Time Value of Money. Solution of the selected work book problems with the aid of
. Financial Calculator ( FC – 200V ): Most of the keys on FC-200V with green ...
Time Value of Money Solution of the selected work book problems with the aid of Financial Calculator ( FC – 200V ): Most of the keys on FC-200V with green font deal with financial calculations. The keys that we shall be using to solve the workbook problems have been explained below: 1. SMPL Key (Simple Interest Mode) : This key lets you calculate the simple interest amount and simple future value (principal plus simple interest amount) given the rate of interest and time period in number of days. 2. CMPD Key (Compound Interest Mode) : This mode lets you calculate the value of any one of the following variables by inputting the value of other variables; a) n or the number of compound periods. b) I% or the rate of interest. c) Present Value (PV) or the principal amount. d) PMT or the payment per period in case of annuities. e) Future Value (FV) or final payment amount. This key is used most frequently in time value questions. 3. CASH Key (Cash Flow Mode) : This mode applies the discounted cash flow (DCF) technique on a series of cash inflows and outflows over a fixed period to find out: a) Net Present Value (NPV). b) Net Future Value (NFV). c) Internal Rate of Return (IRR). d) Payback Period or Discounted Payback Period. The Cash Flow Mode is very useful in the Investment Decision making. 4. AMRT Key (Amortization Mode) : This mode lets you calculate: a) Interest portion of any installment. b) Principal portion of any installment. c) Principal balance upon completion of any installment. d) Total interest paid between any two installments. e) Total principal paid between any two installments. 5. CNVR Key (Conversion Mode) : This mode lets you convert between nominal interest rate (APR) and effective interest rate (EFF) given the frequency of compounding in a year.
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Time Value of Money Work book : Solution to selected problems with FC-200V 3.10 Press CNVR key : On the input screen set : n = 4 I% = 16 Now take the highlighter to APR and solve for it. You get 15.12 as answer. (n is set to 4 because with quarterly compounding, the compounding is done 4 times in a year) 3.11
Press CNVR key : On the input screen set : n = 12 I% = 12 Now take the highlighter to EFF and solve for it. You get 12.68 as answer. (with monthly compounding the number of compounding periods in a year become 12)
3.12
Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 12 30,000 0 0 1 1
Take the highlighter to PMT and solve for it, you get Rs.8322 as answer.
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3.13
Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 120 0 25,00,000 -31,000 0 12 12
Take the highlighter to I% and solve for it, you get 8.50 as answer. 3.14 Step I ---- Press CNVR key : On the input screen set : n = 12 (for monthly compounding) I% = 10 Now solve for EFF. You get 10.471 Step II ---- Press CNVR key again : On the input screen set : n = 4 (for quarterly compounding) I% = 10 Now solve for EFF. You get 10.381 Difference = 10.471 – 10.381 = 0.09 Ans. 3.15
Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 4 12 0 100 1100 1 1
Take the highlighter to PV and solve for it, you get 1002.80 as answer.
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3.16 Press CNVR key : On the input screen set : n = 4 (for quarterly compounding) I% = 10 Now solve for EFF. You get 10.38 as answer. 3.17 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 X 12 8/12 0 -2500 0 1 1
Take the highlighter to FV and solve for it, you get 1,83,692 as answer. (We can keep n = 60, I% = 8 but change P/Y and C/Y to 12 each and we Get the same answer.) 3.18 Press CASH key : On the input screen set : I% = 10 Csh = D.Editor x ---- press EXE key. We get cash flow table. Input the following values in the table: 1 2 3 4 5 6 7 8 9 10 11
0 1500 2000 5000 5000 5000 5000 5000 5000 5000 5000
Press ESC and solve for NPV and you get 25,062 as answer. In the cash flow table cash flow in the year 1 refer to cash flows in the beginning of year 1. If cash flow occurs at the end of year 1, it is shown opposite to year 2.
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3.19 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 4 0 1,00,000 0 -1,51,807 1 1
Take the highlighter to I% and solve for it, you get 10.99 or 11 as answer 3.20
Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 0 12 -1 0 3 1 1
Take the highlighter to n and solve for it, you get 9.69 year as answer. 3.22 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 12 0 0 1 1 1
Take the highlighter to PMT and solve for it, you get 0.056 as answer.
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3.23 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 15 8 0 -70,000 0 1 1
Take the highlighter to FV and solve for it, you get 19,00,648 as answer.
