Advanced Corporate Finance FINA 7330 Capital Structure Issues and Financing Lecture 07 and 08 Fall, 2009

The Theories of Capital Structure Irrelevance Static Tradeoff Pecking Order

The Irrelevance Theorem Perfect Capital Market Setting No Taxes No Contracting Costs Costs of Financial Distress Agency Costs No Information Costs

Irrelevance Theorem LIABILITIES ASSETS DEBT 0 PVA $1,000,000 EQUITY 3,000,000 TOTAL $3,000,000 ASSETS PVA $1,000,000 PVGO 2,000,000 TOTAL $3,000,000

Irrelevance Theorem ASSETS LIABILITIES PVA $1,000,000 DEBT 1,600,000 PVGO 2,000,000 TOTAL $3,000,000 LIABILITIES DEBT 1,600,000 EQUITY 1,400,000 TOTAL $3,000,000

Tax Implications LIABILITIES ASSETS PVA $1,000,000 DEBT 0 EQUITY 2,100,000 TOTAL $2,100,000 ASSETS PVA $1,000,000 PVGO 2,000,000 - PV of Tax Liability 900,000 TOTAL $2,100,000

Tax Implications LIABILITIES ASSETS DEBT 1,600,000 PVA $1,000,000 EQUITY 980,000 TOTAL $2,580,000 ASSETS PVA $1,000,000 PVGO 2,000,000 Less: PV of Tax Liability 420,000 TOTAL $2,580,000

Stockholders’ Wealth Originally: $2,100,000 in Equity Interest Now: 980,000 in Equity Interest $1,600,000 in Cash 2,580,000 Total Stockholders’ Wealth. Notice that Stockholders’ wealth increased by an amount equal to the Present Value of the Tax Shield on Debt.

The Static Tradeoff Theory Benefits versus Costs of Leverage. Benefits Costs Taxes Financial Distress Resolution of Agency Costs Agency Costs Bondholder/Stockholder Manager/Stockholder Bankruptcy Costs Direct and Indirect Information Costs

The Impact of Taxes on the Capital Structure Decisions Firm Value = S Operating Cash Flow (t) (1+ro)t = Market Value of the Firms Liabilities (Including Equity) Let OCF(t) = Operating Cash Flow at time t

With Taxes = S OCF(t) - Tax on operations = Market Value of the Firm Firm Value for an equity financed firm = S OCF(t) - Tax on operations (1+ro)t = Market Value of the Firm = Market Value of Equity = V(u) We call this the Value of the Unlevered Stream (Firm), or the Asset Value of the Firm)

Example Everything is a perpetuity; Cash Revenue $1000 Cash Expense 500 Depreciation 300 Tax Rate = 32% Cost of Capital = 10% ATOCF = (1000-500) -.32*(1000-500-300) {EBIT(1-t) + Depreciation} = 500 - 64 = 436 V(u) = $4,360 Where ATOCF is After Tax Operating Cash Flow

Example ATOCF = (1000-500) -.32*(1000-500-300) {EBIT(1-t) + Depreciation} = 500 - 64 = 436 V(u) = $4,360 Where ATOCF is After Tax Operating Cash Flow

Leverage Effects Now suppose the firm issues 2000 worth of perpetual debt, paying interest at 5%. Then interest will be: INT = .05*2000 = $100

Now lets consider the interest deductions Cash Revenue $1000 Cash Expense 500 Depreciation 300 Interest 100 Tax Rate (t) = 32% CF = (1000-500) -.32*(1000-500-300 -100) = = 500 -32 = 468 Or: = ATOCF + t*INT = 436 + 32 = 468

Now Discount CF = ATOCF + Interest Tax Shield And V = ATOCF + t*INT ro rB V = V(u) + t*B

Now Discount CF = ATOCF + Interest Tax Shield And V = ATOCF + t*INT ro rB V = V(u) + t*B = 4,360 + .32 * 2,000 = $5,000

Value of Debt and Equity Value of firm = $5,000 Value of Debt = $2,000 Value of Equity = $3,000 B/V = .4 E/V = .6

With Taxes In general, V(L) = V(u) Plus Present Value of Tax Shield on Debt. V(L) = V(u) + (Corp. Tax Rate) * Debt, in the special case when debt is thought of as perpetual, or is selling at par.

