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Capital Structure and Leverage. Business vs. financial risk Operating leverage Financial leverage Optimal capital structure Capital structure theory. What is business risk?. Uncertainty about future operating income (EBIT), i.e., how well can we predict operating income?

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capital structure and leverage
Capital Structure and Leverage
  • Business vs. financial risk
  • Operating leverage
  • Financial leverage
  • Optimal capital structure
  • Capital structure theory
what is business risk
What is business risk?
  • Uncertainty about future operating income (EBIT), i.e., how well can we predict operating income?
  • Note that business risk does not include financing effects.

Probability

Low risk

High risk

0

E(EBIT)

EBIT

business risk is affected primarily by
Business risk is affected primarily by:
  • Uncertainty about demand (sales).
  • Uncertainty about output prices.
  • Uncertainty about costs.
  • Product, other types of liability.
  • Operating leverage.
what is operating leverage and how does it affect a firm s business risk
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.
slide5

Rev.

Rev.

$

$

}

TC

Profit

TC

FC

FC

QBE

QBE

Sales

Sales

  • More operating leverage leads to more business risk, for then a small sales decline causes a big profit decline.
operating leverage
Operating Breakeven : Amount of sales that leads to zero EBIT

EBIT = P*Q-V*Q-F=0

QBE=F/(P-V)

Degree of Operating Leverage (DOL)

DOL= % change in EBIT/%change in SALES

Operating Leverage
operating leverage1
EBIT =(P-V)Q-F

dEBIT/dQ=P-V

DOL= dEBIT/dQ * Q/EBIT

= Q*(P-V) /[Q*(P-V) –F]

Operating Leverage
slide8

Probability

Low operating leverage

High operating leverage

EBITL

EBITH

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

what is financial leverage financial risk
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.
financial leverage
Financial Leverage

DFL= % change in EPS/%change in EBIT

EPS=NI /N=(EBIT-I)(1-T) /N

N:number of common stock outstanding

dEPS /dEBIT=(1-T) /N

EBIT /EPS=EBIT /[(EBIT-I)(1-T) /N]

DFL=EBIT /(EBIT-I)

financial breakeven
Financial Breakeven

Amount of EBIT that leads to zero EPS

EPS =(EBIT-I)(1-T) /N=0

EBITBE=I

business risk vs financial risk
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.
slide13

Consider 2 Hypothetical Firms

Firm UFirm L

No debt $10,000 of 12% debt

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

40% tax rate 40% tax rate

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

capial structures of the two firms
Capial Structures of the Two Firms

A=$20,000=D+E for both firms

EU=$20,000 DU=$0

EL=$10,000 DL=$10,000

slide15

Firm U: Unleveraged

Economy

BadAvg.Good

Prob. 0.25 0.50 0.25

EBIT $2,000 $3,000 $4,000

Interest 0 0 0

EBT $2,000 $3,000 $4,000

Taxes (40%) 800 1,200 1,600

NI $1,200 $1,800 $2,400

slide16

Firm L: Leveraged

Economy

BadAvg.Good

Prob.* 0.25 0.50 0.25

EBIT* $2,000 $3,000 $4,000

Interest 1,200 1,200 1,200

EBT $ 800 $1,800 $2,800

Taxes (40%) 320 720 1,120

NI $ 480 $1,080 $1,680

*Same as for Firm U.

slide17

8

8

8

Firm U Bad Avg. Good

BEP* 10.0% 15.0% 20.0%

ROE 6.0% 9.0% 12.0%

TIE

Firm L Bad Avg. Good

BEP* 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.

slide18

Expected Values:

E(BEP) 15.0% 15.0%

E(ROE) 9.0% 10.8%

E(TIE) 2.5x

Risk Measures:

sROE 2.12% 4.24%

CVROE 0.24 0.39

U L

8

slide19

For leverage to raise ROE, must have BEP > kd (avg. and good states).

  • 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.
slide20
NI=[EBIT-Dkd](1-T)

A=D+E

ROE=NI /(A-D)=[EBIT-Dkd](1-T) /(A-D)

=[EBIT/A-(D/A)kd](1-T) /(1-D/A)

=[BEP-DR kd](1-T) /(1-DR)

where DR=D/A

slide21
dROE/dDR=[(1-T)(BEP-kd)] / (1-DR)2

(1-T)(BEP-kd)>0 implies

BEP-kd>0 or BEP>kd q.e.d.

conclusions
Conclusions
  • Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage.
  • L has higher expected ROE because BEP > kd with probability of 0.75.
  • L has much wider ROE (and EPS) swings because of fixed interest charges. Its higher expected return is accompanied by higher risk.
if debt increases tie falls
If debt increases, TIE falls.

TIE =

EBIT

I

EBIT is constant (unaffected by use

of debt), and since I = kdD, as D

increases, TIE must fall.

optimal capital structure
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.
describe the sequence of events in a recapitalization
Describe the sequence of events in a recapitalization.
  • Consider another firm, Hannibal Inc., which announces a recapitalization.
  • New debt is issued.
  • Proceeds are used to repurchase stock.