3.25 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 20 0 -5,000 0 1,00,000 1 1
Take the highlighter to I and solve for it, you get 16.159 as answer.
3.26 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 12 0 0 10,00,000 1 1
Take the highlighter to PMT and solve for it, you get 1,57,410 as answer.
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4.1 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 8 10,000 0 0 1 1
Take the highlighter to FV and solve for it, you get 14693 as answer. By changing the value of I% to 10, 12 and 15 you get the answers for Part (b), (c) and (d). 4.5 Press CMPD key : On the input screen For quarterly compounding, set: Set n I% PV PMT FV P/Y C/Y
End 5x4 12/4 -50,000 0 0 1 1
For annual compounding, set: Set n I% PV PMT FV P/Y C/Y
End 5 12 -50,000 0 0 1 1
Take the highlighter to FV and you get 90,305 for quarterly compounding and 88,117 for annual compounding. For quarterly compounding we can also get the answer by setting C/Y equal to 4 and keeping n and I% at 5 and 12. 4.7 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 6 0 -50 0 99 1 1
Take the highlighter to I% and solve for it, you get 12.058 as answer.
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4.8 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 0 -1 0 3 1 1
Take the highlighter to I% and solve for it, you get 11.612 as answer. 4.10 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 0 -4000 0 15,000 1 1
Take the highlighter to I% and solve for it, you get 14.13 as answer. If your choice of time preference rate is ≥ 14.13%, then you opt for Rs.4000 today. Otherwise you opt for Rs.15,000 after 10 years. 4.12 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 12 0 0 1,00,000 1 1
Take the highlighter to PV and solve for it, you get 32,197 as answer.
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4.14 Press CASH key : On the input screen set : I% = 10 Csh = D.Editor x ---- press EXE key. We get cash flow table. Input the following values in the table: 1 2 3 4 5 6
-10,000 2,000 3,000 4,000 5,000 2,000
Press ESC and solve for NPV and you get 1,959.68 as answer. 5.1 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 5 0 -10,000 0 1 1
Take the highlighter to FV and solve for it, you get 55,256 as answer. 5.2 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 12 0 0 5,00,000 1 1
Take the highlighter to PMT and solve for it, you get 78,705 as answer. 5.3 Press CMPD key : On the input screen set :
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Set n I% PV PMT FV P/Y C/Y
End 10 12 0 0 10,00,000 1 1
Take the highlighter to PMT and solve for it, you get 56,984 as answer. 5.5 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 0 0 -16,000 1,00,000 1 1
Take the highlighter to I% and solve for it, you get 11.18 as answer. 5.6 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 0 10 0 -25,000 2,00,000 1 1
Take the highlighter to n and solve for it, you get 6.167 years as answer. 5.7 Press CMPD key : On the input screen set : Set n I% PV PMT
End 3 10 0 10,000 35
FV P/Y C/Y
0 1 1
Take the highlighter to PV and solve for it, you get 24,869 as answer. 5.8 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 3 x 12 1 0 -10,000 0 1 1
Take the highlighter to PV and solve for it, you get 3,01,075 as answer. 5.9 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 0 1.25 10,00,000 -15,000 0 1 1
Take the highlighter to n and solve for it, you get 144 months as answer. 5.10 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 10 -3,00,000 0 0 1 1
Take the highlighter to PMT and solve for it, you get 48,824 as answer. 36
5.11 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 6 0 -1,00,000 20,000 0 1 1
Take the highlighter to I% and solve for it, you get 5.47 as answer. 5.12 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 15 10,00,000 0 0 1 1
Take the highlighter to PMT and solve for it, you get 2,98,315 as answer. To prepare amortization schedule, now press AMRT key. On the input screen set PM1 = I and also set PM2 = 1. Then scroll down and solve for INT. You will get 1,50,000 which is the interest component of the first installment. Press ESC and now scroll down to PRN and solve for it. You get 1,48,315 which is the principal component of the 1st installment. Then you set PM1 and PM2 equal to 2 and you will get a break up of the 2nd installment into interest and principal component when we solve for INT and PRN again. Install Install. number Amount
