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16 - 1
CHAPTER 16 Capital Structure Decisions: The Basics Impact of leverage on returns Business versus financial risk Capital structure theory Perpetual cash flow example Setting the optimal capital structure in practice Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 2
Consider Two 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 EBIT of $3,000. They differ only with respect to use of debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 3
Impact of Leverage on Returns
EBIT Interest EBT Taxes (40%) NI ROE Copyright © 2002 by Harcourt, Inc.
Firm U $3,000 0 $3,000 1 ,200 $1,800 9.0%
Firm L $3,000 1,200 $1,800 720 $1,080 10.8% All rights reserved.
16 - 4
Why does leveraging increase return? Total dollar return to investors: U: NI = $1,800. L: NI + Int= $1,080 + $1,200 = $2,280. Difference= $480.
Taxes paid: U: $1,200; L: $720. Difference = $480.
More EBIT goes to investors in Firm L. Equity $ proportionally lower than NI. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 5
What is business risk? Uncertainty about future operating income (EBIT). Probability Low risk
High risk
0
E(EBIT)
EBIT
Note that business risk focuses on operating income, so it ignores financing effects. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 6
Factors That Influence Business Risk
Uncertainty about demand (unit sales). Uncertainty about output prices. Uncertainty about input costs. Product and other types of liability. Degree of operating leverage (DOL). Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 7
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. The higher the proportion of fixed costs within a firm’s overall cost structure, the greater the operating leverage. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 8
Higher operating leverage leads to more business risk, because a small sales decline causes a larger profit decline. Rev.
Rev. $ TC
$
} Profit TC FC
FC QBE
Sales
QBE
Sales (More...)
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 9
Probability
Low operating leverage High operating leverage
EBITL
EBITH
In the typical situation, higher operating leverage leads to higher expected EBIT, but also increases risk. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 10
Business Risk versus Financial Risk Business risk: Uncertainty in future EBIT. Depends on business factors such as competition, operating leverage, etc.
Financial risk: Additional business risk concentrated on common stockholders when financial leverage is used. Depends on the amount of debt and preferred stock financing. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 11
From a shareholder’s perspective, how are financial and business risk measured in the stand-alone sense? Stand-alone Business Financial = + . risk risk risk Stand-alone risk = σ ROE. Business risk = σ ROE(U). Financial risk = σ ROE - σ ROE(U). Copyright © 2002 by Harcourt, Inc.
All rights reserved.
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Now consider the fact that EBIT is not known with certainty. What is the impact of uncertainty on stockholder profitability and risk for Firm U and Firm L?
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 13
Firm U: Unleveraged
Prob. EBIT Interest EBT Taxes (40%) NI Copyright © 2002 by Harcourt, Inc.
Bad 0.25 $2,000 0 $2,000 800 $1,200
Economy Avg. 0.50 $3,000 0 $3,000 1,200 $1,800
Good 0.25 $4,000 0 $4,000 1,600 $2,400 All rights reserved.
16 - 14
Firm L: Leveraged Bad Prob.* 0.25 EBIT* $2,000 Interest 1,200 EBT $ 800 Taxes (40%) 320 NI $ 480 *Same as for Firm U. Copyright © 2002 by Harcourt, Inc.
Economy Avg. 0.50 $3,000 1,200 $1,800 720 $1,080
Good 0.25 $4,000 1,200 $2,800 1,120 $1,680 All rights reserved.
16 - 15
Copyright © 2002 by Harcourt, Inc.
8
8
8
Firm U Bad Avg. Good BEP 10.0% 15.0% 20.0% ROI* 6.0% 9.0% 12.0% ROE 6.0% 9.0% 12.0% TIE Firm L Bad Avg. Good BEP 10.0% 15.0% 20.0% ROI* 8.4% 11.4% 14.4% ROE 4.8% 10.8% 16.8% TIE 1.7x 2.5x 3.3x *ROI = (NI + Interest)/Total financing. All rights reserved.
16 - 16
Profitability Measures: L 15.0% 11.4% 10.8%
σROE
2.12%
4.24%
CVROE E(TIE)
0.24
0.39 2.5x
E(BEP) E(ROI) E(ROE) Risk Measures:
Copyright © 2002 by Harcourt, Inc.
8
U 15.0% 9.0% 9.0%
All rights reserved.
