Anıl Sural - Capital Structure and Leverage
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Transcript of Anıl Sural - Capital Structure and Leverage
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.