AMORTIZATION SCHEDULE Interest Part Of Principal Part Principal Installment of Installment Balance
1 2 3
2,98,315 2,98,315 2,98,315
1,50,000 1,27,753 1,02,168
1,48,315 1,70,563 1,96,147
8,51,684 6,81,121 4,84,974
4
2,98,315
72,746
2,25,569
2,59,404
5
2,98,315
38,911
2,59,404
37
0.00
6.1 Press CASH key : On the input screen set : I% = 12 Csh = D.Editor x ---- press EXE key. We get cash flow table. Input the following values in the table: 1 2 3 4 5 6 7 8 9 10 11
0 3000 3000 3000 5000 5000 5000 5000 5000 5000 5000
Press ESC and solve for NFV and you get 72,824 as answer. 6.2 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 10 0 -50,000 10,000 0 1 1
Take the highlighter to I% and solve for it, you get 15.1 as answer. 6.3 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 8 12 0 1,000 4000/0.12 1 1
Take the highlighter to PV and solve for it, you get 18,431 as answer. 38
6.4 Press CASH key : On the input screen set : I% = 10 Csh = D.Editor x ---- press EXE key. We get cash flow table. Input the following values in the table: 1 2 3 4 5 6 7 8 9 10 11
0 15,000 20,000 50,000 50,000 50,000 50,000 50,000 50,000 50,000 50,000
Press ESC and solve for NPV and you get 2,50,617 as answer. 6.5 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 19 12 0 0 10,000/0.12 1 1
Take the highlighter to PV and solve for it, you get 9,675 as answer. 6.6 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 25 8 -2,00,000 0 0 1 1
Take the highlighter to PMT and solve for it, you get 18,736 as answer. 39
6.7 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 20 0 -50,000 8000 0 1 1
Take the highlighter to I% and solve for it, you get 15.03 as answer. This means option A is better for X as foregoing Rs.50,000 today in favour of pension of Rs.8,000 for a period of 20 years provides a return of 15.03%, which is more than his time preference rate of 10%. 6.8 Press CMPD key : On the input screen set : Set Begin n 13 I% 10 PV 0 PMT 0 FV 20,000/0.10 P/Y 1 C/Y 1 Take the highlighter to PV and solve for it, you get 57,933 as answer. We have taken n equal to 13 in this problem because we need accumulated sum at the end of 13th year so that our perpetual income of Rs.20,000 can start from the end of 14th year which is the same as beginning of 15th year. 6.9
Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
Begin 10 10 0 0 25,000 1 1
Take the highlighter to PMT and solve for it, you get 1,426 as answer.
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6.10 Step I : Press CMPD key and input the values : Set n I% PV PMT FV P/Y C/Y
Step II : Press CMPD key again and input the values
Begin 5 10 0 10,000 0 1 1
Set n I% PV PMT FV P/Y C/Y
End 4 10 0 0 41698.65 1 1
In Step I take the highlighter to PV and solve for it and you get 41,698.6. This is the present value of annuity due of Rs.10,000 for 5 years at the end of year 9. In step II, solve for PV again and you get 28480.74. This is the PV of Rs.41,698 (available at the end of year 9) at the end of year 5 after discounting it back by 4 years. Step III : Press CMPD key again and input the values: Set n I% PV PMT FV P/Y C/Y
End 5 10 0 0 28,480.74 1 1
Take the highlighter to PMT and solve for it, you get 4665 as answer. 6.11 Step I :Press CMPD key and set Set n I% PV PMT FV P/Y C/Y
Step II :Press CMPD key and set
End 35 12 0 5,000 0 1 1
Set n I% PV PMT FV P/Y C/Y
End 14 12 0 0 40877.52 1 1
In Step I take the highlighter to PV and solve for it and you get 40877.52. This is the present value of annuity of Rs.5,000 for 35 years at the end of 14th year. In step II we solve for PV again and get 8,364 as answer. 41
6.12 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 24 0 10,000 -500 0 12 12
Take the highlighter to I% and solve for it, you get 18.15 as answer. This is the effective annual rate of interest. If you want to get monthly interest rate keep P/Y and C/Y equal to 1 and then solve for I% and you get1.51 as monthly rate of interest. 6.13 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 12 0 100 1050 1 1
Take the highlighter to PV and solve for it, you get 956.27 as answer. 6.14 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 0 12 -10,000 1500 0 1 1
Take the highlighter to n and solve for it, you get 14.2 years as answer.
