Capital Structure
Capital Structure 1.................................................................................................................. 1
Modigliani and Miller’s (1958) Proposition..........................................................................1
Capital Structure with Corporate Taxes.............................................................................3
Capital Structure with both Corporate and Personal Taxes................................................5
Empirical Evidence on Taxes and Capital Structure..........................................................7
The Low-leverage Puzzle...................................................................................................8
Capital Structure 2:.................................................................................................................9
Bankruptcy Costs and Financial Distress...........................................................................9
The Trade-off Theory of Optimal Capital Structure............................................................9
Asymmetric Information Models.......................................................................................10
Predictions of POT........................................................................................................... 13
Agency Costs of Equity and Corporate Governance............................................................15
1. Corporate Governance definition.................................................................................15
2. Principal-Agent Model..................................................................................................15
3. Agency Problems.........................................................................................................15
4. Solutions to Agency Costs of Equity............................................................................18
Capital Structure 3: Agency cost of debt...............................................................................24
Agency cost of debt......................................................................................................... 24
Source of debtholder-shareholder conflicts......................................................................24
Control Mechanisms........................................................................................................ 26
Theories of capital structure with agency costs................................................................27
Capital Structure 1
Modigliani and Miller’s (1958) Proposition
1. M&M Irrelevance proposition 1:
● Total value of firm is not affected by capital structure under perfect market
condition : Firm value = total cash flow generated by assets
, ● Assumptions of the MM1
○ Perfect capital market without frictions
- No taxes, transaction and insurance costs
- No agency problems and asymmetric information
○ Investors and firm can borrow and lend at the same rate
○ Financing decisions do not change the cash flows generated by
investments
○ No Arbitrage
● Proof of the proposition
○ Arbitrage opportunity are available if MM1 does NOT hold
○ Find 2 identical firms except for capital structures (V l∧V U ¿
○ Arbitrage exists if both firms do not have the same value
○ Example: Homemade leverage, V U > V l
- V U = £100m; V l = £90m where D = £30m and El = £60m
- An investor buy 10% of El (£6m) and 10% of D (£3m)
- And then short(sell) 10% of V U
- Earning a profit of £1 m
○ Arbitrage Profit
- At the t =1, investors receive 10% from levered firms’ share
and bonds: 0.1[X - (1+rD)*D] + 0.1(1+rD)*D
- However, the investors will have to pay out 10% of unlevered
firm ( 0.1X) to cover short sale: 0.1[X - (1+rD)*D] + 0.1(1+rD)*D
- 0.1X = 0
- Earning a profit of £1 m
- Existence of Arbitrage opportunity violates the assumption of
MM1
2. MM’s Irrelevance Proposition 2:
● The cost of equity of a levered firm (r e ¿increases as the D/E increases
(Amount of debt ⇑, cost of equity ⇑, BUT WACCremain unchanged)
● Intuition: debt may be cheaper BUT it increases the financial risk and the
cost of equity
● Derivation of Proposition 2
- Consider levered firm L = a portfolio = debit + equity
- Return on L = WACC (per tax)
E D
r WACC = r e ( ¿+r d ( )
V V
- The overall expected return on L is :
Net operating income(NOI )
r WACC =
V
- Based on MM’s assumption, NOI and V does NOT affected by capital
structure choice, so V l =V U
, - Therefore: r WACC = r U
- Next:
E D
r U = r WACC = r e ( ¿+r d (1−T c )( )
V V
- Equation of MM proposition 2:
D
r e =r U +( )(r −r )
E U d
● Implications of MM2
- Increase the amount of debt does NOT reduce WACC
- Any attempt to decrease the WACC by issuing more debts will offset
by the increase in cost of equity (WACC unchanged)
● Minimising the cost of capital
- r E rises moderately as more debt is used
- WACC ↓ first then ↑
Capital Structure with Corporate Taxes
● The total amount paid to investors is higher with leverage
● Tax advantage of debt financing: tax shield of interest payment
