What capital budgeting is and the four methods
A capital budgeting decision commits money now in return for cash flows over several years: a new machine, a store, a software system. The question is whether the future cash flows justify the cost. Because the cash flows arrive at different times, you need time value of money (see our guide on time value of money) to compare them.
| Method | What it measures | Decision rule | Main weakness |
|---|---|---|---|
| Net present value (NPV) | Value added in today's dollars | Accept if NPV is above zero | Needs a discount rate; gives a dollar figure, not a rate |
| Internal rate of return (IRR) | The project's own annual return | Accept if IRR is above the required return | Can mislead with unusual cash flows or when ranking projects |
| Payback period | Years to recover the investment | Accept if shorter than a cutoff | Ignores timing within the period and cash flows after payback |
| Discounted payback | Years to recover the investment in present-value terms | Accept if shorter than a cutoff | Still ignores later cash flows |
| Profitability index | Present value per dollar invested | Accept if above 1.0 | Can mislead when projects differ in scale |
A worked project
A company can invest $100,000 in new equipment. It expects cash inflows of $30,000, $35,000, $40,000 and $45,000 over the next four years. The required return is 10 percent. All figures are hypothetical.
| Year | Cash flow | Discount factor at 10 percent | Present value | Cumulative cash flow | Cumulative present value |
|---|---|---|---|---|---|
| 0 | -100,000 | 1.0000 | -100,000.00 | -100,000 | -100,000.00 |
| 1 | 30,000 | 0.9091 | 27,272.73 | -70,000 | -72,727.27 |
| 2 | 35,000 | 0.8264 | 28,925.62 | -35,000 | -43,801.65 |
| 3 | 40,000 | 0.7513 | 30,052.59 | 5,000 | -13,749.06 |
| 4 | 45,000 | 0.6830 | 30,735.60 | 50,000 | 16,986.54 |
NPV is the sum of the present values including the initial outlay: 27,272.73 + 28,925.62 + 30,052.59 + 30,735.60 - 100,000 = $16,986.54. It is positive, so the project adds value at a 10 percent required return.
Profitability index is 116,986.54 divided by 100,000, which is 1.17. It earns $1.17 of present value for every $1 invested.
Payback: cumulative cash flow turns positive during year 3. After two years, 65,000 has been recovered, leaving 35,000 to recover from year 3's 40,000. Payback is 2 + 35/40 = 2.88 years.
Discounted payback: cumulative present value turns positive during year 4. After three years, 86,250.94 is recovered, leaving 13,749.06 from year 4's 30,735.60. Discounted payback is 3 + 13,749.06/30,735.60 = 3.45 years.
Internal rate of return
The IRR is the discount rate that makes NPV exactly zero. You cannot solve for it with a simple formula when there are several cash flows, so use a financial calculator, Excel or trial and error. For the project above, test two rates.
| Discount rate | NPV |
|---|---|
| 10.0 percent | +16,986 |
| 17.0 percent | +198 |
| 17.2 percent | -223 |
NPV crosses zero between 17.0 and 17.2 percent, so the IRR is about 17.1 percent. Because it is above the 10 percent required return, the project is acceptable on the IRR rule too. In Excel, enter the cash flows in cells (for example B1 to B5 with the initial outlay as a negative) and use =IRR(B1:B5).
The relationship between the two measures is simple. NPV falls as the discount rate rises, and the IRR is the point where it reaches zero. At any discount rate below the IRR, NPV is positive.
When NPV and IRR disagree
For a single, conventional project (money out first, then money in), NPV and IRR give the same accept or reject answer. They can disagree when you must choose between mutually exclusive projects, especially if they differ in scale or timing.
Scale conflict (hypothetical)
At a 10 percent required return, you can do only one of two projects, each with a single cash inflow after one year.
| Project | Investment | Inflow in year 1 | IRR | NPV at 10 percent |
|---|---|---|---|---|
| X | 100,000 | 120,000 | 20 percent | 9,091 |
| Y | 1,000,000 | 1,150,000 | 15 percent | 45,455 |
IRR prefers X because the percentage return is higher. NPV prefers Y because it creates more value in dollars. When projects are mutually exclusive and capital is not scarce, choose the higher NPV, since it measures how much wealth the decision adds.
