Corporate Finance Lecture 8

Announcements 2nd quiz 2nd case : Boeing 7E7 Opens at midnight tonight Valid for 48 hours Closes at midnight of Thursday 2nd case : Boeing 7E7 Questions will be posted on May 8 Delivery deadline: May 13 Discussion: May 15

Topics covered MM proposition without tax MM proposition with tax Cost of financial distress Direct cost Indirect cost Reducing cost of debt Integration of tax benefit and financial distress cost of debt

Modigliani and Miller (MM) Proposition (no taxes) Proposition I Firm value is not affected by leverage VL = VU Capital structure does not change firm value

Assumptions of the Modigliani-Miller Model Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows Perfect Capital Markets: Perfect competition Firms and investors can borrow/lend at the same rate Equal access to all relevant information No transaction costs No taxes

EPS and ROE Under Both Capital Structures All-Equity 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 Levered 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

Homemade Leverage: An Example Recession Expected Expansion EPS of Levered Firm $1.50 $5.67 $9.83 Earnings for 24 shares $36 $136 $236

Homemade Leverage: An Example Recession Expected Expansion EPS of Unlevered Firm $2.50 $5.00 $7.50 Earnings for 40 shares $100 $200 $300 Less interest on $800 (8%) $64 $64 $64 Net Profits $36 $136 $236 ROE (Net Profits / $1,200) 3% 11% 20% Buying 40 shares of a $50 stock, we get the same ROE as if we bought into a levered firm. Our personal debt equity ratio is: 3 2 200 , 1 $ 800 = S B

The MM Propositions II (No Taxes) Proposition II Leverage increases the risk and return to stockholders rs = r0 + (B / SL) (r0 - rB) rB is the interest rate (cost of debt) rs is the return on (levered) equity (cost of equity) r0 is the return on unlevered equity (cost of capital) B is the value of debt SL is the value of levered equity

The MM Proposition II (No Taxes) The derivation is straightforward: S B WACC r ´ + = set Then r WACC = r S B = ´ + S B + by sides both multiply r S B + = ´ r S B + = ´ ) ( B S r - + = r S B + = ´

MM Proposition II with No Corporate Taxes Cost of capital: r (%) r0 rB rB S B Debt-to-equity Ratio

The MM Proposition I (Corp. Taxes) 1 ( receive firm levered a in rs Shareholde C B T r EBIT - ´ B r receive s Bondholder B r T EBIT C + - ´ ) 1 ( is rs stakeholde all to flow cash total the Thus, The present value of this stream of cash flows is VL = + - ´ B r T EBIT C ) 1 ( B r T EBIT C + - ´ = ) 1 ( BT r T EBIT C B + - ´ = ) 1 ( The present value of the first term is VU The present value of the second term is TCB B T V C U L + = \

The MM Proposition II (Corp. Taxes) Start with M&M Proposition I with taxes: B T V C U L + = Since B S V L + = B T V S C U + = Þ ) 1 ( C U T B S V - + = The balance sheet of a levered firm can be written as Vu=Value of unlevered firm B=Debt TcB=Tax shield S=Equity

The MM Proposition II (Corp. Taxes) The cash flows from each side of the balance sheet must equal: B C U S Br T r V Sr + = B r T S Br Sr C + - = )] 1 ( [ Divide both sides by S B C S r T + - = )] 1 ( [ ) ( 1 B C S r T - ´ + = Which reduces to

The Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate Taxes Cost of capital: r (%) r0 rB Debt-to-equity ratio (B/S)

Total Cash Flow to Investors Under Each Capital Structure with Corp Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes All-Equity Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 EBT $1,000 $2,000 $3,000 Taxes (Tc = 35% $350 $700 $1,050 Total Cash Flow to S/H $650 $1,300 $1,950 Levered Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest ($800 @ 8% ) 640 640 640 EBT $360 $1,360 $2,360 Taxes (Tc = 35%) $126 $476 $826 Total Cash Flow $234+640 $468+$640 $1,534+$640 (to both S/H & B/H): $874 $1,524 $2,174 EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224 $874 $1,524 $2,174

Tax effect of debt In a world without taxes, debt does not affect firm value. When there are corporate taxes, the firm value is positively related to its debt --Debt reduces the firm’s tax liability With taxes, 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 All-equity firm Levered firm S G S G B This is how cutting the pie differently can make the pie larger: the government takes a smaller slice of the pie!

Costs of financial distress Direct costs: Legal and administrative costs Indirect costs: Impaired ability to conduct business Agency costs: conflicts between the shareholders and the debtholders Incentive to take large risks Incentive toward underinvestment Milking the property

Balance Sheet for a Company in Distress Assets BV MV Liabilities BV MV Cash $200 $200 LT bonds $300 Fixed Asset $400 $0 Equity $300 Total $600 $200 Total $600 $200 What happens if the firm is liquidated today? $200 $0 The bondholders get $200; the shareholders get nothing.

Selfish Strategy 1: Take Large Risks The Gamble Probability Payoff Win Big 10% $1,000 Lose Big 90% $0 Cost of investment is $200 (all the firm’s cash) Required return is 50% Expected CF from the Gamble = $1000 × 0.10 + $0 = $100 NPV = –$200 + $100 (1.50) NPV = –$133

Selfish Stockholders Accept Negative NPV Project with Large Risks Expected CF from the Gamble To Bondholders = $300 × 0.10 + $0 = $30 To Stockholders = ($1000 – $300) × 0.10 + $0 = $70 PV of Bonds Without the Gamble = $200 PV of Stocks Without the Gamble = $0 PV of Bonds With the Gamble: PV of Stocks With the Gamble: Debtholder expropriation by shareholders $20 = $30 (1.50) $47 = $70 (1.50)

Selfish Strategy 2: Underinvestment Consider a government-sponsored project that guarantees $350 in one period Cost of investment is $300 the firm only has $200 now the stockholders will have to supply an additional $100 to finance the project Required return is 10% NPV = –$300 + $350 (1.10) NPV = $18.18 Should we accept or reject?

Selfish Strategy 2: underinvestment Firm Debt Equity Without project PV With project CF at t=1

Selfish Strategy 2: Underinvestment Firm Debt Equity Without project PV 200 With project CF at t=1 350 300 50 -300 +350/1.1 =18.18 -200 +300/1.1 =72.73 -100 +50/1.1 =-54.55

Selfish Strategy 3: Milking the Property Liquidating dividends Increase perquisites to shareholders and/or management

Protective Covenants Agreements to protect bondholders Negative covenant: Pay dividends beyond specified amount. Sell more senior debt & amount of new debt is limited. Positive covenant: Maintain good condition of assets. Provide audited financial information. Working capital requirement.

Integration of Tax Effects and Financial Distress Costs Value of firm (V) Value of firm under MM with corporate taxes and debt Present value of tax shield on debt VL = VU + TCB Maximum firm value Present value of financial distress costs V = Actual value of firm VU = Value of firm with no debt Debt (B) B* Optimal amount of debt

The Pie Model VT = S + B + G + L S Marketed claims: VM = S + B B Nonmarketed claims: VN = G + L S B G L

Signaling The firm’s capital structure is optimized where the marginal subsidy to debt equals the marginal cost. Investors view debt as a signal of firm value. A manager that takes on more debt than is optimal in order to fool investors will pay the cost in the long run.