16 - 17
Conclusions Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage. L has higher expected ROI and ROE because of tax savings. L has much wider ROE (and EPS) swings because of fixed interest charges. Its higher expected return is accompanied by higher risk. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 18
In a stand-alone risk sense, Firm L’s stockholders see much more risk than Firm U’s. U and L: σ ROE(U) = 2.12%. U: σ ROE = 2.12%. L: σ ROE = 4.24%.
L’s financial risk is σ ROE - σ ROE(U) = 4.24% - 2.12% = 2.12%. (U’s is zero.) (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 19
For leverage to be positive (increase expected ROE), BEP must be > kd. If kd > BEP, the cost of leveraging will be higher than the inherent profitability of the assets, so the use of financial leverage will depress net income and ROE. In the example, E(BEP) = 15% while interest rate = 12%, so leveraging “works.” Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 20
Capital Structure Theory MM theory Zero taxes Corporate taxes Corporate and personal taxes
Trade-off theory Signaling theory Debt financing as a managerial constraint Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 21
MM Theory: Zero Taxes MM prove, under a very restrictive set of assumptions, that a firm’s value is unaffected by its financing mix. Therefore, capital structure is irrelevant. Any increase in ROE resulting from financial leverage is exactly offset by the increase in risk. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 22
MM Theory: Corporate Taxes Corporate tax laws favor debt financing over equity financing. With corporate taxes, the benefits of financial leverage exceed the risks: More EBIT goes to investors and less to taxes when leverage is used. Firms should use almost 100% debt financing to maximize value. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 23
MM Theory: Corporate and Personal Taxes Personal taxes lessen the advantage of corporate debt: Corporate taxes favor debt financing. Personal taxes favor equity financing.
Use of debt financing remains advantageous, but benefits are less than under only corporate taxes. Firms should still use 100% debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 24
Hamada’s Equation MM theory implies that beta changes with leverage. bU is the beta of a firm when it has no debt (the unlevered beta) bL = bU(1 + (1 - T)(D/E)) In practice, D/E is measured in book values when bL is calculated. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 25
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. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 26
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? Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 27
Debt Financing As a Managerial Constraint One agency problem is that managers can use corporate funds for non-value maximizing purposes. The use of financial leverage: Bonds “free cash flow.” Forces discipline on managers.
However, it also increases risk of financial distress. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 28
Perpetual Cash Flow Example Expected EBIT = $500,000; will remain constant over time. Firm pays out all earnings as dividends (zero growth). Currently is all-equity financed. BV of equity = MV of equity 100,000 shares outstanding. P0 = $20; T = 40%; kRF = 6%; RPM = 4% Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 29
Component Cost Estimates Amount Borrowed (000) $ 0 250 500 750 1,000
kd 10.0% 11.0 13.0 16.0
If company recapitalizes, debt would be issued to repurchase stock. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 30
The MM and Miller models cannot be applied directly because several assumptions are violated. kd is not a constant. Bankruptcy and agency costs exist. In practice, Hamada’s equation is used to find kS for the firm with different levels of debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 31
The Optimal Capital Structure Calculate the cost of equity at each level of debt. Calculate the value of equity at each level of debt. Calculate the total value of the firm (value of equity + value of debt) at each level of debt. The optimal capital structure maximizes the total value of the firm. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 32
Sequence of Events in a Recapitalization Firm announces the recapitalization. Investors reassess their views and estimate a new equity value. New debt is issued and proceeds are used to repurchase stock at the new equilibrium price. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 33
Shares Debt issued = . Bought New price/share After recapitalization firm would have more debt but fewer common shares outstanding. An analysis of several debt levels is given next.
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 34
Cost of Equity at Zero Debt Since the firm has 0 growth, its current value, $2,000,000, is given by Dividends/kS = (EBIT)(1-T)/kS = 500,000 (1 - 0.40)/kS kS = 15.0% = unlevered cost of equity. bU = (kS - kRF)/RPM = (15 - 6)/4 = 2.25 Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 35
Cost of Equity at Each Debt Level Hamada’s equation says that bL = bU (1 + (1-T)(D/E)) Debt(000s) 0 250 500 750 1,000
D/E 0 0.142 0.333 0.600 1.000
Copyright © 2002 by Harcourt, Inc.
bL 2.25 2.44 2.70 3.06 3.60
kS 15.00% 15.77 16.80 18.24 20.40 All rights reserved.
