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Net present value (NPV)

Net present value sums the present value of all future cash flows and subtracts the investment. If NPV is positive, the investment yields better than the discount rate and is profitable. Equal annual cash flows can be summed quickly with the annuity factor.

NPV = -I_0 + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t}

net present value

\text{annuity factor} = \frac{1-(1+r)^{-n}}{r}

for equal cash flows

C

each year

Symbols

$I_0$	investment today	kr
$C_t$	cash flow in year $t$	kr
$r$	discount rate

Example

Investment 100,000 kr, yields 80,000 kr/year for 6 years, $r = 7\%$ :

Annuity factor $\approx 4.7665$ , $NPV \approx -100000 + 80000\cdot 4.7665 \approx 281.323$ kr — profitable.

NPV > 0 means a profitable investment at the given discount rate; NPV < 0 means not profitable.

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Part of Engineering Economics: Investment analysis.