Capital Structure 1.................................................................................................................. 1
Modigliani and Miller’s (1958) Proposition..........................................................................1
Capital Structure with Corporate Taxes.............................................................................3
Capital Structure with both Corporate and Personal Taxes................................................5
Empirical Evidence on Taxes and Capital Structure..........................................................7
The Low-leverage Puzzle...................................................................................................8
Capital Structure 2:.................................................................................................................9
Bankruptcy Costs and Financial Distress...........................................................................9
The Trade-off Theory of Optimal Capital Structure............................................................9
Asymmetric Information Models.......................................................................................10
Predictions of POT........................................................................................................... 13
Agency Costs of Equity and Corporate Governance............................................................15
1. Corporate Governance definition.................................................................................15
2. Principal-Agent Model..................................................................................................15
3. Agency Problems.........................................................................................................15
4. Solutions to Agency Costs of Equity............................................................................18
Capital Structure 3: Agency cost of debt...............................................................................24
Agency cost of debt......................................................................................................... 24
Source of debtholder-shareholder conflicts......................................................................24
Control Mechanisms........................................................................................................ 26
Theories of capital structure with agency costs................................................................27
Capital Structure 1
Modigliani and Miller’s (1958) Proposition
1. M&M Irrelevance proposition 1:
● Total value of firm is not affected by capital structure under perfect market
condition : Firm value = total cash flow generated by assets
, ● Assumptions of the MM1
○ Perfect capital market without frictions
- No taxes, transaction and insurance costs
- No agency problems and asymmetric information
○ Investors and firm can borrow and lend at the same rate
○ Financing decisions do not change the cash flows generated by
investments
○ No Arbitrage
● Proof of the proposition
○ Arbitrage opportunity are available if MM1 does NOT hold
○ Find 2 identical firms except for capital structures (V l∧V U ¿
○ Arbitrage exists if both firms do not have the same value
○ Example: Homemade leverage, V U > V l
- V U = £100m; V l = £90m where D = £30m and El = £60m
- An investor buy 10% of El (£6m) and 10% of D (£3m)
- And then short(sell) 10% of V U
- Earning a profit of £1 m
○ Arbitrage Profit
- At the t =1, investors receive 10% from levered firms’ share
and bonds: 0.1[X - (1+rD)*D] + 0.1(1+rD)*D
- However, the investors will have to pay out 10% of unlevered
firm ( 0.1X) to cover short sale: 0.1[X - (1+rD)*D] + 0.1(1+rD)*D
- 0.1X = 0
- Earning a profit of £1 m
- Existence of Arbitrage opportunity violates the assumption of
MM1
2. MM’s Irrelevance Proposition 2:
● The cost of equity of a levered firm (r e ¿increases as the D/E increases
(Amount of debt ⇑, cost of equity ⇑, BUT WACCremain unchanged)
● Intuition: debt may be cheaper BUT it increases the financial risk and the
cost of equity
● Derivation of Proposition 2
- Consider levered firm L = a portfolio = debit + equity
- Return on L = WACC (per tax)
E D
r WACC = r e ( ¿+r d ( )
V V
- The overall expected return on L is :
Net operating income(NOI )
r WACC =
V
- Based on MM’s assumption, NOI and V does NOT affected by capital
structure choice, so V l =V U
, - Therefore: r WACC = r U
- Next:
E D
r U = r WACC = r e ( ¿+r d (1−T c )( )
V V
- Equation of MM proposition 2:
D
r e =r U +( )(r −r )
E U d
● Implications of MM2
- Increase the amount of debt does NOT reduce WACC
- Any attempt to decrease the WACC by issuing more debts will offset
by the increase in cost of equity (WACC unchanged)
● Minimising the cost of capital
- r E rises moderately as more debt is used
- WACC ↓ first then ↑
Capital Structure with Corporate Taxes
● The total amount paid to investors is higher with leverage
● Tax advantage of debt financing: tax shield of interest payment
