In capital budgeting, what is meant by the crossover rate when comparing two investment projects?

Introduction / Context:
In capital budgeting, companies often have to choose between two mutually exclusive projects, such as two different machines or two possible locations. Net present value (NPV) profiles of these projects may cross at some discount rate, meaning that the preferred project changes depending on the required rate of return. The discount rate at which the NPVs are equal is called the crossover rate. Understanding this concept helps in interpreting NPV and internal rate of return (IRR) conflicts and in making better investment decisions.

Given Data / Assumptions:

• There are at least two projects, often labelled Project A and Project B.
• Each project has its own pattern of cash flows over time.
• NPVs of both projects can be calculated at different discount rates.
• The projects are mutually exclusive, so only one can be chosen.

Concept / Approach:
When plotting NPV against the discount rate for each project, you get NPV profiles. If these profiles intersect, there is a discount rate at which the NPVs are identical. Below this rate, one project may have a higher NPV; above it, the other project becomes more attractive. That intersection point is the crossover rate. It is found by calculating the IRR of the differences in cash flows between the two projects. The crossover rate is useful because it shows the threshold at which investment preference switches from one project to another, given changes in the cost of capital or required return.

Step-by-Step Solution:
Step 1: List the cash flows of Project A and Project B for each period. Step 2: Compute the difference in cash flows between the two projects (for example, cash flow of A minus cash flow of B) for each period. Step 3: Calculate the internal rate of return (IRR) of this series of differential cash flows. Step 4: Interpret this IRR as the discount rate at which the NPVs of Project A and Project B are equal, because at this rate the NPV of the difference is zero. Step 5: Recognise this discount rate as the crossover rate, which indicates the point at which preference between projects changes as the required return varies.

Verification / Alternative check:
Imagine Project A has higher cash flows early in its life but lower cash flows later, while Project B has lower early cash flows but larger later cash flows. At low discount rates, future cash flows are heavily valued, so Project B may have the higher NPV. At high discount rates, early cash flows matter more, making Project A more attractive. The discount rate at which both NPVs are equal is where the NPV profiles cross. This crossing point is found using the IRR of the differential cash flows and is called the crossover rate. It confirms that the crossover rate is the switching point in project preference.

Why Other Options Are Wrong:
Option B incorrectly describes an average of project IRRs, which is not the definition of the crossover rate. Option C refers to a bank maximum lending rate, which is unrelated to NPV equality between projects. Option D incorrectly connects the term to regulatory required returns for public projects, which is not specific to crossover analysis. Option E refers to changing capital structure from debt to equity, which is a financing decision, not a capital budgeting NPV comparison. Only option A properly defines the crossover rate as the discount rate at which the NPVs of two competing projects are equal.

Common Pitfalls:
A common confusion is to think of the crossover rate as just another name for the IRR of each project individually. In fact, it is the IRR of the difference in cash flows between the projects. Another pitfall is to forget that the crossover rate matters only when projects are mutually exclusive and have different cash flow patterns. In interviews, emphasise that the crossover rate reveals at which discount rate the preferred project changes, helping managers understand how sensitive project ranking is to assumptions about the cost of capital.

Final Answer:
In capital budgeting, the crossover rate is the discount rate at which the net present values of two competing projects become equal, causing a switch in preference between them.