4. Capital Structure

1Capital Structure Decisions

Overview and preview of capital structure effects

Business versus financial risk

The impact of debt on returns

Capital structure theory

MM theory MM theory

Zero taxes

Corporate taxes

Bankruptcy cost

Example

Valuing equity as an option

2Basic Definitions

V = value of firm

FCF = free cash flow

WACC = weighted average cost of WACC = weighted average cost of capital

rs and rd are costs of stock and debt

ws and wd are percentages of the firm that are financed with stock anddebt.

3How can capital structure affect value?

)1( tt

WACC

FCFV

1 )1(ttWACC

(Continued)

WACC = wd (1-T) rd + ws rs

4A Preview of Capital Structure Effects

The impact of capital structure on value depends upon the effect of debt on:debt on:

WACC

FCF

(Continued)

5The Effect of Additional Debt

Effect on WACC Debt increases risk of bankruptcy

Causes pre-tax cost of debt, rd, to increase

Debtholders have a prior claim on cash flows relative to stockholders.

Debtholders fixed claim increases risk of Debtholders fixed claim increases risk of stockholders residual claim.

Cost of stock, rs, goes up.

Effect on FCF Tax shield effect

Reduces the taxes paid

Frees up more cash for payments to investors

6 Bankruptcy costs (direct and indirect) Direct costs: Legal fees, fire sales, etc. Indirect costs: Lost customers, reduction in

productivity of managers and line workers, reduction in credit (i.e., accounts payable) offered by suppliers

Additional debt can also affect the behavior of managers.

Reductions in agency costs (FCF problem) )

Imp

(how mangers behave when there is a lot of debt or not debt) debt pre-commits, or bonds, free cash flow

for use in making interest payments. Thus, managers are less likely to waste FCF on perquisites or non-value adding projects.

Increases in agency costs (Underinvestment problem)

debt can make managers too risk-averse, causing underinvestment in risky but positive NPV projects.

Net effect = ?

7Business Risk versus Financial Risk

Business risk:Uncertainty in future EBIT.

Depends on business factors such as competition, operating leverage, etc.competition, operating leverage, etc.

Financial risk:Additional risk concentrated on common

stockholders when financial leverage is used.

Depends on the amount of debt financing.

8Consider Two Hypothetical Firms

Both firms have same total asset of $20,000, EBIT of $3,000, and tax rate of 40%.

They differ only with respect to use of

Firm U Firm L

No debt $10,000 of 12% debt

They differ only with respect to use of debt.

9Impact of Leverage on Returns

EBIT $3,000 $3,000Interest

Firm U Firm L

InterestEBTTaxes (40%)NI

ROE

10

Now consider the fact that EBIT is not known with certainty. What is the

impact of uncertainty on stockholder profitability and risk for Firm U and

Firm L?

Continued

11

Firm U: Unleveraged

Prob. 0.25 0.50 0.25EBIT $2,000 $3,000 $4,000

EconomyBad Avg. Good

EBIT $2,000 $3,000 $4,000InterestEBTTaxes (40%)NI

12

Firm L: Leveraged

Prob.* 0.25 0.50 0.25EBIT* $2,000 $3,000 $4,000

EconomyBad Avg. Good

EBIT* $2,000 $3,000 $4,000InterestEBTTaxes (40%)NI

*Same as for Firm U.

13

Profitability Measures:

E(BEP) 15.0% 15.0%E(ROIC) 9.0% 9.0%E(ROE) 9.0% 10.8%

U L

E(ROE) 9.0% 10.8%

Risk Measures:

ROIC 2.12% 2.12%ROE 2.12% 4.24%

Temur SolievPencil

Temur SolievPencil

Temur SolievPencil

Temur SolievPencil

Temur SolievPencil

Temur SolievPencil

Temur SolievPencil

14

Summary

Ratios such as BEP and ROIC are unaffected by financial leverage.

L has higher expected ROE.

But L also has greater volatility of ROE.

Implication?

For leverage to increase expected ROE, it must be that E(BEP) > rd.

In the example, E(BEP) = 15% while interest rate = 12%.

15

Who are Modigliani and Miller (MM)?

They published theoretical papers that changed the way people thought about financial leverage.

They won Nobel prizes in economics for They won Nobel prizes in economics for their work.

MMs papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes.

16

What assumptions underlie the MMand Miller models?

Firms can be grouped into homogeneous classes based on business risk.business risk.

Investors have identical expectations about firms future earnings.

There are no transactions costs.(More...)

17

No financial distress costs.

All debt is riskless.

both individuals and corporations can borrow unlimited amounts of money at the risk-free rate.

Also, firms have zero growth. This implies expected EBIT is constant over time.

No agency costs. No agency costs.

MMs first paper (1958) assumed zero taxes. Later papers added taxes.

