NPV and IRR calculator

How this NPV and IRR calculator works

A project is worth doing if the cash it brings in is worth more than the cash it costs, once you allow for the fact that money received later is worth less than money in hand today. This calculator builds the project's cash flow after tax for every year and then measures it in four ways.

1. Build the cash flow for each year

Depreciation is not cash, so it is added back. It still matters, because it reduces the tax bill.

2. Net present value (NPV)

Each year's cash flow is divided by (1 + hurdle rate) raised to the number of years away it is, and the results are added up, including the investment made today. NPV is the value the project adds, in today's money, over and above the return the hurdle rate demands. Above zero, the project earns more than the hurdle rate; below zero, it earns less.

3. Internal rate of return (IRR)

IRR is the discount rate at which NPV is exactly zero: the yearly return the project itself earns on the money tied up in it. If the IRR is above the hurdle rate, NPV is positive, and the other way round.

4. Payback and profitability index

Payback is the time the project takes to earn back what was put into it. Discounted payback asks the same question after discounting each year's cash. The profitability index is the present value of all the cash flows after today divided by the amount spent today; above 1.00 means NPV is positive.

When NPV and IRR disagree

For a single project with one outlay followed by inflows, NPV and IRR give the same yes or no. They can disagree when you compare projects, and IRR can break down altogether.

• Scale. IRR is a percentage, so it ignores size. Turning 100 into 150 in a year is an IRR of 50% and, at a 10% hurdle rate, an NPV of about 36. Turning 10,000 into 12,000 is an IRR of only 20% but an NPV of about 909. If you can do only one, the second adds far more value.
• Timing. IRR rewards getting money back quickly. NPV at a low hurdle rate gives more weight to larger cash flows that arrive later. Two projects can therefore rank one way on IRR and the other way on NPV, and the NPV ranking can flip as the hurdle rate changes.
• Several IRRs, or none. If the cash flows change direction more than once, for example an outlay, then income, then a clean-up cost at the end, NPV can be zero at more than one rate. Paying 1,000 today, receiving 2,500 in a year and paying 1,540 a year later has two IRRs: 10% and 40%. Neither is "the" return. This calculator looks for every such rate and, when there are several or none, says so instead of picking one.

When the two disagree, go with NPV: it measures value added in money, which is what the decision is about.

Why payback on its own misleads

Payback ignores everything that happens after the payback date. A project that returns its cost in two years and then stops looks identical to one that returns its cost in two years and keeps earning for another eight. Plain payback also treats cash received in year 3 as equal to cash received today. Discounted payback fixes the second problem but not the first. Use payback as a measure of how long your money is at risk, not as a measure of whether the project is worth doing.

What the calculator assumes

• After tax. Tax is charged on operating profit each year and paid in the same year. A year with a loss gives a tax saving in that year, which assumes the company has other profits to set the loss against.
• No interest. Cash flows are before interest and loan repayments, because the cost of finance is already in the hurdle rate.
• Straight-line depreciation. The initial investment is written off in equal amounts over the project life, down to zero. When the assets are sold at the end, the whole salvage value is therefore a taxable gain.
• Working capital comes back. The money tied up in stock and unpaid invoices is set aside a year ahead of the sales it supports, grows with revenue, and is released in full at the end of the last year. It costs the project only the time the money was tied up.
• Year-end cash flows. Each year's cash is treated as arriving at the end of that year, the same convention as the NPV and IRR functions in a spreadsheet.
• No inflation adjustment. Enter the cash flows and the hurdle rate on the same basis: both including inflation, or both excluding it.

Common questions

What hurdle rate should I use?

The return investors could expect elsewhere for the same risk. For a project of average risk for the company, that is usually its weighted average cost of capital (WACC): the blended return its lenders and shareholders require. Use a higher rate for a riskier project. The calculator raises a flag below 5% and above 25%.

Should I deduct interest or loan repayments from the cash flows?

No. The cost of financing the project is already in the hurdle rate. Deducting interest from the cash flows as well would count it twice and make a good project look worse than it is.

Should the figures include inflation?

Either way works, but be consistent. If revenue and costs include price rises, use a hurdle rate that includes inflation, which is how rates are normally quoted. If the figures are in today's prices, use a rate with inflation taken out. Mixing the two is one of the most common errors in project appraisal.

What does it leave out?

Further capital spending after the start, a depreciation period different from the project life, tax rules that let an asset be written off faster than straight line, tax paid a year in arrears, and the case where a loss cannot be used against other profits. The signed-in version covers later capital spending, a separate depreciation period, losses that can only be carried forward, and cash arriving through the year rather than at the end of it.