Business studies
Net present value and internal rate of return calculator
Type the project's cash flows, from the initial outlay to each year's returns, and the discount rate: get the NPV, the IRR, the payback period and a chart of NPV against the rate.
NPV and IRR: how an investment is appraised
Money today is worth more than the same money in five years, because meanwhile it could earn something. NPV takes that into account: it brings every future flow back to today's value by dividing it by (1 + rate) to the power of the years to wait, and adds everything up. If the result is positive, the project earns more than the required rate.
IRR is the rate that makes NPV exactly zero: the project's implied return. It is compared with the cost of capital; if it is higher, the project is worth doing. With the example flows, 10,000 invested and 3,000, 3,500, 4,000 and 4,000 back, the NPV at 8% is about 1,894 and the IRR about 15.8%.
The payback period says when the money comes back, here after 2.9 years. It is intuitive but ignores the time value of money and later flows; the discounted version fixes the first flaw. To choose between alternative projects, NPV remains the most reliable criterion.
Common mistakes
- Forgetting the sign of the initial investment: without the minus, NPV always comes out positive.
- Choosing between two projects on IRR alone: a small project with a high IRR can create less value than a large one.
- Using IRR when flows change sign more than once: there can be several solutions, none with a clear economic meaning.
Frequently asked questions
Which discount rate should I use?
The return you could get from an investment of similar risk, or the company's weighted average cost of capital (WACC). For an individual, often a government bond yield plus a risk premium.
What is the difference between NPV and IRR?
NPV measures how much wealth the project creates, in today's money. IRR measures its return, as a percentage. They usually point to the same decision, but when they disagree NPV is the one to trust.
What is the profitability index?
The ratio between the present value of inflows and that of outflows. Above 1 the project creates value; it is used to rank projects when capital is limited.
How this calculation works
NPV = Σ Fₜ / (1 + i)^t for t from 0 to n, with Fₜ the flow of period t and i the rate. IRR: the rate r for which Σ Fₜ / (1 + r)^t = 0, found by bisection on every sign change. Payback: the period in which the cumulative flow turns non-negative, linearly interpolated. Profitability index = present value of inflows ÷ present value of outflows.