Question

Your friend promises you a perpetuity of $1 every year, which starts in year 1. However, your friend is an absent-minded guy, paying you $2 at year 9 but no payment at year 10. Except for these two years, in other years, the payment is always $1. Which of the following statements is true?

Select one:

a. your friend is better off for his being absent-minded

b. you are better off for his being absent-minded

c. there is no difference for his being absent-minded

d. no enough information to make decision

e. none of the above

Answer 1

An example can be taken in this regard, for a perpetual cash flow, the Present value of perpetuity is given by CF/k, where CF is the constant cash flow and k is the cost of capital. Assuming cost of capital to be 10%, In case 1 if there is no absent mindedness for the friend, the value of perpetuity = 1/10% = $ 10

For an absent minded friend,

Cash flow from 1 to 8 is $ 1 , $ 2 in year 9 and then $ 1 from year 11, so

PV of cash flows from year 1 to year 9 = 1/10% + 2/(1+10%)^9 = $ 6.18

PV of cash flows from year 11 = (1/0.10)/(1+10%)^11 = 10/(1.1)^11 = $ 3.5

PV of cash flows =$ 6.18 + $ 3.5 = $ 9.69

Answer is a) your friend is better off for his being absent-minded