Advanced Corporate

FinanceFINA 7330

Capital Structure Issues and Financing

Lecture 07 and 08

Fall, 2010

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

• ASSETS

PVA $1,000,000

PVGO 2,000,000

TOTAL $3,000,000

• LIABILITIES

DEBT 0

EQUITY 3,000,000

TOTAL $3,000,000

Irrelevance TheoremASSETS

PVA $1,000,000

PVGO 2,000,000

TOTAL $3,000,000

LIABILITIES

DEBT 1,600,000

EQUITY 1,400,000

TOTAL $3,000,000

Tax Implications ( tax rate of 30%)

ASSETS

PVA $1,000,000

PVGO 2,000,000

- PV of Tax Liability 900,000

TOTAL $2,100,000

LIABILITIES

DEBT 0

EQUITY 2,100,000

TOTAL $2,100,000

Tax Implications

ASSETS

PVA $1,000,000

PVGO 2,000,000

Less: PV of Tax Liability 420,000

TOTAL $2,580,000

LIABILITIES

DEBT 1,600,000

EQUITY ___________

TOTAL $2,580,000

Tax Implications

ASSETS

PVA $1,000,000

PVGO 2,000,000

Less: PV of Tax Liability 420,000

TOTAL $2,580,000

LIABILITIES

DEBT 1,600,000

EQUITY 980,000

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/StockholderManager/Stockholder

Bankruptcy CostsDirect and Indirect

Information Costs

The Impact of Taxes on the Capital Structure Decisions

Firm Value = 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

Firm Value for an equity financed firm

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 $1000Cash Expense 500Depreciation 300Tax Rate = 32%Cost of Capital = 10%ATOCF = Before Tax Operating Cash Flow - TaxBefore Tax Operating Cash Flow = (1000-500) = 500Tax = T*(1000-500-300) .32*200 = 64Thus V(u) = (500 – 64)/r = 436/.1 V(u) = $4,360Where ATOCF is After Tax Operating Cash Flow

Example

Everything is a perpetuity;Cash Revenue $1000Cash Expense 500Depreciation 300Tax Rate = 32%Cost of Capital = 10%

ATOCF = (1000-500) -.32*(1000-500-300) {EBIT(1-t) + Depreciation}

= (1000-500-300)*.68 + 300 = 136 + 300 = 436V(u) = $4,360Where 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 $1000Cash Expense 500Depreciation 300Interest 100Tax 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) + T c

*B

V(u)

Debt

Recall: Cost of CapitalIn the absence of taxes

WACC = ro

rS = ro + (ro-rB)B/S

rB

Cost of Capital (After Tax)

WACC = roB/V) )

rE = ro + (ro-rB)(1-t)B/S

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%

= .07362 +.0136 = 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?

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 = 2.96 (2.95 really, without rounding)

Finally What is Stockholders’ Wealth?

Debt Valuation

• Yield to Maturity

• Coupon rate

• Expected (required) return to Bonds

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’ wealthstockholders’ 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.