金融经济学Capital Structure课件
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VL = VU + TCD
Corporate Finance
Costs of Debt : Bankruptcy costs
➢ So far only benefits of debt
• Firms though don’t have all-debt financial structures There must be costs of debt
➢ There must be thus other costs:
➢ The main cost of debt is the probability of financial distress
➢ FD: situation where a firm can not satisfy its current obligations
Corporate Finance
Direct Costs of FD
0.5 VL = 400 VL = 800
➢ Therefore, VL = VU
➢ To avoid arbitrage, the two firms must have the same value.
Corporate Finance
Proposition II
➢ Under the same assumptions:
➢ No-arbitrage implies that the prices of both strategies be the same
Corporate Finance
Proof
➢ Cost of strategy A = 0.5VU = 0.5 x 800 = 400 ➢ Cost of strategy B = 0.5 VEL + 0.5 VDL = 0.5 VL ➢ They must be equal (why?):
increases the risk of the equity • The two effects must cancel each other (this is MM)
Corporate Finance
Proof
➢ Given expected cash flows {E(X1),E(X2),…,E(XT)}, the firm’s value is:
• If we discount this in perpetuity using the interest rate,
PV TS
TCrD r
TCD
Corporate Finance
MM with taxes:
• The difference between the after-tax cash flows of a levered and an unlevered firm is the tax shield of debt: TCrDD
➢ MM & CAPM
➢ Empirical evidence
Corporate Finance
The capital structure problem
➢ Finding the “optimal mix” of securities:
• Debt, • Equity, • Preferred Stock etc.
• Legal expenses, lawyers etc • In the US, amount to 1-3% of firm’s ex ante value
Corporate Finance
Indirect Costs of FD
➢ Direct costs don’t seem to be significant enough (1% of market value)
Capital Structure
Outline
➢ Modigliani & Miller propositions
• No tax case • Corporate taxes case
➢ Other costs and benefits of debt:
• Bankruptcy costs • FCF Hypothesis • Signaling & risk shifting
that maximises the value of the firm ➢ We focus on two polar securities: equity and debt
Corporate Finance
Proposition I
➢ Assuming:
• Total cash flows to security holders are independent of how the firm is financed;
Corporate Finance
Proof
➢ Suppose firms U and L are identical, except for their capital structures
• U (unlevered) is 100% equity financed, and is worth 800 • L (levered) is (partially) financed with debt. It has a zero
Corporate Finance
Meaning
➢ Intuition:
• More debt decreases the cost of capital (debt is cheaper) • But, it also increases the cost of capital, because it
Corporate Finance
Proof
➢ From (1) follows that the cost of capital (WACC) cannot depend on D (this proves part 1)
➢ Part 2 of the proposition follows from rewriting the WACC:
• The difference between VL and VU is then the present value of the future tax shields:
VL = VU + PVTS
• If debt is constant (perpetuity) this reduces to:
Corporate Finance
Proof
➢ For the levered firm, payoffs to equity and debt are:
xD = 0 xD = 600 xD = xD = 600 xD = 600
xE = 0 xE = 0 xD = xE = 400 xE = 1400
• Taxes • Bankruptcy costs • Agency issues
Corporate Finance
Corporate tax case
➢ Taxes
• Consider a firm with a permanent debt level D, paying r% per year
coupon bond with a face value of 600
➢ Consider two time periods only: t = 0 (now) and t = 1 ➢ CF at t = 1 is random: x {0, 600, 1000, 2000}, all
equally likely
➢ A firm in financial distress:
• Renegotiate the claims • Force liquidation (Chapter 7 in US) • Reorganise operations (Ch 11, uitstel van betaling)
➢ Direct costs are:
• There are no transaction costs, • No arbitrage opportunities exist,
➢ Then the total market value of the firm (the sum of the values all sources of capital) is independent of how the firm is financed
• No-arbitrage (this is a non-restrictive assumption)
Corporate Finance
MM, the other way around
➢ MM show that under those assumptions, CS is irrelevant
WA CC
E D
E E(rE )
D D
EE(rD )
E(rE)
WA CC
D E
(WA CC
E(rD ))
Corporate Finance
Assumptions
➢ The following assumptions are necessary to derive the results:
• No transaction costs (this is not so important and can be relaxed) such as information asymmetries or taxes » Which imply that cash flows are unaffected by capital structure (this is the key of the whole thing)
Corporate Finance
Proof
Cash Flow 0
600 1000 2000
Strategy A 0
300 500 1000
Strategy B 0
300 300+200 300+700
➢ The two strategies provide exactly the same payoffs
1) A firm’s cost of capital does not depend on its capital structure
2) The expected rate of return on a firm’s stock (cost of equity) increases in proportion to its debt-equity ratio
➢ But this means that if those assumptions are not satisfied, CS is relevant
➢ The way to look at CS is to look at how it can affect the real cash flows the firm generates:
Corporate Finance
Proof
➢ Claim: VU = VL ,
➢ where VL = VEL + VDL ➢ Suppose not. Then:
• Strategy A: Buy 50% of firm U • Strategy B: buy 50% of the debt of L and 50% of its equity
V
E(X1) 1 WACC
(1
E(X 2 ) WA C T ) WA CC)T
(1)
➢ By proposition I, the value (V) is independent of the capital structure, and therefore of D
➢ By assumption, {E(X1),E(X2),…,E(XT)} do not change with D either
• Yearly interest expenses are rD, which are tax deductible under current tax law
The firm saves TCrD in taxes every year, where TC is the corporate tax rate
Corporate Finance
Costs of Debt : Bankruptcy costs
➢ So far only benefits of debt
• Firms though don’t have all-debt financial structures There must be costs of debt
➢ There must be thus other costs:
➢ The main cost of debt is the probability of financial distress
➢ FD: situation where a firm can not satisfy its current obligations
Corporate Finance
Direct Costs of FD
0.5 VL = 400 VL = 800
➢ Therefore, VL = VU
➢ To avoid arbitrage, the two firms must have the same value.
