Consider the following two cash flow series of payments: Series A is a geometric

Question

Consider the following two cash flow series of payments: Series A is a geometric series increasing at the rate of 8% per year. The first payment of S1,000 is at the end of year 1. The next seven payments occur at the end of every year (increasing at the rate given). Note that the last payment is at the end of year 8. Series B is a uniform scribes with payments of value X occurring annually at the end of years 2 thru 6 (total of 5 payments). For an interest rate of 5% per year, find the value of X for which the two series are equivalent.

Explanation / Answer

First let us compute present worth (PW) of cash flow series A as follows:

Therefore, for equivalence,

PW of series B = PW of series A

X x PVIFA(5%, 5) x PVIF(5%, 2)** = $8,426.08

X x 4.3295 x 0.907 = $8,426.08

X = $1,765.20

**Discounting end-of-year-2 value to year 0

Year Cash flow ($) PVIF @ 5% Discounted cash flow ($) (1) (2) (1) x (2) 1 1,000.00 0.952381 952.38 2 1,080.00 0.9070295 979.59 3 1,166.40 0.8638376 1,007.58 4 1,259.71 0.8227025 1,036.37 5 1,360.49 0.7835262 1,065.98 6 1,469.33 0.7462154 1,096.44 7 1,586.87 0.7106813 1,127.76 8 1,713.82 0.6768394 1,159.98 PW ($) = 8,426.08

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