Question

Investment A offers to pay you $10,000 per year for 10 years while Investment B offers to pay you $15,000 per year for 6 years.

a. If the annual interest rate (compounded annually) is 10%, which investment is more valuable?

b. Does your answer change if the annual interest rate (compounded annually) is 5%?

c. At what interest rate are the two investments equally attractive?

Answer 1

a: PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

PV of investment A = 10000*(1-1/1.1^10)/0.1 = 6144567

PV of investment B = 15000*(1-1/1.15^6)/0.15= 5676724

Investment A is more valuable

b:

PV of investment A = 10000*(1-1/1.05^10)/0.05 = 77217.35

PV of investment B = 15000*(1-1/1.05^6)/0.05 = 76135.38

Investment A is more valuable

c: The rate at which both are attractive is 5.87%

Using Goalseek function in excel