These assumptions were necessary for MM to prove their propositions on the basis of investor arbitrage.

18

Proposition I:

VL = VU.

MM with Zero Taxes (1958)

VL = VU.

Proposition II:

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

19

Firms U and L are in same business risk class.

EBITU,L = $500,000.

Given the following data, find V, S,rs, and WACC for Firms U and L.

Firm U has no debt; rsU = 14%.

Firm L has $1,000,000 debt at rd = 8%.

The basic MM assumptions hold.

There are no corporate or personal taxes.

20

1. Find VU and VL.

VU = = = $3,571,429.

V = V = $3,571,429.

EBITrsU

$500,0000.14

VL = VU = $3,571,429.

21

VL = D + S = $3,571,429

2. Find the market value of Firm Ls debt and equity.

VL = D + S = $3,571,429

$3,571,429 = $1,000,000 + S

S = $2,571,429.

22

3. Find rsL.

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

= 14.0% + (14.0% - 8.0%)( )$1,000,000= 14.0% + (14.0% - 8.0%)( )= 14.0% + 2.33% = 16.33%.

$1,000,000$2,571,429

23

4. Proposition I implies WACC = rsU.Verify for L using WACC formula.

WACC = wdrd + wsrs = (D/V)rd + (S/V)rsL

( )= ( )(8.0%)+( )(16.33%)

= 2.24% + 11.76% = 14.00%.

$1,000,000$3,571,429

$2,571,429$3,571,429

24

Graph the MM relationships between capital costs and leverage as measured

by D/V.

Without taxesCost of Capital (%)

26

20

14

8

0 20 40 60 80 100Debt/Value Ratio (%)

rsL

WACC

rd

25

The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost.its cost.

Although rd remains constant, rsincreases with leverage. The increase in rs is exactly sufficient to keep the WACC constant.

26

MM Theory: Corporate Taxes

Corporate tax laws favor debt financing over equity financing.

With corporate taxes, more EBIT goes to investors and less to taxes when leverage investors and less to taxes when leverage is used.

With corporate taxes added, the MM propositions become:Proposition I:

VL = VU + TD.

Proposition II:

rsL = rsU + (rsU - rd)(1 - T)(D/S).

27

Notes About the New Propositions

1. When corporate taxes are added,VL VU. VL increases as debt is added to the capital structure, and 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.

28

1. Find VU and VL.

VU = = = $2,142,857.EBIT(1 - T)

rsU

$500,000(0.6)0.14

Note: Represents a 40% decline from the no taxes situation.

VL = VU + TD = $2,142,857 + 0.4($1,000,000)

= $2,142,857 + $400,000

= $2,542,857.

29

VL = D + S = $2,542,857

$2,542,857 = $1,000,000 + S

2. Find market value of Firm Ls debt and equity.

$2,542,857 = $1,000,000 + S

S = $1,542,857.

30

3. Find rsL.

rsL = rsU + (rsU - rd)(1 - T)(D/S)

= 14.0% + (14.0% - 8.0%)(0.6)( )$1,000,000= 14.0% + (14.0% - 8.0%)(0.6)( )= 14.0% + 2.33% = 16.33%.

$1,542,857

31

4. Find Firm Ls WACC.

WACCL= (D/V)rd(1 - T) + (S/V)rsL

= ( )(8.0%)(0.6)$1,000,000$2,542,857( )+( )(16.33%)

= 1.89% + 9.91% = 11.80%.

When corporate taxes are considered, the WACC is lower for L than for U.

$2,542,857

$1,542,857$2,542,857

32

Cost of Capital (%)

MM relationship between capital costs and leverage when corporate taxes are

considered.

rsL26

20

14

8

0 20 40 60 80 100Debt/Value Ratio (%)

rsL

WACC

rd(1 - T)

33

Value of Firm, V (%)

4

3VL

MM relationship between value and debt when corporate taxes are considered.

TD3

2

1

0 0.5 1.0 1.5 2.0 2.5Debt

(Millions of $)

VU

Under MM with corporate taxes, the firms value increases continuously as more and more debt is used.

TD

34

How is all of this analysis different if firms U and L are growing?

Under MM (with taxes and no growth)VL = VU + TD

This assumes the tax shield is This assumes the tax shield is discounted at the cost of debt.

Now, assume the company grows (while maintaining the same capital structure).

The debt tax shield will be larger if the firms grow:

35

7% growth, TS discount rate of rTS

Value of (growing) tax shield =

VTS = rdTD/(rTS g)

So value of levered firm =So value of levered firm =

VL = VU + rdTD/(rTS g)

36

What should rTS be?

The smaller is rTS, the larger the value of the tax shield. If rTS < rsU, then with rapid growth the tax shield then with rapid growth the tax shield becomes unrealistically largerTSmust be equal to rsU to give reasonable results when there is growth. So we assume rTS = rsU.

