# NPV and IRR NPV and IRR are two decision rules from discounted cash flow: the value an investment adds today, and the return at which it breaks even. **The question.** Does this investment add value today at our cost of capital, and does its return clear the hurdle? Also known as: Net present value and internal rate of return. The pair are the usual capital-budgeting rules. ## When to use it - A client is choosing whether to fund a plant, a system, or a product line, and the case is still being made on payback or on an accounting rate of return. - Two mutually exclusive options, such as a large upgrade and a small one, both look attractive, and IRR and NPV may not pick the same one. - A hurdle rate is applied as a yes-or-no on IRR, and nobody has shown the value in money that would be added or given up. - Capital is rationed this year and you need a way to rank projects that does not just sort them by IRR. ## When to avoid it - You are valuing the whole firm. That is a DCF of free cash flow, with a terminal value. This note is the project decision, with a defined life. - There is no basis for a cash forecast. IRR on a made-up series is a made-up rate, and a range of scenarios is more honest. - Cash flows change sign more than once, so several IRRs exist. Quote NPV, or use a modified IRR, and do not pretend there is one rate. - The choice is how to fund the project. NPV and IRR take the mix of capital as given, through the hurdle. They do not say debt or equity. ## Overview NPV and IRR are the two standard decision rules drawn from discounted cash flow. NPV is the value an investment adds today, after discounting its cash at the cost of capital. IRR is the return at which that value is zero. For an independent project with a conventional cash-flow pattern, they agree: take it if NPV is positive, which is IRR above the hurdle. The choice they support is go, stop, or which of two options to take. When the options are mutually exclusive, rank them by NPV. IRR is a rate and will prefer a smaller project that adds less value. Report both, and keep the money figure as the decision. Several sign changes in the cash, a hurdle that does not match the risk, and a single-point forecast are the usual ways the pair is misused. ## The two rules ### Net present value The present value of the project's cash inflows minus the present value of its outflows, discounted at the cost of capital. A positive NPV is value the investment adds today, in money. Independent projects with NPV above zero are accepted. Mutually exclusive ones are ranked by NPV, not by the size of the IRR. ### Internal rate of return The discount rate that sets NPV to zero. It is the break-even return of the project. For a conventional cash-flow pattern, one outlay then inflows, accept if IRR exceeds the hurdle. It is a rate, so it is easy to compare with a cost of capital, and it hides scale. A small project can show a high IRR and add little value. ### The hurdle The discount rate in NPV, and the benchmark for IRR. For average-risk projects it is WACC. For a project with different risk, use a rate that matches that risk. Using the firm's WACC on a riskier bet is how capital drifts to the worst projects. ### Where the rules conflict Mutually exclusive projects can rank differently when they differ in size or in when the cash arrives. NPV measures value and is the rule to keep. IRR remains useful as a communication of the implied return, shown next to NPV, not instead of it. Payback is a liquidity screen, not a third value rule. ## What it is not - A valuation of the company. There is no terminal value here unless the project still has one. Firm DCF is a different note. - A rate you can maximize. Ranking by IRR prefers small, fast projects and can reject a larger one that adds more value. ## The steps 1. **Write the decision and the alternatives.** State what is being chosen, including the do-nothing case, the horizon, and whether the options can both be done. Mutually exclusive and independent projects are ranked differently. 2. **Forecast incremental cash.** Build cash flows from the decision, after tax, with capital spending and working capital. Count only what changes if the project is done. Leave allocated overhead out unless it is incremental. 3. **Set the hurdle.** Take a rate that matches the risk of these cash flows, from the WACC note if the risk is the firm's average. Keep the range, because it will move NPV. 4. **Compute NPV and IRR together.** Discount at the hurdle to get NPV. Solve for IRR. For a conventional pattern, check that they agree on accept or reject. For mutually exclusive options, rank on NPV. If cash flow changes sign more than once, do not report a single IRR. 5. **Show the range and the conflict, if any.** Recompute NPV at the ends of the hurdle range, and at volumes or prices that could fail. If IRR and NPV rank two options differently, state both ranks and take NPV. The output is an accept, reject, or choose-A, with the value in money. ## The formula NPV = CF0 + CF1/(1+r) + CF2/(1+r)^2 + ... + CFN/(1+r)^N. IRR is the rate r* such that NPV(r*) = 0. NPV is each year's cash divided by one plus the discount rate, raised to the year, including the initial outlay as a negative CF0. IRR is the discount rate that makes that sum zero. Accept an independent project if NPV is positive, which for a conventional pattern is the same as IRR above the hurdle. - CFt: incremental cash flow in year t, after tax, including capital spending and the release of working capital at the end. CF0 is usually the initial outlay and is negative. - r: the discount rate, the cost of capital that matches the risk of these cash flows, often WACC. - N: the last year of the project. Do not add a growing perpetuity unless the project actually has one. - IRR: solved from NPV = 