Finance
Net Present Value (NPV)
Present Value applied to a whole stream of future cash flows at once, netted against the upfront cost — the standard way to judge whether an investment is worth making.
Definition
Net present value (NPV)is the sum of the present values of every cash flow an investment is expected to produce — including the upfront cost, counted as a negative cash flow today — discounted back to today's dollars at a chosen rate. If the total is positive, the investment is expected to be worth more, in today's-dollars terms, than it costs; if negative, it's expected to be worth less.
Why this exists
Present Value answers "what is one future amount worth today?" but real investment decisions rarely involve just one future amount — a piece of equipment might cost money today and then generate cash flow for each of the next several years; a business project might require an upfront investment and pay out returns over time. To evaluate a decision like that, every one of those future cash flows needs to be translated back to today's dollars — not just one — and then combined into a single, comparable figure.
Net present value does exactly that: it discounts every expected future cash flow back to today, the same way Present Value discounts a single amount, then adds all of those present values together, including the upfront cost, counted as a negative cash flow happening right now, at time zero. The result is a single number in today's dollars that answers the real underlying question directly: after accounting for the time value of money, is this investment expected to create more value than it costs, or less?
The discount rate matters enormously here, just as it does for Present Value — it should reflect what you could otherwise earn on your money at a similar level of risk. Too low a discount rate makes future cash flows look more valuable than they really are relative to the alternative uses of that money; too high a rate understates them. NPV is only as trustworthy as the discount rate and the cash-flow estimates that go into it. For a company evaluating its own projects, that rate is usually its Cost of Capital (WACC) — the return needed to satisfy everyone who financed the company, and the benchmark used in Capital Budgeting Decision Rules.
Formula & mechanics
Every expected cash flow, discounted and summed:
NPV = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ
CFₜ— the cash flow expected in year t (CF₀is usually negative — the upfront cost)r— the discount rate, matching what you could otherwise earn on your money at a similar level of riskn— the number of years the investment produces cash flow
The decision rule is simple once NPV is calculated: a positive NPV means the investment is expected to create more value than it costs; a negative NPV means the opposite.
Worked example
A small business considers buying a $10,000 machine expected to generate $3,000 of extra cash flow at the end of each of the next 4 years, using an 8% discount rate.
Year 0: −$10,000 Year 1: $3,000 / 1.08¹ ≈ $2,778 Year 2: $3,000 / 1.08² ≈ $2,572 Year 3: $3,000 / 1.08³ ≈ $2,382 Year 4: $3,000 / 1.08⁴ ≈ $2,205 NPV ≈ −$10,000 + $2,778 + $2,572 + $2,382 + $2,205 ≈ −$64
In raw, undiscounted terms, $3,000 × 4 years = $12,000 sounds like a lot more than the $10,000 cost. But once each year's cash flow is discounted back to today, the total is only worth about $9,936 in today's dollars — just barely below the $10,000 cost, for a slightly negative NPV. At an 8% discount rate, this investment is expected to destroy a small amount of value rather than create it. Try the Net Present Value Calculator to see how a different discount rate or cash flow changes the result.
Try it yourself
Net present value
-$63.62
Negative — expected to cost more than the value it creates.
Cash flows, undiscounted
$12,000.00
Cash flows, discounted
$9,936.38
How the math works
The calculator discounts each year's cash flow back to today using PV = CF / (1 + r)^t, adds all of those present values together, and subtracts the initial investment (the cash flow at time zero):
Year 1: $3,000.00 → $2,777.78 today Year 2: $3,000.00 → $2,572.02 today Year 3: $3,000.00 → $2,381.50 today Year 4: $3,000.00 → $2,205.09 today
Undiscounted, the 4-year stream of cash flows totals $12,000.00 — but discounted back to today at 8%, it's only worth $9,936.38. Subtracting the $10,000.00 upfront cost leaves an NPV of -$63.62 — the difference between the naive undiscounted sum and NPV is exactly the cost of waiting for the money.
Common misconceptions
“If the total, undiscounted cash flows are bigger than the cost, the investment is worth it.”
Summing raw future cash flows ignores that money received later is worth less than money received now. NPV can be negative even when the simple sum of future cash flows exceeds the upfront cost, exactly as in the worked example above.
“A higher discount rate makes an investment's NPV look better.”
It's the opposite. A higher discount rate shrinks the present value of future cash flows more heavily, pushing NPV lower, because it implies a higher bar — a higher opportunity cost — the investment has to clear.
“NPV tells you with certainty whether an investment will succeed.”
NPV is only as good as its inputs. The cash-flow estimates and the discount rate are both assumptions about the future, not guarantees, and a modest change in either can flip NPV's sign.
Also in the Glossary: Net Present Value (NPV)