Can someone walk through a two-stage DDM with actual numbers? I keep getting the terminal value calculation wrong.

Question

AcadiFi · Accepted Answer

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**

```mermaid
flowchart LR
    subgraph "High Growth Phase (15%)" 
        D1["D1=$2.30"] --> D2["D2=$2.65"]
        D2 --> D3["D3=$3.04"]
        D3 --> D4["D4=$3.50"]
    end
    subgraph "Stable Phase (4%)" 
        D5["D5=$3.64"] --> INF["...forever"]
    end
    D4 --> D5
    D4 -. "TV4 = D5/(r-g)
= $60.63" .-> TV["Terminal
Value"]
    TV -. "Discount to
today at r" .-> V0["V0 = $50.36"]
```

**Common Mistakes to Avoid**

1. **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.
2. **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).
3. **Forgetting to discount TV:** TV4 sits 4 years in the future. You must bring it back: TV4/(1+r)^4.
4. **Growth rate exceeds required return:** If g >= r, the model breaks. Always check this.

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Can someone walk through a two-stage DDM with actual numbers? I keep getting the terminal value calculation wrong.

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Practice Questions

Input	Value
D0 (just paid)	$2.00
High growth rate (years 1-4)	15%
Stable growth rate (year 5+)	4%
Required return (r)	10%

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