16 - 36
D = $250, kd = 10%, ks = 15.77%. (EBIT - kdD)(1 - T) S1 = ks [$500 - 0.1($250)](0.6) = = $1,807. 0.1577 V1 = S1 + D1 = $1,807 + $250 = $2,057. $2,05 P1 = 7 = $20.57. 100 Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 37
Shares $250 = = 12.15. repurchased $20.57 Shares = n1 = 100 - 12.15 = 87.85. remaining Check on stock price: S1 $1,807 P1 = = = $20.57. n1 87.85 Other debt levels treated similarly. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 38
Value of Equity at Each Debt Level Equity Value = Dividends/kS Debt(000s) 0 250 500 750 1,000
kD na 10% 11% 13% 16%
Copyright © 2002 by Harcourt, Inc.
Divs 300 285 267 241.5 204
kS 15.00% 15.77 16.80 18.24 20.40
E 2,000 1,807 1,589 1,324 1,000 All rights reserved.
16 - 39
Total Value of Firm
Debt (000s) 0 250 500 750 1,000
E 2,000 1,807 1,589 1,324 1,000
Total Value 2,000 2,057 2,089 2,074 2,000
Copyright © 2002 by Harcourt, Inc.
Price per Share $20.00 20.57 20.89 20.74 20.00
Total Value is Maximized with 500,000 in debt. All rights reserved.
16 - 40
Calculate EPS at debt of $0, $250K, $500K, and $750K, assuming that the firm begins at zero debt and recapitalizes to each level in a single step. Net income = NI = [EBIT - kd D](1 - T). EPS = NI/n. D $ 0 250 500 750
NI $300 285 267 242
Copyright © 2002 by Harcourt, Inc.
n 100.00 87.85 76.07 63.84
EPS $3.00 3.24 3.51 3.78
All rights reserved.
16 - 41
EPS continues to increase beyond the $500,000 optimal debt level. Does this mean that the optimal debt level is $750,000, or even higher?
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 42
Find the WACC at each debt level. D $ 0 250 500 750 1,000
S $2,000 1,807 1,589 1,324 1,000
V $2,000 2,057 2,089 2,074 2,000
kd Ks WACC -15.00% 15.0% 10% 15.77 14.6 11.0 16.80 14.4 13.0 18.24 14.5 13.0 20.40 15.0
e.g. D = $250: WACC = ($250/$2,057)(10%)(0.6) + ($1,807/$2,057)(15.77%) = 14.6%. Copyright © 2002 by Harcourt, Inc. All rights reserved.
16 - 43
The WACC is minimized at D = $500,000, the same debt level that maximizes stock price. Since the value of a firm is the present value of future operating income, the lowest discount rate (WACC) leads to the highest value.
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 44
How would higher or lower business risk affect the optimal capital structure? At any debt level, the firm’s probability of financial distress would be higher. Both kd and ks would rise faster than before. The end result would be an optimal capital structure with less debt. Lower business risk would have the opposite effect. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 45
Is it possible to do an analysis exactly like the one above for most firms?
No. The analysis above was based on the assumption of zero growth, and most firms do not fit this category. Further, it would be very difficult, if not impossible, to estimate ks with any confidence. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 46
What type of analysis should firms conduct to help find their optimal, or target, capital structure? Financial forecasting models can help show how capital structure changes are likely to affect stock prices, coverage ratios, and so on. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 47
Forecasting models can generate results under various scenarios, but the financial manager must specify appropriate input values, interpret the output, and eventually decide on a target capital structure. In the end, capital structure decision will be based on a combination of analysis and judgment. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 48
What other factors would managers consider when setting the target capital structure? Debt ratios of other firms in the industry. Pro forma coverage ratios at different capital structures under different economic scenarios. Lender and rating agency attitudes (impact on bond ratings). Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 49
Reserve borrowing capacity. Effects on control. Type of assets: Are they tangible, and hence suitable as collateral? Tax rates.
