Can someone walk through a two-stage DDM with a timeline? I keep getting the terminal value timing wrong.

Question

AcadiFi · Accepted Answer

The two-stage DDM is the workhorse valuation model for CFA Level II equity questions. The key insight is getting the **terminal value timing** right — it sits at the *beginning* of the stable-growth phase, which is the *end* of the high-growth phase. ```mermaid graph LR T0[Year 0
D0 = $2.00
Current] --> T1[Year 1
D1 = $2.30
g = 15%] T1 --> T2[Year 2
D2 = $2.645
g = 15%] T2 --> T3[Year 3
D3 = $3.042
g = 15%] T3 --> T4[Year 4
D4 = $3.194
g = 5% stable] T3 -.-> TV[Terminal Value at T3
TV3 = D4 / r - g
= $3.194 / 0.06
= $53.23] style T0 fill:#0a0a0f,color:#c9a84c style T4 fill:#1e3a5f,color:#fff style TV fill:#c9a84c,color:#000 ``` **The Setup — Valuing Silverton Corp:** | Parameter | Value | |---|---| | Current dividend (D0) | $2.00 | | High-growth rate (years 1-3) | 15% | | Stable growth rate (year 4+) | 5% | | Required return (r) | 11% | **Step 1: Project dividends during the high-growth phase.** - D1 = $2.00 x 1.15 = **$2.300** - D2 = $2.30 x 1.15 = **$2.645** - D3 = $2.645 x 1.15 = **$3.042** **Step 2: Calculate the terminal value at the END of the high-growth phase.** The terminal value uses the Gordon Growth Model starting from the first stable-growth dividend: - D4 = D3 x (1 + g_stable) = $3.042 x 1.05 = **$3.194** - TV_3 = D4 / (r - g_stable) = $3.194 / (0.11 - 0.05) = $3.194 / 0.06 = **$53.233** This terminal value sits at **time 3** — it represents the value at year 3 of all dividends from year 4 to infinity. **Step 3: Discount everything back to today (time 0).** - PV of D1 = $2.300 / (1.11)^1 = **$2.072** - PV of D2 = $2.645 / (1.11)^2 = **$2.147** - PV of D3 = $3.042 / (1.11)^3 = **$2.224** - PV of TV_3 = $53.233 / (1.11)^3 = **$38.919** **Step 4: Sum all present values.** V0 = $2.072 + $2.147 + $2.224 + $38.919 = **$45.36** Silverton is worth $45.36 per share. If it trades at $40, it is undervalued. **The Most Common Mistakes:** 1. **Terminal value timing error:** Students calculate TV using D3 instead of D4. The Gordon model needs the *next period's* dividend. TV_3 = D4/(r-g), NOT D3/(r-g). 2. **Discounting TV to the wrong period:** TV_3 must be discounted 3 periods back, not 4. It represents value *at* time 3. 3. **Using the wrong growth rate for D4:** D4 grows at the *stable* rate (5%), not the high-growth rate (15%). 4. **Forgetting to add D3 and TV_3 separately:** Some students discount (D3 + TV_3) together, which is correct — but others forget D3 entirely. **When to Use Multi-Stage DDM vs. Other Models:** - Use DDM when the company pays regular dividends and dividends are related to earnings. - Use FCFE when dividends are not paid or diverge significantly from free cash flow. - Use residual income when book value data is reliable and the company has volatile earnings. Practice more multi-stage DDM problems in our CFA Level II equity question bank.

Can someone walk through a two-stage DDM with a timeline? I keep getting the terminal value timing wrong.

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