Crossover Rate Calculator

Formula

The formula to calculate the crossover rate is:

\[ CR = \frac{NPV1 \times (1 + r)^n}{NPV2 \times (1 + r)^n - NPV1} \]

Where:

$ CR $ is the crossover rate
$ NPV1 $ is the net present value of the first investment
$ NPV2 $ is the net present value of the second investment
$ r $ is the discount rate
$ n $ is the number of periods

What is a Crossover Rate?

The crossover rate is a specific point on the cost of capital curve in the field of corporate finance. It is the rate at which two comparable projects have the same net present value (NPV). The crossover rate is used in capital budgeting to compare the desirability of projects, especially when comparing projects of different sizes or lengths. It helps to identify which project would be more profitable under different circumstances.

Example Calculation

Let's assume the following values:

Net Present Value of First Investment (NPV1): $50,000
Net Present Value of Second Investment (NPV2): $70,000
Discount Rate (r): 0.08
Number of Periods (n): 5

Using the formula to calculate the crossover rate:

\[ CR = \frac{50000 \times (1 + 0.08)^5}{70000 \times (1 + 0.08)^5 - 50000} \approx 1.39 \]

The crossover rate is approximately 0.1.39.