1.2c Present Value

Present Value

The present value is the current worth of a compounded sum of money or stream of cash flows, given a specific rate of return $r$, and a time period of $t$ years over $n$ periods. It is calculated by discounting the future amount(s) back to the present using the formula
$\text{PV}=\frac{\text{FV}}{(1+\frac{r}{n}{)}^{nt}}.$

Given multiple cashflows $C_1,\dots ,C_N$, the net future value of the cashflows is calculated by compounding each cashflow to a common future date using the appropriate interest rate, and then summing these compounded amounts. Mathematically,
$\text{NPV}={\sum }_{i=0}^{nt}\frac{C_i}{{\left(1+\frac{r}{n}\right)}^i}.$