Week 4: Payout Policy Section A Focus

Master MM Dividend Irrelevance, share repurchases, and payout mechanics for the 30-mark news analysis section.

      🎯 Exam Relevance: Payout policy is one of four core topics for Section A (news analysis). You need to: explain MM dividend irrelevance, demonstrate homemade dividends, compare dividends vs repurchases, and discuss signaling effects. Remember: 4 sentences per answer — identify issue, cite theory, apply to facts, state implication.
    

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Core Exam Concepts

🎯 MM Dividend Irrelevance Proposition

"With perfect capital markets, dividend policy does NOT affect the value of the firm."

Key insight: A dividend merely exchanges cash in the firm for cash in investors' pockets. When a dividend is paid, the firm value falls by exactly the dividend amount. The investor gets a capital loss that exactly matches their extra cash.

Price relationship:

P_ex-div = P_cum-div − Dividend per share

📊 Three Payout Mechanisms (All Equivalent Under MM)

Mechanism	How it works	Effect on shareholders
Cash Dividend	Firm pays cash to all shareholders proportionally	Cash ↑, Stock price ↓ by dividend amount
Share Repurchase	Firm buys back shares at market price	Sellers get cash; non-sellers own larger % of smaller firm
New Equity + Higher Dividend	Issue new shares to fund larger dividend	Old shareholders diluted but receive more cash

Under MM assumptions, shareholders are indifferent between all three — total wealth unchanged.

🔄 Homemade Dividends — The Key to Irrelevance

Shareholders can replicate ANY dividend policy by buying/selling shares:

Want more cash than dividend? → Sell shares ex-dividend
Want less cash than dividend? → Use dividend to buy more shares

📝 Section A Answer Template (4 Sentences)

1 Identify: "The article discusses [company]'s dividend/repurchase decision..."

2 Theory: "Under MM's dividend irrelevance, in perfect markets, payout policy doesn't affect firm value because..."

3 Apply: "In this case, [specific application to the article facts]..."

4 Implication: "Therefore, the market reaction should be [neutral/explained by other factors]..."

⚠️ When MM Breaks Down (Real World)

Dividend policy DOES matter when perfect market assumptions fail:

Taxes: Dividends vs capital gains taxed differently
Transaction costs: Buying/selling shares isn't free
Signaling: Dividend changes convey information (Lintner model)
Agency costs: Dividends reduce free cash flow for wasteful spending
Clientele effects: Some investors prefer dividends, others prefer gains

Key Formulas for Section B

Firm Value (with growing perpetuity):

V₀ = Cash + FCF₁/(1+r) + FCF₂/(1+r)² + ... + [FCF_n × (1+g)] / [(r-g) × (1+r)ⁿ]

Share Repurchase:

Number of shares repurchased = Cash for repurchase / Current stock price Stock price = Firm Value / Shares outstanding

Ex-Dividend vs Cum-Dividend Price:

P_cum = V₀ / Shares P_ex = (V₀ − Total Dividend) / Shares = P_cum − Dividend per share

Practice Problems (Exam-Style)

Work through these step-by-step. Show all formulas and calculations for partial credit.

Section B Style

Problem 1: Replicating Dividend Policies

MM Dividend Irrelevance • Homemade Dividends • ~15 mins

MC Company has excess cash and is considering two dividend policies:

Policy 1: £4 per share dividend
Policy 2: £8 per share dividend

Current share price: £20. An investor owns 20 shares.

Questions:

a) Show how the investor can replicate Policy 2 if MC adopts Policy 1, and vice-versa.

b) What is the investor's net worth in each case?

Step-by-Step Solution:

Part A: Replicating Policy 2 under Policy 1

Given: Dividend = £4/share, Current price = £20

Formula: P_ex-div = P_cum − Dividend = £20 − £4 = £16

Investor receives: 20 × £4 = £80

Investor wants: 20 × £8 = £160 (as if Policy 2)

Shortfall: £160 − £80 = £80

Shares to sell: £80 ÷ £16 = 5 shares

Result: 15 shares remaining + £160 cash

Part A: Replicating Policy 1 under Policy 2

Given: Dividend = £8/share

Formula: P_ex-div = £20 − £8 = £12

Investor receives: 20 × £8 = £160

Investor wants: 20 × £4 = £80

Excess cash: £160 − £80 = £80

Shares to buy: £80 ÷ £12 = 6.67 shares

Result: 26.67 shares + £80 cash

Part B: Net Worth Verification

Original: 20 × £20 = £400

Policy 1 replicated as 2: 15 × £16 + £160 = £240 + £160 = £400 ✓

Policy 2 replicated as 1: 26.67 × £12 + £80 = £320 + £80 = £400 ✓

              🎯 Exam Takeaway: Dividend policy is irrelevant because shareholders can create their preferred payout by buying/selling shares. Net worth remains unchanged.
            

Section B Style

Problem 2: Share Repurchase & Valuation

Firm Valuation • Repurchase Mechanics • Growing Perpetuity • ~20 mins

Iomega Corporation has:

$30 million excess cash (no debt)
Expected FCF: $110M (Year 1), $121M (Year 2), $133.1M (Year 3)
After Year 3: FCF grows at 2% perpetually
10 million shares outstanding
Cost of capital: 10%

Iomega uses $30M to repurchase shares, then distributes all future FCF as dividends.

