Enter the cash flows for Project A and Project B (comma-separated, starting at time 0) to calculate the crossover rate—the discount rate at which both projects have the same net present value (NPV). Optionally, enter a discount rate to compare each project’s NPV at that rate.

Crossover Rate Calculator

Enter cash flows as a comma-separated list from time 0 to time n (example: -5000, 2500, 2500, 2500).

Enter cash flows above, then click Calculate.

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Crossover Rate Formula

The crossover rate is the discount rate CR at which two projects have the same NPV. Equivalently, it is the internal rate of return (IRR) of the incremental cash flows (Project A minus Project B).

\sum_{t=0}^{n}\frac{CF_{A,t}-CF_{B,t}}{(1+CR)^t}=0

Variables:

  • CR is the crossover rate (discount rate per period)
  • CFA,t is the cash flow of Project A at time period t
  • CFB,t is the cash flow of Project B at time period t
  • t is the time period index (starting at 0)
  • n is the final period in the cash-flow series

Because CR appears inside the discounting term, there is generally no closed-form expression for the crossover rate for multi-period cash flows; it is typically found using numerical methods (the calculator above uses a bracketing and bisection approach).

What is a Crossover Rate?

The crossover rate is the discount rate at which two mutually exclusive projects have the same net present value (NPV). Graphically, it is the point where the projects’ NPV profiles (NPV versus discount rate) intersect. In capital budgeting, the crossover rate helps identify which project has the higher NPV at different costs of capital: below the crossover rate one project has the higher NPV, and above it the other project has the higher NPV.

How to Calculate Crossover Rate?

The following steps outline how to calculate the Crossover Rate:

  1. List the cash flows for Project A by period (including the time-0 cash flow, which is typically negative).
  2. List the cash flows for Project B by period (including the time-0 cash flow).
  3. Compute the incremental cash flows for each period: Incremental CF = CFA − CFB.
  4. Calculate the IRR of the incremental cash flows (solve for the discount rate that makes the incremental NPV equal to 0). This IRR is the crossover rate.
  5. Check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Project A cash flows = -5000, 2500, 2500, 2500

Project B cash flows = -4000, 2000, 2000, 2000 (incremental cash flows A − B = -1000, 500, 500, 500; crossover rate ≈ 23.3% per period)