Advanced Corporate
Finance
FINA 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
• LIABILITIES
• ASSETS
PVA
$1,000,000
DEBT
0
PVGO
2,000,000
EQUITY
3,000,000
TOTAL
$3,000,000
TOTAL $3,000,000
Irrelevance Theorem
ASSETS
LIABILITIES
PVA
$1,000,000
DEBT
PVGO
2,000,000
EQUITY 1,400,000
TOTAL $3,000,000
1,600,000
TOTAL $3,000,000
Tax Implications
( tax rate of 30%)
LIABILITIES
ASSETS
PVA
PVGO
$1,000,000
2,000,000
- PV of Tax Liability 900,000
TOTAL
$2,100,000
DEBT
0
EQUITY
2,100,000
TOTAL
$2,100,000
Tax Implications
LIABILITIES
ASSETS
PVA
PVGO
$1,000,000
DEBT
1,600,000
2,000,000
Less:
PV of Tax Liability 420,000
EQUITY
___________
TOTAL
TOTAL
$2,580,000
$2,580,000
Tax Implications
LIABILITIES
ASSETS
PVA
PVGO
$1,000,000
DEBT
1,600,000
2,000,000
Less:
PV of Tax Liability 420,000
EQUITY
TOTAL
TOTAL
$2,580,000
980,000
$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
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 = Before Tax Operating Cash Flow - Tax
Before Tax Operating Cash Flow = (1000-500) = 500
Tax = T*(1000-500-300) .32*200 = 64
Thus V(u) = (500 – 64)/r = 436/.1
V(u)
= $4,360
Where ATOCF is After Tax Operating Cash Flow
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}
= (1000-500-300)*.68 + 300
= 136 + 300 = 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(u)
Debt
Recall: Cost of Capital
In the absence of taxes
rS = ro + (ro-rB)B/S
r
WACC = ro
rB
Cost of Capital (After Tax)
rE = ro + (ro-rB)(1-t)B/S
r
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
Debt
4.2 million
Equity
6.8 million
Stockholders’ Wealth
V = $6 million
B = 3.2/(1.05) = $3.05
E = $6 - $3.05 = $2.95
2.2 million
2.2 million
0
6.6
3.2
3.4
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
Probability of each state is 50%
Stockholders’ Wealth
V = $6 million
E = $6 million
2.2 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
– Total
11 million
Bankruptcy cost
• Net
11 million
Bad (Default)
2.2 million
0.1 million
2.1 million
Impact of Bankruptcy Costs
•
Good State
– Total
11 million
Bankruptcy cost
•
•
•
•
•
•
•
Bad (Default)
2.2 million
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.