpex lease (see above) where increases escalated @ OP % p.a. from the base date to valuation or sale date is deducted from the total OPEX to arrive at the NetOpex (see below). N.B lower case letters are shown to indicate a per period (p.p.) factor or adaptation Contract premises rental (for occupied space) if separated in lease schedule from parking spaces rental. Otherwise = total contract rental, Co, entered as PRent. Number of rental payments in renewal rent review periods: r_r = P x RR. RA F ⇐ (YA +Ie +Gr ) �1 −

(1+Ie +Gr )F − 1 � (1+YA +Ie +Gr )F − 1

Based on BOP rental payments p.p.: (1+ie+gr)f –1 ya+ie+gr RA f = � � �1– � �� (1+ya+ie+gr)f –1 1+ya where EOP rental payments ×(1+ya) 204


RA F

ARRY annual (p.a.) cap rate where F x P = f payment period rent reviews

RA m

ARRY per payment period (p.p.) cap rate for m payment period reviews

RA M

ARRY annual (p.a.) cap rate where P x M = m_ payment period rent reviews

RA

m_

ARRY per period (p.p.) cap rate for m_ payment period reviews

RA O

ARRY annual (p.a.) OPEX nominal OP escalating cap rate for P = 12 payments p.a. i.e. monthly and p payment periods OPEX increases

RAop

ARRY OPEX per payment period (p.p.) cap rate for p months payment period reviews

RA

OP

RAr_r

RARR

RA T

RA t

ARRY annual (p.a.) OPEX nominal OP escalating cap rate for P = 12 payments p.a. i.e. monthly and p payment periods OPEX increases ARRY per period (p.p.) cap rate for r_r payment period reviews

Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: RAF = P × RAf where: EOP rental payments ×(1+ya)

Based on BOP rental payments p.p.: (1+ie+gr)m –1 ya+ie+gr RA m = � � �1– � �� (1+ya+ie+gr)m –1 1+ya where EOP payments ×(1+ya) Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: RAM = P × RAm_ ; where: EOP rental payments ×(1+ya) Based on BOP rental payments p.p.: (1+ie+gr)m_ –1 ya+ie+gr RA m_ = � � �1– � �� (1+ya+ie+gr)m_ –1 1+ya where EOP rental payments ×(1+ya)

RAOP replaces RAOp previously in Chapter 6. Based on nominal annual OPEX p.a.; where: p = 1×P = 1×12 = 12 BOP payments p.p.: RAOP = P×RAop ; where EOP ×(1+ya)

Based on monthly BOP OPEX payments p.p.:

(1+op)P –1 ya+ie+gr RA op = � � �1– � �� (1+ya+ie+gr)P –1 1+ya

where EOP payments ×(1+ya) N.B. (1+op) replaces (1+ie+gr) as growth rate in the second term of above cap rate formula. Based on nominal annual OPEX p.a.; where: p = 1 × P = 1 × 12 = 12 BOP payments p.p.: RAOP = P × RAop ; where EOP × (1+ya)

Based on BOP rental payments p.p.: (1+ie+gr)r_r –1 ya+ie+gr RA r_r = � � �1– � �� (1+ya+ie+gr)r_r –1 1+ya where EOP rental payments ×(1+ya) Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: RARR = P × RAr_r ; where EOP rental payments ×(1+ya)

ARRY annual (p.a.) cap rate where P x RR = r_r payment period rent reviews ARRY annual (p.a.) EOP (1+Ie +Gr )T − 1 rental payment cap rate RA T ⇐ (YA +Ie +Gr ) �1 − � (1+YA +Ie +Gr )T − 1 where T years rent review frequency Based on BOP rental payments p.p.: ARRY per period (p.p.) (1+ie+gr)t –1 ya+ie+gr t cap rate for t payment RA = � � �1– � �� (1+ya+ie+gr)t –1 1+ya period reviews where EOP rental payments ×(1+ya) 205

Real Value Valuation for Real Estate Investments (Jefferies, 2017) ARRY annual (p.a.) cap rate where F x P = t payment period rent reviews

RA T

RentComm

Rescf

F

REsc

Rescr_r

REscRR

Resc

t

REscT

ReviewDate

RF RL

Rental commencement date ARRY per period (p.p.) prescribed nominal escalation cap rate for f payment period reviews ARRY annual (p.a.) prescribed nominal escalation cap rate for F year reviews p.a. ARRY per period (p.p.) prescribed nominal escalation cap rate for r_r payment period reviews ARRY annual (p.a.) prescribed nominal escalation cap rate for P x RR = r_r payment period rent reviews ARRY per period (p.p.) prescribed nominal escalation cap rate for t payment period reviews ARRY annual (p.a.) prescribed nominal escalation cap rate for T year reviews Next rental review date Re-leasing rent-free fitting out period and/or rent-free incentive period in months Re-leasing on contract lease expiry

