Net Present Value of a Cash Flow Series
Net Present Value of a Cash Flow Series
Net present value (NPV) answers the central question of capital budgeting: is this investment worth making? By discounting every future cash flow back to today's dollars at a chosen discount rate and summing them (including the negative upfront investment), NPV converts a whole stream of future money into a single comparable number.A positive NPV means the investment is expected to create value above the discount rate's required return, while a negative NPV means the money would be better invested elsewhere at that same rate — which is why NPV is the standard decision rule used to compare competing capital projects, from a new factory line to a piece of equipment.
The net present value is NPV = CF_0 + CF_1/(1+r) + CF_2/(1+r)² + CF_3/(1+r)³, summing the discounted value of each period's cash flow. where CF_0 is the initial investment (negative), CF_1 through CF_3 are the cash flows received in each following year, r_disc is the discount rate, and NPV_calc is the resulting net present value, all in dollars (plain numbers, no currency unit).
Inputs
CF_0 := -100000=-100000
CF_1 := 30000=30000
CF_2 := 40000=40000
CF_3 := 50000=50000
r_disc := 0.08=0.08
Discount each future cash flow back to present value and add them to the (already-present-value) initial investment — later cash flows get discounted more heavily since (1+r) is raised to a higher power.
NPV_calc := CF_0 + CF_1/(1+r_disc)^1 + CF_2/(1+r_disc)^2 + CF_3/(1+r_disc)^3=1762.94
Results
A positive NPV here means the discounted future cash flows more than repay the $100,000 initial investment at an 8% required return, making the project attractive on a purely financial basis. Raising the discount rate (reflecting higher perceived risk or a higher required return elsewhere) shrinks the present value of the later cash flows fastest, so a project that looks good at 8% can easily turn negative at 15% — which is why the choice of discount rate is itself a critical, often debated, input.
Assumptions & limitations
- Cash flows and timing are known with certainty (no risk adjustment beyond the discount rate).
- A single constant discount rate applies to all periods.
- Cash flows occur at the end of each period.
- Monetary amounts are plain numbers (dollars implied).