Investment decisions
Net present value (NPV)
Decide whether a project creates value — and avoid the most common spreadsheet NPV mistake.
Learning objectives
- Calculate NPV from a cash-flow forecast
- Apply the NPV decision rule
- Use the NPV() function correctly with a time-0 investment
Net present value is the value a project adds today: the present value of everything it will pay you, minus what it costs. Discount at the return investors require for a project of that risk (the cost of capital).
- NPV > 0: the project earns more than the required return — it creates value.
- NPV < 0: you would do better investing elsewhere at the same risk.
NPV = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ
- CF₀
- today's cash flow — usually the negative investment
- CFₜ
- net cash flow at the end of year t
- r
- cost of capital
What NPV really measures. Imagine funding the project above with a 50,000 loan at 10% and using every inflow to pay it down. After year 1 you owe 35,000; after year 2, 13,500; the year 3 inflow then clears the loan and leaves 150 over. That surplus, discounted back three years, is the NPV of 112.70. A positive NPV means the project can repay all the capital and its required return, with something left for the owners; a negative NPV means it cannot.
What goes into the cash flows. Only incremental cash: the cash that changes because the project goes ahead. Money already spent (a feasibility study last year, a sunk cost) is left out because no decision can recover it. Interest payments are left out too, because the cost of financing is already charged through the discount rate; deducting interest as well would count it twice. And it is cash, not accounting profit: depreciation is not a cash flow, but the purchase of the equipment is.
A method you can follow: (1) lay out a timeline from year 0; (2) put each incremental cash flow in the year it happens, including investment, working capital and salvage value; (3) discount each year's net figure at the cost of capital; (4) add them up; (5) accept if the total is positive. When two projects compete for the same money, the one with the higher NPV adds more value. The next lesson asks the reverse question: at what rate would the NPV be exactly zero?
Calculate
You invest 1,000 today and receive 1,200 in 2 years. Nothing in between. At 8%, what is the NPV?
NPV of an equipment investment
The machine costs 250,000 today and generates the cash flows shown. In column C calculate each year's discount factor at the cost of capital in B1; in column D the present value; and in D10 the project's NPV. Any correct method for D10 earns full marks.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Cost of capital | 9.0% | ||
| 2 | ||||
| 3 | Year | Cash flow | Discount factor | Present value |
| 4 | 0 | (250,000.00) | ||
| 5 | 1 | 70,000.00 | ||
| 6 | 2 | 85,000.00 | ||
| 7 | 3 | 90,000.00 | ||
| 8 | 4 | 80,000.00 | ||
| 9 | ||||
| 10 | NPV |
Check your understanding
A project's NPV at a 9% cost of capital is +11,934. What does that tell you?
Getting the cash flows right
NPV is only as good as the cash flows that go in. Two items are easy to miss: working capital (inventory and receivables tied up to run the project, paid out at the start and released at the end) and salvage value (what the assets fetch when the project ends). Both are cash, so both belong on the timeline in the year they happen.
Calculate
A new product line needs 400,000 of equipment and 50,000 of working capital, both today. It generates 110,000 of cash a year for 5 years, and the working capital is recovered in full at the end of year 5. The cost of capital is 11%. What is the NPV?
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