Saving & investing
Net present value (NPV): Definition, Formula and Example
NPV is the sum of cash inflows and outflows discounted to one valuation date using a stated discount rate.
Scope: General financial concept; examples are hypothetical.
Other names and related labels: NPV; Discounted net value.
How it works
A positive NPV means the modeled cash flows exceed the return represented by the discount rate. It depends on the amounts, timing and chosen rate; it is not a guaranteed profit. Include the initial outlay and any terminal value once, with consistent signs.
NPV = Σ[cash flow at period t / (1 + discount rate)^t]
Use a rate per cash-flow period and consistent nominal or real amounts. The t = 0 cash flow is not discounted.
$1,000 paid now for $1,100 in one year
Use a hypothetical 5% annual discount rate.
- Present value of receipt: $1,100 / 1.05 ≈ $1,047.619.
- Subtract initial cost: $1,047.619 − $1,000 ≈ $47.619.
NPV is about $47.62 at a 5% discount rate.
One certain modeled receipt at year end; the rate is an input, not an investment recommendation.
Try these example inputsThe discount rate can change the conclusion
For the same cash flows, NPV is zero at 10%. An optimistic receipt or an unrealistically low discount rate can inflate NPV. Undiscounted payback ignores this time-value effect and also ignores later receipts.
Explore with a calculator
- Payback Period Calculator
Inspect NPV and payback for the same modeled cash-flow stream.
- Present Value Calculator
Discount individual payments or regular payment streams.
Sources and checks
Definition and example arithmetic checked . Sources explain the concepts; numerical examples use the assumptions stated above.
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