Question

You are offered the following deal: if you give me $1200 today, I will provide you with a 40-year annuity that grows at 5% per year. Each payment is received at the end of each year and the first payment (one year from now) is equal to $100. The appropriate interest rate for an investment of this risk is 15%. What is the PV of this stream of cash flows and should you accept the offer?

A. PV is approximately $974. Accept the offer.

B. PV is approximately $974. Reject the offer.

C. PV is approximately $664. Reject the offer.

D. PV is approximately $1267 Accept the offer.

Answer 1

The present value of cash flows (excluding rhe inital $1200 outflow) can be calculated as  

PV = 100/1.15 + 100*1.05/1.15² + 100*1.05²/1.15³ + ...... + .100*1.05³⁹/1.15⁴⁰

As this is a Geometric progression, we can apply the sum of a GP formula and write

= 100/1.15 * (1- (1.05/1.15)⁴⁰) / (1- (1.05/1.15)

= 100 / (1.15-1.05) * (1- 0.913⁴⁰)

= 100 / 0.1 * (1-0.02628) = $ 973.71 or Apx $ 974

Now, if we were to calculate the NPV of this deal,we would get the NPV as

NPV = -1200+ 974 = -226

As the NPV is negative , we should not accept the deal

Hence the correct option is Option B