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Finance formula

How to calculate net present value

NPV turns uneven future cash flows into a single present-day value.

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Direct answer
Formula
NPV = -C0 + sum(Ct / (1 + r)^t)

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Net present value formula
Start here when you only need the equation and variable names.
Formula
NPV = -C0 + sum(Ct / (1 + r)^t)

NPV turns uneven future cash flows into a single present-day value.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
C0Initial investmentCash paid at the start.currency
CtCash flowCash received or paid in period t.currency
rDiscount rateRequired return per period as a decimal.Depends on inputs
tPeriodNumber of periods from today.Depends on inputs
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Use NPV when projects, investments, or purchases have cash flows spread across several years.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1List the upfront investment as a negative cash flow.
  2. 2Choose a discount rate that matches the risk and time value of money.
  3. 3Discount each future cash flow by year.
  4. 4Add the discounted cash flows and subtract the initial investment.
Examples
These sample numbers show the order of operations and units.
Small project
C0
$10,000
r
8%
C1
$3,000
C2
$4,000
C3
$5,000
  1. 1.NPV = -10000 + 3000 / 1.08 + 4000 / 1.08^2 + 5000 / 1.08^3
  2. 2.NPV = -10000 + 2777.78 + 3429.36 + 3969.16
  3. 3.NPV = 176.29
Result
The project has an NPV of $176.29.
Large purchase
C0
$50,000
r
10%
C1
$15,000
C2
$18,000
C3
$22,000
  1. 1.NPV = -50000 + 15000 / 1.10 + 18000 / 1.10^2 + 22000 / 1.10^3
  2. 2.NPV = -50000 + 13636.36 + 14876.03 + 16528.93
  3. 3.NPV = -4958.68
Result
The project has an NPV of -$4,958.68.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Using an annual rate where the net present value formula needs a monthly or period rate.
  • Entering 8 instead of 0.08 when the formula calls for a decimal rate.
  • Comparing results across different time periods without converting them first.
  • Rounding each step instead of rounding the final answer.
Open the Net Present Value (NPV) Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Net Present Value (NPV) Calculator
FAQs
Short answers for common formula questions.
Can I calculate Net present value by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Net present value result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the NPV Calculator better than hand math?

Open the NPV Calculator to check several scenarios or skip the hand arithmetic.