Capital budgeting is how a company decides whether a long-term investment (new equipment, a new product line, a new facility) is worth the money. The capital budgeting techniques your course covers are all versions of the same question: does this project return more than it costs, once you account for the time value of money? That is project appraisal, or investment appraisal, depending on your textbook.
The time value of money in one sentence
A dollar today is worth more than a dollar a year from now, because today’s dollar can be invested. So future cash flows have to be discounted back to today’s value, at the return the company requires, before they can be compared with the upfront cost.
The four main capital budgeting methods
- Payback period = initial investment ÷ annual cash inflow (for even cash flows). It measures how long it takes to recover the investment. It ignores the time value of money and any cash after payback. A discounted payback period fixes the first problem by using discounted cash flows.
- Net present value (NPV) = present value of all future cash inflows − initial investment. Accept the project if NPV is above zero.
- Internal rate of return (IRR) = the discount rate that makes NPV exactly zero. Accept the project if the IRR is above the required rate of return.
- Profitability index = present value of future cash flows ÷ initial investment. Accept the project if it’s above 1.
Some courses also cover the accounting rate of return (ARR), which uses accounting profit instead of cash flow and ignores the time value of money.
Worked example
A project costs $10,000 and returns $4,000 a year for three years. The required return is 10%.
Payback: 10,000 ÷ 4,000 = 2.5 years
Present values: Year 1: 4,000 ÷ 1.10 = 3,636.36. Year 2: 4,000 ÷ 1.21 = 3,305.79. Year 3: 4,000 ÷ 1.331 = 3,005.26. Total = 9,947.41.
NPV = 9,947.41 − 10,000 = −52.59
Profitability index = 9,947.41 ÷ 10,000 = 0.99
IRR is about 9.7%, just under the 10% required return.
NPV, the profitability index, and IRR all agree: reject the project, narrowly. Notice that a 2.5-year payback might look fine on its own, which is why payback shouldn’t be the only test.
A tip for doing it in Excel
The NPV function in Excel discounts the first value in the range by one full period, as if it arrives at the end of Year 1. So don’t include the initial investment in the range. Subtract it separately: =NPV(10%, 4000, 4000, 4000) − 10000. For IRR, put the initial investment in as a negative number in the first cell and use =IRR(range).
Common mistakes
Including the initial investment inside Excel’s NPV function. It treats that cash outflow as happening in Year 1 and discounts it, which understates the cost.
Relying on payback alone. It ignores both the time value of money and everything after the payback point.
Mixing up the decision rules. Accept if NPV is above zero, IRR is above the required return, or the profitability index is above 1. They should point the same way for a single project.
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