Net Present Value (NPV)
Present value of an arbitrary cash flow stream discounted at the required rate of return. Sums each cash flow CF_t divided by (1+k)^t. Positive NPV = project creates value; negative NPV = destroys value.
When to use: The single most-used capital-budgeting metric. Use to evaluate any investment or project by discounting its expected cash flows at the cost of capital (or your required return) and comparing the result to zero.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| NPV | Net Present Value | Present value of all cash flows discounted at the required rate | $ |
| CashFlows | Cash Flows | Sequence of cash flows starting at period 0 (negative for outflows, positive for inflows) | $ |
| k | Discount Rate | Cost of capital or required rate of return as a decimal (e.g. 0.10 for 10%) | % |
Real-Life Examples
Example 1: 4-Year Project
Invest $1,000 today, receive $400/year for 4 years. Required return is 10%. What is the NPV?
Given
Step-by-Step
NPV is +$267.95 — the project creates $267.95 of value above the 10% required return. Accept.
Example 2: Marginal Project (Reject)
Invest $5,000, receive $1,200, $1,500, $1,800, $2,000 over 4 years. Required return 12%.
Given
Step-by-Step
NPV is negative — the project earns less than the 12% required return. Reject (or renegotiate to lower the upfront cost).
Frequently Asked Questions
NPV gives a dollar-value answer at a specific discount rate (your cost of capital). IRR gives a single rate of return regardless of capital cost. NPV is usually preferred because it scales with project size and assumes intermediate cash flows are reinvested at the cost of capital — a more realistic assumption than IRR's implicit reinvestment-at-IRR assumption.
For corporate projects, the weighted average cost of capital (WACC). For personal investments, your required rate of return — often the rate available on a comparable-risk alternative. The discount rate must reflect the risk of the cash flows being discounted.
Because t=0 is "today" — no time has passed, so no discounting is needed. By convention, the initial investment is entered as a negative cash flow at index 0, with subsequent cash flows discounted by 1, 2, …, n periods.
Yes — that is its main strength. Unlike PV-of-annuity (which requires constant payments), NPV accepts any sequence of cash flows including zeros, sign changes, growth, or one-time payments. This makes it the workhorse of project finance.