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.
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
You are offered the following deal: if you give me $1200 today, I will provide you...
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