Two projects being considered are mutually exclusive and have the following projected cash flows:
Year Project A Project B -
0-$50,000-$50,000
115,9900
215,9900
315,9900
415,9900
515,990100,560
At what rate (approximately) do the NPV profiles of Projects A and B cross?
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A. B. C. D. E.Explanation
Solve for numerical PVIFA and PVIF and obtain corresponding interest rates from table. Project A:50,000 = 15,990(PVIFA(Irr,5))
3.12695 = PVIFA(IrrA,5)
IRR(A) = 18%
Project B:50,000 = 100,560(PVIF(IrrB,5)0
0.49722 = PVIF(IrrB,5)
IRR(B) = 15%
Solving for the crossover rate of 11.49% requires interpolation, which is not covered in the text. However, by using trial and error and an NPV profile drawing, the student can select the correct multiple choice answer, 11.5%. Drawing an NPV profile drawing using the calculated IRRs, and the NPVs at k = 0%, shows that there is a crossover rate. Of the responses listed in the problem, 16.5% and 20.0% are clearly too high, since the IRR(B) is 15%. At k = 6.5% the NPVs are not equal, thus 11.5% must be the correct response.