NPV Calculator
Discount a series of future cash flows to today’s dollars and see whether an investment adds value.
NPV is positive, so at a 10% discount rate the project is expected to add value — accept it.
| Year | Cash flow | Discounted value |
|---|---|---|
| 1 | $3,000.00 | $2,727.27 |
| 2 | $4,000.00 | $3,305.79 |
| 3 | $5,000.00 | $3,756.57 |
| 4 | $3,000.00 | $2,049.04 |
Each year’s cash flow is divided by (1 + r) raised to that year, so later money counts for less.
Net present value discounts every future cash flow back to today and subtracts the upfront cost: NPV = −C₀ + Σ CF_t ÷ (1 + r)^t. Invest $10,000 for inflows of $3,000, $4,000, $5,000, and $3,000 at a 10% rate and the NPV is $1,838.67. Because NPV > 0, the rule says accept the investment.
What net present value tells you
Net present value (NPV) measures how much wealth an investment is expected to create in today’s dollars. A dollar received in three years is worth less than a dollar today, so NPV shrinks each future cash flow by a discount rate that reflects your required return, then adds them up and subtracts the initial outlay. The decision rule is simple: if NPV is positive the project is expected to earn more than your required return and should be accepted; if it is negative, your money is better used elsewhere.
C₀ is the initial investment, CF_t the cash flow in year t, r the discount rate as a decimal, and t the year number.
Worked example
Invest $10,000 today for four years of cash flows — $3,000, $4,000, $5,000, then $3,000 — with a 10% discount rate.
- 1 Write the discount rate as a decimal. r = 10% ÷ 100 = 0.10.
- 2 Discount each cash flow to today. Divide each by (1 + r)^t: 3,000 ÷ 1.1 = 2,727.27; 4,000 ÷ 1.21 = 3,305.79; 5,000 ÷ 1.331 = 3,756.57; 3,000 ÷ 1.4641 = 2,049.04.
- 3 Add the discounted cash flows. 2,727.27 + 3,305.79 + 3,756.57 + 2,049.04 = $11,838.67 — the present value of all inflows.
- 4 Subtract the initial investment. $11,838.67 − $10,000 = $1,838.67, the net present value.
- 5 Apply the decision rule. NPV of $1,838.67 is greater than zero, so the project clears the 10% hurdle and adds value — accept it.
How the discount factor shrinks later cash flows
The discount factor is 1 ÷ (1 + r)^t at a 10% rate. Money arriving further out is multiplied by a smaller factor, so a distant dollar is worth much less today.
| Year (t) | (1 + r)^t | Discount factor | $1,000 becomes |
|---|---|---|---|
| 1 | 1.1000 | 0.9091 | $909.09 |
| 2 | 1.2100 | 0.8264 | $826.45 |
| 3 | 1.3310 | 0.7513 | $751.31 |
| 4 | 1.4641 | 0.6830 | $683.01 |
| 5 | 1.6105 | 0.6209 | $620.92 |
Choosing a discount rate — and NPV vs. IRR
The discount rate drives the answer. It represents the return you could earn on a comparable-risk alternative — often a company’s weighted average cost of capital, or simply the return you require. Raise the rate and future cash flows are discounted harder, so NPV falls; a project that looks great at 8% can turn negative at 15%. Because the choice of rate matters so much, it’s worth testing a range rather than trusting a single figure.
NPV vs. IRR. The internal rate of return (IRR) is the discount rate that makes NPV exactly zero. IRR is quoted as a percentage, which feels intuitive, but NPV is generally the more reliable decision tool: it reports value in dollars, handles unconventional cash-flow patterns without giving multiple answers, and ranks competing projects correctly. When the two disagree on which project to pick, follow NPV.