Net Present Value (NPV)

NPV discounts future cash flows to today and subtracts the initial investment to determine value creation at a given discount rate.

Formula

NPV = \u2211 CF_t / (1 + r)^t \u2212 Initial investment

Where r is the discount rate, CF_t are cash flows at time t. Positive NPV indicates the project adds value at rate r.

Example

Initial outlay $100,000. Cash inflows over 3 years: $40,000, $45,000, $50,000. Discount rate r = 10%.

• PV year 1 = 40,000 / 1.1 = $36,364
• PV year 2 = 45,000 / 1.1^2 = $37,190
• PV year 3 = 50,000 / 1.1^3 = $37,565

Total PV = 36,364 + 37,190 + 37,565 = $111,119; NPV = 111,119 − 100,000 = $11,119 (acceptable).

Step-by-Step

1. List initial outlay and future cash flows by period.
2. Choose discount rate r based on risk and cost of capital.
3. Discount each cash flow to present value and sum.
4. Subtract initial investment to get NPV.

Sensitivity & Pitfalls

• Results are sensitive to r; test multiple scenarios.
• Use consistent timing (end-of-period vs mid-year conventions).
• Exclude sunk costs; include working capital changes if relevant.