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
CHAPTER 16 Capital Structure Decisions: The Basics Impact of leverage on returns Business versus financial risk Capital structure theory Perpetual cash flow example Setting the optimal capital structure in practice Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 2
Consider Two 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 EBIT of $3,000. They differ only with respect to use of debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 3
Impact of Leverage on Returns
EBIT Interest EBT Taxes (40%) NI ROE Copyright © 2002 by Harcourt, Inc.
Firm U $3,000 0 $3,000 1 ,200 $1,800 9.0%
Firm L $3,000 1,200 $1,800 720 $1,080 10.8% All rights reserved.
16 - 4
Why does leveraging increase return? Total dollar return to investors: U: NI = $1,800. L: NI + Int= $1,080 + $1,200 = $2,280. Difference= $480.
Taxes paid: U: $1,200; L: $720. Difference = $480.
More EBIT goes to investors in Firm L. Equity $ proportionally lower than NI. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 5
What is business risk? Uncertainty about future operating income (EBIT). Probability Low risk
High risk
0
E(EBIT)
EBIT
Note that business risk focuses on operating income, so it ignores financing effects. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 6
Factors That Influence Business Risk
Uncertainty about demand (unit sales). Uncertainty about output prices. Uncertainty about input costs. Product and other types of liability. Degree of operating leverage (DOL). Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 7
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. The higher the proportion of fixed costs within a firm’s overall cost structure, the greater the operating leverage. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 8
Higher operating leverage leads to more business risk, because a small sales decline causes a larger profit decline. Rev.
Rev. $ TC
$
} Profit TC FC
FC QBE
Sales
QBE
Sales (More...)
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 9
Probability
Low operating leverage High operating leverage
EBITL
EBITH
In the typical situation, higher operating leverage leads to higher expected EBIT, but also increases risk. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 10
Business Risk versus Financial Risk Business risk: Uncertainty in future EBIT. Depends on business factors such as competition, operating leverage, etc.
Financial risk: Additional business risk concentrated on common stockholders when financial leverage is used. Depends on the amount of debt and preferred stock financing. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 11
From a shareholder’s perspective, how are financial and business risk measured in the stand-alone sense? Stand-alone Business Financial = + . risk risk risk Stand-alone risk = σ ROE. Business risk = σ ROE(U). Financial risk = σ ROE - σ ROE(U). Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 12
Now consider the fact that EBIT is not known with certainty. What is the impact of uncertainty on stockholder profitability and risk for Firm U and Firm L?
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 13
Firm U: Unleveraged
Prob. EBIT Interest EBT Taxes (40%) NI Copyright © 2002 by Harcourt, Inc.
Bad 0.25 $2,000 0 $2,000 800 $1,200
Economy Avg. 0.50 $3,000 0 $3,000 1,200 $1,800
Good 0.25 $4,000 0 $4,000 1,600 $2,400 All rights reserved.
16 - 14
Firm L: Leveraged Bad Prob.* 0.25 EBIT* $2,000 Interest 1,200 EBT $ 800 Taxes (40%) 320 NI $ 480 *Same as for Firm U. Copyright © 2002 by Harcourt, Inc.
Economy Avg. 0.50 $3,000 1,200 $1,800 720 $1,080
Good 0.25 $4,000 1,200 $2,800 1,120 $1,680 All rights reserved.
16 - 15
Copyright © 2002 by Harcourt, Inc.
8
8
8
Firm U Bad Avg. Good BEP 10.0% 15.0% 20.0% ROI* 6.0% 9.0% 12.0% ROE 6.0% 9.0% 12.0% TIE Firm L Bad Avg. Good BEP 10.0% 15.0% 20.0% ROI* 8.4% 11.4% 14.4% ROE 4.8% 10.8% 16.8% TIE 1.7x 2.5x 3.3x *ROI = (NI + Interest)/Total financing. All rights reserved.
16 - 16
Profitability Measures: L 15.0% 11.4% 10.8%
σROE
2.12%
4.24%
CVROE E(TIE)
0.24
0.39 2.5x
E(BEP) E(ROI) E(ROE) Risk Measures:
Copyright © 2002 by Harcourt, Inc.
8
U 15.0% 9.0% 9.0%
All rights reserved.
16 - 17
Conclusions Basic earning power = BEP = EBIT/Total assets is unaffected by financial leverage. L has higher expected ROI and ROE because of tax savings. L has much wider ROE (and EPS) swings because of fixed interest charges. Its higher expected return is accompanied by higher risk. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 18
In a stand-alone risk sense, Firm L’s stockholders see much more risk than Firm U’s. U and L: σ ROE(U) = 2.12%. U: σ ROE = 2.12%. L: σ ROE = 4.24%.