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6.15
Step I : Press CMPD key and input the values : Set n I% PV PMT FV P/Y C/Y
Step II : Press CMPD key again and input the values
End 3 9 17,00,000 0 0 1 1
Set n I% PV PMT FV P/Y C/Y
End 8 9 22,01,549 0 0 1 1
In Step I take the highlighter to FV and solve for it and you get 2201549. This is the FV of deferred loan of Rs.17,00,000 at the end of year three on the basis of which repayment will start in the form of annuity from the end of year 4. In step II, solve for PMT and you get 3,97,763 as answer. 6.16
Step I : Press CMPD key and input the values : Set n I% PV PMT FV P/Y C/Y
Step II : Press CMPD key again and input the values
End 16 10 0 3,000 0 1 1
Set n I% PV PMT FV P/Y C/Y
End 9 10 0 0 23,471.12 1 1
In Step I take the highlighter to PV and solve for it and you get 23,471.12. This is the PV of 16 year annuity of Rs.3000 at the end of year 9. In step II, solve for PV and you get 9,954 as answer. This is the PV of Rs.23471 to be received at the end of year 9. 6.17 Step I : Press CMPD key and input the values : Set n I% PV PMT FV P/Y C/Y
Step II : Press CMPD key again and input the values
End 25 10 0 -4500 0 1 1
Set n I% PV PMT FV P/Y C/Y 43
End 20 10 4,42,562 0 0 1 1
In Step I take the highlighter to FV and solve for it and you get 4,42,562. This is the FV of 25 year annuity of Rs.4500 at the end of year 25. In step II, solve for PMT and you get 51,983 as answer. This is the fixed amount you can withdraw annually for 20 years starting from the end of 26th year. 6.18 Press CMPD key Set n I% PV PMT FV P/Y C/Y
: On the input screen set : End 4 8 0 0 1100/8 1 1
Take the highlighter to PV and solve for it, you get 10,106. We should accept this offer because the PV of perpetuity of Rs.1100 stating from 5th year at 8% interest is Rs.10,106 which is more than Rs.10,000. 6.19 Step I : Press CMPD key and input the values : Set n I% PV PMT FV P/Y C/Y
Step II : Press CMPD key again and input the values
End 3 10 0 0 50,000 1 2
Set n I% PV PMT FV P/Y C/Y
End 5 10 0 0 70,000 1 2
Solve for the PV in step I and you get Rs.37,310.76. Solve for the PV in step II and you get Rs.42,973.9. Add both the PV’s and you get the answer which is Rs.80,285. 6.21 Press CMPD key : On the input screen set : Set End n 0 I% 1 PV 10,00,000 PMT -12,000 FV 0 P/Y 1 C/Y 1 44
Take the highlighter to n and solve for it, you get 180 months as answer. To calculate the interest portion and principal portion of installment 72, press AMRT key. Set PM1 and PM2 equal to 72 and then scroll down to INT and solve for it and you get Rs.7,964 as answer. Press ESC and scroll down to PRN and solve for it and you get Rs.4,054 as answer. 6.22
Press CASH key : On the input screen set : I% = 10 Csh = D.Editor x ---- press EXE key. We get cash flow table. Input the following values in the table: 1 2 3 4 5 6
-10,000 2,000 3,000 4,000 5,000 3,000
Press ESC and solve for NPV and you get 2,580 as answer. Press ESC and solve for NFV and you get 4,156 as answer. Press ESC and solve for IRR and you get 18.69 as answer. 6.23 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
Begin 24 1.25 80,000 0 0 1 1
Take the highlighter to PMT and solve for it, you get 3,831 as answer. 6.26 Press CMPD key : On the input screen set : Set n I% PV PMT FV
End 1 0 -96 0 5+105
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P/Y C/Y
1 1
Take the highlighter to 1% and solve for it, you get 14.58 as answer. 6.28 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 5 X 12 1 0 -10,000 0 1 1
Take the highlighter to PV and solve for it, you get 4,49,550 as answer. 6.29 Press CMPD key : On the input screen set : Set n I% PV PMT FV P/Y C/Y
End 0 12 0 -5,00,000 100,00,000 1 1
Take the highlighter to n and solve for it, you get 10.8 years as answer. 6.30 Step I :Press CMPD key and set : Set n I% PV PMT FV P/Y C/Y
Step II :Press CMPD key and set:
End 6 8 1,00,000 0 0 1 1
Set n I% PV PMT FV P/Y C/Y
Begin 3 8 0 21,631.53 0 1 1
In step I solve for PMT and you get 21,631.53. In step I solve for PV and you get 60,206 as answer.
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