Session 6: Capital Structure I C15.0008 Corporate Finance Topics.
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Transcript of Session 6: Capital Structure I C15.0008 Corporate Finance Topics.
![Page 1: Session 6: Capital Structure I C15.0008 Corporate Finance Topics.](https://reader035.fdocuments.net/reader035/viewer/2022062404/551a87b4550346761a8b539f/html5/thumbnails/1.jpg)
Session 6: Capital Structure I
C15.0008 Corporate Finance Topics
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Outline
• Basic capital structure theory—irrelevance
• Debt and equity as options
• Tax effects
• Valuation
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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.
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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
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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.
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Equity and Debt Payoffs
Firm value10 Firm value10
Equity Debt
• Equity: a call option on the firm • Debt: firm - call = risk-free bond - put
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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
60
99
44
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Introducing Debt
The firm finances itself through Debt of $55 million to be paid after 1 year.
Firm
60
99
44
Equity
?
44
0
Debt
?
55
44
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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
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Replicating Debt
Replicate debt with a position in the firm and a position in risk-free debt:99 H - 1.1 B* = 5544 H - 1.1 B* = 44 H = 0.2, B* = -32B = 0.2(60) + 32 = $44 million V = S + B = 16 + 44 = $60 mill.
Remained the same!
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Assumptions
• Perfect capital markets (no taxes or transaction costs)
• Personal and corporate borrowing at the
same rate No information effects
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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
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Intuition
• Buying equity in the levered firm is firm-generated 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
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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.
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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)
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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 = bROEb — earnings retention rate, i.e., D=(1-b)EROE—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)
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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.
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Introducing Corporate Taxes
• Earnings are taxed at the corporate rate
• Interest expense is tax deductible
• Dividends are not tax deductible
• Tax rate: TC
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Example..
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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
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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
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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
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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%
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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
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Income Statement
Bad GoodProbability 0.5 0.5
EBIT 1,000 2,000 Interest Exp. - -
EBT 1,000 2,000 Taxes 400 800
Net Income 600 1,200 EPS 0.60 1.20
E[EPS]Stock Price
Stock Return 6.67% 13.33%E[return]
0.90
10.00%
9.00
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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)
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Income Statement
Bad GoodProbability 0.5 0.5
EBIT 1,000 2,000 Interest Exp. 400 400
EBT 600 1,600 Taxes 240 640
Net Income 360 960 EPS 0.66 1.76
E[EPS]Stock Price
Stock Return 6.00% 16.00%E[return]
11.00
11.00%
1.21
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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