Streams of Cash Flows

Discounting a Stream (NPV)

NPV adds present values of every time-stamped flow and discounts each according to its time period.

highlighted = computed this step

Each inflow’s present value

The first inflow of $605.00 is discounted to $550.00 one period out; the second inflow is worth $500.00 two periods out.

$550.00$500.00PV1=$605.001+r,PV2=$605.00(1+r)2\$550.00\$500.00\text{PV}_{1} =\frac{\$605.00}{1+r},\text{PV}_{2} =\frac{\$605.00}{(1+r)^2}
Discounting a streamA cost today and inflows later are worth the net of discounted value. 012$1,000.00$605.00$605.00NPV: $50.00

Net present value

The net present value is $50.00: a positive net means the inflows are worth more than the initial outflow at this discount rate — a descriptive statement about value, not investment advice.

NPV=−$1,000.00+PV1+PV2=$50.00\text{NPV}= -\$1,000.00 + \text{PV}_{1} + \text{PV}_{2} =\$50.00
Discounting a streamA cost today and inflows later are worth the net of discounted value. 012$1,000.00$605.00$605.00NPV: $50.00

Rounding and assumptions

Round-half-up to the cent is applied only to displayed values. This model ignores taxes and fees and focuses only on the time value of cash flows. Institutions and regulations can define different rounding rules (for example, banker's rounding or round-half-to-even).

NPV=$50.00\text{NPV}=\$50.00