chapter 16 capital structure decisions: part ii. 16-2 topics in chapter mm models: without corporate...
TRANSCRIPT
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Chapter 16
Capital Structure Decisions: Part II
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16-2
Topics in Chapter
MM models: Without corporate taxes (1958) With corporate taxes (1963)
Miller model: (1977) With corporate and personal taxes
Extension to MM with growth and the tax shield is risky
Equity as an option
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16-3
Modigliani and Miller (MM) Published theoretical papers that
changed the way people thought about financial leverage
Nobel prizes in economics MM 1958 MM 1963 Miller 1977 The papers differed in their assumptions
about taxes.
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16-4
Model Assumptions
1. No taxes2. Business risk measured by σEBIT
Firms with same risk = “homogeneous risk class”
3. Homogeneous expectationsAll investors have same estimates of firm’s future EBIT
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16-5
4. Perfect capital marketsNo transactions costsAll can borrow and lend at riskfree rate
5. Debt is risklessInterest rate on all debt = rf
6. All cash flows are perpetuitiesAll firms are expect zero growthAll bonds are perpetuities
Model Assumptions
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16-6
Proposition I:
MM with Zero Taxes (1958)No agency or financial distress costs.VF = EBIT capitalized at WACC
L = Levered rrL = levered return
U = Unlevered rrU =unlevered return
sUr
EBIT
WACC
EBIT UL VV (16-1)
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16-7
MM (1958) Proposition I
Implications: When there are no taxes, the value of
the firm is independent of its leverage The WACC is completely independent
of a firm’s capital structure Regardless of the amount of debt a
firm uses, its WACC = cost of equity that it would have if it used no debt
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16-8
Proposition II:
rsL = rsU + (rsU - rd)(D/S)
MM with Zero Taxes (1958)
rrL = levered return
rrU =unlevered returnD = market value of firm’s debtS = market value of firm’s equityrd = constant cost of debt
(16-2)
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16-9
MM (1958) Proposition II When there are no taxes:
(1) The cost of equity to an unlevered firm in the same risk class, rsU, plus
(2) A risk premium depending on the difference between an unlevered firm’s costs of debt and equity and the amount of debt used
As debt increases, the cost of equity also increases, and in a mathematically precise manner.
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16-10
MM (1958) Implications
Using more debt will noe increase the value of the firm The benefits of additional debt will be
exactly offset by the increase in the cost of equity
In a world without taxes, both the value of the firm and its WACC would be unaffected by its capital structure.
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16-11
MM (1958) Arbitrage Proof
Assume all firms = 0 growth EBIT remains constant All earnings paid out as dividends
sL
d
sLsL r
Dr-(EBIT
r
IncomeNet
r
DividendsS
) (16-3)
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16-12
Firms U and L are in same risk class EBIT (U,L) = $900,000 Firm U has no debt; rsU = 10% Firm L has $4,000,000 debt at rd = 7.5% All net income is paid out as dividends No corporate or personal taxes Both firms are “no growth” (g=0)
MM (1958) Arbitrage Proof
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16-13
Before Any Arbitrage
000,000,10 $
000,000,6$000,000,4$SDV
000,000,6$
10.0
)000,000,4($75.0000,000,9$
r
DrEBITS
000,000,9$r
DrEBITSV
LLL
sU
dL
sU
dUU
0.10
$600,000
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16-14
VU = $9,000,000 Dis-equilibrium VL = $10,000,000 Situation
Suppose you own 10% of L’s stock Market value = $600,000
If VL >VU, then you can increase your income without increasing your risk
Before Any Arbitrage
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16-15
Arbitrage Proof
1. Sell your 10% of L’s stock for $600,000
2. Borrow an amount = 10% of L’s debt($400,000)
3. Buy 10% of U’s stock for $900,0004. Invest the remaining $100,000 at
7.5%
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16-16
Before & After Arbitrage
10% of L's $600,000 10% of U's $900,000equity income $60,000 equity income 90,000
Less 7.5% interest on $400,000 loan (30,000)Plus 7.5% interest on extra $100,000 7,500
TOTAL INCOME $60,000 TOTAL INCOME $67,500
Old Portfolio New Portfolio
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16-17
Arbitrage ProofPropositions I and II
Substitute $400,000 of “homemade leverage” for L’s leverage
Neither effective debt nor risk has changed
Profit motive would force price of L’s stock down and U’s up until market values are equal.
