Net Present Value — Definition, Formula & Examples

Net Present Value (NPV) is the total value today of a series of future cash flows minus the initial investment cost. A positive NPV means the investment is expected to earn more than the required rate of return, while a negative NPV means it falls short.

Net Present Value is the sum of the present values of all future cash inflows and outflows associated with an investment, discounted at a specified rate. Formally, it equals the algebraic sum of each period's cash flow divided by $(1 + r)^t$ , where $r$ is the discount rate and $t$ is the time period.

Key Formula

NPV = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t}

Where:

$C_t$ = Cash flow at time period t (negative for costs, positive for income)
$r$ = Discount rate per period (as a decimal)
$n$ = Total number of time periods
$t$ = Time period (0, 1, 2, ...)

How It Works

To find NPV, you discount each future cash flow back to its present value using a chosen discount rate, then add them all together, including the initial cost (which is typically negative). If the result is positive, the investment earns more than the discount rate and is considered worthwhile. If negative, the investment destroys value relative to that rate. The discount rate often reflects the cost of borrowing money or the return you could earn elsewhere.

Worked Example

Problem: You invest $10,000 today in a project that returns $4,000 at the end of each year for 3 years. The discount rate is 10%. Find the NPV.

Step 1: Identify the cash flows. At t = 0, you pay $10,000. At t = 1, 2, and 3 you receive $4,000 each.

C_0 = -10{,}000, \quad C_1 = C_2 = C_3 = 4{,}000

Step 2: Discount each future cash flow to present value using r = 0.10.

PV_1 = \frac{4{,}000}{1.10^1} = 3{,}636.36, \quad PV_2 = \frac{4{,}000}{1.10^2} = 3{,}305.79, \quad PV_3 = \frac{4{,}000}{1.10^3} = 3{,}005.26

Step 3: Sum all present values including the initial cost.

NPV = -10{,}000 + 3{,}636.36 + 3{,}305.79 + 3{,}005.26 = -52.59

Answer: The NPV is approximately −$52.59. Since it is negative, this investment barely fails to meet the 10% return threshold.

Why It Matters

NPV is the standard tool for evaluating business investments, capital projects, and financial decisions in economics and finance courses. Anyone working in corporate finance, real estate, or entrepreneurship uses NPV to decide whether a project is worth pursuing at a given cost of capital.

Common Mistakes

Mistake: Forgetting that the initial investment at t = 0 is not discounted.

Correction: When t = 0, the denominator

(1 + r)^0 = 1

, so the initial cost enters the sum at its full value. Only future cash flows get discounted.