Questions:

a) Determine firm value before repurchase

b) How many shares repurchased and at what price?

c) If instead paying $3/share dividend immediately, find cum-div and ex-div prices

Step-by-Step Solution:

Part A: Firm Valuation

Formula: V₀ = Cash + PV(FCFs) + PV(Terminal Value)

V₀ = 30 + 110/1.1 + 121/1.1² + 133.1/1.1³ + [133.1 × 1.02] / [(0.10 - 0.02) × 1.1³]

Calculate each term:

Cash = $30M
PV(FCF₁) = 110/1.1 = $100M
PV(FCF₂) = 121/1.21 = $100M
PV(FCF₃) = 133.1/1.331 = $100M
Terminal Value at t=3 = (133.1 × 1.02)/0.08 = $1,697.025M
PV(TV) = 1697.025/1.331 = $1,275M

V₀ = 30 + 100 + 100 + 100 + 1275 = $1,605 million

Part B: Share Repurchase

Stock price before repurchase:

P₀ = V₀ / Shares = $1,605M / 10M = $160.50 per share

Shares repurchased:

n = $30M / $160.50 = 0.187 million shares

Remaining shares: 10M − 0.187M = 9.813M shares

Part C: Dividend Alternative

Cum-dividend price:

P_cum = V₀ / Shares = $1,605M / 10M = $160.50

Total dividend: $3 × 10M = $30M

Ex-dividend price:

P_ex = (V₀ − Dividend) / Shares = ($1,605M − $30M) / 10M = $157.50

Or simply: P_ex = P_cum − Div/share = $160.50 − $3 = $157.50

              🎯 Exam Takeaway: Whether firm uses cash for repurchase or dividend, shareholder wealth is identical under MM. The key is correctly calculating firm value using the growing perpetuity formula.
            

Section B Style

Problem 3: Dividend vs Negative NPV Project

NPV • Investment Decision • Shareholder Wealth • ~10 mins

Quick Quiz — Test Your Knowledge

These MCQs test core concepts. Aim for 100% before the exam!

0 / 5

Correct Answers

1. Under MM's dividend irrelevance proposition, when a firm pays a $2 dividend, what happens to the stock price?

Stock price stays the same Stock price drops by exactly $2 Stock price increases by $2 Stock price drops by more than $2 due to signaling

Correct! Under MM, the stock price drops by exactly the dividend amount. The investor's capital loss equals their cash gain, leaving total wealth unchanged.

2. A company has 1,000 shares outstanding at $50/share. It uses $5,000 to repurchase shares. Under MM, how many shares are bought back?

100 shares at $50 each 111 shares at $45 each 50 shares at $100 each Cannot determine without more information

Correct! Shares repurchased = Cash / Price = $5,000 / $50 = 100 shares. Under MM, repurchase happens at the current market price.

3. An investor prefers $100 in cash but the firm only pays $60 dividend. The ex-dividend price is $40. What should the investor do?

Buy 1 share for $40 Sell 1 share for $40 Wait for the next dividend The investor cannot achieve their preferred payout

Correct! This is "homemade dividends." Investor receives $60, needs $40 more. Sell 1 share at $40 ex-div price. Total cash = $60 + $40 = $100. ✓

4. Which assumption is NOT required for MM dividend irrelevance to hold?

No taxes No transaction costs Constant dividend growth rate No information asymmetry

Correct! MM requires perfect markets: no taxes, no transaction costs, no information asymmetry, and the investment decision is separate from dividend decision. Constant growth is just a valuation assumption, not a market perfection requirement.

5. Firm value is $1,000M with 10M shares. After a $5/share dividend, what is the ex-dividend share price?

$100 $95 $50 $105

Correct! P_cum = $1,000M / 10M = $100. P_ex = $100 − $5 = $95. Or: Total dividend = $5 × 10M = $50M. P_ex = ($1,000M − $50M) / 10M = $95.

Interactive Calculators

Practice your calculations before the exam. These mirror Section B problem types.

📊 Dividend Impact Calculator

Firm Value ($M)

Shares Outstanding (M)

Dividend per Share ($)

$100.00

Cum-Dividend Price

$95.00

Ex-Dividend Price

$50M

Total Dividend Paid

🔄 Share Repurchase Calculator

Firm Value ($M)

Shares Outstanding (M)

Cash for Repurchase ($M)

$160.50

Share Price

0.187M

Shares Repurchased

9.813M

Shares Remaining

📈 Growing Perpetuity (Terminal Value)

Final Year FCF ($M)

Growth Rate (%)

Discount Rate (%)

Years to TV

$1,697M

Terminal Value (at year n)

$1,275M

PV of Terminal Value

Formula: TV = FCF_n × (1+g) / (r−g) | PV(TV) = TV / (1+r)ⁿ

📅 Cash Flow Timeline (Iomega Example)

Today

$30M Cash

Year 1

$110M

Year 2

$121M

Year 3

$133.1M

∞

Perpetuity

g = 2%

📋 Week 4 Exam Checklist

Before moving on, make sure you can:

☐ Explain MM dividend irrelevance and its assumptions
☐ Calculate cum-dividend and ex-dividend prices
☐ Demonstrate homemade dividends (replicating any payout)
☐ Compare dividends vs share repurchases under MM
☐ Calculate shares repurchased given cash and price
☐ Value a firm using growing perpetuity for terminal value
☐ Explain why MM breaks down in real markets (taxes, signaling, etc.)
☐ Section A: Use the 4-sentence answer template