What net present value actually measures
NPV is the amount of value a project creates after paying for the capital it consumes. It is denominated in today's dollars, and it is additive: the NPV of two independent projects is the sum of their NPVs. No other capital budgeting measure has both properties, which is why NPV is the rule finance theory endorses and the one every other rule gets compared against.
The logic runs in three moves. A dollar arriving in five years is worth less than a dollar today, because today's dollar can be invested. The rate at which you trade future dollars for present ones is your required return, r. So you shrink each future flow by 1 ÷ (1 + r)t, add the shrunken values, and subtract what you pay now.
That surplus has a concrete meaning. An NPV of $48,000 says the project pays back its cost, earns your required return on the capital while it is tied up, and still leaves $48,000 of extra value in today's money. An NPV of −$12,000 says the project earns something, just not enough.
The decision rule is therefore blunt. Accept every independent project with a positive NPV, reject every negative one, and when capital is rationed rank by value created per dollar committed rather than by NPV alone.
Why the formula discounts each period separately
Each cash flow gets its own discount factor because each one waits a different length of time. The factor for period t is (1 + r)−t, the present value of $1 received t periods from now. At 10% that factor is 0.9091 after one period, 0.6209 after five and 0.3855 after ten: the same dollar loses about 61% of its present value over a decade.
Three details in the formula do most of the work in practice.
The rate must match the period. If your cash flows are quarterly, r is a quarterly rate: a 12% annual rate becomes 1.120.25 − 1 = 2.874% per quarter when compounding. Mixing an annual rate with quarterly flows overstates NPV badly.
The rate must match the risk of the cash flows, not the source of the money. A firm with cheap debt does not get to discount a risky project at its borrowing rate. The discount rate belongs to the project. Build it from the weighted average cost of capital of a business with the same risk profile, and use CAPM for the equity leg.
Cash flows are cash, not accounting profit. Add depreciation back, subtract capital expenditure and the change in working capital, use after-tax operating numbers, exclude interest (the discount rate already charges for financing), and ignore sunk costs entirely. Include opportunity costs and any incremental effect on other product lines. The free cash flow to the firm definition is the one to work from.
Because the discount factor shrinks geometrically, cutting the forecast at year five throws away everything after it — which is why most valuation models bolt on a terminal value to represent the tail.
Worked example: a $100,000 machine with five uneven years
A plant manager wants to buy a $100,000 packaging line. After-tax cash flows are forecast at $30,000, $35,000, $40,000, $45,000 and $50,000 over five years. The company's cost of capital is 10%. Work it through period by period.
- Convert the rate. r = 10 ÷ 100 = 0.10 per year.
- Year 1. Factor = 1 ÷ 1.10 = 0.909091. PV = $30,000 × 0.909091 = $27,272.73.
- Year 2. 1.102 = 1.21, factor = 0.826446. PV = $35,000 × 0.826446 = $28,925.62.
- Year 3. 1.103 = 1.331, factor = 0.751315. PV = $40,000 × 0.751315 = $30,052.59.
- Year 4. 1.104 = 1.4641, factor = 0.683013. PV = $45,000 × 0.683013 = $30,735.61.
- Year 5. 1.105 = 1.61051, factor = 0.620921. PV = $50,000 × 0.620921 = $31,046.07.
- Add the present values. 27,272.73 + 28,925.62 + 30,052.59 + 30,735.61 + 31,046.07 = $148,032.61.
- Subtract the outlay. $148,032.61 − $100,000 = NPV of $48,032.61.
Two checks fall out of the same numbers. The undiscounted flows total $200,000, so discounting removed $51,967 of apparent profit — the cost of waiting. And the profitability index is $148,032.61 ÷ $100,000 = 1.4803, so every dollar committed comes back as $1.48 of present value. The rate at which NPV would cross zero is the internal rate of return, 25.75% here; the gap to the 10% hurdle is the project's margin of safety on the discount rate.
How to read the number you get
Read the sign first, then the size relative to the outlay, then the sensitivity.
The sign is the decision. Positive means accept, negative means reject, and there is no threshold beyond zero — NPV is already net of your required return, so a $500 NPV on a $10m project is technically an accept. In practice a result that close to zero is inside the noise of your own forecast and should be treated as a coin flip, not a green light.
The size only means something relative to the money at risk. Use the profitability index for that. A PI of 1.48 is strong; 1.05 is marginal; below 1.00 the project destroys value. When you are choosing among projects that compete for the same limited budget, rank by PI and fill the budget from the top — that produces more total NPV than ranking by NPV when capital binds.
Sensitivity tells you how much to trust it. The NPV profile chart plots NPV against the discount rate. A steep profile means the answer is dominated by distant cash flows and is fragile to the rate you picked. Recompute at your hurdle rate ±3 percentage points and shave 20% off the last two forecast years; if NPV survives both, the accept decision is robust.