37

Relevant information for valuation

EBIT1 = $500,000

T = 40%

rTS =rsU = 14% rTS =rsU = 14%

rd = 8%

Required net reinvestment in operating assets = 10% of EBIT = $50,000.

Debt = $1,000,000

Growth rate=7%

38

Calculating VU

NOPAT1 = EBIT1(1-T)

= $500,000 (.60) = $300,000

Investment in net op. assets Investment in net op. assets

= EBIT1 (0.10) = $50,000

FCF1 = NOPAT1 Inv. in net op. assets

= $300,000 - $50,000

= $250,000 (this is expected FCF next year)

39

Value of unlevered firm, VU

Value of unlevered firm =

VU = FCF1/(rsU g)

= $250,000/(0.14 0.07)= $250,000/(0.14 0.07)

= $3,571,429

40

Value of tax shield, VTS and VL

VTS = rdTD/(rsU g)

= 0.08(0.40)$1,000,000/(0.14-0.07)

= $457,143= $457,143

VL = VU + VTS= $3,571,429 + $457,143

= $4,028,571

41

Levered cost of equity

In this case, the levered cost of equity is rsL = rsU + (rsU rd)(D/S)

This looks just like MM without taxesThis looks just like MM without taxeseven though we allow taxes and allow for growth.

42

Cost of equity and WACC

Just like with MM with taxes, the cost of equity increases with D/V, and the WACC declines. WACC declines.

But since rsL doesn't have the (1-T) factor in it, for a given D/V, rsL is greater than MM would predict, and WACC is greater than MM would predict.

43

Bankruptcy cost

MM theory ignores bankruptcy (financial distress) costs, which increase as more leverage is used.

At low leverage levels, tax benefits At low leverage levels, tax benefits outweigh bankruptcy costs.

At high levels, bankruptcy costs outweigh tax benefits.

An optimal capital structure exists that balances these costs and benefits.

Temur SolievHighlight

44

Choosing the Optimal Capital Structure: Example

Currently is all-equity financed.

Expected EBIT = $500,000.

Firm expects zero growth.Firm expects zero growth.

100,000 shares outstanding; rs = 12%;

P0 = $25; T = 40%; b = 1.0; rRF = 6%;

RPM = 6%.

45

Estimates of Cost of Debt

Percent financedwith debt, wd rd

0% -

20% 8.0%20% 8.0%

30% 8.5%

40% 10.0%

50% 12.0%If company recapitalizes, debt would be issued to repurchase stock.

Temur SolievHighlight

46

The Cost of Equity at Different Levels of Debt: Hamadas Equation

MM theory implies that beta changes with leverage.

b is the beta of a firm when it has no bU is the beta of a firm when it has no debt (the unlevered beta)

bL = bU [1 + (1 - T)(D/S)]

47

The Cost of Equity for wd = 20%

Use Hamadas equation to find beta:

bL = bU [1 + (1 - T)(D/S)]

= 1.0 [1 + (1-0.4) (20% / 80%) ]= 1.0 [1 + (1-0.4) (20% / 80%) ]

= 1.15

Use CAPM to find the cost of equity:

rs = rRF + bL (RPM)

= 6% + 1.15 (6%) = 12.9%

48

Cost of Equity vs. Leverage

wd D/S bL rs

0% 0.00 1.000 12.00%

20% 0.25 1.150 12.90%20% 0.25 1.150 12.90%

30% 0.43 1.257 13.54%

40% 0.67 1.400 14.40%

50% 1.00 1.600 15.60%

49

The WACC for wd = 20%

WACC = wd (1-T) rd + ws rs

WACC = 0.2 (1 0.4) (8%) + 0.8 (12.9%)

WACC = 11.28%

Repeat this for all capital structures

under consideration.

50

WACC vs. Leverage

wd rd rs WACC

0% 0.0% 12.00% 12.00%

20% 8.0% 12.90% 11.28%20% 8.0% 12.90% 11.28%

30% 8.5% 13.54% 11.01%

40% 10.0% 14.40% 11.04%

50% 12.0% 15.60% 11.40%

51

Corporate Value for wd = 20%

V = FCF / (WACC-g)

g=0, so FCF = NOPAT = EBIT (1-T)=

($500,000)(1-0.40) = $300,000.($500,000)(1-0.40) = $300,000.

V = $300,000 / 0.1128 = $2,659,574.

52

Corporate Value vs. Leverage

wd WACC Corp. Value

0% 12.00% $2,500,000

20% 11.28% $2,659,57420% 11.28% $2,659,574

30% 11.01% $2,724,796

40% 11.04% $2,717,391

50% 11.40% $2,631,579

53

Debt and Equity for wd = 20%

The dollar value of debt is:

D = wd V = 0.2 ($2,659,574) = $531,915.

