DCF valuation · Net present value
Net Present Value (NPV): Formula, Decision Rule & Worked Example
NPV is the single number that answers whether an investment creates or destroys value above the hurdle rate. Every DCF model and every capital allocation decision reduces to one question: is the present value of future cash flows greater than what you pay today?
Net present value (NPV) measures whether an investment creates value by summing the present value of all expected future cash flows and subtracting the upfront cost. NPV = Σ [CFt ÷ (1 + r)^t] − I₀, where CFt is the cash flow in period t, r is the discount rate (WACC), and I₀ is the initial investment. NPV > 0 signals value creation; NPV < 0 signals destruction; NPV = 0 means the investment earns exactly the hurdle rate.
The NPV Formula: What Each Variable Means
The formula has four inputs. The cash flow projection (CFt) is the hardest to get right; the discount rate (r) has the most leverage on the final answer.
Worked Example: 3-Year Project at 9% WACC
A company evaluates a $45B product investment expected to generate $15B, $20B, and $25B in free cash flow over three years, discounted at a 9% WACC:
- Year 1: $15B ÷ (1.09)¹
- PV = $13.76B
- Year 2: $20B ÷ (1.09)²
- PV = $16.84B
- Year 3: $25B ÷ (1.09)³
- PV = $19.31B
- Sum of discounted cash flows
- $49.91B
- NPV = $49.91B − $45B initial investment
- +$4.91B
The NPV of +$4.91B means this investment creates $4.91B of value above what the 9% hurdle rate requires. Because NPV is positive, the project clears the bar. Add a terminal value at year 3 and you have a complete DCF model.
The NPV Decision Rule
The decision rule is mechanically simple — but it only works as well as the cash flow and discount rate assumptions behind it:
- NPV > 0: Invest. The project earns above the required return. Every dollar above zero is value created for shareholders above the hurdle rate. The larger the NPV, the more value is created.
- NPV = 0: Breakeven. The project earns exactly the cost of capital. It neither creates nor destroys value. Proceed only if there are strategic or optionality reasons; otherwise capital may be deployed elsewhere.
- NPV < 0: Reject. The project earns less than the cost of capital, destroying shareholder value — even if it is profitable in absolute terms. A 5% return against a 9% hurdle rate is a loss in economic terms.
- Between competing projects, choose the higher NPV. When two mutually exclusive options both have positive NPVs, the one with the larger NPV creates more absolute dollar value — regardless of which has the higher IRR.
NPV vs. IRR: Which to Use?
IRR (internal rate of return) is the discount rate that makes NPV equal to zero. It is expressed as a percentage: if IRR is 14% and WACC is 9%, the project clears the bar. The appeal is intuitive — it summarizes a project's return as a single rate comparable to the cost of capital.
The problem with IRR is scale blindness. A $1M project with a 30% IRR is not necessarily better than a $1B project with a 15% IRR — the second project creates far more absolute value. NPV captures this; IRR does not. When ranking mutually exclusive investments, always prefer NPV. Use IRR only to screen whether a project clears the hurdle rate.
A second IRR limitation: it assumes all interim cash flows are reinvested at the IRR itself, which is usually unrealistic. NPV avoids this by discounting all flows at the actual cost of capital.
NPV in a DCF Stock Valuation
A discounted cash flow (DCF) model is an NPV calculation applied to a stock. Projected free cash flows — typically five to ten years of explicit forecasts plus a terminal value representing everything beyond the forecast window — are discounted back to today at the WACC. The output is the present value of the entire business.
To get intrinsic value per share, subtract net debt from enterprise value and divide by shares outstanding. If intrinsic value exceeds the current market price, the stock has a positive NPV — the market is pricing it below what the cash flows justify. If intrinsic value is below the market price, NPV is negative: buying here earns less than the hurdle rate.
This is why discount rate sensitivity dominates DCF analysis. A WACC shift from 9% to 10% can swing intrinsic value by 20–30% because every future cash flow is discounted at that rate. The DCF calculator runs this sensitivity table automatically so you see the valuation band, not a false-precision single number. The CAPM guide covers how to build the cost of equity that feeds into WACC.