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16-18
Propositions I & II
sUr
EBIT
WACC
EBIT UL VV
rsL = rsU + (rsU - rd)(D/S)
Proposition I:
Proposition II:
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16-19
Without taxesCost of Capital (%)
26
20
14
8
0 20 40 60 80 100Debt/Value Ratio (%)
rs
WACC
rd
MM Relationships Between Capital Costs and Leverage (D/V)
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16-20
The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost.
Although rd remains constant, rs
increases with leverage. The increase in rs is exactly sufficient
to keep the WACC constant.
MM Relationships Between Capital Costs and Leverage (D/V)
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16-21
With corporate taxes added, the MM propositions become:
Proposition I:
VL = VU + TD
Proposition II:
rsL = rsU + (rsU - rd)(1 - T)(D/S)
MM (1963) with Corporate Taxes
(16-4)
(16-6)
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16-22
Tax Shield and Value of U
sUU
D
D
r
)T1(EBITSV
r
DTrTD
Shield Tax
(16-5)
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16-23
Hamada’s Equation
)]SD)T1(1[bb U (16-7)
Beta increases with leverage
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16-24
Notes About the New Propositions
1. When corporate taxes are added,VL ≠ VU. VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm.
2. rsL increases with leverage at a slower rate when corporate taxes are considered.
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16-25
Frederickson Water Company No debt E(EBIT) = $2,400,000 No growth All income paid out as dividends If uses debt, rD=8%
Any debt would be used to repurchase stock Beta = 0.80 (bU) Risk-free rate = 8% rsU = 12% Market risk premium = 5%
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16-26
VU = = = $20.0mEBIT
rsU
$2.4 m0.12
Value of FWC (No Taxes)
With No Debt & No Taxes
With $10.0m Debt & No Taxes
S=V-D = $20 m - $10 m = $10 m
rsL = rsU + (rsU - rd)(D/S)
= 12% + (12%-8%)($10/$10) = 16%
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16-27
FWC’s WACC
12.0% 16%)($10/$20)( 8%)(1.0)($10/$20)(
sLD r)VS()T1)(r)(V
D(WACC
• Value of the firm and the firm’s WACC are independent of the amount of debt
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16-28
FWCC with Corporate Taxes Tax rate = 40% Debt = $10 m EBIT = $4,000,000*
Taxes will reduce net income and EBIT
EBIT increased to make comparison easier
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16-29
m14$m10$m24$DVS
m24$)m10($4.0m20$TDVV
m20$12.0
)60.0(m4$
r
)T1(EBITSV
UL
sUU
FWCC With Corporate Taxes
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16-30
1429.1
]SD)T1(1[bb
r)V/S()T1)(r)(V/D(WACC
%71.13)m14$/m10)($6.0%)(8%12(%12
)SD)(T1)(rr(rr
U
sLd
dsUsUsL
$14m$10m0.40)-(10.80[1
10.0% 13.71%)($14/$24)(8%)(0.6)($10/$24)(
FWCC with Corporate Taxes
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16-31
Cost of Capital (%)
26
20
14
8
0 20 40 60 80 100Debt/Value Ratio (%)
rs
WACCrd(1 - T)
MM: Capital Costs vs. Leverage with Corporate Taxes
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16-32
Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.
