NPV Profiles of Projects A and B: Cross Rate Calculation

Rate at Which NPV Profiles of Projects A and B Cross

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Question

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?

Answers

Explanations

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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.