NPV, IRR and payback
Investment appraisal turns a stream of future cash flows into a decision. The net present value is NPV = Σ CFₜ / (1 + r)ᵗ − C₀: discount every future cash flow to today and subtract the initial outlay. A positive NPV means the project adds value at the required return r. The internal rate of return is the discount rate that makes NPV = 0, and the payback is how long the cash flows take to recover the investment.
Why discount cash flows
A dollar today is worth more than a dollar next year, because it can be invested — the time value of money. The discount rate r captures the opportunity cost of capital and the project's risk; a higher rate weighs distant cash flows less. Discounting is what lets you compare projects with different timing on the same footing.
How to use the calculator
List the cash flows (a negative initial investment followed by the returns), set the discount rate, and read the NPV, the IRR and both payback measures. Comparing NPV across mutually exclusive projects tells you which one creates the most value.
Note: IRR can be unreliable when cash flows change sign more than once (a project can then have several IRRs or none) and it implicitly assumes reinvestment at the IRR itself. When NPV and IRR disagree on ranking, corporate-finance texts recommend NPV.
Frequently asked questions
What is net present value (NPV)?
NPV is the sum of a project's future cash flows each discounted to today, minus the initial investment: NPV = sum(CF_t / (1+r)^t) - C0. A positive NPV means the project is expected to add value at the discount rate r.
What is the internal rate of return (IRR)?
The IRR is the discount rate at which a project's NPV equals zero. A project is generally attractive if its IRR exceeds the required rate of return (the cost of capital).
What is the payback period?
The payback period is the time it takes for cumulative cash flows to recover the initial investment. The discounted payback uses discounted cash flows, so it is always at least as long as the simple payback.
Should I use NPV or IRR?
Both are useful, but when they rank projects differently, finance theory favors NPV because it measures value added directly and avoids IRR's problems with non-conventional cash flows and reinvestment assumptions.
References
- R. A. Brealey, S. C. Myers & F. Allen, Principles of Corporate Finance (McGraw-Hill) — NPV, IRR and capital budgeting.
- S. A. Ross, R. W. Westerfield & J. Jaffe, Corporate Finance (McGraw-Hill).
- The time value of money and discounting: present value PV = CF / (1 + r)^t.