Can someone walk through a two-stage DDM with actual numbers? I keep getting the terminal value calculation wrong.
Struggling with the multi-stage dividend discount model for CFA Level II. I understand the single-stage Gordon model fine, but when the question says 'high growth for 5 years then stable growth forever,' I keep messing up the terminal value and discounting. A step-by-step numerical example would save my life right now.
The two-stage DDM trips up a lot of candidates because there are two common errors: (1) computing the terminal value at the wrong point in time, and (2) forgetting to discount the terminal value back to today. Let me walk through this carefully.
Setup: Dunleavy Consumer Brands (fictional)
| Input | Value |
|---|---|
| D0 (just paid) | $2.00 |
| High growth rate (years 1-4) | 15% |
| Stable growth rate (year 5+) | 4% |
| Required return (r) | 10% |
Step 1: Project dividends during the high-growth phase
| Year | Dividend Calculation | Dividend | PV Factor | PV |
|---|---|---|---|---|
| 1 | $2.00 x 1.15 | $2.300 | 1/(1.10)^1 | $2.091 |
| 2 | $2.30 x 1.15 | $2.645 | 1/(1.10)^2 | $2.186 |
| 3 | $2.645 x 1.15 | $3.042 | 1/(1.10)^3 | $2.285 |
| 4 | $3.042 x 1.15 | $3.498 | 1/(1.10)^4 | $2.389 |
PV of high-growth dividends = $2.091 + $2.186 + $2.285 + $2.389 = $8.951
Step 2: Calculate terminal value at the END of year 4
The terminal value uses the Gordon model applied at the transition point. The first stable-growth dividend is D5:
D5 = D4 x (1 + g_stable) = $3.498 x 1.04 = $3.638
TV4 = D5 / (r - g_stable) = $3.638 / (0.10 - 0.04) = $3.638 / 0.06 = $60.633
Step 3: Discount terminal value back to today
PV of TV = $60.633 / (1.10)^4 = $60.633 / 1.4641 = $41.413
Step 4: Sum everything
V0 = $8.951 + $41.413 = $50.36
Common Mistakes to Avoid
- Wrong terminal value timing: TV4 is the value AT time 4, not time 5. It captures all dividends from year 5 onward, valued at the end of year 4.
- Using D4 instead of D5 in terminal value: The Gordon model needs the NEXT period's dividend. TV4 = D5/(r-g), not D4/(r-g).
- Forgetting to discount TV: TV4 sits 4 years in the future. You must bring it back: TV4/(1+r)^4.
- Growth rate exceeds required return: If g >= r, the model breaks. Always check this.
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