Transcript Capital Structure and Leverage
Capital Structure and Leverage
Business vs. financial risk
Operating leverage
Financial leverage
Optimal capital structure
Capital structure theory
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What is business risk?
Uncertainty about future operating income (EBIT), i.e., how well can we predict operating income?
Probability Low risk High risk 0 E(EBIT)
Note that business risk does not financing effects.
EBIT include
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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.
$ Rev.
$ Rev.
TC
}
Profit TC FC FC Q BE Sales Q BE Sales
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Operating Leverage Operating Breakeven : Amount of sales that leads to zero EBIT EBIT = P*Q-V*Q-F=0 Q BE =F/(P-V) Degree of Operating Leverage (DOL) DOL= % change in EBIT/%change in SALES
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Operating Leverage EBIT =(P-V)Q-F dEBIT/dQ=P-V DOL= dEBIT/dQ * Q/EBIT = Q*(P-V) /[Q*(P-V) –F]
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Probability Low operating leverage High operating leverage EBIT L EBIT H Typical situation: Can use operating leverage to get higher E(EBIT), but risk increases.
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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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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)
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Financial Breakeven Amount of EBIT that leads to zero EPS EPS =(EBIT-I)(1-T) /N=0 EBIT BE =I
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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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Consider 2 Hypothetical Firms Firm U No debt $20,000 in assets 40% tax rate Firm L $10,000 of 12% debt $20,000 in assets 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) .
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Capial Structures of the Two Firms A=$20,000=D+E for both firms E U =$20,000 D U =$0 E L =$10,000 D L =$10,000
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Firm U: Unleveraged Prob.
EBIT Interest EBT Taxes (40%) NI Bad 0.25
$2,000 0 $2,000 800 $1,200 Economy Avg.
Good 0.50
$3,000 0 $3,000 1,200 $1,800 0.25
$4,000 0 $4,000 1,600 $2,400
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Firm L: Leveraged Bad Economy Avg.
Good Prob.* EBIT* Interest EBT Taxes (40%) NI 0.25
$2,000 1,200 $ 800 320 $ 480 0.50
$3,000 1,200 $1,800 720 $1,080 0.25
$4,000 1,200 $2,800 1,120 $1,680 *Same as for Firm U.
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Firm U BEP* ROE TIE Bad 10.0% 6.0% Avg.
15.0% 9.0% Good 20.0% 12.0%
Firm L
Bad Avg.
BEP* ROE TIE 10.0% 4.8% 1.67x
15.0% 10.8% 2.5x
*BEP same for Firms U and L.
Good 20.0% 16.8% 3.3x
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Expected Values: E(BEP) E(ROE) E(TIE) Risk Measures:
s
ROE CV ROE U 15.0% 9.0% L 15.0% 10.8% 2.5x
2.12% 0.24 4.24% 0.39
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For leverage to raise ROE, must have
BEP > k
d (avg. and good states).
Why?
If k d > 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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NI=[EBIT-Dk d ](1-T) A=D+E ROE=NI /(A-D)=[EBIT-Dk d ](1-T) /(A-D) =[EBIT/A-(D/A)k d ](1-T) /(1-D/A) =[BEP-DR k d ](1-T) /(1-DR) where DR=D/A
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dROE/dDR=[(1-T)(BEP-k d )] / (1-DR) 2 (1-T)(BEP-k d )>0 implies BEP-k d >0 or BEP>k d q.e.d.
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Conclusions
Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage.
L has higher expected ROE because BEP > k d 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.
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If debt increases, TIE falls.
TIE = EBIT I EBIT is constant (unaffected by use of debt), and since I = k d D, as D increases, TIE must fall.
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Optimal Capital Structure
That capital structure (mix of debt, preferred, and common equity) at which P 0 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.
Consider another firm, Hannibal Inc., which
announces
a recapitalization.
New debt is
issued
.
Proceeds are used to
repurchase
stock.
Price per share
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Cost of debt at different debt levels after recapitalization Amount D/A D/E Bond borrowed ratio ratio rating k d K$ 0 0 0 - - 250 500 0.125
0.250
0.1429 AA 0.3333 A 8% 9% 750 1,000 0.375
0.500
0.6000 BBB 1.0000 BB 11.5% 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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What would the earnings per share be if 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 P 0 = $25.Nu=80,000 D = 0: EPS 0 = (EBIT – k d D)(1 – T) Shares outstanding ($400,000)(0.6) 80,000
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D = $250K, k
d
= 8%.
