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Dividend Theories: Walter, Gordon, and MM Models

Prerequisites

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1. WALTER'S MODEL

Proposed by: Professor James E. Walter (1963)

1.1 Basic Proposition

Dividend policy affects firm value when internal rate of return (r) differs from cost of equity (Ke).

1.2 Walter's Formula

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1.3 Walter's Optimal Dividend Policy

Case 1: r > Ke (Growth Firm)

  • Return on investment > Cost of equity
  • Optimal Policy: ZERO dividend (100% retention)
  • Retain all earnings to invest at higher return
  • Share price maximized when D = 0

Case 2: r < Ke (Declining Firm)

  • Return < Cost of equity
  • Optimal Policy: 100% payout (no retention)
  • Distribute all earnings; don't invest at low returns
  • Share price maximized when D = E

Case 3: r = Ke (Normal Firm)

  • Return = Cost of equity
  • Optimal Policy: Dividend policy IRRELEVANT
  • Share price same regardless of payout
  • Any policy gives same value

1.4 Numerical Problem (Exam Format)

Problem: Calculate market price per share using Walter's model:

EPS (E) = ₹10
Cost of Equity (Ke) = 10% = 0.10
Internal Rate of Return (r) = 15% = 0.15
Dividend per share (D) = ₹4

Solution:

Step 1: Apply Walter's Formula

P = [D + (E - D) × (r/Ke)] / Ke
P = [₹4 + (₹10 - ₹4) × (0.15/0.10)] / 0.10
P = [₹4 + ₹6 × 1.5] / 0.10
P = [₹4 + ₹9] / 0.10
P = ₹13 / 0.10
P = ₹130

Answer: Market price per share = ₹130

Interpretation: Since r (15%) > Ke (10%), this is a growth firm. Lowering dividend (increasing retention) would increase share price further.

1.5 Assumptions of Walter's Model

  1. All financing through retained earnings (no external financing)
  2. r and Ke constant
  3. 100% payout ratio or 100% retention
  4. Constant EPS
  5. Infinite life of firm

1.6 Criticisms

  • Unrealistic to assume no external financing
  • r and Ke change over time
  • Ignores risk differences
  • Not applicable to real-world scenarios

2. GORDON'S MODEL

Proposed by: Myron J. Gordon (1962)

2.1 Basic Proposition

"Bird-in-hand" theory: Investors prefer current dividends (certain) over future capital gains (uncertain).

2.2 Gordon's Growth Model Formula

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2.3 Gordon's Optimal Policy

Depends on r vs Ke:

  • If r > Ke: Retain more (low payout) → Higher P
  • If r < Ke: Distribute more (high payout) → Higher P
  • If r = Ke: Irrelevant

Similar conclusion to Walter, but Gordon emphasizes uncertainty resolution through dividends.

2.4 Numerical Problem (Exam Format)

Problem: Calculate share price using Gordon's model:

EPS (E) = ₹20
Retention Ratio (b) = 60% = 0.60
Return on Investment (r) = 12% = 0.12
Cost of Equity (Ke) = 10% = 0.10

Solution:

Step 1: Calculate Growth Rate

g = b × r
g = 0.60 × 0.12
g = 0.072 or 7.2%

Step 2: Calculate Dividend

Dividend (D1) = E(1 - b)
D1 = ₹20 × (1 - 0.60)
D1 = ₹20 × 0.40
D1 = ₹8

Step 3: Apply Gordon's Formula

P = D1 / (Ke - g)
P = ₹8 / (0.10 - 0.072)
P = ₹8 / 0.028
P = ₹285.71

Alternative Method:

P = E(1-b) / (Ke - br)
P = ₹20(1-0.60) / (0.10 - 0.60×0.12)
P = ₹20 × 0.40 / (0.10 - 0.072)
P = ₹8 / 0.028
P = ₹285.71

Answer: Market price per share = ₹285.71

2.5 Assumptions of Gordon

  1. All-equity financed firm (no debt)
  2. No external equity
  3. r and Ke constant
  4. Retention ratio (b) constant
  5. Ke > br (otherwise formula breaks down)

2.6 Criticisms

  • Assumes r constant (unrealistic)
  • Ignores external financing
  • Not applicable when Ke < g (formula gives negative/infinite values)

3. MODIGLIANI-MILLER (MM) APPROACH

Proposed by: Franco Modigliani and Merton Miller (1961)

3.1 Basic Proposition

Dividend policy is IRRELEVANT to firm value in perfect capital markets.

Why? Shareholders are indifferent between:

  • Receiving dividends now, OR
  • Receiving capital gains later (from retained earnings invested)

3.2 MM Logic

Homemade Dividends:

  • If shareholder wants cash: Sell some shares (create own dividend)
  • If shareholder doesn't need cash: Reinvest dividends in more shares
  • Result: Can replicate any payout policy personally

3.3 MM Value Formula

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3.4 MM Assumptions (Perfect Market)

  1. No Taxes (or same tax on dividends and capital gains)
  2. No Transaction Costs (free to buy/sell shares)
  3. No Flotation Costs
  4. Perfect Information (all investors have same info)
  5. Rational Investors

3.5 Criticisms

Real World Violations:

  1. Taxes: Dividends often taxed higher than capital gains
  2. Transaction Costs: Selling shares costs money (brokerage)
  3. Flotation Costs: Issuing new shares is expensive
  4. Information Asymmetry: Insiders know more than outsiders
  5. Behavioral Factors: Investors prefer dividends psychologically

Conclusion: In reality, dividend policy DOES matter.

4. Comparison of Three Theories

TheoryRelevance?Optimal PolicyKey AssumptionPractical?
WalterRelevantDepends on r vs KeAll internal financingNo
GordonRelevantDepends on r vs KeBird-in-hand preferenceSomewhat
MMIrrelevantAny policy equivalentPerfect marketsNo (theoretical)

Consensus: r > Ke → Retain; r < Ke → Distribute; r = Ke → Irrelevant

Exam Pattern Questions and Answers

Question 1: "Calculate market price using Walter's Model." (6 Marks)

Given: E = ₹8, Ke = 12%, r = 16%, D = ₹3

Solution:

P = [D + (E - D)(r/Ke)] / Ke
P = [₹3 + (₹8 - ₹3)(0.16/0.12)] / 0.12
P = [₹3 + ₹5 × 1.33] / 0.12
P = [₹3 + ₹6.67] / 0.12
P = ₹9.67 / 0.12
P = ₹80.58

Answer: ₹80.58

Question 2: "State MM hypothesis on dividend irrelevance." (4 Marks)

Answer: Modigliani-Miller proposed that in a perfect capital market, dividend policy is irrelevant to firm value. Shareholders can create "homemade dividends" by selling shares if they need cash, or reinvest dividends if they don't. The value is determined by investment decisions and earning power, not by how earnings are distributed. Assumptions include no taxes, no transaction costs, and perfect information - which don't hold in reality, making the theory more theoretical than practical.

Summary

Three Major Theories:

  1. Walter: r vs Ke determines optimal policy
  2. Gordon: Similar to Walter + Bird-in-hand argument
  3. MM: Dividend irrelevant in perfect markets

Common Thread (Walter & Gordon):

  • If r > Ke → Retain (growth firm)
  • If r < Ke → Distribute (declining firm)
  • If r = Ke → Irrelevant (normal firm)

Real World: Dividend policy DOES matter due to taxes, costs, and behavioral factors.

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Quiz Time! 🎯

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