Overview

Crossover rate is the rate of return (or the weighted average cost of capital - WACC) at which the net present value (NPV) of two projects are identical. It is the point of rate of return at which the NPV of one project intersects the NPV of another project. The crossover rate is calculated with the NPV functions of two projects with different cash flows and investment periods.

Example: Project A requires an initial investment of A0 and will generate a constant stream of cash flow (C1, C2, C3, C4, C5) over a 5-year period. Project B has an initial investment of B0 and generate steady cash flow streams (F1, F2, F3) over 3 years. The net present value of the two projects are as follows:

NPV A = C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 + C4/(1+r)^4 + C5/(1+r)^5 - A0

NPV B = F1/(1+r) + F2/(1+r)^2 + F3/(1+r)^3 - B0

Crossover rate is the rate of return at which NPV A = NPV B. Therefore, the two formulas can be combined to solve for the crossover rate (r):

C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 + C4/(1+r)^4 + C5/(1+r)^5 - A0 = F1/(1+r) + F2/(1+r)^2 + F3/(1+r)^3 - B0

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