Suppose project Acquisition and project Merger are mutually exclusive.Project Acquisition requires an initial cash outlay of $50,000 and is expected to provide after-tax cash flows of $15,000 in year 1, $25,000 in year 2, $20,000 in year 3, and $15,000 in year 4.Project Merger requires an initial cash outlay of $75,000 and is expected to provide after-tax cash flows of $20,000 in year 1, $28,000 in year 2, $35,000 in year 3, and $20,000 in year 4.The appropriate discount rate is 12%.What is the crossover rate?

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Quizplus · Accepted Answer

The crossover rate is the discount rate at which the NPVs of the two projects are equal. To find the crossover rate, we can set the NPV of Project Acquisition equal to the NPV of Project Merger and solve for the discount rate.The NPV of Project Acquisition is:NPV = -50,000 + 15,000/(1+r) + 25,000/(1+r)^2 + 20,000/(1+r)^3 + 15,000/(1+r)^4The NPV of Project Merger is:NPV = -75,000 + 20,000/(1+r) + 28,000/(1+r)^2 + 35,000/(1+r)^3 + 20,000/(1+r)^4Setting the two NPVs equal to each other, we get:-50,000 + 15,000/(1+r) + 25,000/(1+r)^2 + 20,000/(1+r)^3 + 15,000/(1+r)^4 = -75,000 + 20,000/(1+r) + 28,000/(1+r)^2 + 35,000/(1+r)^3 + 20,000/(1+r)^4Simplifying, we get:25,000 = 20,000/(1+r) + 3,000/(1+r)^2 + 15,000/(1+r)^3 + 5,000/(1+r)^4Using a financial calculator, we can solve for the discount rate that makes the two NPVs equal. The crossover rate is approximately 4.30%.

Suppose Project Acquisition and Project Merger Are Mutually Exclusive