13 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. CHAPTER 13 Capital Structure and Leverage Business vs. financial risk Optimal capital structure

13 - 1

Copyright © 2002 by Harcourt, Inc. All rights reserved.

CHAPTER 13Capital Structure and Leverage

Business vs. financial risk

Optimal capital structure

Operating leverage

Capital structure theory

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

Note that business risk does not include financing effects.

What is business risk?

Probability

EBITE(EBIT)0

Low risk

High risk

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Business risk is affected primarily by:

Uncertainty about demand (sales).

Uncertainty about output prices.

Uncertainty about costs.

Product, other types of liability.

Operating leverage.

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

Operating leverage is the use of fixed costs rather than variable costs.

If most costs are fixed, hence do not decline when demand falls, then the firm has high operating leverage.

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

What happens if variable costs change?

Sales

$ Rev.TC

FC

QBE Sales

$ Rev.

TC

FC

QBE

} Profit

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Probability

EBITL

Low operating leverage

High operating leverage

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

EBITH

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What is financial leverage?Financial risk?

Financial leverage is the use of debt and preferred stock.

Financial risk is the additional risk concentrated on common stockholders as a result of financial leverage.

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Business Risk vs. Financial Risk

Business risk depends on business factors such as competition, product liability, and operating leverage.

Financial risk depends only on the types of securities issued: More debt, more financial risk. Concentrates business risk on stockholders.

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Firm U Firm L

No debt $10,000 of 12% debt

$20,000 in assets $20,000 in assets

40% tax rate 40% tax rate

Consider 2 Hypothetical Firms

Both firms have same operating leverage, business risk, and probability distribution of EBIT. Differ only with respect to use of debt (capital structure).

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Firm U: Unleveraged

Prob. 0.25 0.50 0.25EBIT $2,000 $3,000 $4,000Interest 0 0 0EBT $2,000 $3,000 $4,000Taxes (40%) 800 1,200 1,600NI $1,200 $1,800 $2,400

Economy Bad Avg. Good

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Prob.* 0.25 0.50 0.25EBIT* $2,000 $3,000 $4,000Interest 1,200 1,200 1,200EBT $ 800 $1,800 $2,800Taxes (40%) 320 720 1,120NI $ 480 $1,080 $1,680

*Same as for Firm U.

Firm L: Leveraged

Economy Bad Avg. Good

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Firm U Bad Avg. GoodBEP* 10.0% 15.0% 20.0%ROE 6.0% 9.0% 12.0%TIE

Firm L Bad Avg. GoodBEP* 10.0% 15.0% 20.0%ROE 4.8% 10.8% 16.8%TIE 1.67x 2.5x 3.3x*BEP same for Firms U and L.

8 8 8

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Expected Values:

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

E(TIE) 2.5x

Risk Measures:ROE 2.12% 4.24%

CVROE 0.24 0.39

U L

8

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For leverage to raise expected ROE, must have BEP > kd.

Why? If kd > BEP, then the interest expense will be higher than the operating income produced by debt-financed assets, so leverage will depress income.

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Conclusions

Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage.

L has higher expected ROE because BEP > kd.

L has much wider ROE (and EPS) swings because of fixed interest charges. Its higher expected return is accompanied by higher risk.

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If debt increases, TIE falls.

EBIT is constant (unaffected by useof debt), and since Int = kdD, as Dincreases, TIE must fall.

TIE = .EBITInt

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Optimal Capital Structure

That capital structure (mix of debt, preferred, and common equity) at which P0 is maximized. Trades off higher E(ROE) and EPS against higher risk. The tax-related benefits of leverage are exactly offset by the debt’s risk-related costs.

The target capital structure is the mix of debt, preferred stock, and common equity with which the firm intends to raise capital.

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Describe the sequence of events in a recapitalization.

Campus Deli announces the recapitalization.

New debt is issued.

Proceeds are used to repurchase stock.

Debt issued Price per share

Shares bought = .

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Amount D/A D/E Bondborrowed ratio ratio rating kd

Cost of Debt at Different Debt Levels after Recapitalization

$ 0 0 0 -- --

250 0.125 0.1429 AA 8%

500 0.250 0.3333 A 9%

750 0.375 0.6000 BBB 11.5%

1,000 0.500 1.0000 BB 14%

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Why does the bond rating and cost of debt depend upon the amount

borrowed?

As the firm borrows more money, the firm increases its risk causing the firm’s bond rating to decrease, and its cost of debt to increase.

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EPS0 =

= = $3.00.

What would the earnings per share be if Campus Deli recapitalized and used these amounts of debt: $0, $250,000, $500,000, $750,000? Assume EBIT = $400,000, T = 40%, and shares can be

repurchased at P0 = $25.

D = 0: (EBIT – kdD)(1 – T)

Shares outstanding

($400,000)(0.6)80,000

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D = $250, kd = 8%.

= = 10,000.Shares

repurchased$250,000

$25

TIE = = = 20×.$400$20

EBITI

EPS1 =

= $3.26.

[$400 – 0.08($250)](0.6)80 – 10

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D = $500, kd = 9%.

= = 20.Shares

repurchased$500$25

TIE = = = 8.9×.$400$45

EBITI

EPS2 =

= $3.55.

[$400 – 0.09($500)](0.6) 80 – 20

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D = $750, kd = 11.5%.

= = 30.Shares

repurchased$750$25

TIE = = = 4.6×.$400

$86.25EBIT

I

EPS3 =

= $3.77.

[$400 – 0.115($750)](0.6) 80 – 30

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D = $1,000, kd = 14%.

