1. Consider a perpetuity that pays $100 per year. The market rate of interest is 10%....

1. Consider a perpetuity that pays $100 per year. The market rate of interest is 10%.

a. What is the PV of the perpetuity?

b. What is the PV of the perpetuity three years from now?

c. What is the present value of the perpetuity "n" years from now?

d. Under what circumstances does the value of a perpetuity change?

Solutions

Expert Solution

a) PV of perpetuity = annuity / interest rate = $ 100 / 10% = $ 1000

b) Value of perpetuity three years from now will also be $ 1000 (since after 3 years also, investor will receive $100 per year for infinite years)

c) Value of perpetuity n years from now will be same $ 1000 (since after n years also, investor will receive $100 per year for infinite years)

d) Value of perpetuity will change only if:

1) interest rate changes or

2) Annuity amount changes or

3) both change

If interest rate goes down, value of annuity will increase and vice-versa. (Interest rate and PV of annuity are inversely related)

If annuity amount ($100) increases, value of annuity will go up and vice versa.(Annuity amount and PV are directly related)

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