Crossover Point in NPV Profile Graph | CFA® Level 1 Capital Budgeting Question

Is there a Crossover Point in the Relevant NPV Profile Graph?

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Question

As the director of capital budgeting for Raleigh/Durham Company, you are evaluating two mutually exclusive projects with the following net cash flows:

Year Project XProject Z -

0-$100-$100

150 10

240 30

330 40

410 60

Is there a crossover point in the relevant part of the NPV profile graph (the northeast, or upper right, quadrant)?

Answers

Explanations

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A. B. C. D. E.

Explanation

Financial calculator solution:

Project X -

Inputs: CF(0) = -100; CF(1) = 50; CF(2) = 40; CF(3) = 30; CF(4) = 10.

Output: IRR = 14.489%.

Project Y -

Inputs: CF(0) = -100; CF(1) = 10; CF(2) = 30; CF(3) = 40; CF(4) = 60.

Output: IRR = 11.79%.

Calculate the NPVs of the projects at k = 0 discount rate.

NPV(X,k = 0%) = -100 + 50+ 40 + 30 + 10 = 30.

NPV(Y,k = 0%0 = -100 + 10 + 30 + 40 + 60 = 40.

Calculate the IRR of the differential project, i.e., Project(X - Y)

IRR(X - Y)Inputs: CF(0) = 0; CF(1) = 40; CF(2) = 10; CF(3) = -10; CF(4) = -50.

Output: IRR = 7.167%.

Solely using the calculator we can determine that there is a crossover point in the relevant part of an NPV profile graph. Project X has the higher IRR. Project Y has the higher NPV at k = 0. The crossover rate is 7.17% and occurs in the upper right quadrant.

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