Other problems with IRR: projects with alternating signs can have more than one IRR, and the method assumes cash flows are reinvested at the IRR itself, which is often unrealistic. A modified IRR (MIRR) fixes the reinvestment assumption by using a stated reinvestment rate. This is a good point to mention in an evaluation.
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Get an instant quoteEstimating the cash flows
The calculation is mechanical. The harder skill, and often the bigger source of marks, is deciding which cash flows to include. Follow these principles.
| Include or exclude | Principle | Example |
|---|---|---|
| Include | Only incremental cash flows, the change caused by the project | Extra revenue minus extra costs |
| Include | Cash flows after tax | Tax on additional profit |
| Include | Working capital changes | Extra stock and receivables, recovered at the end |
| Include | Opportunity costs | Rent forgone by using a building the firm already owns |
| Include | Salvage value at the end | Sale of equipment after year 4 |
| Exclude | Sunk costs | A feasibility study already paid for |
| Exclude | Financing costs in the cash flows | Interest is reflected in the discount rate |
| Include as a tax effect | Depreciation is not cash, but it reduces tax | Depreciation tax shield = depreciation x tax rate |
Depreciation tax shield
Equipment costing $100,000 is depreciated on a straight-line basis over four years, $25,000 a year. At a 25 percent tax rate, depreciation saves 25,000 x 0.25 = $6,250 in tax each year. That saving is a real cash benefit and belongs in the project's cash flows, even though depreciation itself is not a cash payment.
Practice problem with solution
A project costs $50,000 and returns $20,000 at the end of each of three years. The required return is 12 percent. Calculate NPV, IRR, payback, discounted payback and the profitability index, and make a decision.
Solution
- NPV: the inflows are an annuity. PV = 20,000 x [1 - 1.12^-3] / 0.12 = 20,000 x 2.4018 = 48,036.62. NPV = 48,036.62 - 50,000 = -$1,963.38.
- Profitability index: 48,036.62 / 50,000 = 0.96, which is below 1.
- IRR: we need an annuity factor of 50,000 / 20,000 = 2.5. At 9 percent the three-year factor is 2.5313 and at 10 percent it is 2.4869, so the IRR is about 9.7 percent, below the 12 percent required.
- Payback: 50,000 / 20,000 = 2.5 years.
- Discounted payback: the present value of all three inflows is only 48,036.62, so the investment is not recovered within the project's life.
Decision: reject. NPV is negative, IRR is below the required return and the profitability index is under 1. Payback of 2.5 years looks acceptable alone, which shows why payback should not be the only test.
Risk, sensitivity and the discount rate
The discount rate should reflect the risk of the project, usually the firm's cost of capital adjusted for how risky the project is compared with its normal business. A higher rate makes future cash flows worth less. It is common to test how the decision changes if inputs are wrong.
| Technique | What it does |
|---|---|
| Sensitivity analysis | Changes one input at a time, such as sales or the discount rate, and shows the effect on NPV |
| Scenario analysis | Combines inputs into best, expected and worst cases |
| Break-even analysis | Finds the value of an input, such as annual sales, at which NPV is zero |
| Simulation | Runs many random combinations of inputs to see the spread of NPV |
For the worked project, a useful sensitivity is the discount rate. NPV is still positive at 15 percent but turns negative at about 17.1 percent, so the project is robust to quite a large increase in the required return. You can also compare it with the cost behavior ideas in our guide to break-even analysis.
Excel pitfalls
Excel's NPV function assumes the first cash flow occurs at the end of period 1, not at time 0. If your initial outlay is at time 0, do not include it in the NPV range. Add it separately.
=NPV(0.10, C2:C5) + C1 where C1 = -100,000 and C2:C5 = the four inflows
Using =NPV(0.10, C1:C5) would wrongly discount the initial outlay by a year. IRR, by contrast, takes the full range including the time 0 cash flow. Set up a clear inputs area for the rate and cash flows so that you can change assumptions quickly, and label every row.
- Use incremental, after-tax cash flows Ignore sunk costs and financing costs; include working capital and salvage.
- Show the discount factor or formula Marks are for the method as well as the answer.
- State the decision rule and the decision For example, accept because NPV is positive at 10 percent.
- Compare methods Say why NPV is preferred, and mention payback as a liquidity measure.
- Discuss risk Include at least one sensitivity or scenario comment.
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