CAPITAL STRUCTURE AND LEVERAGE

•Business Risk vs. Financial Risk•Operating Leverage•Capital Structure Theory

Business Risk, Operating LeverageFinancial Risk, Financial Leverage

PART 1

Uncertainty about future operating income (EBIT), i.e., how well can we predict operating income?

Note that business risk does not include effect of financial leverage.

What is business risk?

Probability

EBITE(EBIT)0

Low risk

High risk

What determines business risk?

Uncertainty about demand (sales). Uncertainty about output prices. Uncertainty about costs. Product, other types of liability. Competition. Operating leverage.

What is operating leverage, and how does it affect a firm’s business risk?

Operating Leverage is defined as (%change in EBIT)/(%change in sales).

Operating leverage is high if the production requires higher fixed costs and low variable costs.

High fixed cost can leverage small increase in sales into high increase in EBIT.

Effect of operating leverage

More operating leverage leads to more business risk, for then a small sales decline causes a big profit decline.

Sales

$ Rev.TC

FC

QBE Sales

$ Rev.

TCFC

QBE

} Profit

Using operating leverage

Typical situation: Can use operating leverage to get higher E(EBIT), but risk also increases.

Probability

EBITL

Low operating leverage

High operating leverage

EBITH

8

Business Risk versus Financial Risk

Business risk:◦ Uncertainty in future EBIT. It is measured by

the CV of EBIT or by the CV of ROE of a firm that does not use debt (or PS) financing.

Financial risk:◦ Additional risk placed on common stockholders

when financial leverage is used. It is measured by the increase in the CV of ROE.

◦ Financial risk depends on the amount of debt (or preferred stock) financing the firm uses.

Two firms with the same operating leverage, business risk, and probability distribution of EBIT.

Only differ with respect to their use of debt (capital structure).

Firm U Firm LNo debt $5,000 of 8% debt$20,000 in assets $20,000 in assets40% tax rate 40% tax rate

Group Problem

Economic State Probability EBIT

Bad 0.20 $500 Average 0.50 $600 Good 0.30 $700

Both firms have the same probability distribution of EBIT and the same business risk

11

Expected EBIT, Standard Deviation, and the Coefficient of Variation

n

iii PEBITEEBIT

1

2

)(

CV = σ / E(EBIT)

E(EBIT) = Σ EBITi . Pi

E (EBIT) = (0.20)($500) + (0.50)($600) +(0.30)($700)=$610 EBIT = ($500 - $610)2 (0.20) +

($600 - $610)2 (0.50) + ($700 - $610)2 (0.30)

= $70

CVEBIT = $70 / $610 = 0.115 (Business Risk)

Business Risk for Both Firms

13

Total Risk Total risk is the risk born by the stockholders.

It is measured by the volatility of ROE.

Total Risk = Business Risk + Financial Risk

Only firms that use financial leverage (e.g., debt or PS) would have financial risk.

Firms that use no financial leverage would have only business risk. These firms’ total risk is equal to their business risk, i.e., the volatility of their ROE would be the same as the volatility of their EBIT.

Firm U: Unleveraged

Economy Bad Avg. GoodProb. 0.20 0.50 0.30EBIT $500 $600 $700Interest 0 0 0EBT $500 $600 $700Taxes (40%) 200 240 280NI $300 $360 $420

ROE 6% 9% 12%

Firm L: Leveraged

Economy Bad Avg. GoodProb. 0.20 0.50 0.30EBIT $500 $600 $700Interest 400 400 400EBT $100 $200 $300Taxes (40%) 40 80 120NI $60 $120 $180

ROE 6% 12%

18%

16

Firm U has only business risk and no financial risk

E (ROE) = (0.20)(6%) + (0.50)(9%) + (0.30)(12%) = 9.3%

ROE = (6-9.3)2 (0.20) + (9-9.3)2 (0.50) (12-9.3)2 (0.30)

= 2.1%

CVROE = 2.1% / 9.3%

= 0.226 (Total Risk )

17

Firm L has financial risk in addition

to business risk E (ROE) = (0.20)(6%) + (0.50)(12%) + (0.30)(18%) = 12.6%

ROE = (6-12.6)2 (0.20) + (12-12.6)2(0.50) (18-12.6)2 (0.30)

= 4.2%

CVROE = 4.2% / 12.6% = 0.333 (Total Risk)

Fin. Risk = Total Risk (0.333) - Bus. Risk (0.115) =0.218

18

The Effect of Financial Leverage

Probability Firm

U Firm L

CV(U)=0.226 CV(L)=0.333

6% 9% 12% 12% 18% ROE

Firm L has a higher expected ROE but it also has more risk because in addition to business risk it also has financial risk.

19

PART 2Capital Structure Theory

MM theory◦ Zero taxes◦ Corporate taxes

Trade-off theory Signaling theory Pecking order

20

MM Theory: Zero Taxes

MM assume: (1) no transactions costs; (2) individuals can borrow at the same rate as corporations.

MM prove that there would be no difference between firms using leverage or investors borrowing and investing (home made leverage). The total values of Firm U and Firm L should be equal:

VL = VU

Therefore, capital structure is irrelevant.

21

MM Theory with Zero Taxes: Capital Structure is

Irrelevant

$

VLVU

Financial Leverage

22

MM Theory with Corporate Taxes

Corporate tax laws allow interest to be deducted, which reduces taxes paid by levered firms.

