Chapter 16

Capital Structure Decisions: Part II

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

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.

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

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

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)

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

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)

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.

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.

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)

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

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

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

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%

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

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.

16-18

Propositions I & II

sUr

EBIT

WACC

EBIT UL VV

rsL = rsU + (rsU - rd)(D/S)

Proposition I:

Proposition II:

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)

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)

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)

16-22

Tax Shield and Value of U

sUU

D

D

r

)T1(EBITSV

r

DTrTD

Shield Tax

(16-5)

16-23

Hamada’s Equation

)]SD)T1(1[bb U (16-7)

Beta increases with leverage

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.

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%

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%

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

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

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

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

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

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

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)

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.

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.

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)

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)

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

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

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

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

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)

16-43

Risky Debt

MM and Hamada assume riskless debt Βd = 0

If Bd ≠ 0:

MRFdd

MdRFd

RP/)rr(b

RPbrr

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%

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

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%

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

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)

16-49

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

16-50

Kunkel Variables

P = $20 million (firm value) X = $10 million (face value of

debt) T = 5 years (maturity of debt) rRF = 6% σ = 40%

16-51

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)

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.

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

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

16-55

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

16-56

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.

16-57

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

16-58

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

16-59

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.

16-60

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

16-61

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)

16-62

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