S = V D

S = $2,659,574 - $531,915 = $2,127,659.

54

Debt and Stock Value vs. Leverage

wd Debt, D Stock Value, S

0% $0 $2,500,000

20% $531,915 $2,127,66020% $531,915 $2,127,660

30% $817,439 $1,907,357

40% $1,086,956 $1,630,435

50% $1,315,790 $1,315,790

Note: numbers are rounded

55

Stock Price for wd = 20%

The firm issues debt, and uses debt proceeds

to repurchase stock.

Stock price changes after debt is issued.

S : value of stock after debt issuance S : value of stock after debt issuance

D : value of debt after debt issuance

56

Stock Price for wd = 20% (Continued)

D0 and n0 are debt and outstanding

shares before recap.

D - D0 is equal to cash that will be used D - D0 is equal to cash that will be used

to repurchase stock.

S + (D - D0) is wealth of shareholders

after the debt is issued but immediately

before the repurchase.(More)

57

Stock Price for wd = 20% (Continued)

P = S + (D D0)

n0

P = $2,127,660 + ($531,915 0) P = $2,127,660 + ($531,915 0)

100,000

P = $26.596 per share.

58

Number of Shares Repurchased

# Repurchased = (D - D0) / P

# Rep. = ($531,915 0) / $26.596

= 20,000.

# Remaining = 100,000-20,000=80,000

OR, # Remaining = n = S / P

n = $2,127,660 / $26.596

= 80,000.

P can also be found by

59

Price per Share vs. Leverage

# shares # shares

wd P Repurch. Remaining

0% $25.00 0 100,0000% $25.00 0 100,000

20% $26.60 20,000 80,000

30% $27.41 30,416 69,584

40% $27.30 40,287 59,713

50% $25.87 49,134 50,866

60

Optimal Capital Structure

wd = 30% gives:

Lowest WACC

Highest corporate valueHighest corporate value

Highest stock price per share

61

How companies determine capital structure:Theory and Reality

In theory

WACC, firm value, stock price

According to survey, companies consider

A good credit rating

When issuing equity,

Consider EPS dilution

Consider recent stock appreciation (Market timing)

62

Equity as an option

Suppose the firm has $2 million face value of 1-year zero coupon debt, and the current value of the firm (debt plus equity) is $4 million.is $4 million.

If the firm pays off the debt when it matures, the equity holders get to keep the firm. If not, they get nothing.

63

Equity as an option

The equity holder's position looks like a call option with

P = underlying value of firm = $4 million

P = underlying value of firm = $4 million

X = exercise price = $2 million

t = time to maturity = 1 year

Suppose rRF = 6%

= volatility of firm (debt + equity) = 0.60

64

Use Black-Scholes to price this option

V = P[N(d1)] - Xe-rRFt[N(d2)].

d1 = . t

ln(P/X) + [rRF + (2/2)]t

d1 = . t

d2 = d1 - t.

65

Black-Scholes Solution

V = $4[N(d1)] - $2e-(0.06)(1.0)[N(d2)].

ln($4/$2) + [(0.06 + 0.36/2)](1.0)

(0.60)(1.0)d1 = (0.60)(1.0)

= 1.5552.

d2 = d1 - (0.60)(1.0) = d1 - 0.60

= 1.5552 - 0.6000 = 0.9552.

66

N(d1) = N(1.5552) = 0.9401

N(d2) = N(0.9552) = 0.8383Note: Values obtained from Excel using NORMSDIST function.

V = $4(0.9401) - $2e-0.06(0.8303)

= $3.7604 - $2(0.9418)(0.8303)

= $2.196 Million = Value of Equity

67

Value of Debt

Value of debt = Total Value Equity

= $4 million 2.196 million= $4 million 2.196 million

= $1.804 million

68

This value of debt gives us a yield

Debt yield for 1-year zero coupon debt

= (face value / price) 1

= ($2 million/ 1.804 million) 1 = ($2 million/ 1.804 million) 1

= 10.9%

69

How does affect an option's value?

Higher volatility means higher option value.

70

Values of Debt and Equity for Different Volatilities

1.50

2.00

2.50

3.00

Val

ue

(mil

lion

s)

Equity

Debt

0.00

0.50

1.00

1.50

0.00 0.20 0.40 0.60 0.80 1.00

Volatility (sigma)

Val

ue

(mil

lion

s)

Debt

71

Managerial Incentives

Manager can change a firm's by changing the assets the firm invests in. And changing can change the value of the equity. the equity.

So increasing can 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.

72

Bait and Switch

Managers who know this might tell debtholders they are going to invest in one kind of asset, and, instead, in one kind of asset, and, instead, invest in riskier assets. This is called bait and switch and bondholders will require higher interest rates for firms that has a history of doing this.