Net Present Value (NPV)

Net present value is the difference between the discounted value of everything a project or purchase brings in and the discounted value of everything it costs. Office of Management and Budget Circular A-94, the federal guidance for benefit-cost analysis, defines it as "the difference between the discounted present value of benefits and the discounted present value of costs," and states the rule that follows from it: "Programs with positive net present value increase social resources and are generally preferred. Programs with negative net present value should generally be avoided."

The word doing the work is "net." Present value answers what a future amount or a future stream is worth today; it is a valuation and it has no opinion. Net present value takes that valuation and subtracts what you have to pay to get it, which converts a number into a verdict. A present value is always positive. A net present value can be negative, and when it is, the arithmetic is telling you the purchase costs more than the discounted worth of what it delivers.

The outlay is a cash flow, not a separate consideration, and that is the structural point. In a net present value calculation the money you pay today sits in the same column as the money you receive later, with a negative sign and a discount factor of one, because a dollar paid now needs no discounting. Everything after it is discounted back. The total is a single signed number in today's dollars. Positive means the discounted receipts exceed the discounted payments; negative means they do not; zero means the project exactly earns the rate you discounted at, and nothing more.

Because the answer is in dollars, it ranks. Because a rate is not, it does not. This is the practical division of labor between net present value and the internal rate of return, and it is the reason both figures exist. A percentage tells you the rate a commitment earned without telling you how large the commitment was, so it cannot say which of two opportunities produces more money. Net present value can, because two dollar amounts are directly comparable. The cost is that it cannot be computed at all until you name a discount rate, which is a judgment rather than an observation.

The verdict is only as firm as the rate, and honest practice is to show the range rather than a single answer. Circular A-94 directs exactly that: "Analyses should show the sensitivity of the discounted net present value and other outcomes to variations in the discount rate." A project whose net present value is a large positive number at every plausible rate is a different proposition from one that turns negative if the rate moves a percentage point, even though both look like an accept at the rate first chosen. When a decision hangs on the rate, the rate is the thing to argue about, and the choice of it is a subject in its own right.

Two mechanical points that quietly change answers. First, dating: a flow treated as arriving at the end of a year discounts more heavily than the same flow treated as arriving in the middle of it, and Circular A-94's appendix supplies both conventions and shows the same project's net present value moving when the assumption changes. Second, what is included: taxes, fees, resale or salvage value, and the cost of doing nothing all belong in the columns, and each omission biases the answer in a predictable direction. Federal energy-project rules are unusually explicit about this. Under 10 CFR 436.19 a project's life cycle costs are "the sum of the present values of" investment costs "less salvage values at the end of the study period," non-fuel operation and maintenance costs, replacement costs less salvage, and energy or water costs. 10 CFR 436.20 then provides that for a retrofit project net savings "may be found by subtracting life cycle costs based on the proposed project from life cycle costs based on not having it." That second comparison is the one households skip: the alternative to buying is not zero, it is whatever doing nothing costs. A comparison between two net present values computed on different inclusion rules is not a comparison.

List every amount the decision moves, with its date and its sign: the purchase price and any later costs as negatives, the savings, income or resale proceeds as positives. Discount each one back to today at a chosen rate, add the results, and read the sign. Then repeat at a higher and a lower rate to see whether the sign holds.

A hypothetical example, run twice on purpose. A $9,000 heat pump is projected to cut $1,000 a year from a household's energy bills for 12 years, with no resale value at the end.

Discounted at 4 percent, the twelve annual savings are worth $9,385.07 today, so the net present value is $9,385.07 − $9,000 = +$385.07. The project clears, though not by much.

Discounted at 8 percent, the same twelve savings are worth $7,536.08 today, and the net present value is $7,536.08 − $9,000 = −$1,463.92. The same equipment, the same savings, the same twelve years, and now the project fails.

Nothing about the heat pump changed between those two lines. What changed was the assumption about what else the $9,000 could have earned. The rate at which the answer crosses zero is about 4.73 percent, which is this project's internal rate of return, and it is the cleanest single summary of the decision: the heat pump is worth buying if the household's realistic alternative earns less than roughly 4.7 percent, and is not if it earns more.

Pros

• Answers the actual question, which is whether a purchase or project is worth its cost, rather than only what its returns are worth.
• Reported in dollars, so opportunities of different sizes can be ranked against each other.
• Handles irregular, uneven and long-dated cash flows without any special treatment.
• Has a single unambiguous value for any given rate, unlike the internal rate of return, which can have several.
• Sensitivity to the rate can be shown explicitly, which turns a hidden assumption into a visible one.

Cons

• Cannot be computed without choosing a discount rate, and the choice can change the verdict.
• The output is only as good as the projected cash flows, which for a household decision are usually estimates of savings that have not happened yet.
• Ignores taxes, fees and inflation unless they are deliberately built into the flows and the rate.
• Says nothing about liquidity or risk of ruin: a project with a positive net present value can still require money the household cannot afford to tie up.
• Lends an air of precision to a calculation resting on a rate assumption and a forecast.