Let the interest rate be 10 percent (r = .10) at all maturities. a. Calculate th

Question

Let the interest rate be 10 percent (r = .10) at all maturities.

a. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being $1000. Let the payments grow at an annual rate of 7 percent (g = .07).

b. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being $1000. Let the payments grow at an annual rate of 9 percent (g = .09).

c. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being $1000. Let the payments grow at an annual rate of 9.5 percent (g = .095).

d. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being $1000. Let the payments grow at an annual rate of 9.9 percent (g = .099).

e. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being $1000. Let the payments grow at an annual rate of 10.5 percent (g = .105). Hint: Consider the trend in the present values as the growth rate increases by comparing your answers to a through d. If you use the standard growing perpetuity formula when g > r, you get a silly answer. Using your intuition from your answers to a through d, what is the real answer?

Explanation / Answer

a. present value= 1000/.07= $14285.71 b. present value = 1000/.09= $11111.11 c. present value = 1000/.095= $10526.32 d. present value =1000/.099= $10101.01 e. present value =1000/.105= $9523.81

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