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Unformatted text preview: 1 CAPITAL STRUCTURE: THE BASIC CONCEPTS Ross, Westerfield & Jaffe “Corporate Finance” 7th ed. Chapter 15 The Capital‐Structure Question and The Pie Theory 2 The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity. V = D + E If the goal of the management of
ED
S the firm is to make the firm as
valuable as possible, the firm
should pick the debtequity ratio
that makes the pie as big as
possible. Value of the Firm The Capital‐Structure Question 3 1. 2. There are really two important questions: Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value. What is the ratio of debt‐to‐equity that maximizes the shareholder’s value? Capital Restructuring 4 Capital restructuring involves changing the amount of leverage a firm has without changing the firm’s assets A firm can issue bonds and use the proceeds to buy back some shares, increasing the debt to equity ratio. Or issue shares and use the proceeds to pay back existing debt, decreasing the debt to equity ratio The firm can consider capital restructuring decisions in isolation from its investment decisions Choosing a Capital Structure 5 What is a company’s purpose? Maximize shareholder wealth So we want to choose a capital structure that will maximize shareholder wealth by maximizing firm value Financial Leverage, EPS, and ROE 6 Consider an allequity firm that is considering going into debt. (Maybe some of
the original shareholders want to cash out.) Current Assets $20,000 Debt $0 Equity $20,000 Debt/Equity ratio 0.00 Interest rate n/a Shares outstanding 400 Share price $50 Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50 7 EPS and ROE Under Current Capital Structure Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 Net income $1,000 $2,000 $3,000 EPS $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current Shares Outstanding = 400 shares 8 EPS and ROE Under Proposed Capital Structure Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 640 640 640 Net income $360 $1,360 $2,360 EPS $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20% Proposed Shares Outstanding = 240 shares EPS and ROE Under Both Capital Structures 9 AllEquity
Recession
EBIT
$1,000
Interest
0
Net income
$1,000
EPS
$2.50
ROA
5%
ROE
5%
Current Shares Outstanding = 400 shares Levered Recession EBIT $1,000 Interest 640 Net income $360 EPS $1.50 ROA 5% ROE 3% Proposed Shares Outstanding = 240 shares Expected
$2,000
0
$2,000
$5.00
10%
10% Expected $2,000 640 $1,360 $5.67 10% 11% Expansion
$3,000
0
$3,000
$7.50
15%
15% Expansion $3,000 640 $2,360 $9.83 15% 20% 15‐10 Financial Leverage and EPS 12.00
10.00 EPS 8.00 No Debt 6.00
4.00
2.00
0.00
1,000
(2.00) 2,000 3,000 EBIT in dollars, no taxes Example: The Effect of Leverage 11 What happens to EPS and ROE when we issue debt and buy back shares of stock? A firm currently has no debt in its capital structure. The management is considering restructuring which will involve taking on some debt to buyback shares The firm assets are valued at $8m. There are 400,000 shares outstanding at $20 per share. The proposed debt issue will raise $4m at 10% interest rate allowing a buy back of 200,000 shares. The new capital structure will involve a debt to equity ratio of 1. Example: The Effect of Leverage 12 Current Capital Structure: No Debt Recession Expected Expansion $500,000 $1,000,000 $1,500,000 0 0 0 $500,000 $1,000,000 $1,500,000 ROE 6.25% 12.5% 18.75% EPS $1.25 $2.50 $3.75 EBIT Interest Net Income Proposed Capital Structure: Debt = $4 million Recession Expected Expansion EBIT $500,000 $1,000,000 $1,500,000 Interest 400,000 400,000 400,000 Net Income $100,000 $600,000 $1,100,000 ROE 2.50% 15.0% 27.50% EPS $0.50 $3.00 $5.50 Example: The Effect of Leverage 13 Variability in ROE Current: ROE ranges from 6.25% to 18.75% Proposed: ROE ranges from 2.50% to 27.50% Variability in EPS Current: EPS ranges from $1.25 to $3.75 Proposed: EPS ranges from $0.50 to $5.50 The variability in both ROE and EPS increases when financial leverage is increased Example: The Effect of Leverage 14 Earnings per share ($) 4 With debt No debt 3 2 1 Break‐even point Disadvantage due to debt Earnings before interest and taxes ($) 0
400,000
1 2 800,000 1,200,000 1,600,000 Break‐even EBIT 15 If we expect EBIT to be greater than the break‐
