NPV profile

An NPV profile is a graph plotting a project's net present value against a range of discount rates, showing the IRR where the line crosses zero and how project rankings can shift across rates.

ByHoang TruongUpdated July 5, 2026

See it move

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A project costing €10,000 with €4,000 a year for three years has an NPV of €2,000 at a 0% discount rate, falling to about −€53 at 10%. Because the line crosses from positive to negative between those rates, the project's internal rate of return sits just under 10%, close to 9.7%.

Where it fits

TopicCapital Budgeting & Investment AppraisalCoreSubjectCorporate FinanceCore

The formula

LaTeX

NPV(r) = -C_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t}

Variables

$C_{0}$: Initial outlay (€)
$C F_{t}$: Cash flow in year t (€)
$r$: Discount rate (decimal)
$n$: Final year of the project (years)
$t$: Year index (year)

Evaluating this expression at many discount rates r and plotting the resulting NPV values produces the project's NPV profile.

Check yourself

PracticeCORE

GreenPeak Ltd is evaluating a project with an initial outlay of €15,000 and expected inflows of €6,000 a year for three years. Its NPV profile shows an NPV of €1,339 at a 5% discount rate and an NPV of −€1,301 at a 15% discount rate. Reading the NPV profile, which of the following is the best estimate of the project's IRR?

Select an answer to check your understanding.