What are IRR and NPV and how are they calculated?

IRR and NPV: what they are for

Before putting money into a project, a property to rent or a piece of equipment, the question is always the same: is it worth it? IRR (internal rate of return) and NPV (net present value) are the two numbers that answer it rigorously¹. Both start from the same information: the initial investment and the cash flows the investment generates over the years. You can work them out on our IRR & NPV calculator.

NPV brings the future back to today

A euro received in five years is worth less than a euro today: it could have been invested in the meantime. NPV corrects for this, bringing each cash flow back to today's value with a discount rate and subtracting the investment:

NPV = minus the investment, plus the sum of each cash flow divided by (1 + rate) to the power of the year

If the NPV is positive, the investment earns more than the required rate and creates value. If it is negative, it falls below that bar. It is the same logic as the compounding of compound interest, but in reverse: instead of projecting a value into the future, it brings future values into the present.

IRR is the project's annual return

The IRR is the discount rate that makes the NPV exactly zero. In other words, it is the implied annual return of the investment. The decision rule is direct:

It is worth it when the IRR is higher than the discount rate (your cost of capital).

There is no closed formula for IRR: you search for the rate that zeroes the NPV by trial and error, something the calculator does for you. When the IRR is higher than the discount rate, the NPV is positive, the two numbers agree.

Payback and ROI: the complements

Two simpler numbers go alongside the analysis:

Payback is intuitive (how long until "I get back what I put in"), but it does not count what happens afterwards nor the time value of money. ROI (return on investment) measures the size of the gain, but a 50% ROI can be excellent over 2 years and mediocre over 20. That is why NPV and IRR are the main criteria and these two are the complement.

Worked example

Imagine a 10,000 € investment that generates 3,000 € a year for 5 years, with a discount rate of 5%:

• sum of cash flows = 5 × 3,000 = 15,000 €, so the total ROI = (15,000 − 10,000) ÷ 10,000 = 50%;
• bringing each 3,000 € back to today at 5%, the NPV = 2,988 € (positive, creates value);
• the IRR is about 15.2%, well above the 5% required, so it pays off;
• the payback is 3.3 years (the 10,000 € is recovered after three years and a third).

Because the IRR (15.2%) is well above the discount rate (5%), the NPV is positive and the investment creates value. See how it changes when you alter the cash flows or the rate on the IRR & NPV calculator.

The discount rate is your choice

The discount rate is not in the law: it is your cost of capital or the minimum return you require of the money. You can use the return of a safe alternative (a term deposit, savings certificates) or the cost of your financing. The higher the rate, the more demanding the calculation and the lower the NPV, so the choice of rate is decisive.

What this analysis does not include

The calculation assumes yearly, net, nominal cash flows. It does not handle taxation (income or corporate tax on the profit), nor inflation eroding the real value, nor a residual value at the end (selling the asset), nor the modified IRR (MIRR) used when intermediate flows are reinvested at another rate. To compare in real terms, use inflation-adjusted cash flows and a real discount rate too. Use the estimate to decide with confidence and confirm the figures with your accountant or adviser.