L’s financial risk is σ ROE - σ ROE(U) = 4.24% - 2.12% = 2.12%. (U’s is zero.) (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 19
For leverage to be positive (increase expected ROE), BEP must be > kd. If kd > BEP, the cost of leveraging will be higher than the inherent profitability of the assets, so the use of financial leverage will depress net income and ROE. In the example, E(BEP) = 15% while interest rate = 12%, so leveraging “works.” Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 20
Capital Structure Theory MM theory Zero taxes Corporate taxes Corporate and personal taxes
Trade-off theory Signaling theory Debt financing as a managerial constraint Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 21
MM Theory: Zero Taxes MM prove, under a very restrictive set of assumptions, that a firm’s value is unaffected by its financing mix. Therefore, capital structure is irrelevant. Any increase in ROE resulting from financial leverage is exactly offset by the increase in risk. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 22
MM Theory: Corporate Taxes Corporate tax laws favor debt financing over equity financing. With corporate taxes, the benefits of financial leverage exceed the risks: More EBIT goes to investors and less to taxes when leverage is used. Firms should use almost 100% debt financing to maximize value. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 23
MM Theory: Corporate and Personal Taxes Personal taxes lessen the advantage of corporate debt: Corporate taxes favor debt financing. Personal taxes favor equity financing.
Use of debt financing remains advantageous, but benefits are less than under only corporate taxes. Firms should still use 100% debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 24
Hamada’s Equation MM theory implies that beta changes with leverage. bU is the beta of a firm when it has no debt (the unlevered beta) bL = bU(1 + (1 - T)(D/E)) In practice, D/E is measured in book values when bL is calculated. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 25
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. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 26
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? Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 27
Debt Financing As a Managerial Constraint One agency problem is that managers can use corporate funds for non-value maximizing purposes. The use of financial leverage: Bonds “free cash flow.” Forces discipline on managers.
However, it also increases risk of financial distress. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 28
Perpetual Cash Flow Example Expected EBIT = $500,000; will remain constant over time. Firm pays out all earnings as dividends (zero growth). Currently is all-equity financed. BV of equity = MV of equity 100,000 shares outstanding. P0 = $20; T = 40%; kRF = 6%; RPM = 4% Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 29
Component Cost Estimates Amount Borrowed (000) $ 0 250 500 750 1,000
kd 10.0% 11.0 13.0 16.0
If company recapitalizes, debt would be issued to repurchase stock. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 30
The MM and Miller models cannot be applied directly because several assumptions are violated. kd is not a constant. Bankruptcy and agency costs exist. In practice, Hamada’s equation is used to find kS for the firm with different levels of debt. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 31
The Optimal Capital Structure Calculate the cost of equity at each level of debt. Calculate the value of equity at each level of debt. Calculate the total value of the firm (value of equity + value of debt) at each level of debt. The optimal capital structure maximizes the total value of the firm. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 32
Sequence of Events in a Recapitalization Firm announces the recapitalization. Investors reassess their views and estimate a new equity value. New debt is issued and proceeds are used to repurchase stock at the new equilibrium price. (More...) Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 33
Shares Debt issued = . Bought New price/share After recapitalization firm would have more debt but fewer common shares outstanding. An analysis of several debt levels is given next.
Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 34
Cost of Equity at Zero Debt Since the firm has 0 growth, its current value, $2,000,000, is given by Dividends/kS = (EBIT)(1-T)/kS = 500,000 (1 - 0.40)/kS kS = 15.0% = unlevered cost of equity. bU = (kS - kRF)/RPM = (15 - 6)/4 = 2.25 Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 35
Cost of Equity at Each Debt Level Hamada’s equation says that bL = bU (1 + (1-T)(D/E)) Debt(000s) 0 250 500 750 1,000
D/E 0 0.142 0.333 0.600 1.000
Copyright © 2002 by Harcourt, Inc.
bL 2.25 2.44 2.70 3.06 3.60
kS 15.00% 15.77 16.80 18.24 20.40 All rights reserved.
