Why (1+g) in DCF Terminal Value (Perpetuity Growth Method)?
⚡ The Root Problem
In the Perpetuity Growth Model, the Terminal Value formula is:
TV = CFt+1 / (r - g)
NOT: TV = CFt / (r - g)
🧠 Why "t+1" Not "t"?
- At the end of Year 5 (or Year N), you're standing at the end of that year.
- The value of the business is based on the future cash flows, starting next year (Year 6).
- A buyer pays for all future cash flows, not today’s cash flow.
🔥 Slower Walkthrough — Building the Perpetuity
Example:
- End of Year 5 FCF = $100.
- FCF grows forever at 2% per year.
Thus:
- Year 6 FCF = $100 × (1+0.02) = $102
- Year 7 FCF = $102 × (1+0.02) = $104.04
- Year 8 FCF = $104.04 × (1+0.02) = $106.12
- ... and so on, growing forever.
📚 Why Is the Growing Perpetuity Formula Like That?
The perpetuity cash flows form a growing geometric series:
PV = C₁ / (r - g)
Where:
- C₁ = Cash Flow at Year 6 (NOT Year 5)
- r = Discount Rate
- g = Growth Rate
🥇 Simple Memory Hack
- End of Year 5 → Start of Year 6 → Must "grow once" by (1+g).
- Thus: multiply Final Year FCF × (1+g) before applying the perpetuity formula.
🚫 Contrast: Exit Multiple Method
- Exit Multiple Method is just applying a static sale price multiple.
- No (1+g) needed — it prices the company based on current EBITDA, not future cash flows.
🎯 Final Recap (Simple Table)
| Method | Do (1+g)? | Why? |
|---|---|---|
| Perpetuity Growth (DCF) | Yes | Need future cash flow (Year 6) |
| Exit Multiple | No | Valuing current cash flow |
🧠 Human Intuitive Summary:
"In DCF, when we use perpetuity growth, we're pricing future cash flows that start growing immediately after the last forecasted year. Thus, we must grow the final year’s cash flow once by (1+g) to capture the first cash flow of the endless series."