Debt issued

Price per share

Shares bought = .

cost of debt at different debt levels after recapitalization
Cost of debt at different debt levels after recapitalization

Amount D/A D/E Bond

borrowed ratio ratio rating kd

K$ 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%

why does the bond rating and cost of debt depend upon the amount borrowed
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.

slide28

(EBIT – kdD)(1 – T)

Shares outstanding

What would the earnings per share beif Hannibal 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.Nu=80,000

D = 0:

EPS0 =

= = $3.00.

($400,000)(0.6)

80,000

slide29

$250,000

$25

Sharesrepurchased

= = 10,000.

[$400 – 0.08($250)](0.6)

80 – 10

EPS1 =

= $3.26.

EBIT

I

$400

$20

TIE = = = 20×.

D = $250K, kd = 8%.

slide30

$500

$25

Sharesrepurchased

= = 20.

[$400 – 0.09($500)](0.6)

80 – 20

EPS2 =

= $3.55.

EBIT

I

$400

$45

TIE = = = 8.9×.

D = $500K, kd = 9%.

slide31

$750

$25

Sharesrepurchased

= = 30.

[$400 – 0.115($750)](0.6)

80 – 30

EPS3 =

= $3.77.

D = $750K, kd = 11.5%.

EBIT

I

$400

$86.25

TIE = = = 4.6×.

slide32

$1,000

$25

Sharesrepurchased

= = 40.

[$400 – 0.14($1,000)](0.6)

80 – 40

EPS4 =

= $3.90.

EBIT

I

$400

$140

TIE = = = 2.9×.

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

stock price zero growth
Stock Price (Zero Growth)

D1ks – g

EPSks

DPSks

P0 = = = .

If payout = 100%, then EPS = DPS and

E(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.

what effect would increasing debt have on the cost of equity for the firm
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.
the hamada equation
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.
the hamada equation cont d
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(80K*$25).

calculating levered betas
Calculating Levered Betas

D = $250K

ks = kRF + (kM – kRF)bL

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%.

table for calculating levered betas
Table for Calculating Levered Betas

ks

12.00%

12.51

13.20

14.16

15.60

Amount borrowed

K$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

D/E ratio

0.00%

14.29

33.33

60.00

100.00

Levered Beta

1.00

1.09

1.20

1.36

1.60

minimizing the wacc
Minimizing the WACC

ks

12.00%

12.51

13.20

14.16

15.60

kd (1 – T)

0.00%

4.80

5.40

6.90

8.40

Amount borrowed

K$ 0

250

500

750

1,000

D/A ratio

0.00%

12.50

25.00

37.50

50.00

E/A ratio

100.00%

87.50

75.00

62.50

50.00

WACC

12.00%

11.55

11.25

11.44

12.00

p 0 dps k s
P0 = DPS/ks

Amount

Borrowed

DPS

k

P

s

0

$ 0

$3.00

$25.00

12.00%

3.26

26.03

250,000

12.51

3.55

26.89*

500,000

13.20

3.77

26.59

14.16

750,000

15.60

3.90

25.00

1,000,000

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

what debt ratio maximizes eps
What debt ratio maximizes EPS?

See preceding slide. Maximum EPS = $3.90 at D = $1,000,000, and D/A = 50%.

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

what is hannibal s optimal capital structure
What is Hannibal’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).

slide43

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).

slide44

%

ks

15

WACC

kd(1 – T)

D/A

0

.25

.50

.75

$

P0

EPS

D/A

.25

.50

slide45
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 of more debt.

total risk
Total risk

Total risk is the combination of business risk and financial risk.

Degree of total leverage:

DTL= DOL* DFL

=% change in EPS/%change in SALES

If DOL then DFL should  to keep DTL

constant

total breakeven
Total Breakeven

The amount of sales that leads to zero EPS

[(P-V)Q-F-I](1-T) /N=0

QBE=(F-I)/(P-V)

other factors to consider when establishing the firm s target capital structure
Other factors to consider when establishing the firm’s target capital structure?

1. Industry average debt ratio

2. TIE ratios under different scenarios

3. Lender/rating agency attitudes

4. Reserve borrowing capacity

5. Effects of financing on control

6. Asset structure

7. Expected tax rate

how would these factors affect the target capital structure
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?

long term debt ratios for selected industries
Long-term Debt Ratios for Selected Industries

IndustryLong-Term Debt Ratio

Pharmaceuticals 20.00%

Computers 25.93

Steel 39.76

Aerospace 43.18

Airlines 56.33

Utilities 56.52

Source: Dow Jones News Retrieval. Data collected through December 17, 1999.

slide51

Value of Stock

MM result

Actual

No leverage

D/A

0

D1

D2

slide52
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.
slide53

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

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

what are signaling effects in capital structure
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:

therefore managers can be expected to
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.

conclusions on capital structure
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.