0. Spreadsheet IRR routines assume equally spaced periods and can miss multiple roots if the sign of cash flow flips more than once. - Decision: independent project, accept if NPV > 0. Mutually exclusive, choose the higher NPV. Capital rationing, rank by NPV per dollar invested, not by IRR. ## In practice Two mutually exclusive upgrades. The large one costs $10 million now and is expected to produce free cash flow of $2.5, $3.0, $3.0, $3.0, and $3.5 million over five years, then nothing. WACC is 10 percent. Discounted inflows are 2.273 + 2.479 + 2.254 + 2.049 + 2.173 = $11.228 million. NPV = 11.228 − 10 = +$1.23 million. IRR is about 14.5 percent, above the 10 percent hurdle. On its own, the large project clears both rules. The small one costs $2 million and produces $0.9 million a year for four years. Present value of that annuity at 10 percent is 0.9 × 3.170 = $2.853 million. NPV = 2.853 − 2 = +$0.85 million. IRR is about 28 percent. IRR ranks the small project first, 28 percent against 14.5 percent. NPV ranks the large one first, $1.23 million against $0.85 million. They cannot both be done. The value added is $1.23 million on the large upgrade, so that is the choice. Reporting only IRR would have funded the smaller one and left about $0.38 million of value on the table. If capital is limited to $2 million, the small one is then the project that fits, which is a budget constraint, not an IRR result. ## What you leave with - NPV at the chosen hurdle, and at a rate a point above and below. - IRR, with a note if the cash-flow pattern could produce more than one. - The ranking of mutually exclusive options by NPV, with IRR shown beside it. - Incremental cash flows, with each operating assumption and its evidence. - A short list of the assumptions that would flip the sign of NPV. ## Failure points ### Ranking by IRR Capital goes to small, fast projects. A larger project with a lower IRR and a higher NPV is rejected, as in the example, and value is left unbuilt. ### The firm's WACC on a different risk A riskier project clears a hurdle that is too low, and a safer one is rejected. Same error as in the WACC note, applied one project at a time. ### Several IRRs ignored An outlay in a later year, such as decommissioning, flips the sign of cash flow twice. The spreadsheet still returns one rate, and the accept-or-reject reading is arbitrary. ### Payback as the decision A two-year payback rule kills a four-year project with a large NPV, or accepts a quick project with a negative NPV. Payback can screen liquidity. It cannot measure value. ### A single-point cash forecast One case is discounted and presented as the answer. Volume and price are uncertain, and a modest miss flips the sign. Show the cases that still pay and the ones that do not. The failures above are usually [Commercial Acumen](https://usefulconsultingframeworks.com/your-edge/#commercial): the work was not tied to money, for the client and/or for you. ## Origin The present-value arithmetic is the same as in a discounted-cash-flow valuation of a firm. Irving Fisher's The Theory of Interest (1930) set out the comparison of investments by discounted cash, and the related "rate of return over cost." John Burr Williams applied present value to shares in 1938. What this note covers is the project form: accept an independent investment if the present value of its cash inflows exceeds the outlay, or if the rate that sets that net present value to zero exceeds the cost of capital. Joel Dean's Capital Budgeting (Columbia University Press, 1951) is the book that put those two rules into corporate practice, alongside payback. Internal rate of return is also close to Keynes's marginal efficiency of capital. Later textbooks, especially Brealey and Myers, documented the cases where the two rules rank mutually exclusive projects differently, because of scale and the timing of cash, and treated NPV as the rule that matches value. WACC, or another hurdle that fits the risk of the cash flows, is the rate both rules need. See the DCF and WACC notes for how that rate is built. ## Further reading - [Net present value](https://en.wikipedia.org/wiki/Net_present_value). Wikipedia's overview of the NPV rule, the comparison with IRR, and the usual caveats, including mutually exclusive projects. Free. - [Internal rate of return](https://en.wikipedia.org/wiki/Internal_rate_of_return). Wikipedia's account of the definition, the accept rule, multiple roots, and why NPV is preferred when the two conflict. Free. ## Related frameworks - [Discounted Cash Flow](https://usefulconsultingframeworks.com/frameworks/dcf/): The same present-value arithmetic applied to a whole business, with a terminal value. Pick DCF to value the firm. Pick NPV and IRR to accept or reject a project. - [Weighted Average Cost of Capital](https://usefulconsultingframeworks.com/frameworks/wacc/): Supplies the hurdle for average-risk cash flows. Build it first, with its range, before running either rule. - [Economic Value Added](https://usefulconsultingframeworks.com/frameworks/eva/): Measures one year's profit after a capital charge. Pick it for ongoing performance. Pick NPV for the go or no-go on an investment. - [Break-Even and Contribution Margin](https://usefulconsultingframeworks.com/frameworks/break-even/): Finds the volume that covers operating fixed cost, with no cost of capital and no discounting. Use it as a first volume hurdle, then NPV for the investment that changes that cost base. - [Three Horizons of Growth](https://usefulconsultingframeworks.com/frameworks/three-horizons/): Sorts growth bets by how far they sit from the current business. Horizon 3 options often fail a short-horizon IRR. NPV with an honest risk-adjusted rate is the fairer screen, and some options should stay small on purpose. Last updated October 20, 2026.