Practice Problem – Crossover Rate

Practice Question

Intro to Finance
Capital Budgeting
Crossover Rate
Short Answer

Nike has the following cash flows for two mutually exclusive projects: You have also estimated that the IRR of project A is 15.86% and the IRR of project B is 14.1%. The payback period of Project A is 2 years, while the payback period of project B is 3.2 years. When is Project B more lucrative than Project A? That is, over what range of discount rate (k) does Project B have a higher NPV than Project A?

Answer +
Correct Answer: Accept Project A if the discount rate (k) is between 10.064% and 15.86%. Accept Project B if the discount rate (k) is between 0.00% and 10.064%.
Explanation +

Step 1: Highlight Relevant Information

IRR of Project A = 15.86%
IRR of Project B = 14.1%
Payback Period of Project A = 2 years
Payback Period of Project B = 3.2 years

Step 2: Understand Crossover Rate Logic

The crossover rate is the discount rate at which the NPVs of both projects are equal. Below this rate, the project with greater early cash flows (typically Project B) may be more favorable. Above it, the higher IRR project (Project A) becomes superior.

Step 3: Determine Preference Ranges

Since Project A has a higher IRR (15.86%) and Project B has a lower IRR (14.1%), we accept Project A if the required return (k) is between 10.064% and 15.86%, and accept Project B if k is between 0.00% and 10.064%.

Step 4: Conclusion

Project B is more lucrative than Project A when the discount rate is below the crossover point of 10.064%. Once the required return exceeds that, Project A becomes the better investment due to its higher IRR.