Given an interest rate of 6.0 % per year, what is the value at date t=5 of a per

Question

Given an interest rate of 6.0 % per year, what is the value at date t=5 of a perpetual stream of $1,500 payments that begins at date t=15?

Note: Valuing a perpetuity is easy: PVp=C/r. The trick here is that this equation gives you the value one period before the cash flows start. But in this problem the cash flows don't start in one period, so when you use the equation you are actually calculating the value of the perpetuity at time t=14, or one period before the cash flows begin. You much then turn that FV into a FV at time t=5 by discounting (14-5)=9 more periods using the equation for single cash flows.

Answer options:

14,797.46

25,000

13,959.87

15,093.41

Explanation / Answer

Value at T-5 is required if $ 1,500 is invested for perpetuity from t-15 at 6%, therefore value of perpetuity will be given by Cash Flow / 6% at T-15 will be = $ 25,000. Now we need to find the present value of this $ 25,000 at T-15 on T-5.

This can be done by using the following formula:

Present Value of Cash Flow at T-15 / (1 + 6%) ^ 10

= $ 25,000 / ( 1 + 6% ) ^ 10

= $ 13,959.87

Therefore value at date t=5 of a perpetual stream of $1,500 payments that begins at date t=15 is $ 13,959.87.

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