Session 6: Capital Structure I C15.0008 Corporate Finance Topics

Session 6: Capital Structure I
C15.0008 Corporate Finance
Topics
Outline
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Basic capital structure theory—irrelevance
Debt and equity as options
Tax effects
Valuation
Introduction to Capital Structure
Problem: What is the optimal mix of debt
and equity, i.e., the capital structure that
maximizes the value of the firm?
Approach: Begin with a simple model (a
framework) that identifies the relevant
issues, then add realism.
A Road Map
• Perfect markets (no taxes)  capital
structure is irrelevant
• +corporate taxes  more debt is better
• +financial distress and agency costs 
optimal capital structure
Options and Corporate Finance
Consider a firm that will liquidate in 1 year, with
$10 million of 1-year zero coupon debt
outstanding.
If the firm is worth less than $10 million in 1 year,
the debtholders receive everything and the
stockholders receive nothing. Otherwise, the
debtholders receive $10 million and the
stockholders receive the residual.
Equity and Debt Payoffs
Equity
10
Debt
Firm value
10
• Equity: a call option on the firm
• Debt: firm - call = risk-free bond - put
Firm value
An example
A firm undertakes a risky, zero NPV project and
will be worth either $99 mill. or $44 mill. in 1
year. Value of the unlevered firm is $60 mill.
Risk free rate is 10%
Firm
99
60
44
Introducing Debt
The firm finances itself through Debt of $55
million to be paid after 1 year.
Firm
Debt
Equity
99
60
?
?
44
55
44
0
44
Replicating Equity
Replicate equity with a position in the firm
financed by borrowing:
99 H - 1.1 B* = 44
44 H - 1.1 B* = 0
 H = 0.8, B* = 32
 S = 0.8(60) - 32 = $16 million
Replicating Debt
Replicate debt with a position in the firm and a
position in risk-free debt:
99 H - 1.1 B* = 55
44 H - 1.1 B* = 44
 H = 0.2, B* = -32
B = 0.2(60) + 32 = $44 million
V = S + B = 16 + 44 = $60 mill.
Remained the same!
Assumptions
• Perfect capital markets (no taxes or
transaction costs)
• Personal and corporate borrowing at the
same rate
 No information effects
The Primary Result
The value of the firm is independent of its
capital structure, i.e., the financing mix is
irrelevant (Miller & Modigliani).
Proposition I: VU = VL
Intuition
• Buying equity in the levered firm is firmgenerated leverage
• Buying equity in the unlevered firm and
borrowing is do-it-yourself leverage
 Conclusion: no one is willing to pay the
firm for levering up when they are “free” to
lever up individually
Discount Rates
The value result also has implications for discount
rates (r0 is the cost of unlevered equity).
Proposition II:
rS = r0 + (B/S)(r0 - rB)
WACC = r0
The WACC is constant and the cost of equity can
be decomposed into business risk and financial
risk.
Valuation: The Dividend Discount
Model
• The stock price today should be the discounted
value of expected future dividends
P = t Dt/(1+rS)t
• If dividends are growing at a constant rate, then
the price of the stock (not including current
dividend) is
P0 = D1 / (rS - g)
Expected Returns, Growth and P/E Ratios
• The valuation formula can be inverted to get
expected returns: rS = (D1 / P0) + g
• Where does growth come from?
g = bROE
b — earnings retention rate, i.e., D=(1-b)E
ROE—return on equity
• What are the implied P/E ratios?
P0 = D1 / (rS - g) = (1-b) E1 / (rS – b ROE)
P0 / E1 = (1-b) / (rS – b ROE)
Equity Valuation
The value of all the equity is just the
aggregate value of all the shares
outstanding, i.e., the discounted value of
aggregate dividends.
All the previous results apply.
Introducing Corporate Taxes
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Earnings are taxed at the corporate rate
Interest expense is tax deductible
Dividends are not tax deductible
Tax rate: TC
Example..
Value Implications
Proposition I: VL = VU + PV(tax shield)
PV(tax shield) = t [TC(interest expense)t] / (1+ rB)t
• Debt reduces the firm’s tax liability and
therefore increases value
• The more debt, the higher the value of the
firm
An Example
All equity firm with pre-tax earnings (cash
flow) of $X in year 1, a retention rate of b,
and growth rate g in perpetuity:
VU = [(1-b)(1- TC)X] / (r0-g)
If this firm adds $B of perpetual debt:
PV(tax shield) = [TC (rB B)] / rB = TC B
VL = VU + TC B
Discount Rates
Prop. II:
rS = r0 + (1- TC)(B/S)(r0 - rB)
WACC = [(S+(1- TC)B)/(S+B)] r0
• Equity risk increases with leverage (but
more slowly than in the no tax case)
• WACC decreases as the amount of debt
increases
Recapitalization: An Example
Firm characteristics:
• EBIT: 50% prob. of $1 million, 50% prob. of $2
million (in perpetuity)
• Depreciation = Cap. Ex.
• ΔNWC=0
• 100% payout (no growth, dividends = earnings)
• r0 = 10% (required return on unlevered equity)
• TC = 40%
Unlevered Value
VU = [(1- TC)EBIT] / r0
= [(1-0.4)1.5] / 0.1 = $9 mill.
n = 1 million (shares outstanding)
Share price:
P = VU / n = $9.00
Income Statement
Probability
EBIT
Interest Exp.
EBT
Taxes
Net Income
EPS
E[EPS]
Stock Price
Stock Return
E[return]
Bad
0.5
Good
0.5
1,000 2,000
1,000 2,000
400
800
600 1,200
0.60
1.20
0.90
9.00
6.67% 13.33%
10.00%
Recapitalization
Firm issues $5 million of perpetual debt (rB = 8%)
and uses the proceeds to repurchase equity.
On announcement:
• Shareholders revalue the firm:
VL = VU + TC B = 9 + 0.4 (5) = $11 million
• Share price moves to $11/share
$ 5 million repurchases 454.5 shares (n = 545.5)
Income Statement
Probability
EBIT
Interest Exp.
EBT
Taxes
Net Income
EPS
E[EPS]
Stock Price
Stock Return
E[return]
Bad
0.5
Good
0.5
1,000 2,000
400
400
600 1,600
240
640
360
960
0.66
1.76
1.21
11.00
6.00% 16.00%
11.00%
Assignments
• Reading
– RWJ: Chapters 16.1-16.9, Appendix 16B
– Problems: 16.2, 16.6, 16.8
• Problem sets
– Problem Set 2 due monday
• Cases
– AHP due in 1 week