How does Lintner's dividend smoothing model work mathematically?

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AcadiFi · Accepted Answer

**John Lintner (1956)** observed that managers follow a partial adjustment model toward a target payout ratio rather than paying a fixed fraction of each period's earnings. **Lintner model formula:** ΔD_t = α + β × (D_t* − D_{t-1}) + ε_t Where: - ΔD_t = change in dividend at time t - D_t* = target dividend = target payout ratio × EPS_t - D_{t-1} = prior period dividend - β = speed of adjustment (0 < β < 1) - α = constant (usually positive, small) **Interpretation:** - β = 0.3 (typical) means firms close ~30% of the gap between target and current dividend each period - High β = quick adjustment to earnings changes - Low β = smoother, slower adjustment **Example — Meadowvale Communications:** - Target payout ratio: 40% - Speed of adjustment β: 0.30 - Year 1: EPS = $3.00, D_{t-1} = $1.00. Target = 0.40 × $3.00 = $1.20. ΔD = 0.30 × ($1.20 − $1.00) = $0.06. New D = $1.06. - Year 2: EPS spikes to $5.00 (one-time). Target = $2.00. ΔD = 0.30 × ($2.00 − $1.06) = $0.28. New D = $1.34. - Year 3: EPS normalizes to $3.20. Target = $1.28. ΔD = 0.30 × ($1.28 − $1.34) = −$0.018. D drops slightly to $1.32. ```mermaid flowchart LR A[Current EPS] --> B[Target
Dividend] C[Prior
Dividend] --> D[Gap] B --> D D --> E[Partial
Adjustment] E --> F[New
Dividend] ``` **Implication:** Dividends are much less volatile than earnings. Analysts should not use current-year dividend / current-year EPS as the 'true' payout policy — it must be normalized over a cycle. **Modern applicability:** Holds well for mature dividend payers; weaker for tech firms that lean on buybacks.

How does Lintner's dividend smoothing model work mathematically?

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