Two figures deserve equal weight next to NPV. The internal rate of return converts the surplus into a rate, which is easier to compare against a hurdle. The discounted payback period tells you how long your capital is exposed before it is recovered in present-value terms.
Present value of $1 received in period t
| Period | 5% | 8% | 10% | 12% | 15% |
|---|---|---|---|---|---|
| 1 | 0.9524 | 0.9259 | 0.9091 | 0.8929 | 0.8696 |
| 2 | 0.9070 | 0.8573 | 0.8264 | 0.7972 | 0.7561 |
| 3 | 0.8638 | 0.7938 | 0.7513 | 0.7118 | 0.6575 |
| 4 | 0.8227 | 0.7350 | 0.6830 | 0.6355 | 0.5718 |
| 5 | 0.7835 | 0.6806 | 0.6209 | 0.5674 | 0.4972 |
| 10 | 0.6139 | 0.4632 | 0.3855 | 0.3220 | 0.2472 |
| 15 | 0.4810 | 0.3152 | 0.2394 | 0.1827 | 0.1229 |
| 20 | 0.3769 | 0.2145 | 0.1486 | 0.1037 | 0.0611 |
Each factor is (1 + r)⁻ᵗ, rounded to four places. Notice the 20-year row: at 15% a dollar two decades out is worth six cents, which is why long-dated forecasts contribute almost nothing to NPV at high discount rates.
Where the discount rate comes from
For a project with the same risk as the firm's existing business, use the after-tax weighted average cost of capital. For a project that is riskier or safer than the firm, use the WACC of a pure-play comparable — unlever its beta, relever at your own capital structure, and rebuild the rate. Never use the interest rate on the loan that happens to fund the project.
Public-sector work in the United States follows OMB Circular A-94, which prescribes the discount rates for federal benefit-cost analysis and requires real rates applied to real cash flows. Whatever rate you pick, keep it consistent with the flows: nominal with nominal, real with real.
Mistakes that make an NPV wrong
- Discounting profit instead of cash. Net income contains depreciation, accruals and non-cash charges. Convert to free cash flow first: after-tax operating profit, plus depreciation, minus capital expenditure, minus the increase in working capital.
- Subtracting interest from the cash flows. The discount rate already prices financing. Charging interest as well double-counts the cost of capital and understates NPV.
- Mixing nominal and real. A 10% nominal rate applied to cash flows held flat in today's prices silently assumes zero inflation and biases every long-dated project toward rejection.
- Including sunk costs, or ignoring working-capital release. The feasibility study you already paid for is irrelevant; only incremental future cash matters. But inventory and receivables tied up at the start do come back at the end, so put that recovery in the final period.
- Truncating the forecast without a terminal value. Stopping at year five implicitly assumes the asset is worthless afterwards. Either add salvage value or extend the horizon.
- Reading NPV as a return. It is a dollar amount, not a rate, and it scales with project size. Compare projects of different sizes on profitability index, never on raw NPV.
NPV against IRR, payback and the profitability index
Every alternative rule is a shortcut that fails in an identifiable way, and knowing the failure mode tells you when the shortcut is safe.
IRR answers the same question as a rate rather than a dollar amount, which makes it far easier to communicate. It matches NPV's verdict for a conventional stream — one outflow followed by inflows. It breaks in three cases: streams that change sign more than once can have several IRRs or none; ranking mutually exclusive projects by IRR can pick the smaller one; and IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself. The MIRR fixes that last assumption explicitly.
Payback ignores the time value of money and everything after recovery, so it is a liquidity screen rather than a value measure. It still earns its place: just over half the CFOs in Graham and Harvey's survey of corporate practice reported using it. Use the payback period calculator for the raw version.
Profitability index is NPV per dollar of outlay. It is the right ranking tool under capital rationing and gives the same accept/reject answer as NPV for a standalone project, because PI > 1 and NPV > 0 are the same statement.
Most finance teams settle on the same protocol: compute NPV as the decision, quote IRR as the headline, check payback as a risk screen, rank by profitability index when the budget binds. When cash flows arrive on irregular calendar dates, switch to a date-aware method such as XIRR rather than forcing them into equal periods.
Key terms
- Discount factor
- The present value of $1 received in period t, equal to (1 + r)−t. Multiply a cash flow by it to move the money back to today.
- Free cash flow
- Cash available to all investors after taxes and reinvestment: after-tax operating profit plus depreciation, less capital expenditure and less the increase in working capital. This is what belongs in an NPV, not net income.
- Hurdle rate
- The minimum return a project must earn to be funded. Usually the cost of capital, sometimes the cost of capital plus a management premium for optimism in the forecasts.
- Profitability index
- Present value of the inflows divided by the initial outlay, equal to 1 + NPV ÷ C₀. Ranks projects by value created per dollar committed.
- NPV profile
- A plot of NPV against the discount rate. Its intercept on the horizontal axis is the IRR, and its steepness shows how sensitive the project is to the rate you assume.