Time value of money: NPV, IRR and payback for investment decisions

Should you buy the new machine, open the second site, or build the software tool that saves your team ten hours a week? Each of these means spending money now in return for cash or savings later. The question is whether the later money is worth more than the money you give up today.

Three methods answer that question: net present value (NPV), internal rate of return (IRR) and payback. They all start from the same idea, the time value of money, but they answer slightly different questions. This guide explains each one, works through an example, and shows which to trust when they disagree.

Why a pound today is worth more than a pound later

Money you have now can be put to work. You could pay down a loan, invest in stock that sells at a profit, or simply hold it in a savings account. Money promised in three years cannot do any of that until it arrives, and there is always some risk it will not arrive in full.

So future cash has to be discounted to compare it fairly with cash today. The present value of a future amount is that amount divided by (1 + r) raised to the power of the number of years, where r is the discount rate. At 10%, £1,100 in one year has a present value of £1,000. £1,000 in five years has a present value of about £621.

The discount rate is the return you require for taking on the investment. Companies often use their weighted average cost of capital (the blended cost of their debt and equity). A small business might use its borrowing rate plus a margin for risk, or the return it could get from its next best use of the money. Riskier projects deserve a higher rate.

Net present value

NPV adds up the present value of every cash flow from a project, including the upfront cost as a negative number.

• NPV above zero: the project earns more than your required return and adds value.
• NPV below zero: it earns less than your required return and destroys value.
• NPV of zero: it earns exactly your required return.

NPV gives an answer in pounds, which makes it easy to compare projects and to add them up. Its main weakness is that the result depends heavily on your cash flow estimates and the discount rate you choose.

Internal rate of return

IRR is the discount rate that makes NPV exactly zero. Think of it as the project’s own annual rate of return. If the IRR is higher than your required return (often called the hurdle rate), the project passes.

IRR is popular because a percentage is easy to communicate. It has known traps, though:

• It ignores scale. A small project with a high IRR can add less value in pounds than a large project with a lower IRR.
• If cash flows switch between negative and positive more than once (for example, a large clean-up cost at the end), there can be more than one IRR, or none.
• It is often criticised for assuming interim cash can be reinvested at the IRR itself, which can flatter high-return projects. The modified IRR (MIRR) uses your cost of capital for reinvestment instead.

For a single, conventional project (one outflow followed by inflows), IRR and NPV give the same accept or reject answer. When you must choose between projects, they can disagree, and NPV is the better guide to total value.

Payback period

Payback is the time it takes to get your money back. If you spend £30,000 and the project returns £9,000 a year, payback is £30,000 divided by £9,000, or 3.3 years.

Payback is simple and speaks directly to risk and cash: the shorter it is, the sooner your money is free again. But it ignores the time value of money and everything that happens after the payback date. A project that pays back in two years and then stops can look better than one that pays back in three years and then earns for a decade. The discounted payback period fixes the first problem by using present values, but not the second.

A worked example

An example (illustration only): a small food producer is considering a packing machine for £30,000. It would save £9,000 a year in labour for five years, with no resale value at the end. The owner uses a 10% discount rate.

• NPV: about £4,117, so the machine beats the 10% required return.
• IRR: about 15.2%, comfortably above the 10% hurdle.
• Simple payback: 3.3 years.
• Discounted payback: about 4.3 years.

Now a second option: a smaller machine costing £12,000 that saves £4,500 a year for four years. Its NPV at 10% is about £2,264 and its IRR is about 18.5%. By IRR, the small machine wins. By NPV, the large one adds nearly twice as much value. If the business can only afford one and the money has no better use, the large machine is the better choice, because NPV measures value in pounds.

How to run the numbers yourself

1. List the upfront cost, including installation, training and any extra stock or working capital the project needs.
2. Estimate the extra cash the project brings in or saves each year. Use cash, not accounting profit, and leave out depreciation.
3. Include the end: resale value, clean-up or replacement costs.
4. Pick a discount rate that reflects your cost of funding and the project’s risk.
5. Use a spreadsheet: NPV and IRR functions handle the arithmetic. In Excel, the NPV function treats the first value as one period away, so add the year 0 cost separately, or use XNPV and XIRR for irregular dates.
6. Test the result. Change the savings by 20% and the rate by a few points, and see whether the decision still holds.

Common mistakes and when to use each method

• Using profit instead of cash. Depreciation is not a cash cost, and timing of receipts matters.
• Forgetting working capital. A new product line may tie up cash in stock and customer debts.
• Choosing the discount rate after seeing the answer. Set it first.
• Ranking projects by IRR alone. Check NPV when projects differ in size or length.
• Trusting one number. Every method depends on forecasts, so show a range.

Use NPV as your main decision tool, since it measures value directly. Use IRR as a cross-check and a way to communicate returns. Use payback when cash is tight or the future is very uncertain, as a measure of how long your money is at risk. For small, routine purchases, payback alone is often enough. For anything large or long-lived, run all three and let NPV have the final say.