Crossover rate

The crossover rate is the discount rate at which two mutually exclusive projects' NPV profiles intersect, so the NPV ranking between them flips on either side of it.

ByHoang TruongUpdated July 5, 2026

See it move

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Projects A and B each require a €20,000 outlay. A returns €12,000 in both year 1 and year 2; B returns €4,000 in year 1 and €24,000 in year 2. Setting the present value of their incremental cash flows to zero gives a crossover rate of 50% — below it B has the higher NPV, above it A does.

Where it fits

TopicCapital Budgeting & Investment AppraisalAdvancedSubjectCorporate FinanceAdvanced

The formula

LaTeX

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

Variables

$C F_{A, t}$: Project A's cash flow in year t (€)
$C F_{B, t}$: Project B's cash flow in year t (€)
$r^{*}$: Crossover rate (decimal)
$n$: Final year common to both projects (years)
$t$: Year index (year)

The crossover rate r* is the discount rate that makes the present value of the incremental cash flows between two mutually exclusive projects equal to zero.