Value of Firm, V (%)
4
3
2
10 0.5 1.0 1.5 2.0 2.5
Debt(Millions of $)
VL
VU
TD
MM: Value vs. Debt with Corporate Taxes
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16-33
Miller’s Proposition I:
VL = VU + [1 - ]D
Tc = corporate tax rateTd = personal tax rate on debt incomeTs = personal tax rate on stock income
(1 - Tc)(1 - Ts)(1 - Td)
Miller Model with Personal Taxes
(16-12)
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16-34
VL = VU + [1 - ]D
= VU + (1 - 0.75)D
= VU + 0.25D
(1 - 0.40)(1 - 0.12)(1 - 0.30)
Tc = 40%, Td = 30%, Ts = 12%
Value rises with debt; each $100 increase in debt raises L’s value by $25.
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16-35
Miller vs. MM Model with Corporate Taxes
If only corporate taxes, thenVL = VU + TcD = VU + 0.40D
Here $100 of debt raises value by $40.
Personal taxes lowers the gain from leverage, but the net effect depends on tax rates.
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16-36
Miller Model Implications
1. The right-hand term = gain from leverage
2. If taxes ignored, then Miller=Original MM
3. If personal taxes ignored, then Miller = MM with corporate taxes
D)T1(
)T1)(T1(1VV
d
scUL
(16-12)
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16-37
Miller Model Implications
4. If Ts=Td, right-hand term = Tc
5. If (1-T)(1-T) =(1-T), right-hand term= 0
No gain to leverage
D)T1(
)T1)(T1(1VV
d
scUL
(16-12)
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16-38
Criticisms of MM and Miller
No one believes the models holds precisely Models assume personal and corporate
leverage are perfect substitutes Homemade leverage puts stockholders
in grater risk of bankruptcy Brokerage costs are assumed to be 0
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16-39
Criticisms of MM and Miller
No one believes the models holds precisely
4. Individuals cannot borrow at the risk-free rate
5. For the Miller equilibrium to be reached, the tax benefit from debt mustbe the same for all firms
6. MM and Miller assumed no cost to financial distress
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16-40
Under MM (with taxes; no growth) VL = VU + TD
This assumes the tax shield is discounted at the cost of debt.
The debt tax shield will be larger if the firms grow
MM with Nonzero Growth & A Risky Tax Shield
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16-41
MM with Nonzero Growth & a Risky Tax Shield
Value of (growing) tax shield =
Value of levered firm with growth:
gr
TDrV
TS
dTS
(16-14)
(16-15)TDgr
rVV
TS
dUL
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16-42
MM with Nonzero Growth & a Risky Tax Shield
If rTS = rsU:
(16-16)
S
D)bb(bb
SD)rr(rr
TDgr
rVV
dUU
dsUsUsL
sU
dUL
(16-17)
(16-18)
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16-43
Risky Debt
MM and Hamada assume riskless debt Βd = 0
If Bd ≠ 0:
MRFdd
MdRFd
RP/)rr(b
RPbrr
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16-44
MM Extension with GrowthPeterson Power Illustration
E(FCF) = $1 m G = 7% rsU = 12% T = 40% VU = $20 m $10 m debt rd= 8%
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16-45
Peterson Power
%78.10%44.14)3788.00.1(%8)40.01(3788.0WACC
%44.14)6212.0
3788.0%)(8%12(%12S
D)rr(rr
m4.16$m10$m4.26$DVS
m4.26$07.012.0
m10$40.008.0m20$TD
gr
rVV
dsUsUsL
L
sU
dUL
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16-46
FWC vs. PPIFrederickson Peterson
Debt $10 m $10 mr(d) 8% 8%E(EBIT) $4 mE(FCF) $1 mg 0 7%r(sU) 12% 12%T 40% 40%V(U) $20 m $20V(L) $24 m $26.4 mS $14 m $16.4 mr(sL) 13.71% 14.44%WACC 10% 10,78%
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16-47
Cost of Capital for MM and Extension
0%
5%
10%
15%
20%
25%
30%
35%
40%
0% 10% 20% 30% 40% 50% 60% 70% 80%
D/V
MM cost of equity
MM WACC
Extension cost ofequityExtension WACC
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16-48
Equity as an Option: Kunkel, Inc.
