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Question 9.P.17: Illustrate the reinvestment fallacy by supposing that, in Pr......

Illustrate the reinvestment fallacy by supposing that, in Problem 9.15, the revenues from system 2 could be reinvested at 40% in years 3 through 5.

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At the end of five years, the net future worth of system 1 is:

FW_1 = -$50 000(F/P, 15%, 5) + $22 000(F/A, 15%, 5)

= -$50 000(2.0114) + $22 000(6.7424) = $47 762.80

and the net future worth of system 2 is (draw a time diagram):

FW_2 = -$75 000(F/P, 15%, 5) + $24 000(F/P, 15%, 1)(F/P, 40%, 3) + $24 000(F/A, 40%, 4)

= -$75 000(2.0114) + $24 000(1.15)(2.7440) + $24 000(7.1040)

= $95 375.40

The effect of the reinvestment is to reverse the conclusion of Problem 9.15: now, system 2 is the better.

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