even point, then leverage is beneficial to our stockholders If we expect EBIT to be less than the break‐even point, then leverage is detrimental to our stockholders 16 Example: Homemade leverage and ROE Assume markets are complete, investors are rational and risk averse Investors can use ‘Home‐made’ leverage to change the amount of overall leverage they are exposed to Suppose an investor buys $2000 worth of equity if the proposed capital structure is adopted. Can s/he use private borrowing to replicate these payoffs with the current capital structure? 17 Example: Homemade Leverage and ROE Proposed Capital Structure Recession Expected Expansion EPS $ 0.50 $ 3.00 $ 5.50 Earnings for 100 shares 50.00 300.00 550.00 Net cost = 100 shares at $20 = $2,000 Original Capital Structure and Homemade Leverage Recession Expected Expansion EPS $ 1.25 $ 2.50 $ 3.75 Earnings for 200 shares 250.00 500.00 750.00 Capital Structure Theory 18 Modigliani and Miller Theory of Capital Structure: The value of the firm is determined by the firm’s cash flow and riskiness of assets Proposition I: The value of the firm is independent of the capital structure Proposition II: Cost of capital is constant and cost of equity is a linear function of its capital structure Assumptions: complete markets, complete info, no taxes, no bankruptcy costs, no transaction costs, the value of the assets of the firms are unaffected by the capital structure The MM Propositions I & II (No Taxes) 19 Proposition I Firm value is not affected by leverage VL = VU Proposition II Leverage increases the risk and return to stockholders rE = rU + (D / EL) (rU ‐ rD) rD is the interest rate (cost of debt) rE is the return on (levered) equity (cost of equity) rU (or rA) is the return on unlevered equity (cost of capital) D is the value of debt EL is the value of levered equity Proof of MM Proposition I 20 Rests on the no‐arbitrage argument Suppose Firm U is unlevered, i.e. VU = EU Invest in 1% of Firm U’s shares Dollar Investment
Dollar Return 0.01VU 0.01Profits Suppose Firm L is levered Invest in 1% of Firm L’s debt and equity Dollar Investment Debt Equity Total Dollar Return The MM Proposition I (No Taxes) 21 The derivation is straightforward:
Shareholders in a levered firm receive Bondholder s receive EBIT rD D rD D Thus, the total cash flow to all stakeholders is
( EBIT rD D) rD D The present value of this stream of cash flows is VL
Clearly
( EBIT rD D) rD D EBIT
The present value of this stream of cash flows is VU VL V
U MM Proposition II 22 WACC = RA = (E/V)RE + (D/V)RD RE = RA + (RA – RD)(D/E) RA is the “cost” of the firm’s business risk, i.e., the risk of the firm’s assets and nature of operations (RA – RD)(D/E) is the “cost” of the firm’s financial risk, i.e., the additional return required by stockholders to compensate for the risk of leverage and chosen capital structure The MM Proposition II (No Taxes) 23 The derivation is straightforward:
rWACC
D
D E r D
E r
r
E D D E E
D D E
D E r E r
A Then set rWACC rA
D E
multiply both sides by
E D E
D
D E
E
D E
´
rD rE rA
E
E
D E
E
D E
D
D E rE rD
rA
E
E D
D
rD rE rA rA
E
E rE rA D
(rA rD )
E The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate Taxes Cost of capital: r
(%) 24 rA rE rA rW ACC D (rA rD )
EL D
E rD rE
DE
DE
rB rB D Debttoequity
Ratio E The Risk‐Return Tradeoff 25 Proposition I says that financial leverage has no effect on shareholder wealth Proposition II says the rate of return to equity increases as the firm’s debt to equity ratio increases How can shareholders be indifferent to leverage when it increases expected returns? The CAPM and Proposition II 26 How does financial leverage affect systematic risk? CAPM: RA = Rf + A(RM – Rf) Where A measures the systematic risk of the firm’s assets Proposition II Replace RA with the CAPM and assume that the debt is riskless (RD = Rf) RE = [Rf + A(RM ‐ Rf)](1+ D/E) – Rf(1+D/E) RE = Rf + A(1+D/E)(RM – Rf) The CAPM and Proposition II 27 RE = Rf + A(1+D/E)(RM – Rf) CAPM: RE = Rf + E(RM – Rf) E = A(1 + D/E) Therefore, the systematic risk of the stock depends on: Systematic risk of the assets, A, (Business risk) Level of leverage, D/E, (Financial risk) 28 The Modigliani Miller Propositions : Incorporating Taxes Interest is tax deductible Therefore, when a firm adds debt, it reduces taxes, all else equal The reduction in taxes increases the cash flow of the firm How should an increase in cash flows affect the value of the firm? Example: Incorporating Taxes 29 Consider two firms, Firm U(unlevered) and Firm L (levered). The value of their assets and operations is identical. EBIT (current and expected) is $5000 for both firms. Firm L issues debt