Firm value (Debt + Equity) = $20 m Firm has $10 million face value of 5-year
zero coupon debt coming due soon If the current value of the firm (D+S) = $9
m: Firm will default on debt; equity holders get 0
If firm value > $10 m: Firm pays off the debt; equity holders keep the
firm Payoff to stockholders = Max(P-$10m,0)
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Notation
V = Value of the option P = Value of the firm (S+D) X = strike = value of debt rRF = risk-free rate σ = volatility of the underlying
asset T = time to maturity in years
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Kunkel Variables
P = $20 million (firm value) X = $10 million (face value of
debt) T = 5 years (maturity of debt) rRF = 6% σ = 40%
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The Black-Scholes Formulas
Tdd
T
T)2/2r()X/Pln(d
)d(N[eX)]d(N[PV
12
RF1
2Tr
1RF
: where
] (16-19)
(16-21)
(16-20)
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16-52
Formula Functions
ln = natural log N(x) = the probability that a normally
distributed variable with a mean of zero and a standard deviation of 1 is less than x
N(d1) and N(d2) denote the standard normal probability for the values of
d1 and d2.
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16-53
BSOPM Kunkel Example
P = $20 rRF = 6% σ = 40%
X = $10 T = 5
6632.0540.05576.1d
Tdd
5576.1540.0
5)240.006.0()1020ln(d
T
T)2/2r()X/Pln(d
2
12
2
1
RF1
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16-54
BSOPMCall Price Example
m $6.72 $13.28m - $20mV
Equity of Value $13.28 V
(0.7464)10e - 20(0.9403) V
d
s
5.06-
)d(NeX)d(NPV 2rT
1
d1 = 1.5576 N(1.5576) = 0.9403
d2 = 0.6632 N(0.6632) = 0.7464
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Zero-Coupon Debt Yield Debt yield for 5-year zero coupon debt
= (Face value / Price)1/5 – 1= ($10 million/ $6.72 million) – 1 = 8.27%
Yield on debt depends on: Probability of default Value of the option
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Managerial Incentives Managers can change a firm's by
changing the assets the firm invests in.
Changing can: Change the value of the equity, even if it
doesn't change the expected cash flows Transfer wealth from bondholders to
stockholders by making the option value of the stock worth more, which makes what is left, the debt value, worth less.
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Effect on Option Values Volatility = σ
Increased volatility increased upside potential and downside risk
Increased volatility is NOT good for the holder of a share of stock
Increased volatility is good for an option holder Option holder has no downside risk Greater potential for higher upside
payoff
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Bait and Switch Managers who know the effect of
volatility, might tell debtholders they are going to invest in one kind of asset, and, instead, invest in riskier assets.
“Bait and Switch” Bondholders will require:
Higher coupon rates Strict bond covenants as protection
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Risky Coupon Debt
More complex analysis With each coupon payment
management has an option on an option: If it makes the interest payment then it
purchases the right to later make the principal payment and keep the firm
This is called a compound option.
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Capital Structure TheoryThe Authors’ View
1. Debt financing has the benefit of tax deductibility so firms should have some debt in their capital structure
2. Financial distress and agency costs place limits on debt usage
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Capital Structure TheoryThe Authors’ View
3. “Pecking Order” Due to problems from asymmetric
information and flotation costs, low-growth firms should follow a pecking order in raising funds (R/E, debt, new equity)
High-growth firms whose growth involves tangible assets should follow the same pecking order (r/e, debt. Equity)
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Capital Structure TheoryThe Authors’ View
3. “Pecking Order” High-growth firms whose growth is
primarily in intangible assets should emphasize stock rather than debt
4. Firms should maintain reserve borrowing power