RLContr

Contribution by landlord expected as an re-leasing leasing incentive to secure a tenant e.g. a material incentive or cost

RM

Market rental capitalisation rate

Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: RAT = P × RAt where: EOP rental payments ×(1+ya) The last rent review date if reviewed since commencement, if not, as per the lease commencement date, Comm (above), or where an unexpired rent-free period, the date the rental is to commence, input in dd/mm/yyyy format. Based on rental BOP payments p.p.: (1+esc)f − 1 ya+ie+gr Resc f = � � �1 − � �� (1+ya+ie+gr)f − 1 1+ya


Based on nominal annual rental p.a.; where 1/P BOP payments p.p.: REscF = P × Rescf ; where EOP ×(1+ya) Based on rental BOP payments p.p.: Rescr_r = �

(1+esc)r_r − 1 ya+ie+gr � �1 − � �� (1+ya+ie+gr)r_r − 1 1+ya


Based on nominal annual rental p.a.; where 1/P BOP payments p.p.: REscRR = P × Rescr_r ; where EOP rental payments ×(1+ya) Based on rental BOP payments p.p.:

(1+esc)t − 1 ya+ie+gr Resc t = � � �1 − � �� (1+ya+ie+gr)t − 1 1+ya


Based on nominal annual rental p.a.; where 1/P BOP rental payments p.p.: REscT = P × Resct ; where EOP ×(1+ya)

Template calculates automatically (if applicable) and should be as in the lease schedule, input in dd/mm/yyyy format. Expected on re-leasing, the ARRY valuation model delays the PRVs of the subsequent rental receipts by these periods. When it is assumed it will be re-leased on current ADLS lease market terms. Y= yes; N = no. This requires the calculation of the PRV of any incentive, other than a rent-free period, calculated as a current monetary input (i.e. in real terms). This might be a contribution to a fitout; or a refurbishment; or assuming a liability for the lessee's rental payable for prior premises, or other ex-gratia inducement payments. Where R = rate; and subscript M is a capital letter) = market.

206

Real Value Valuation for Real Estate Investments (Jefferies, 2017) RNF

Net of growth capitalisation rate

RO

Over-all capitalisation rate

ROF

RoRs ROT RR

RrF r_r (lower case) RT

Nominal annual (p.a.) rental cap rate where F years rent review frequency Perpetually renewable or number of rights of renewal Nominal annual (p.a.) rental cap rate where T years term to run Contract renewal rental review frequency (in years) Nominal annual (p.a.) real yield rental cap rate where F years rent review frequency Contract renewal rental review frequency (in payment periods) Length of contract lease renewal terms in years.

T

Term to run

t (lower-case)

Number of payment periods to run to next rent review

Term

Contract lease term in years, [previously an input in template]

To_Exp

Length of contract lease including assumed renewal terms in years, if applicable – years to final termination.

VAltUse

Current redevelopment or alternative use value for property in current condition at valuation or sale date

(1+GO )F − 1 (Y ) (Y ) RN = N +GO − N +GO � � (1+YN +GO)F − 1 Where R = rate, the subscript O is a capital letter: Co not 0 (zero) = overall. RO ⇐ CMV F

Based on nominal annual rental p.a in arrears: RO F ⇐ YO �1 −

(1+GO )F − 1 � (1+YO )F − 1

P used for perpetually renewable, or a number (if any) for number of lease renewals assumed. Based on nominal annual rental p.a. in arrears: RO F ⇐ YO �1 −

(1+GO )T − 1 � (1+YO )T − 1

In decimals of years (if applicable).Not to be confused with “real rate” as in ARRY. Based on nominal annual rental p.a in arrears: Rr F ⇐ (Yr +Ie ) �1 −

(1+Ie +Gr )F − 1 � (1+Yr +Ie )F − 1

Number of rental payments in renewal rent review periods: r_r = P × RR. Number of years in each lease renewal term, in decimals of years. T = Term to next rent review or renewal, whichever is the lesser, in years t = P × T, normally truncated to an integer, used as a superscript "t" in p.p. capitalisation rate formula: i.e. RAt Template calculates this in decimals (displayed rounded up to 2 decimal places), of years to run to expiry (excluding any renewal terms). Template calculates on number of days, on a 365.25 days per years basis allowing for leap years): = (ExpDate-Comm)/365.25 Template calculates automatically (if applicable) and should be as in lease schedule. Template calculates this in decimals (displayed rounded up to 2 decimal places), of years to run to expiry (including any renewal terms). Template calculates on number of days, on a 365.25 days per years basis (to allow for leap years): = EX+(RT × RoRs). Includes (deduction) for any current demolition/site clearance costs to make land suitable for rebuilding.

