How to calculate net present value, step by step
Net present value is one subtraction that answers one question: does this investment create value? The calculation needs four numbers: the initial investment, the annual cash inflow, the discount rate and the number of years. On $10,000 invested with $3,000 a year coming back for 5 years at a 10% discount rate, the net present value is $1,372.36 — a positive number, so the investment creates value.
The formula is net present value = present value of the inflows − initial investment. The present value of the inflows is each year’s inflow divided by (1 + rate) raised to that year, added up: year one’s $3,000 divided by 1.10, year two’s $3,000 divided by 1.10 squared, and so on for five years. The discount rate is what a dollar next year is worth today — a dollar a year from now is worth less than a dollar today, because today’s dollar could be invested. The sign of the answer is the verdict: positive means the investment creates value, negative means it destroys value, and zero means it breaks even.
The worked example, line by line. Step 1 — the investment: $10,000. Step 2 — the annual cash inflow: $3,000. Step 3 — the discount rate: 10%. Step 4 — the years: 5. Step 5 — the present value of each year’s inflow: year 1 is $2,727.27, year 2 is $2,479.34, year 3 is $2,253.94, year 4 is $2,049.04 and year 5 is $1,862.76. Step 6 — the present value of the inflows: $11,372.36. Step 7 — the net present value: $11,372.36 − $10,000 = $1,372.36. Work it yourself in the net present value calculator.
A note on the rounding: the five yearly figures are each rounded to two decimals, and the rounded figures add to $11,372.35 — one cent less than the $11,372.36 the unrounded figures add to. The one cent is rounding, not a mistake.
What the answer means
A net present value of $1,372.36 means the investment creates $1,372.36 of value in today’s dollars, so on $10,000 invested the inflows are worth $11,372.36 today — for every dollar of the investment, the inflows return about $1.14 in present value. A positive net present value means the project earns more than the discount rate asks of it. A negative net present value means the project earns less than the discount rate asks of it — the money would be worth more kept and invested elsewhere. A net present value of zero means the project earns exactly the discount rate — it neither creates nor destroys value. The number on its own never says whether $1,372.36 is a lot or a little — that depends on the size of the investment. Compare the net present value against the investment, and against the net present value of the next best project, before you decide.
When the discount rate is zero
If the discount rate is zero, a dollar next year is worth a dollar today — there is no discounting at all. The present value of the inflows is just the inflows added up: on $10,000 invested with $3,000 a year coming back for 5 years, the present value is 5 × $3,000 = $15,000, and the net present value is $15,000 − $10,000 = $5,000.00. The zero-rate case is the ceiling of the calculation: no positive rate can give a higher net present value, because every positive rate shrinks each year’s inflow.
Uneven cash flows
The simple formula only fits a steady inflow — the same $3,000 coming back every year. When the cash comes back unevenly, discount each year separately and add the results. Take a $10,000 investment that returns $3,000 in year one, $4,000 in year two and $4,000 in year three at a 10% discount rate: year one’s $3,000 is worth $2,727.27 today, year two’s $4,000 is worth $3,305.79, and year three’s $4,000 is worth $3,005.26 — so the present value of the inflows is $9,038.32, and the net present value is $9,038.32 − $10,000 = −$961.68. The investment destroys value, even though the inflows add to $11,000 — more than the $10,000 invested — because the later dollars are discounted hardest.
NPV vs payback
Net present value and the payback period answer different questions, and mixing them up is the most common mistake. Net present value counts value: how much the investment creates in today’s dollars. The payback period counts time: how many years until the cash coming back covers the investment. On $10,000 invested with $3,000 a year coming back, the net present value at a 10% discount rate is $1,372.36, and the payback period is 3.33 years. One is a value, the other is a clock. A project can pay back quickly and still destroy value — if the discount rate is high enough, the inflows are worth less today than the investment even when they arrive fast. Use net present value when you want to know whether the investment creates value, and use the payback period when you want to know how long the money takes to come back. Work out the years in the payback period calculator.
NPV vs IRR
The internal rate of return is the discount rate at which the net present value is exactly zero — the rate the project itself earns. On $10,000 invested with $3,000 a year coming back for 5 years, the internal rate of return is 15.24%: at a 15% discount rate the net present value is still positive, and at 16% it is negative, so the rate where it crosses zero sits between them, at 15.24%. If your discount rate is below 15.24%, the net present value is positive and the project creates value; if it is above 15.24%, the net present value is negative and the project destroys value. Use net present value when you want the value in dollars, and use the internal rate of return when you want the rate to compare against other projects.
Common mistakes
The first mistake is forgetting to discount — adding the inflows as $15,000 and calling the net present value $5,000.00, which is the zero-rate figure, not the 10% one. The second is using revenue instead of cash inflow — revenue is what comes in before costs, and net present value needs the cash left after costs, so the answer comes out far too high. The third is mixing up the discount rate and the return — a 10% discount rate is what a dollar is worth today, not what the project earns, and the project earns 15.24% here. The fourth is rounding each year’s present value and adding the rounded figures — the rounded figures add to $11,372.35, a cent short of the $11,372.36 the unrounded figures give. Work it out in the net present value calculator, and check the payback period calculator and the future value calculator before you decide what the answer means.