Question

You are evaluating an investment that will pay ​$70 in 1​ year, and it will continue to make payments at annual intervals​ thereafter, but the payments will grow by 3​% forever.

a. What is the present value of the first ​$70 payment if the discount rate is 11​%?

b. How much cash will this investment pay 100 years from​ now? What is the present value of the 100th​ payment? Again use a 11​% discount rate.

c. What is the present value of the entire growing stream of perpetual cash​ flows?

d. Explain why the answers to parts a and b help to explain why an infinite stream of growing cash flows has a finite present value.

Answer 1

Answer a.

First payment = $70
Discount rate = 11%

Present Value = $70 / 1.11
Present Value = $63.06

Answer b.

First payment = $70
Growth rate = 3%
Discount rate = 11%

100^th payment = $70 * 1.03^99
100^th payment = $1,306.121

Present Value = $1,306.121 / 1.11^100
Present Value = $0.04

Answer c.

First payment = $70
Growth rate = 3%
Discount rate = 11%

Present value of perpetuity = First payment / (Discount rate - Growth rate)
Present value of perpetuity = $70 / (0.11 - 0.03)
Present value of perpetuity = $875.00

Answer d.

Present value of growing perpetuity is a finite number as after certain number of payment, present value of each payment will be equivalent to 0.