Time Value of Money Examples

Time Value of Money Examples Ten Questions with Answers Worked Example A project management team have projected that income from a capital project will start to flow in 10 years after completion of the build. From then on they project income of 500,000 p.a. (assumed to come in continuously over the year) growing at a rate of 2.5% p.a. If the project is planned to have a life of 25 years from completion and they wish to make a 20% profit from the build what is the maximum the accumulated spend can be at the end of the 10 year build? Assume that all monies receive a return of 6.5%p.a.

Exercises 1. What is the price of a 10 year zero coupon bond with redemption value 100 if the interest rate is assumed to be 6%p.a.? 2. What is the price of a 15 year fixed interest bond with coupons six monthly of 5% and redemption value 100 if interest rates are assumed to be 5.5%p.a.? 3. If a share has an annual dividend with the next dividend being 6.5 in one years time and dividend growth is assumed to be 3% p.a. What is the fair price of the share assuming interest rates of 7%p.a. and assuming we hold the share indefinitely? 4. The rental income for a property is 500 p.c.m. with rent reviews every 3 years. Assuming that rents will increase by 3% at each rent review what is the present value of the income stream over the next 30 years assuming interest rates are 6.5% p.a.? 5. What is the price of a 20 year zero coupon bond with redemption value 100 if the interest rate is assumed to be 6.5%p.a.? 1

6. What is the price of a 20 year fixed interest bond with coupons six monthly of 4% and redemption value 100 if interest rates are assumed to be 5.5%p.a. for the first 10 years and 6.0% for the last 10 years. 7. If a share has an annual dividend with the next dividend being 6.5 in six months time and dividend growth is assumed to be 2.5% p.a. What is the fair price of the share assuming interest rates of 6.7%p.a. and assuming we hold the share indefinitely? 8. The mortgage for a property is 1,500 p.c.m. for a 25 year mortgage. If interest rates are assumed to be 4.5% p.a. and I paid a 20% deposit what was the original price of the house? 9. A 15 year index linked bond has coupons of 1.5% above inflation and is redeemed at 100 real. If interest rates are assumed to be 6.5% p.a. and inflation is assumed to be 2%p.a. what is the fair price of the bond? 10. A corporate bond with a term of 25 years, redemption of 100 and a coupon of 6.5% is priced at 140. What rate of return does this offer?

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