Given an interest rate of 4 percent per year, what is the value at date t = 5 of a perpetual stream of $2,400 payments that begins at date t = 10? (do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

perpetuity value $

The answer is $49,315.63

Explanation:

In order to get this value some formulas has to be used, the perpetutiy and the present value of a future payment. First, we get the value of the perpetuity, in this case payment = 2,400 and interest rate = 0.04 (4%). The calculation is Perpetuity = 2,400/0.04 = 60,000. This is the value of the perpetuity in year 10, so we have to bring that value to year 5. To do so, we subtract 5 to 10 to get the gap of years between the future payment and the present value we want to get, in this case: t=10-5 = 5. Finally, using the discount factor 1/(1+r)^t, we have: PV at year 5 = 60,000*(1/1.04)^5=49,315.63

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