207

Real Value Valuation for Real Estate Investments (Jefferies, 2017) VDate

Valuation date or sale date

Vi

Initial vacancy, in months, to lease commencement (if applicable and unexpired)

Vr

Re-leasing vacancy period in months

ya (lower-case)

The per payment period all-risks real yield (ARRY)

ya0_

ARRY OPEX per payment period (p.p.) for zero growth cap rate for P payments per annum. N.B. 0 is a zero not a capital letter O.

YA 0

ARRY annual (p.a.) zero growth cap rate for P payments p.a. N.B. superscript 0 is a zero not a capital letter O

YN

Net of growth yield

YO

Over-all yield

YO

Required annual overall yield rate, or nominal rate of return on investment; where O is a subscript capital letter O, not a zero 0 The per payment period (p.p.) nominal rate of return on investment

Valuation date - or if analysing a sale, the sale date, input in dd/mm/yyyy format. Number of whole months between the valuation (or sale) date and commencement date of the lease. This does not include any rent-free period (see IRF above). The template calculates and displays this based on the date inputs. The number of whole months expected between the lease expiry date and commencement date of a new lease. As a decimal or % p.p.: P ya = (1+YA)1/P –1, or = �(1+YA) −1 Based on monthly BOP fixed payments p.p.: (1+0)P –1 ya+ie+gr Ya0_ = � � �1– � �� (1+ya+ie+gr)P –1 1+ya As (ya+ie+gr) = yo , and (1+0)P = 1 this simplifies the equation to: yo yo 0 Ya0_ = � � �1– � �� = P (1+yo) –1 1+ya 1+ya where EOP payments ×(1+ya) = yo

Applied to a fixed annual payment, e.g. CPOpex p.a.; where p = 1×P, e.g. 1×12 = 12 BOP monthly payments p.p.: YA0 = ya0_ ×P; where EOP payments ×(1+ya) The Y = yield, the N is a subscript capital letter N = net of growth. The Y = yield, the subscript O is a capital letter, not 0 (zero) = overall (See redefined below).

Considers all expected property benefits and risks, without financing or tax similar to IRR where: NPV = 0; in nominal terms Yo = Ro+Go; also Yo = Ro+Ie+Gr

YP

Years purchase

As a decimal or % p.p.: P yo = (1+YO)1/P –1, or = �(1+YO) −1

Yr

Real yield

Where Y = yield; and r (subscript, lower case) = real

yo (lower case)

1

An income multiplier used in the UK, YP = Yo

208


Appendix B The Appendix B.1 ARRY Valuation template property or tenancy worksheet – complete over two pages in Figure 86 and Figure 87 at pages 210 and 211 is an A3 sized copy* of a whole property worksheet with highlighted comments boxes of the main features and changes from the earlier 2010 and 2011 versions of the template used in Chapter 4 and further developed for the special adaptations in Chapter5. An explanation of this template, its features and its key inputs, yield data and output areas are fully detailed in Appendix B.2 at page 212, with enlarged sections of key parts of this worksheet in follows the copy of the template in Appendix B.2 at page 212. * To view on screen Use your View – Zoom 200% to read or print to an A4 to A3 enlargement.

209


B.1 ARRY Valuation template property or tenancy worksheet – complete ARRY Valuation - Separate Single Tenant Properties (Up to 10 Properties) -©Copyright R L Jefferies, May 2013 Model example: vacancies, rent-free periods, and leasing costs; plus GRL; CAPEX Valuation (or Sale) date: VDate Expected (nominal ) inflation rate: I e [from summary sheet] Real growth rate: G r Nominal value growth rate: G o = I e + G r All-risks real rield (ARRY) rate: Y A Over-all required nominal yield (disc. rate): (Y A + I e + G r ) = Y o

`

20/03/2012

YELLOW highlighted data input

2.00000% p.a.

cells are unlocked and have validation boxes with data entry message. If invalid data is entered an Error Alert is shown.

