The discounted cash flow formula calculates the present value of a series of future cash flows by discounting them back to today using a required rate of return. It is the mathematical foundation of investment valuation, expressed as:
Where $CF$ is the cash flow for a given year and $r$ is the discount rate (the WACC or required return).
The Formula:
> DCF = CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³ + … + CFₙ/(1+r)ⁿ
Or in summation notation:
> DCF = Σ [CFₜ / (1 + r)ᵗ] for t = 1 to n
Breaking Down Each Component
| Component | What It Is | How to Find It |
|---|---|---|
| CFₜ | Cash flow in period t | From financial projections or historical data |
| r | Discount rate | Cost of capital (WACC), hurdle rate, or required return |
| t | Time period | Year 1, Year 2, etc. |
| (1 + r)ᵗ | Discount factor | Calculated for each year |
| n | Total number of periods | The length of your forecast |
The Discount Factor Table
The discount factor converts future cash into today’s value. At a 10% discount rate:
| Year (t) | Discount Factor = 1/(1.10)ᵗ | $1 Future → Today |
|---|---|---|
| 1 | 0.909 | $0.91 |
| 2 | 0.826 | $0.83 |
| 3 | 0.751 | $0.75 |
| 4 | 0.683 | $0.68 |
| 5 | 0.621 | $0.62 |
| 10 | 0.386 | $0.39 |
The further out the cash flow, the less it’s worth today – this is the time value of money in action.
Full DCF Calculation Example
A project generates these annual cash flows with a 12% discount rate:
| Year | Cash Flow | Discount Factor (12%) | Present Value |
|---|---|---|---|
| 1 | $50,000 | 0.893 | $44,650 |
| 2 | $60,000 | 0.797 | $47,820 |
| 3 | $70,000 | 0.712 | $49,840 |
| 4 | $65,000 | 0.636 | $41,340 |
| 5 | $55,000 | 0.567 | $31,185 |
| Total DCF Value | $214,835 |
If you can acquire this stream of cash flows for less than $214,835 today – the investment creates value. If it costs more, you’d be better off elsewhere.
Adding Terminal Value
In business valuation, cash flows beyond the explicit forecast period are captured in a terminal value – typically using the Gordon Growth Model:
> Terminal Value = FCFₙ × (1 + g) / (r − g)
Where:
- FCFₙ = Free cash flow in the final projected year
- g = Perpetual growth rate (usually 2-3%)
- r = Discount rate
The terminal value is then discounted back to today using the same discount factor as year n.
Why it matters: In most DCF models, terminal value represents 60-80% of the total estimated value. This means the valuation is highly sensitive to the perpetual growth rate assumption – a good reason to test multiple scenarios.
DCF in Excel
For a simple cash flow series:
=NPV(discount_rate, CF1, CF2, CF3, CF4, CF5)
Note: Excel’s NPV function assumes the first cash flow occurs at end of Period 1. If there’s an initial investment at Period 0, add it separately:
=NPV(0.12, 50000, 60000, 70000, 65000, 55000) + (−initial_investment)
Sensitivity to the Discount Rate
The discount rate is the most important – and most argued – input in any DCF:
| Discount Rate | Total PV of Example Cash Flows |
|---|---|
| 8% | $232,500 |
| 10% | $223,100 |
| 12% | |
| 15% |
A 3-point change in the discount rate changes the valuation by nearly 10%. Always present DCF results as a range.
The Bottom Line
The discounted cash flow formula is the mathematical expression of a simple idea: future money is worth less than today’s money, so discount it back at your required rate of return. Master the formula, understand each component, and always stress-test your assumptions – especially the discount rate and terminal growth rate, which drive the bulk of the valuation.