Shares repurchased $250,000 = = 10,000.
$25 EPS 1 = [$400 – 0.08($250)](0.6) 80 – 10 = $3.26.
EBIT TIE = = = 20 I $400 $20 ×.
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D = $500K, k
d
= 9%.
Shares repurchased $500 = = 20.
$25 EPS 2 = [$400 – 0.09($500)](0.6) 80 – 20 = $3.55.
EBIT TIE = = = 8.9
I $400 $45 ×.
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D = $750K, k
d
= 11.5%.
Shares repurchased $750 = = 30.
$25 EPS 3 = [$400 – 0.115($750)](0.6) 80 – 30 = $3.77.
EBIT TIE = = = 4.6
I $400 $86.25
×.
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D = $1,000K, k
d
= 14%.
Shares repurchased $1,000 = = 40.
$25 EPS 4 = [$400 – 0.14($1,000)](0.6) 80 – 40 = $3.90.
EBIT TIE = = = 2.9
I $400 $140 ×.
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Stock Price (Zero Growth) P 0 k s D – g EPS k s DPS k s If payout = 100%, then EPS = DPS and E(g) = 0.
We just calculated EPS = DPS. To find the expected stock price (P 0 ), we must find the appropriate k s at each of the debt levels discussed.
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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 k s.
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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) b L = b U [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).
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Calculating Levered Betas
D = $250K
k s = k RF + (k M – k RF )b L b L b L = b U [1 + (1 – T)(D/E)] = 1.0[1 + (1 – 0.4)($250/$1,750)] b L = 1.0[1 + (0.6)(0.1429)] b L = 1.0857.
k s k s = k RF + (k M – k RF )b L = 6.0% + (6.0%)1.0857 = 12.51%.
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Table for Calculating Levered Betas Amount borrowed K$ 0 250 500 750 1,000 D/A ratio 0.00% 12.50
25.00
37.50
50.00
D/E ratio 0.00% Levered Beta 1.00
k s 12.00% 14.29
1.09
12.51
33.33
1.20
13.20
60.00
1.36
14.16
100.00
1.60
15.60
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Minimizing the WACC Amount D/A ratio borrowed 0.00% K$ 0 12.50
250 25.00
500 37.50
750 50.00
1,000 E/A ratio 100.00% 87.50
75.00
62.50
50.00
k s 12.00% k d (1 – T) WACC 0.00% 12.00% 12.51
4.80
11.55
13.20
5.40
11.25
14.16
6.90
11.44
15.60
8.40
12.00
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P 0 = DPS/k s Amount Borrowed $ 0 250,000 500,000 750,000 1,000,000 DPS $3.00
3.26
3.55
3.77
3.90
k s 12.00% 12.51
13.20
14.16
15.60
P 0 $25.00
26.03
26.89* 26.59
25.00
*Maximum: Since D = $500,000 and assets = $2,000,000, optimal D/A = 25%.
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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%.
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What is Hannibal’s optimal capital structure?
P 0 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
.50
.75
k s WACC k d (1 – T) D/A .25
P 0 EPS .50
D/A
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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 of more debt.
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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
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Total Breakeven The amount of sales that leads to zero EPS [(P-V)Q-F-I](1-T) /N=0 Q BE =(F-I)/(P-V)
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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
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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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Long-term Debt Ratios for Selected Industries Industry Pharmaceuticals Computers Steel Aerospace Airlines Utilities Long-Term Debt Ratio 20.00% 25.93
39.76
43.18
56.33
56.52
Source: Dow Jones News Retrieval. Data collected through December 17, 1999.
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Value of Stock MM result 0 D 1 D 2 Actual No leverage D/A
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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, discussed earlier, suggests firms should use less debt than MM suggest.
This
unused debt capacity
helps avoid stock sales, which depress P 0 because of signaling effects.
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What are “signaling” effects in capital structure?
Assumptions:
Managers have better information about a firm’s long-run value than outside investors.
Managers act in the best interests of current stockholders.
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Therefore, managers can be expected to:
issue stock overvalued .
if they think stock is
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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