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What is the present value (PV) today of a stable perpetuity that pays $15,000 every 4...

What is the present value (PV) today of a stable perpetuity that pays $15,000 every 4 years, starting 2 years from today? The appropriate annual discount rate is 19% p.a. Round your answer to the nearest dollar.

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Answer #1

PV = CF/r

This formula gives the present value one period before the first payment. Our one period = 4 years

Since the first payment is in two years, this formula gives the present value as of two years ago. That is 4 years before the first payment.

Four-year interest rate, r = (1 + 0.19)^4 - 1

r = 1.00533921

PV(-2) = 15,000/1.00533921

PV(-2) = 14,920.3371864905

Present value today, P0 = PV(-2) * (1 + one year rate)^n

one year rate = 19%

n = 2 years

P0 = 14,920.3371864905 * 1.19^2

P0 = $21,128.6894897892

The present value today of the perpetuity, P0 = $21,129

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