NPV Formula (Net Present Value)

Net present value (NPV) sums the present value of a series of future cash flows, discounting later money back to today at a chosen rate. A positive NPV means the project is expected to create value above its cost of capital; a negative NPV means it destroys value.

The formula

Sums the present values of a series of future cash flows. Positive NPV means the project is profitable; negative means it loses money.

What goes into it

This calculation works from a series of period cash flows rather than single variables — enter them in the live calculator below.

Worked example

Pre-loaded example — five periods (t = 0…4) at R = 5%:

The decision rule

Accept the project when NPV > 0, reject it when NPV < 0. Between two options, prefer the higher NPV. The discount rate is your required return — raise it for riskier projects and the same cash flows are worth less today.

NPV in Excel

In a spreadsheet, =NPV(rate, value1, value2, …) discounts a stream of period-end cash flows. Note Excel's NPV assumes the first value is one period out, so a cash flow at time 0 (your initial outlay) is added separately: =initial + NPV(rate, future_flows). The calculator below handles the period-0 flow for you.

This calculator applies a single rate R to every period. In practice, later-stage cash flows often warrant a lower discount rate as the risk profile improves.

Worked example: iRobot Select, one subscriber

In 2021 iRobot launched Select: a premium Roomba, accessory replenishment, a protection plan and an upgrade every three years, for $29 a month plus a $149 activation fee. Chapter 23 of Tangibles runs the NPV of one subscriber to ask whether the programme could beat an outright sale. The inputs are illustrative (the book says so), but the method is the one you would use for any hardware subscription.

Step 1: build the cash-flow series. Month 1 to 12 each bring $29. From month 13 the expected fee shrinks by 5% a month: $27.55, $26.17, $24.86 and so on, down to about $4.60 in month 48. Undiscounted, the 48 months sum to roughly $812.

Step 2: discount each month. Divide month t's fee by (1 + 0.004167)^t. The first year is worth $338.76 today; months 13 to 48 are worth $418.13, because churn and discounting compound against them. Total present value of fees: $756.89.

Step 3: add period 0. The activation fee comes in and the robot goes out on day one, neither discounted: +$149 − $179.67 = −$30.67.

Step 4: sum. NPV = $756.89 − $30.67 = $726.22, or $729.37 with the book's convention of collecting each fee at the start of its month rather than the end. Positive, so a subscriber creates value. But the book then runs the same arithmetic for a customer who pays $799.99 up front and buys consumables for four years and gets $1,116.54. Each subscriber was worth about $387 less than the buyer they replaced. Select was discontinued.

To reproduce it in the calculator below: set the discount rate to 0.4167, the initial outflow to −30.67, then add 48 periods of 29 × the surviving share (1.00 for the first twelve, 0.95, 0.9025, 0.857 and so on after that). The calculator also returns the IRR and, if you extend the horizon, a terminal value.

When to use NPV, and when not

Use it for any decision where money goes out now and comes back over years: a tooling investment against the unit-cost saving it buys, a subscription against an outright sale, a cloud back-end against the service revenue it enables, one product programme against another competing for the same budget. Use it whenever someone says “it pays back in three years” and you want to know what those three years are worth today.

Do not use it on its own when the cash-flow timing is the question, not the total. The Select programme had a positive NPV and still opened a hole in the ledger, because production cost hit in month 1 while revenue arrived over 48. Pair NPV with a cash-flow forecast. Do not use a single rate for projects whose risk falls over time, and do not compare projects of different lengths by NPV alone; use the IRR, or an annualised equivalent, alongside it.

Frequently asked questions

Go further

• Chapter 20 of Tangibles introduces NPV, cost of capital and terminal value for hardware product decisions; Chapter 23 runs the iRobot Select case in full.
• Present value: one cash flow at a time, the building block of NPV.
• Customer lifetime value: NPV applied to a customer relationship, with retention built in.
• Contribution margin and break-even: the unit economics that feed each period's cash flow.
• Market risk premium: how the discount rate is built.

Related: all business formulas — the live directory includes NPV, contribution margin, customer lifetime value, and more.