Graphically Firm Value (V) V = V(u) + Tc*B V(u) Debt

Cost of Capital rS = ro + (ro-rB)B/S WACC = ro r rB

Cost of Capital (After Tax) rE = ro + (ro-rB)(1-t)B/S r WACC = ro(1-t(B/V) ) rd

Weighted Average Cost of Capital WACC is the discount rate we use to discount the firm’s after tax Operating Cash Flow: (ATOCF) So in the example we just had: WACC = ro(1-T(B/V) ) = 8.72% = rE(E/V) + (1-T)rB(B/V), and rE = .10 + (.10-.05)(1-.32)(.6) = 12.27% WACC = .1227*.6 + .68*.05*.4 = 8.72%

Firm Value and the Tax Shield on Debt Notice that the value of the firm is simply the ATOCF discounted by the WACC! The greater is the amount of debt issued, the lower is the WACC, and thus the higher is the value of the firm. By assumption, the ATOCF is unaffected by the firm’s capital structure.

Static Tradeoff Theorem Costs of Financial Distress Potential Bankruptcy Costs Underinvestment Risk Shifting Agency Costs

General Approach Assume: No Taxes Single period Cost of Capital = 10%

Perfect Capital Market Widgets International Good State Bad State Pure Equity 11 million 2.2 million Probability of each state is 50% Stockholders’ Wealth V = $6 million E = $6 million

Bond and Stock Valuation Suppose the firm issued 1 year Debt paying a 5% coupon and principal in the amount of $4 million. What is the market value of this debt? It will depend on the required return to the debt. Suppose the required return (rB) is 5% Then the value is B = E{Cash Flows}/1.05

Debt valuation What is the Yield to Maturity? (YTM) What is the Expected Return? This will require some work

Perfect Capital Markets Let the Firm issue a bond paying $4 million in principal, 0.2 million in interest. (Coupon rate is 5%) Widgets International Good State Bad State Expected Total 11 million 2.2 million 6.6 Debt 4.2 million 2.2 million 3.2 Equity 6.8 million 0 3.4 Stockholders’ Wealth V = $6 million B = 3.2/(1.05) = $3.05 E = $6 - $3.05 = $2.95 IF The Value of the Firm remains unchanged

Valuation of Equity If the value of the firm is independent of capital structure, rE = ro + (ro-rB)B/V Therefore; rE = .10 + (.05)(3.05/2.95) = = 15.17% And: E = 3.4/1.1517 = ??? Finally What is Stockholders’ Wealth?

Debt Valuation Yield to Maturity Coupon rate Expected (required) return to Bonds

Widgets International Bankruptcy Costs Widgets International Good State Bad State Pure Equity 11 million 2.2 million Probability of each state is 50% Stockholders’ Wealth V = $6 million E = $6 million

Direct Bankruptcy Costs Typically amounts to 2% to 5% of the distressed value of the firm Widgets International Again assume the same leverage of a bond promising to pay 4.4 million Good State Bad (Default) Total 11 million 2.2 million Bankruptcy cost 0.1 million Net 11 million 2.1 million

Impact of Bankruptcy Costs Good State Bad (Default) Total 11 million 2.2 million Bankruptcy cost 0.1 million Net 11 million 2.1 million Value 5.95 million Debt 3 million Equity 2.95 million Thus stockholders’ wealth declines by $50,000 (SHW = 2.95 + 3 = 5.95 not 6) Notice that it is the stockholders that pays the expected bankruptcy costs.