MM show that the total CF to Firm L’s investors is equal to the total CF to Firm U’s investor plus an additional amount due to interest deductibility:

VL = VU + TD If T=40%, then every dollar of debt adds

40 cents of extra value to firm.

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

Value of Firm

0 Financial Leverage

VL = VU + TD

V

U

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

TD

24

Trade-off Theory

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

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.

Tax Shield vs. Cost of Financial Distress

Value of Firm

0 Financial Leverage

VL

VU

Tax Shield

Distress Costs

Maximum Firm Value

Optimal Capital Structure

26

Choosing the Optimal Capital Structure: A Numerical Example

• Currently, the firm is all-equity financed.

• Expected EBIT = $200,000.

• The firm expects zero growth.

• Currently the firm’s rs = 10%; b = 1.0;

T = 40%; rRF = 4%; RPM = 6%.

27

Equations Used in theCalculations

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

rs = rRF + bL (RPM)

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

28

Estimates of Cost of Debt

% financed with debt, wd

rd

0% -20% 7.0%

30% 8.0%40% 10.0%50% 12.5%

29

Finding the Beta at Different Levels of

Debt Beta changes with leverage.

bU is the beta of a firm when it has no debt (the unlevered beta). bL is the beta of a firm when it uses debt financing (leverage).

Hamada’s Equation showing the relationship between bL and bU

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

30

Using Hamada’s equation to find beta at different

leverage levels 20% Debt:

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

= 1.0 [1 + (1 - 0.4) (20% / 80%)] = 1.15

30% Debt:

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

= 1.0 [1 + (1 - 0.4) (30% / 70%)] = 1.257

31

Using Hamada’s equation to find beta at different leverage levels

40% Debt:

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

= 1.0 [1 + (1 - 0.4) (40% / 60%)] = 1.4

50% Debt:

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

= 1.0 [1 + (1 - 0.4) (50% / 50%)] = 1.6

32

Using CAPM to find the cost of equity

20% debt, bL = 1.15:

rs = rRF + bL (RPM) = 4% + 1.15 (6%) = 10.9%

30% debt, bL = 1.257:

rs = rRF + bL (RPM) = 4% + 1.257 (6%) = 11.54%

33

Using CAPM to find the cost of equity

40% debt, bL = 1.4:

rs = rRF + bL (RPM) = 4% + 1.4 (6%) = 12.4%

50% debt, bL = 1.6:

rs = rRF + bL (RPM) = 4% + 1.6 (6%) = 13.6%

34

The WACC for of the firm

at different leverage levels

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

0% debt (current position):

WACC = 0.0 + 1.0(10%) = 10%

20% debt:

WACC=0.2(1- 0.4)(7%)+0.8(10.9%)=9.56%

35

The WACC for of the firm

at different leverage levels

30% debt:

WACC=0.3(1-0.4)(8%)+0.7(11.54%)= 9.52%

40% debt:

WACC=0.4(1-0.4)(10%)+0.6(12.4%)=9.84%

50% debt:

WACC=0.5(1-0.4)(12.5%)+0.5(13.6%)=10.55%

36

WACC vs. Leverage

wd rd rs WACC

0% 0.0% 10.00% 10.00%

20% 7.0% 10.90% 9.56%

30% 8.0% 11.54% 9.52%

40% 10.0% 12.40% 9.84%

50% 12.5% 13.60% 10.55%

LowestWACC

OptimalCapitalStructure

37

Leverage and Corporate

Value

V = FCF1 / (WACC - g) (Gordon’s Formula)

g = 0, therefore:

V = FCF / WACC

FCF = NOPAT = EBIT (1 - T)

= ($200,000)(1 - 0.40) = $120,000

38

Leverage and Corporate Value

V = FCF / WACC

Currently, with no debt: V = $120,000 / 0.10

= $1,200,000

20% debt: V = $120,000 / 0.0956

= $1,255,230

39

Leverage and Corporate Value

30% debt V = $120,000 / 0.0952 = $1,260,504

40% debt:

V = $120,000 / 0.0984 = $1,219,512

50% debt V = $120,000 / 0.1055 = $1,137,441

40

Corporate Value vs. Leverage

wd WACC Corp. Value

0% 10.00% $1,200,000

20% 9.56% $1,255,230

30% 9.52% $1,260,504

40% 9.84% $1,219,512

50% 10.55% $1,137,441

MaximumValue

MinimumWACC

The corporation’s value is maximized when WACC is minimized.

41

Optimal Capital Structure

wd = 30% gives:

◦ Lowest WACC

◦ Highest corporate value

But wd = 20% is close. Optimal range is

pretty flat between 20% and 30%.

42

WACC

rs

rd(1-T)

10%

0% 20% 30% 40% 50% Debt/Assetsx

Optimal

Cost ofCapital

Optimal Capital Structure

9.56% 9.52% 9.84%

10.55%

4.2% 4.8% 6%7.5%

10.90%11.54%

12.4%

13.6%

43

Signaling Theory

MM assumed that investors and managers have the same information.

But, managers often have better information. Thus, they would:◦Sell stock if stock is overvalued.◦Sell bonds if stock is undervalued.

Investors understand this, so view new stock sales as a negative signal.

Implications for managers?

44

Pecking Order Theory

Firms use internally generated funds first, because there are no flotation costs or negative signals.

If more funds are needed, firms then issue debt because it has lower flotation costs than equity and not negative signals.

If more funds are needed, firms then issue equity.