Question

Perpetuities Suppose that today's date is January 1,2019. You have the opportunity to make an investment that will pay you $100 on January 1 of every year, starting in 2020 and continuing forever.

Assume the relevant discount rate is 7%.

a. What would you pay now for this investment?

b. Suppose the investment's first cash flow comes immediately, on January 1,2019, P5-27 with subsequent cash payments every January 1 thereafter. Now how much would you pay? It might be helpful to draw the first few years of a timeline here and compare it to the situation in part a.

c. Suppose the investment's first cash flow is 3 years from now, on January 1, 2022. On every January 1 thereafter you will receive $100. How much is this worth to you today, January 1, 2019?

Answer 1

a) Value of a perpetuity =$1,428.57

b) Present value of perpetuity due will include extra cash flow received at start: =$1,528.57

c) Present value = 1428.57/(1.07^2)=$1,247.77

Step-by-step explanation:

a) Value of a perpetuity = Cash flow/rate=100/0.07=$1,428.57

b) Present value of perpetuity due will include extra cash flow received at start:

=Cash flow/rate+Cash flow=100+(100/0.07)=$1,528.57

c) This will be equal to PV of perpetuity at end of year 2=100/0.07=$1428.57 after 2 years

Present value = 1428.57/(1.07^2)=$1,247.77