Investment Appraisal
Is a project worth its price? Enter what you pay now and what it brings in each year, and see the three classic answers side by side: the net present value (how much richer it makes you in today’s money), the internal rate of return (the yearly return the project earns on its own) and the payback period (how long until your money is back).
How is an Investment Judged?
Money now is worth more than the same amount later, because money now can earn a return in the meantime. At 8% a year, 1 080 next year is worth 1 000 today. Discounting turns every future cash flow into its value today. The net present value is the sum of those values minus what you pay now: if it is positive, the project beats the return you could get elsewhere, and makes you richer by exactly that amount.
The higher the discount rate, the lower the NPV. At one rate it is exactly zero: the internal rate of return, the yearly return the project itself earns. Accept when it is above the return you require. If the cash flows change sign more than once there can be several IRRs, or none; the modified IRR always gives one answer by reinvesting at the required return.
The payback period is the time until the cash coming in adds up to the investment: a quick measure of risk. The discounted payback counts in today’s money and is always a little longer. Both ignore everything after the payback moment, so use them next to the NPV, not instead of it.
Cash Flows and Money Back Over Time
NPVNPV at Every Discount Rate
IRRYear by Year
| Year | Cash flow | Cash so far | Discount factor | Value today | In today’s money so far |
|---|
Worked Techniques
When the project brings in the same amount every year, one formula (the annuity) replaces the whole sum.
There is no formula for the IRR: try rates until the NPV is zero. This page scans every rate from −99% to 1000% and narrows each crossing down, so it finds all IRRs. Out, in and out again (−1600, +10 000, −10 000) gives two: 25% and 400%.
Add up the cash year by year. In the year it passes the investment, take the part of that year that was still needed. Do the same in today’s money for the discounted payback.
Sources & Verification
- R. A. Brealey, S. C. Myers & F. Allen, Principles of Corporate Finance, 13th ed., McGraw-Hill Education, 2020 — Ch. 2 (How to Calculate Present Values) and Ch. 5 (Net Present Value and Other Investment Criteria: the IRR rule, its pitfalls, and the payback rule).
- J. Berk & P. DeMarzo, Corporate Finance, 5th ed., Pearson, 2020 — Ch. 4 (The Time Value of Money) and Ch. 7 (Investment Decision Rules: multiple IRRs, the modified IRR and payback).