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24 June, 18:13

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 $

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  1. 24 June, 18:49
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    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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