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**Session 6: Capital Structure I**

C Corporate Finance Topics

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**Outline Basic capital structure theory—irrelevance**

Debt and equity as options Tax effects Valuation The first part should be review!

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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 This whole process will take 2 weeks!

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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. Assumes absolute priority rules are followed (we’ll talk about this later!)

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**Equity and Debt Payoffs**

Firm value 10 Firm value V=B+S debt and equity sum to the firm Simple apllication of put-call parity 10 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 Zero NPV implies V is unchanged. Spreadsheet available.

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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 Debt ? 55 44 Equity ? 44 Zero NPV implies V is unchanged. Spreadsheet available.

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Replicating Equity Replicate equity with a position in the firm financed by borrowing: 99 H B* = 44 44 H B* = 0 H = 0.8, B* = 32 S = 0.8(60) - 32 = $16 million Increasing volatility increases the value of the equity (and decreases the value of the debt). This is the agency conflict that generates the agency costs we will talk about later.

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Replicating Debt Replicate debt with a position in the firm and a position in risk-free debt: 99 H B* = 55 44 H B* = 44 H = 0.2, B* = -32 B = 0.2(60) + 32 = $44 million V = S + B = = $60 mill. Remained the same! H(S)+H(B)=1, B*(S)+B*(B)=0 YTM=55/44-1=25% E(r)=0.5(55/44-1)+0.5(44/44-1)=12.5% Expected return is less than promised yield because this is risky debt, I.e., expected cash flows are not promised cash flows.

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**Assumptions Perfect capital markets (no taxes or transaction costs)**

Personal and corporate borrowing at the same rate No information effects Personal and corporate borrowing at the same rate is a result of the other assumptions NOT an additional assumption.

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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 U-unlevered (no debt) V-levered (with debt)

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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 You need to borrow at the same rate as the company. Why is this reasonable? Borrowing secured by unlevered equity (i.e., assets), which is the same thing that the company is doing (and in the same proportions). What is do-it-yourself unleverage, i.e., how do you generate unlevered equity payoffs when the firm is levered? Buy levered equity and debt in proportion to their market values.

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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. Under DCF there are 3 variables—cash flows, discount rates, and value. If cash flows are fixed, then values and discount rates must move together. If you plug r(S) into the definition of WACC you get WACC=r(0). These equations are saying the same thing.

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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) Think about dividends defined broadly as all cash flows to the equity holders, i.e., dividends, stock repurchases, cash acquisitions. Watch the timing—price today, next period’s dividend

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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 = bROE 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) The expected return formulation can be used at the market level to get expected returns and hence the market risk premium (although they usually use the earnings/payout version). ROE is accounting ROE (on a cash flow basis), i.e., the denominator is book equity not market value equity. Why? What we want is the return on the actual dollars of equity invested in the projected. Market value includes not just the amount invested but also the NPV of the investment. An aside—when should you retain more earnings, i.e., increase b? When doing so increases the stock price. dP/db > 0 when ROE > r(S). ROE > r(S) is the same thing as the IRR rule (for equity investments) and hence the same thing as the NPV rule.

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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 Total cash flows are fixed (i.e., the projects are fixed). All we are doing is dividing these cash flows among claimants. Reduce the value of the governments claim, and the residual value goes up.

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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 This is just an example. These formulas do not apply generally!

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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 Business risk/financial risk. B=0, WACC=r(0) S=0, WACC=(1-T)r(0) As before plugging r(S) into WACC definition gives WACC formula.

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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% Standard no growth assumptions: Depr=capex, dNWC=0, 100% payout.

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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 E[EBIT]=0.5(1)+0.5(2)=1.5

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**Income Statement EPS=NI/n E[EPS]=E[DPS] (100% payout)**

P=E[DPS]/r(0)=0.9/0.1=9 (forward looking so it is constant) Stock return=dividend yield (no capital gains) E[return]=required return Coincidence? I don’t think so. How does it work? Stock price depends on required return and determines expected return. Try it yourself, spreadsheet available.

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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 = (5) = $11 million Share price moves to $11/share $ 5 million repurchases shares (n = 545.5) Time line Announce Stock price moves Sell debt and use proceeds to buy back equity at new price

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**Income Statement r(S)=D(1)/P(0)=1.21/11=11%**

Leverage increases risk (return more volatile) and increases value (less tax)

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**Assignments Reading Problem sets Cases**

RWJ: Chapters , Appendix 16B Problems: 16.2, 16.6, 16.8 Problem sets Problem Set 2 due monday Cases AHP due in 1 week

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