1.00000% p.a. 3.00000% p.a. 7.00000% p.a. 10.00000% p.a.

New input cell: Lease commenecement date from which the Term is calculated.

CONTRACT LEASE DATES (Existing contract lease or assumed leasing terms if initial vacancy allowed). Lease commencement date: Comm Term in years: Term

20/06/2012 19/06/2018 6.00 years 20/09/2012

Rental commencement date, (i.e. last rent review date if not Comm above), or after initial rent-free period if any: RentComm Initial rent-free payment periods (If any): IRF Pre initial leasing refurbishment, free lessee's fit out or other incentive cost -$ : Contr Initial vacancy, in whole rental payment periods, to lease commencement (if applicable and unexpired): V i

New input cell: Rental commencement date, from which the term to run (T), next rent review (ReviewDate) and years to expiry (EX) is calculated.

VDate Ie Gr Go YA Yo

3 months -$

50,000 3 months

Comm ExpDate Term RentComm IRF Contr Vi

CONTRACT RENTAL DATA (Existing contract lease or assumed leasing terms if initial vacancy allowed). Premises annual rental: PRent Car parks annual rental: CpRent Total annual contract rental: Co Monthly contract rental: Co_pcm Rental and OPEX payments frequency per annum: P

For clearest viewing and for data inputting select Columns A:B; on menu View Tab, Click on

New input cell: For any separate car parking rental.

38,000 1,500

$

39,500 $3,292 p.c.m. 12 1 2.00 years

Rental review frequency, or fixed rental term, during contract lease term - in years: F New input cell: For ratchet options Hard or Soft choice from drop-down list.

IF prescribed rental - current escalated rental if reviewed $p.a. : CEsc Ratchet clause?: Rcht If soft ratchet clause above - minimum rental: Min

New Input Cell: For minimum rent if Soft ratchet

Next rental review date (If applicable): ReviewDate

4.00000% p.a. $

39,115 Hard

$

38,000 20/06/2014

Period to run in years, to next rental review, or to expiry if fixed term or no further review, incl. any unexpired vacancy & rent-free: T

2.25 years

Current contract lease expires in years: EX

6.25 years

New input cell: For number of lease renewals allowed and assumed to be taken up.

LEASE RENEWAL DATA - assuming rights of renewal (If any) are exercised: Perpetually renewable or number of rights of renewal (If any) assumed: RoRs Contract renewal rental review frequency or fixed rental term during renewal term (in years): RR

1 3.00 years 3.00 years

New input cell: For rent review frequency during renewals.

Contract lease with assumed renewals - if applicable - terminating in years: To_Exp Final expiry date, - if applicable - i.e. termination at end of assumed renewals: FinalExp

Total current OPEX –$p.a. for gross lease (if above); or of re-leasing as gross lease; or if vacancy allowed: OPEX

9.25 years 19/06/2021

New input cell: For Gross lease or Net lease Option - from drop-down list.

OPEX (operating expenses) - default is an ADLS net lease with 100% of outgoings recovered from tenant: IF gross lease - (nil, or partial i.e. 0

N

>0

Blank

Y

0

N

>0

Blank

Y

>0

Y

>0

Blank

Y

Y

0

Y

>0

Blank

Y

Y

P

Blank

Blank

Blank

Y

P

Blank

0

N

0

N

Blank

0

Y

Blank

Blank

Y

Y

>0

Y

0

Y

Blank

0

Blank

Y

>0

Blank

=IF(ISTEXT(GRL),GRL,"")

=IF(AND(Gross="Y",RoRs>0,RL="Y",BDOpex>0,ISBLANK(CPOpex)), IF(GRL="Y",(-BDOpex/YA0)*(1-PV(YA,To_Exp,,-1,0))+(OPEX/RAO) *PV(YA,To_Exp,,-1,0),(-BDOpex/YA0)*(1-PV(YA,To_Exp,,-1,0))),0)

=IF($K$770

Blank

=IF(ISTEXT(GRL),GRL,"")

=IF(AND(Gross="Y",RoRs=0,RL="Y",BDOpex>0,ISBLANK(CPOpex)), IF(GRL="Y",(-BDOpex/YA0)*(1-PV(YA,EX,,-1,0))+(OPEX/RAO) *PV(YA,EX,,-1,0),(-BDOpex/YA0)*(1-PV(YA,EX,,-1,0))),0)

=IF($K$78