NPV, IRR and payback
Discount a five-year cash-flow forecast back to today, solve the internal rate of return, and see exactly where the project pays back its initial outlay. Every result recalculates locally as you move the inputs.
| Year | Cash flow | Discount factor | Present value | Cumulative PV |
|---|---|---|---|---|
| Year 0 | -$100,000 | 1.0000 | -$100,000 | -$100,000 |
| Y1 | $30,000 | 0.9091 | $27,273 | -$72,727 |
| Y2 | $35,000 | 0.8264 | $28,926 | -$43,802 |
| Y3 | $40,000 | 0.7513 | $30,053 | -$13,749 |
| Y4 | $45,000 | 0.6830 | $30,736 | +$16,987 |
| Y5 | $50,000 | 0.6209 | $31,046 | +$48,033 |
Cash flows are treated as end-of-year. The salvage or terminal value is added to the final year.
NPV = −C₀ + Σ CFₜ / (1+r)ᵗ · summed over t = 1…T
0 = −C₀ + Σ CFₜ / (1+IRR)ᵗ · the rate that zeroes NPV
PI = PV(inflows) / C₀ · accept when PI > 1
DPB = t* + |cumPVₜ*| / PVₜ*₊₁ · interpolated at the first sign change
A clear path from inputs to results.
Net present value asks a single question: after paying for the project and waiting for its cash flows, are you better off in today’s money? This engine discounts each forecast year at your hurdle rate, solves the internal rate of return on the same flow vector, and shows the sensitivity of the answer to both the discount rate and the cash-flow forecast.
How to use
- Enter the initial outlay — the cash committed at time zero, before any inflows arrive.
- Set the discount rate. This is your hurdle rate: the return the project must beat to be worth doing.
- Fill in the five annual net cash flows. Negative years are allowed, which is how ramp-up costs are modelled.
- Add a salvage or terminal value if the asset has residual worth at the end of year five.
- Read the verdict from the NPV sign, then check the IRR against your hurdle rate. They agree for conventional cash flows.
- Use the sensitivity grid to see how much forecast error the decision can absorb before NPV turns negative.
The formula
Reference: Brealey, Myers & Allen, "Principles of Corporate Finance", ch. 5–6; Graham & Harvey (2001) survey of CFO hurdle-rate practice.
Worked example
Five-year project, 10% hurdle rate (default inputs)
- Initial outlay $100,000 at t = 0.
- Discount rate 10% per year.
- Cash flows: $30,000, $35,000, $40,000, $45,000, $50,000 for years one to five.
- No salvage value.
- 1
Discount each year: 30,000/1.10 = 27,273; 35,000/1.21 = 28,926; 40,000/1.331 = 30,053; 45,000/1.4641 = 30,736; 50,000/1.61051 = 31,046.
- 2
Sum the present values to get $148,033 of discounted inflows.
- 3
Subtract the outlay: 148,033 − 100,000 = $48,033 of net present value.
- 4
Solve for the rate that zeroes that expression. Bisection converges on 25.75%.
- 5
Divide inflows by outlay for the profitability index: 148,033 / 100,000 = 1.48.
NPV $48,033 · IRR 25.75% · PI 1.48 · the project clears a 10% hurdle with 15.75 points of spread.
Interpreting the result
A positive NPV means the project adds value at your hurdle rate; the size of the number is the value added in today’s money. The IRR restates the same fact as a rate, which is easier to compare against borrowing costs but misleading when cash flows change sign more than once. The profitability index is the ratio version, useful when capital is rationed and you must rank projects of different sizes.
Assumptions & limitations
- A single constant discount rate applies to every year. Projects with time-varying risk need a term structure of rates.
- Cash flows arrive at year end. Mid-year convention would raise the NPV slightly.
- The forecast flows are point estimates. The sensitivity grid exists because they are not.
- Conventional cash flows (one sign change) guarantee a unique IRR. Multiple sign changes can produce multiple roots.
- No taxes, financing costs or working-capital effects are modelled separately; fold them into the cash flows if they matter.
Frequently asked questions
What discount rate should I use?
The rate should reflect the risk of the cash flows, not the cost of the money. A company typically uses its WACC for average-risk projects and a higher rate for ventures riskier than the existing business. Using the borrowing rate understates risk and overstates NPV.
Is a higher IRR always better?
No. A small project can have a spectacular IRR and add little value, while a large project with a modest IRR adds far more. IRR also breaks down when cash flows alternate sign, producing more than one mathematically valid answer.
How should salvage value be treated?
Add it to the final year’s cash flow before discounting. If the salvage is uncertain, run the sensitivity grid with and without it — a large terminal value is often doing most of the work in a marginal NPV.
Why do NPV and IRR sometimes disagree?
They disagree when projects differ in scale or timing. NPV measures absolute value added, IRR measures the percentage return on the outlay. When ranking mutually exclusive projects, NPV is the correct criterion because it is additive across projects.
What does the profitability index tell me?
It is value per dollar invested. A PI of 1.48 means each dollar of outlay returns $1.48 of present value. It is the right ranking tool when you have more acceptable projects than capital to fund them.
Does this model handle taxes?
Not separately. Enter after-tax cash flows if you want an after-tax answer, and use an after-tax discount rate. Depreciation tax shields belong in the annual flows, not in the discount rate.
Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.