Corporate Finance
Proposition II
➢ Under the same assumptions:
➢ No-arbitrage implies that the prices of both strategies be the same
Corporate Finance
Proof
➢ Cost of strategy A = 0.5VU = 0.5 x 800 = 400 ➢ Cost of strategy B = 0.5 VEL + 0.5 VDL = 0.5 VL ➢ They must be equal (why?):
increases the risk of the equity • The two effects must cancel each other (this is MM)
Corporate Finance
Proof
➢ Given expected cash flows {E(X1),E(X2),…,E(XT)}, the firm’s value is:
• If we discount this in perpetuity using the interest rate,
PV TS
TCrD r
TCD
Corporate Finance
MM with taxes:
• The difference between the after-tax cash flows of a levered and an unlevered firm is the tax shield of debt: TCrDD
➢ MM & CAPM
➢ Empirical evidence
Corporate Finance
The capital structure problem
➢ Finding the “optimal mix” of securities:
• Debt, • Equity, • Preferred Stock etc.
• Legal expenses, lawyers etc • In the US, amount to 1-3% of firm’s ex ante value
Corporate Finance
Indirect Costs of FD
➢ Direct costs don’t seem to be significant enough (1% of market value)
Capital Structure
Outline
➢ Modigliani & Miller propositions
• No tax case • Corporate taxes case
➢ Other costs and benefits of debt:
• Bankruptcy costs • FCF Hypothesis • Signaling & risk shifting
that maximises the value of the firm ➢ We focus on two polar securities: equity and debt
Corporate Finance
Proposition I
➢ Assuming:
• Total cash flows to security holders are independent of how the firm is financed;
Corporate Finance
Proof
➢ Suppose firms U and L are identical, except for their capital structures
• U (unlevered) is 100% equity financed, and is worth 800 • L (levered) is (partially) financed with debt. It has a zero
Corporate Finance
Meaning
➢ Intuition:
• More debt decreases the cost of capital (debt is cheaper) • But, it also increases the cost of capital, because it
Corporate Finance
Proof
➢ From (1) follows that the cost of capital (WACC) cannot depend on D (this proves part 1)
➢ Part 2 of the proposition follows from rewriting the WACC:
• The difference between VL and VU is then the present value of the future tax shields:
VL = VU + PVTS
• If debt is constant (perpetuity) this reduces to:
Corporate Finance
Proof
➢ For the levered firm, payoffs to equity and debt are:
xD = 0 xD = 600 xD = xD = 600 xD = 600
xE = 0 xE = 0 xD = xE = 400 xE = 1400
• Taxes • Bankruptcy costs • Agency issues
Corporate Finance
Corporate tax case
➢ Taxes
• Consider a firm with a permanent debt level D, paying r% per year
coupon bond with a face value of 600
➢ Consider two time periods only: t = 0 (now) and t = 1 ➢ CF at t = 1 is random: x {0, 600, 1000, 2000}, all
equally likely
➢ A firm in financial distress:
• Renegotiate the claims • Force liquidation (Chapter 7 in US) • Reorganise operations (Ch 11, uitstel van betaling)
➢ Direct costs are:
• There are no transaction costs, • No arbitrage opportunities exist,
➢ Then the total market value of the firm (the sum of the values all sources of capital) is independent of how the firm is financed
• No-arbitrage (this is a non-restrictive assumption)
Corporate Finance
MM, the other way around
➢ MM show that under those assumptions, CS is irrelevant
WA CC
E D
E E(rE )
D D
EE(rD )
E(rE)
WA CC
D E
(WA CC
E(rD ))
Corporate Finance
Assumptions
➢ The following assumptions are necessary to derive the results:
• No transaction costs (this is not so important and can be relaxed) such as information asymmetries or taxes » Which imply that cash flows are unaffected by capital structure (this is the key of the whole thing)
Corporate Finance
Proof
Cash Flow 0
600 1000 2000
Strategy A 0
300 500 1000
Strategy B 0
300 300+200 300+700
➢ The two strategies provide exactly the same payoffs
1) A firm’s cost of capital does not depend on its capital structure
2) The expected rate of return on a firm’s stock (cost of equity) increases in proportion to its debt-equity ratio
➢ But this means that if those assumptions are not satisfied, CS is relevant
➢ The way to look at CS is to look at how it can affect the real cash flows the firm generates:
Corporate Finance
Proof
➢ Claim: VU = VL ,
➢ where VL = VEL + VDL ➢ Suppose not. Then:
• Strategy A: Buy 50% of firm U • Strategy B: buy 50% of the debt of L and 50% of its equity
V
E(X1) 1 WACC
(1
E(X 2 ) WA C T ) WA CC)T
(1)
➢ By proposition I, the value (V) is independent of the capital structure, and therefore of D
➢ By assumption, {E(X1),E(X2),…,E(XT)} do not change with D either
• Yearly interest expenses are rD, which are tax deductible under current tax law
The firm saves TCrD in taxes every year, where TC is the corporate tax rate