Net Present Value (NPV)
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 measures value in currency at the chosen discount rate. IRR is a rate at which NPV is zero. NPV accounts for project scale; IRR rankings can differ for mutually exclusive projects.
The valuation equation discounts cash flows at an opportunity cost; it does not require that each cash flow actually be reinvested. Terminal-wealth comparisons need a separate reinvestment assumption.
The first entry is time zero; subsequent entries are equally spaced year-end cash flows. Use rates matching the period if interpreting the periods differently.