Question

A contract specifies that you will receive $1000 in one year, $1040 in two years, and annual payments that continue to grow at a 4% rate forever. If the appropriate discount rate is 7.5%, what is the value of this contract?

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Answer #1

We can use the Gordon growth model to solve this problem. The present value of all future cash flows will be the value of the contract.

a) Present value of amount received after year 1 = 1000 / (1 + Discount Rate)

= 1000 / (1 + 7.5%)

= 930.2325

b) Present value of amount received after year 2 = 1040 / (1 + Discount Rate)^2

= 899.9459

Total value of payments after year 2 by using Gordon growth model = Payment for the next period / (Discount rate - growth rate)

= 1040(1 + 4%) / (7.5% - 4%)

= 30,902.8571

c) Present value of terminal amount = 30,902.8571 / (1 + 7.5%)^2

= 26,741.25

Adding a + b + c

= 28,571.4284

So the value of the contract will be $28,571.4284

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