of $5000 at 10% interest rate. The interest rate bill is 5000x0.1=500 every year indefinitely. The tax rate is 34%. Example: MM with taxes 30 Unlevered Firm U Levered Firm L 5000 5000 0 500 Taxable Income 5000 4500 Tax ( 34%) 1700 1530 Net Income 3300 2970 EBIT Interest Assuming no capital expenditure or net working capital changes: EBIT 5000 5000 Less: Taxes 1700 1530 Cash Flow From Assets 3300 3470 Cash Flow to Stockholders 3300 2970 Cash Flow to Bondholders 0 500 Example: MM with Taxes 31 Annual interest tax shield Tax rate times interest payment 5000 in 10% debt = 500 in interest expense Annual tax shield = 0.34(500) = 170 Present value of annual interest tax shield Assume perpetual debt for simplicity PV = 170 / .10 = 1700 PV = D(RD)(TC) / RD = DTC = 5000(0.34) = 1700 MM with taxes: Proposition I 32 The value of the firm increases by the present value of the annual interest tax shield Value of a levered firm = value of an unlevered firm + PV of interest tax shield Value of equity = Value of the firm – Value of debt Assuming perpetual cash flows VU = EBIT(1‐T) / RU VL = VU + DTC The MM Proposition I (Corp. Taxes) 33 Shareholders in a levered firm receive Bondholder s receive
( EBIT r D) (1 T )
D rD C D Thus, the total cash flow to all stakeholders is
( EBIT r D) (1 T ) r D
D C D The present value of this stream of cash flows is VL
Clearly ( EBIT r D) (1 T ) r D D C EBIT EBIT D (1 T ) r D (1 T ) r D
C D C D (1 T ) r D r DT r D
C
D
DC
D
The present value of the first term is VU
The present value of the second term is TCD V L V U T D
C MM with taxes: Proposition I 34 Example: MM with taxes 35 Suppose a firm has EBIT = $25 million; Corporate tax rate = 35%; Debt = $75 million; Cost of debt = 9%; Unlevered cost of capital = 12%. (For simplicity assume these to be current and expected future values) The MM Proposition II (Corp. Taxes) 36 Now, with taxes :
rA E rE D rD (1 TC )
V
V
then :
rE V rA D rD (1 TC )
E
E
rE (1 D )rA D rD (1 TC )
E
E
rE rA D (rA rD )(1 TC )
E MM with taxes : Proposition II 37 The WACC decreases as D/E increases because of the government subsidy on interest payments RA = (E/V)RE + (D/V)(RD)(1‐TC) RD < RE and RD gets greater weight RA approaches RD as debt increases Cost of equity increases as D/E increases RE = RU + (RU – RD)(D/E)(1‐TC) RE increases by (RU – RD)(1 – TC) for every increase in the debt to equity ratio The Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate Taxes 38 Cost of capital: r
(%) rE rA D (rA rD )
EL rA rD Debttoequity
ratio (D/E) Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes 39 AllEquity
EBIT
Interest
EBT
Taxes (Tc = 35%)
Total Cash Flow to E EBIT Interest ($800 @ 8% ) EBT Taxes (Tc = 35%) Total Cash Flow (to both E & D): EBIT(1‐Tc)+TCrBB Recession
$1,000
0
$1,000
$350 Expected
$2,000
0
$2,000
$700 Expansion
$3,000
0
$3,000
$1,050 $650 $1,300 $1,950 Recession $1,000 640 $360 $126 $234+640 $874 $650+$224 $874 Expected $2,000 640 $1,360 $476 $884+$640 $1,524 $1,300+$224 $1,524 Expansion $3,000 640 $2,360 $826 $1,534+$640 $2,174 $1,950+$224 $2,174 Levered Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes 40 Allequity firm
E G Levered firm
E G D The levered firm pays less in taxes than does the allequity firm.
Thus, the sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm. Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes 41 Allequity firm
E
G Levered firm
E G D The sum of the debt plus the equity of the levered firm is greater
than the equity of the unlevered firm.
This is how cutting the pie differently can make the pie larger: the
government takes a smaller slice of the pie! Summary: No Taxes 42 In a world of no taxes, the value of the firm is unaffected by capital structure. This is M&M Proposition I: VL = VU Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of no taxes, M&M Proposition II states that leverage increases the risk and return to stockholders D
rE rA EL (rA rD ) Summary: Taxes 43 In a world of taxes, but no bankruptcy costs, the value of the firm increases with leverage. This is M&M Proposition I: VL = VU + TC D Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of taxes, M&M Proposition II states that leverage increases the risk and return to D
stockholders. rE rA EL (1 TC ) (rA rD ) ...
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This note was uploaded on 04/09/2012 for the course FINN 321 taught by Professor Farahsaid during the Spring '12 term at Alvin CC.
 Spring '12
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