Finance Crossover Rate Example

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Finance Crossover Rate Example

Understanding the Crossover Rate with an Example

The crossover rate, also known as the Fisher rate, is a crucial concept in capital budgeting. It’s the discount rate at which the net present values (NPVs) of two projects are equal. This rate helps determine which project is more profitable at different cost of capital scenarios. It’s especially useful when projects have differing cash flow patterns; one might have a higher initial investment but generate more cash later, while the other might have a lower initial investment with quicker, smaller returns.

Let’s illustrate this with a practical example. Suppose a company, Acme Corp, is considering two mutually exclusive projects: Project A and Project B.

Project Details:

  • Project A: Requires an initial investment of $100,000 and generates cash inflows of $30,000 per year for 5 years.
  • Project B: Requires an initial investment of $70,000 and generates cash inflows of $22,000 per year for 5 years.

To find the crossover rate, we need to determine the discount rate (r) where NPV(A) = NPV(B). This means finding the ‘r’ that satisfies the following equation:

-$100,000 + $30,000/(1+r) + $30,000/(1+r)² + $30,000/(1+r)³ + $30,000/(1+r)⁴ + $30,000/(1+r)⁵ = -$70,000 + $22,000/(1+r) + $22,000/(1+r)² + $22,000/(1+r)³ + $22,000/(1+r)⁴ + $22,000/(1+r)⁵

Solving this equation manually is complex and often requires iterative methods or financial calculators. We can simplify the equation by bringing all terms to one side and finding the ‘r’ where the NPV difference is zero:

NPV(A) – NPV(B) = 0

Using a financial calculator or spreadsheet software, we find that the crossover rate is approximately 8.69%.

Interpreting the Results:

  • If Acme Corp’s cost of capital is less than 8.69%: Project A has a higher NPV than Project B. This means that even though Project A requires a larger initial investment, its higher cash inflows outweigh the cost of capital, making it the more profitable choice.
  • If Acme Corp’s cost of capital is greater than 8.69%: Project B has a higher NPV than Project A. In this scenario, the lower initial investment and quicker returns of Project B become more attractive, as the higher cost of capital makes the later cash flows of Project A less valuable in present terms.
  • If Acme Corp’s cost of capital is exactly 8.69%: Both projects have the same NPV. The company would then need to consider other factors, such as strategic alignment, risk profile, or qualitative aspects, to make a decision.

The crossover rate helps Acme Corp understand how their project selection should change depending on their cost of capital. It’s a crucial tool for making informed investment decisions, especially when comparing projects with different cash flow patterns and investment amounts. Ignoring the crossover rate can lead to selecting a suboptimal project, potentially costing the company significant profits.

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