CalculatorMine

Crossover Rate Calculator

%
Project A ($)Project B ($)Investment
Year 1
Year 2
Year 3
Year 4

Your Results

The two projects have the same NPV at a discount rate of 11.97%. Below that rate, Project B is worth more; above it, Project A is worth more. At your 10% cost of capital, Project A is worth $78.82 and Project B is worth $100.40, so Project B is the better choice.

11.97%
Crossover rate: the NPVs of A and B are equal
$78.82
NPV of A at 10%
$100.40
NPV of B at 10%
14.49%
IRR of Project A
13.55%
IRR of Project B

NPV profile of each project

  • Project A
  • Project B
  • Crossover
Cash Flow Table
YearABA − BDiscount RatePresent Value
0-$1,000.00-$1,000-$1,000.00-$1,000$0.00$011.97%$0.00$0
1$500.00$500$100.00$100$400.00$40011.97%$357.22$357
2$400.00$400$300.00$300$100.00$10011.97%$79.76$80
3$300.00$300$400.00$400-$100.00-$10011.97%-$71.23-$71
4$100.00$100$675.00$675-$575.00-$57511.97%-$365.75-$366
Total––––$0.00$0

Discounted at the crossover rate, the differences between the projects add up to $0. That's what makes it a crossover rate.

What Is a Crossover Rate?

When you can choose only one of two projects, the crossover rate is the discount rate at which both have the same net present value (NPV). On a chart of each project's NPV at different discount rates, called its NPV profile, it's the point where the two lines cross, which is why it's also called the crossover point.

Why it matters

  • It shows which project to choose: below the crossover rate, one project has the higher NPV; above it, the other does. Compare it with your cost of capital.
  • Timing drives it: a project with bigger cash flows later loses more value as the discount rate rises, so projects with different timing often cross.
  • It explains IRR conflicts: when NPV and IRR favor different projects, the crossover rate shows the range of rates where they disagree.

Some pairs of projects never cross, because one is better at every rate, and a few cross more than once. The calculator tells you when either happens.

How to Calculate the Crossover Rate

Subtract Project B's cash flow from Project A's for each year, then find the rate that makes the NPV of those differences zero:

∑t=0n At−Bt (1+r)t =0
  • At and Bt: each project's cash flow in year t. Year 0 is the investment, as a negative number.
  • r: the crossover rate.
  • n: the number of years of cash flows.

This is the same as finding the IRR of the differences. It can't be rearranged to give r directly, so r is found by trial and error, which the calculator does for you.

Example

Both projects cost $1,000. Project A pays $500, $400, $300 and $100. Project B pays $100, $300, $400 and $675.

  • Differences (A − B): $0.00, $400.00, $100.00, -$100.00, -$575.00
  • Discounted at 11.97%, their present values are $0.00, $357.22, $79.76, -$71.23, -$365.75, which add up to $0.
  • So the crossover rate is 11.97%. Below it Project B is worth more; above it Project A is.
  • At a 10% cost of capital, Project A's NPV is $78.82 and Project B's is $100.40, so Project B is better.

How to Use the Crossover Rate Calculator

"I can fund only one of two $1,000 projects. One pays back sooner, the other pays more later. At what rate does my choice change, and which should I pick at a 10% cost of capital?" This calculator answers that.

Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own projects.

  • Number of Years: Choose 4, which is how many years of cash flows each project has, from 1 to 12.
  • Cost of Capital: Enter 10, which is the yearly return you need from a project. It decides which project is better for you, but doesn't change the crossover rate. It must be from 0 to 99.99.
  • Investment: Enter 1,000 for Project A and 1,000 for Project B, which is what each costs at the start. Enter a positive number; the calculator treats it as money going out.
  • Year 1: Enter 500 for A and 100 for B, which is the cash each project pays that year.
  • Year 2: Enter 400 for A and 300 for B.
  • Year 3: Enter 300 for A and 400 for B.
  • Year 4: Enter 100 for A and 675 for B. A later cash flow can be negative if a project costs you money that year.

Calculate and Reset

Click Calculate to see your results. If a box has a problem, such as an investment of 0, a message pops up under that box instead. With the default numbers you get:

  • Your Results: a short summary in words: the crossover rate (11.97%), which project wins on each side, and which is better at your cost of capital.
  • Crossover Rate: the headline number. It says None if the projects never cross, and lists every rate if they cross more than once.
  • NPV of A, NPV of B, IRR of Project A and IRR of Project B: $78.82, $100.40, 14.49% and 13.55%. The better NPV is highlighted.
  • NPV profile chart: each project's NPV at different discount rates, with a dot where the lines cross.
  • Table: each year's cash flows, their difference, the discount rate (the crossover rate) and the present value, adding up to $0. If the projects never cross, it uses your cost of capital instead. Download Excel saves it with the formulas, so you can change a number and see the results update.
  • Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.

Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put every box back to its default and show the default results again.

Video: How to Use the Crossover Rate Calculator