16 - 36
D = $250, kd = 10%, ks = 15.77%. (EBIT - kdD)(1 - T) S1 = ks [$500 - 0.1($250)](0.6) = = $1,807. 0.1577 V1 = S1 + D1 = $1,807 + $250 = $2,057. $2,05 P1 = 7 = $20.57. 100 Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 37
Shares $250 = = 12.15. repurchased $20.57 Shares = n1 = 100 - 12.15 = 87.85. remaining Check on stock price: S1 $1,807 P1 = = = $20.57. n1 87.85 Other debt levels treated similarly. Copyright © 2002 by Harcourt, Inc.
All rights reserved.
16 - 38
Value of Equity at Each Debt Level Equity Value = Dividends/kS Debt(000s) 0 250 500 750 1,000
kD na 10% 11% 13% 16%
Copyright © 2002 by Harcourt, Inc.
Divs 300 285 267 241.5 204
kS 15.00% 15.77 16.80 18.24 20.40
E 2,000 1,807 1,589 1,324 1,000 All rights reserved.
16 - 39
Total Value of Firm
Debt (000s) 0 250 500 750 1,000
E 2,000 1,807 1,589 1,324 1,000
Total Value 2,000 2,057 2,089 2,074 2,000
Copyright © 2002 by Harcourt, Inc.
Price per Share $20.00 20.57 20.89 20.74 20.00
Total Value is Maximized with 500,000 in debt. All rights reserved.
16 - 40
Calculate EPS at debt of $0, $250K, $500K, and $750K, assuming that the firm begins at zero debt and recapitalizes to each level in a single step. Net income = NI = [EBIT - kd D](1 - T). EPS = NI/n. D $ 0 250 500 750
NI $300 285 267 242
Copyright © 2002 by Harcourt, Inc.
n 100.00 87.85 76.07 63.84
EPS $3.00 3.24 3.51 3.78
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EPS continues to increase beyond the $500,000 optimal debt level. Does this mean that the optimal debt level is $750,000, or even higher?
Copyright © 2002 by Harcourt, Inc.
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16 - 42
Find the WACC at each debt level. D $ 0 250 500 750 1,000
S $2,000 1,807 1,589 1,324 1,000
V $2,000 2,057 2,089 2,074 2,000
kd Ks WACC -15.00% 15.0% 10% 15.77 14.6 11.0 16.80 14.4 13.0 18.24 14.5 13.0 20.40 15.0
e.g. D = $250: WACC = ($250/$2,057)(10%)(0.6) + ($1,807/$2,057)(15.77%) = 14.6%. Copyright © 2002 by Harcourt, Inc. All rights reserved.
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The WACC is minimized at D = $500,000, the same debt level that maximizes stock price. Since the value of a firm is the present value of future operating income, the lowest discount rate (WACC) leads to the highest value.
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16 - 44
How would higher or lower business risk affect the optimal capital structure? At any debt level, the firm’s probability of financial distress would be higher. Both kd and ks would rise faster than before. The end result would be an optimal capital structure with less debt. Lower business risk would have the opposite effect. Copyright © 2002 by Harcourt, Inc.
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Is it possible to do an analysis exactly like the one above for most firms?
No. The analysis above was based on the assumption of zero growth, and most firms do not fit this category. Further, it would be very difficult, if not impossible, to estimate ks with any confidence. Copyright © 2002 by Harcourt, Inc.
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What type of analysis should firms conduct to help find their optimal, or target, capital structure? Financial forecasting models can help show how capital structure changes are likely to affect stock prices, coverage ratios, and so on. (More...) Copyright © 2002 by Harcourt, Inc.
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Forecasting models can generate results under various scenarios, but the financial manager must specify appropriate input values, interpret the output, and eventually decide on a target capital structure. In the end, capital structure decision will be based on a combination of analysis and judgment. Copyright © 2002 by Harcourt, Inc.
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What other factors would managers consider when setting the target capital structure? Debt ratios of other firms in the industry. Pro forma coverage ratios at different capital structures under different economic scenarios. Lender and rating agency attitudes (impact on bond ratings). Copyright © 2002 by Harcourt, Inc.
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Reserve borrowing capacity. Effects on control. Type of assets: Are they tangible, and hence suitable as collateral? Tax rates.
Copyright © 2002 by Harcourt, Inc.
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