## Net Present Value (NPV)
NPV is a discounted cash flow method that values a project as the amount, in current (present) value terms, that the investment earns after paying the cost of capital in each period.
Using a specified discount rate, all cash inflows after the initial investment are brought back to their present values (the initial investment occurs at year 0).
### Formula
$$\text{NPV} = \frac{C_1}{(1+k)} + \frac{C_2}{(1+k)^2} + \frac{C_3}{(1+k)^3} + \dots + \frac{C_n}{(1+k)^n} - I$$
In words:
$$\text{NPV} = \text{PV of net cash inflows} - \text{Total net initial investment}$$
Where C = cash flow of each year, k = discount rate, n = project life, I = investment.
### Steps to compute NPV
1. Determine the net cash inflow for each year.
2. Select the desired rate of return / discount rate (often WACC).
3. Find the discount factor (PVF) for each year at that rate.
4. Multiply each year's cash flow by its discount factor → PV of cash flows.
5. Total all the PVs and subtract the initial investment.
### Decision rule
| Condition | Decision |
|---|---|
| NPV ≥ 0 | Accept the proposal |
| NPV < 0 | Reject the proposal |
For mutually exclusive projects, choose the one with the higher NPV.
> NPV's reinvestment assumption: it assumes interim cash flows are reinvested at the discount rate — a logical assumption, since any project earning more than the discount rate is accepted.