NPV calculator
NPV discounts a stream of future cash back to today and subtracts what it cost. Positive means the project beats the discount rate.
%
Net present value
3439.50
- Present value of the cash flows
- 103 439.50
- Profitability index
- 1.0344
- Simple payback period
- 5.56 years
- Undiscounted profit
- 44 000.00
Show the working
- Initial investment = 100 000
- Cash flow per year = 18 000
- Number of years = 8
- Discount rate = 8
- i = 8 / 100 = 0.08
- annuity_factor = (1 - (1 + 0.08)^(-8)) / 0.08 = 5.746 64
- Present value of the cash flows = 18 000 * 5.746 64 = 103 440
- Net present value = 103 440 - 100 000 = 3439.5
- Profitability index = 100 000 > 0 ? 103 440 / 100 000 : 0 = 1.0344
- Simple payback period = 18 000 > 0 ? 100 000 / 18 000 : 0 = 5.555 56
- Undiscounted profit = 18 000 * 8 - 100 000 = 44 000
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- annuity factor = (1 - (1+i)^-n) / i
- NPV = cash flow x annuity factor - initial investment
This assumes an even annual cash flow. Uneven flows need each year discounted separately.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.