= = 40.Shares

repurchased$1,000

$25

TIE = = = 2.9×.$400$140

EBITI

EPS4 =

= $3.90.

[$400 – 0.14($1,000)](0.6) 80 – 40

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Stock Price (Zero Growth)

If payout = 100%, then EPS = DPS andE(g) = 0.

We just calculated EPS = DPS. To find the expected stock price (P0), we must find the appropriate ks at each of the debt levels discussed.

P0 = = = .D1

ks – gEPS

ks

DPSks

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What effect would increasing debt have on the cost of equity for the firm?

If the level of debt increases, the riskiness of the firm increases.

We have already observed the increase in the cost of debt.

However, the riskiness of the firm’s equity also increases, resulting in a higher ks.

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The Hamada Equation

Because the increased use of debt causes both the costs of debt and equity to increase, we need to estimate the new cost of equity.

The Hamada equation attempts to quantify the increased cost of equity due to financial leverage.

Uses the unlevered beta of a firm, which represents the business risk of a firm as if it had no debt.

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The Hamada Equation (cont’d)

bL = bU[1 + (1 – T)(D/E)].

The risk-free rate is 6%, as is the market risk premium. The unlevered beta of the firm is 1.0. We were previously told that total assets were $2,000,000.

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Calculating Levered Betas

D = $250

bL = bU[1 + (1 – T)(D/E)]

bL = 1.0[1 + (1 – 0.4)($250/$1,750)]

bL = 1.0[1 + (0.6)(0.1429)]

bL = 1.0857.

ks = kRF + (kM – kRF)bL

ks = 6.0% + (6.0%)1.0857 = 12.51%.

ks = kRF + (kM – kRF)bL

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Table for Calculating Levered Betas

Amount borrowed

$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

Levered Beta

1.00

1.09

1.20

1.36

1.60

D/E ratio

0.00%

14.29

33.33

60.00

100.00

ks

12.00%

12.51

13.20

14.16

15.60

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Finding Optimal Capital Structure

The firm’s optimal capital structure can be determined two ways:

Minimizes WACC.

Maximizes stock price.

Both methods yield the same results.

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Minimizing the WACC

Amount borrowed

$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

WACC

12.00%

11.55

11.25

11.44

12.00

E/A ratio

100.00%

87.50

75.00

62.50

50.00

ks

12.00%

12.51

13.20

14.16

15.60

kd (1 – T)

0.00%

4.80

5.40

6.90

8.40

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AmountBorrowed DPS ks P0

$ 0 $3.00 12.00% $25.00

250,000 3.26 12.51

500,000 3.55 13.20

26.03

26.89*

750,000 3.77 14.16 26.59

1,000,000 3.90 15.60 25.00

*Maximum: Since D = $500,000 and assets = $2,000,000, optimal D/A = 25%.

Maximizing Stock Price

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See preceding slide. Maximum EPS = $3.90 at D = $1,000,000, and D/A = 50%. (Remember DPS = EPS because payout = 100%.)

Risk is too high at D/A = 50%.

What debt ratio maximizes EPS?

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What is Campus Deli’s optimal capital structure?

P0 is maximized ($26.89) at D/A = $500,000/$2,000,000 = 25%, so optimal D/A = 25%.

EPS is maximized at 50%, but primary interest is stock price, not E(EPS).

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The example shows that we can push up E(EPS) by using more debt, but the risk resulting from increased leverage more than offsets the benefit of higher E(EPS).

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%

15

0 .25 .75.50 D/A

ks

WACCkd(1 – T)

$

D/A.25 .50

P0

EPS

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If it were discovered that the firm had more/less business risk than originally estimated, how would the analysis be

affected?

If there were higher business risk, then the probability of financial distress would be greater at any debt level, and the optimal capital structure would be one that had less debt. On the other hand, lower business risk would lead to an optimal capital structure with more debt.

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Other Factors to Consider When Establishing the Firm’s Target Capital

Structure

1. Industry average debt ratio2. TIE ratios under different scenarios3. Lender/rating agency attitudes4. Reserve borrowing capacity5. Effects of financing on control6. Asset structure7. Expected tax rate

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How would these factors affect the Target Capital Structure?

1. Sales stability?

2. High operating leverage?

3. Increase in the corporate tax rate?

4. Increase in the personal tax rate?

5. Increase in bankruptcy costs?

6. Management spending lots of money on lavish perks?

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Value of Stock

0 D1 D2

D/A

MM result

Actual

No leverage

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The graph shows MM’s tax benefit vs. bankruptcy cost theory.

Logical, but doesn’t tell whole capital structure story. Main problem--assumes investors have same information as managers.

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Signaling theory suggests firms should use less debt than MM suggest.

This unused debt capacity helps avoid stock sales, which depress P0 because of signaling effects.

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What are “signaling” effects in capital structure?

Managers have better information about a firm’s long-run value than outside investors.

Managers act in the best interests of current stockholders.

Assumptions:

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Therefore, managers can be expected to:

Issue stock if they think stock is overvalued.

Issue debt if they think stock is undervalued.

As a result, investors view a common stock offering as a negative signal--managers think stock is overvalued.

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Conclusions on Capital Structure

1. Need to make calculations as we did, but should also recognize inputs are “guesstimates.”

2. As a result of imprecise numbers, capital structure decisions have a large judgmental content.

3. We end up with capital structures varying widely among firms, even similar ones in same industry.

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13 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. CHAPTER 13 Capital Structure and Leverage Business vs. financial risk Optimal capital structure