Question

How much would you be willing to pay for an investment that will pay you and your heirs $16,000 each year in perpetuity if the first payment is to be received in 9 years?

a) Assuming your opportunity cost is 6%?

b) if you want the payments to grow by 2% indefinitely.

problem must be in excel

Answer 1

(a) Computation of the present value of investment that will pay today.We have,

Step1: Computation of the present value of perpetuity at 9th years.We have,

Present value of perpetuity at 9th year = Constant annual payment / opprotunity cost

Present value of perpetuity at 9th year = 16,000 / 0.06 = $ 266,667

Present value of perpetuity at 9th year = $ 266,667

Step2: Computation of the current investment using future annuity method.We have,

FVIFA_{(n=9, r= 6%)} = ((1+r)ⁿ - 1) / r

FVIFA_{(n=9, r= 6%)} = ((1.06)⁹ - 1) / 0.06 = (1.6895 - 1) / 0.06 = 11.491

Current investment = Value of perpetuity / FVIFA_{(n=9, r= 6%)}

Current Investment = 266,667 / 11.491 = $ 23,206

Current Investment

$ 23,206

(b) Computation of the present value of investment that will pay today.We have,

Step1: Computation of the present value of perpetuity at 9th years if growth rate is 2%indefinitely.We have,

Present value of perpetuity at 9th year = Constant annual payment / (opprotunity cost - growth rate)

Present value of perpetuity at 9th year = 16,000 / (0.06 - 0.02) = $ 400,000

Present value of perpetuity at 9th year = $400,000

Step2: Computation of the current investment using annuity method.We have,

FVIFA_{(n=9, r= 6%)} = ((1+r)ⁿ - 1) / r

FVIFA_{(n=9, r= 6%)} = ((1.06)⁹ - 1) / 0.06 = (1.6895 - 1) / 0.06 = 11.491

Current investment = Value of perpetuity / FVIFA_{(n=9, r= 6%)}

Current Investment = 400,000 / 11.491 = $ 34,810

Current Investment

$ 34,810