Capital Structure in a Perfect MarketChapter 14

outline

• Equity and or debt financing • Return on levered equity• Modigliani-Miller theorems:– MM1: firm value not affected– MM2: expected returns are affected

• Application to levered beta’s• Thinking about cash• Leverage and EPS• dilution

What is capital structure

• Composition of liabilities– Need to finance a project…how much debt to

raise/how much equity?– Firms often recapitalize or change their capital

structure using secondary market• Does capital structure affects the value of

assets?• Focus on Cash-Flow rights

ExampleEquity financing (issuing stock)

• Consider the project that requires an initial investment of $800 and generates risky cash flows one year from now. Cash flows are either $1400 or $900 with probability one half (0.5) depending on the state of the economy.

-$800

$1400

$900

BOOM

BUST

NPV of the Project under Equity financing

• Investors require a 10% risk premium for holding equity in this firm due to the sensitivity of cash flows to the state of the economy (assume a risk free rate of 5%).

• What is the NPV of the project?

Firm value under equity financing

• If the project is financed all with equity, how much will investors be willing to pay for the firms’ shares?

• Assuming that equity markets are competitive (remember we are considering perfect markets here) investors will break even on their investment.

• Equity holders are the residual claimants and are entitled to all future cash flows. They will be willing to pay

Who benefits from positive NPV projects?

• The entrepreneur can sell the equity of the firm, cover the initial investment of $800 and remain with profit of $200.

• Notice – the value of the profit is determined by the NPV of the project.

• The returns earned by the investors are 40% in the good state and -10% in the bad state. Expected return is 15% - exactly as determined by the risk premium of 10%.

• Notice: here the risk of the project is the same as the risk of equity since there is no debt. Equity in a firm with no debt is called unlevered equity.

Debt and Equity financing

• Suppose that $500 is raised via debt in addition to selling equity.

• Debt holders will require at the end of the year:

• Remember - Debt claims are senior to equity claims (debt holders are paid first and only if funds remain then equity holders are paid)

Levered equity

• Equity in a firm with debt is called leveraged equity. Payments to equity holders are:

• Payments to debt holders

The value of levered equityUsing the MM1 theorem• What is the price E of the levered equity?• Modigliani and Miller (1958) argued that in perfect capital

markets the total value of the firm should not depend on its capital structure.

• The firm’s cash flows equal exactly the cash flows generated by the firm’s debt and (levered) equity. Therefore they should have the same value (law of one price).

• Since the value of debt is $500 and the total value of the firm is $1000 we conclude that the value of levered equity is $500 which is less than the value of equity of the unlevered firm. What is the preferred financing method here?

The value of levered equityDiscounting Cash Flows

• Lets find the value of levered equity by calculating the present value of the payoffs to equity holders:

• But this is not consistent with the MM argument! Did the value of the firm now go up to $1043? What is wrong here?

Return on levered equity• To see the effect of leverage on the risk of equity lets compare

the return distributions when the entrepreneur raises $500 from issuing equity and $500 from issuing debt:

Risk and Return

• The higher risk leads to an expected return of 25% on levered equity relative to the 15% on unlevered equity.

• Leverage increases the risk of equity!• But, considering both sources of capital

together, the firm’s average cost of capital with leverage is of the unlevered firm:

Assumptions by Modigliani-Miller

• Perfect capital markets mean:– Investors and firms can trade same securities at

competitive market prices– There are no taxes, transaction costs and security

issuance costs– Firms’ financing decisions do not affect the cash

flows generated by its investments nor do they reveal new information about them

Modigliani - Miller

• MM Proposition 1: In a perfect capital market the total value of the firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.

• There is no gain or loss from using leverage and the value of the firm is determined by the present value of its cash flows from its current and future investments.

Proof of MM1 by no-arbitrage principle• Counter example: Suppose that a firm which is

exactly the same as the non-levered firm in our example is financed $500 with debt, and its levered equity is selling for $450, while the unlevered firm’s equity is selling for $1000.

• Is there an arbitrage opportunity here?• Strategy: buy the levered firm’s equity and buy a risk

free bond worth $500. This will cost you $950 today. To finance this investment short sell the unlevered firm’s equity and receive $1000. You will end up with current profit of $50 and no future obligations.

Arbitrage trading strategy details

strategy Time 0 payoff Time 1 payoff

Buy levered firm equity

-$450 BOOM: $875 BUST: $375

Buy risk free bond -$500 $525

Short sell unlevered firm

$1000 BOOM: -$1400BUST: -$900

TOTAL PAYOFF $50 $0

Leveraged Recapitalization (using MM1)New Example

• Harrison Industries is an all equity firm with 50 million shares outstanding with price $4 per-share.

• Harrison Industries is planning to borrow $80 million and use the funds to repurchase 20 million of its outstanding shares.

• Lets follow Harrison Industries’ market value balance sheet throughout the transaction

Leveraged Recapitalizationstarting point

• Initial Balance sheet

Leveraged Recapitalizationdebt issuance

• After borrowing $80M but before repurchase

Leveraged Recapitalizationrepurchase

• After Share Repurchase of $80M

Modigliani – Miller continued• We are now convinced that the value of the

firm is not affected by its capital structure.• We saw earlier that the risk of equity returns

and the equity cost of capital increase with leverage.

• E and D are the market values of Equity and Debt respectively if the firm is levered.

• U is the market value of equity if unlevered.• A is the market value of the firm’s assets.

The Firm as a Portfolioof Risky Assets

• Proposition I implies thatU = A = E + D

• Since the realized return on a portfolio equals the weighted average of the realized returns of the securities in it:

Modigliani – Miller

• MM Proposition II: The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio

Modigliani - Miller

• Back to our example• We can calculate the equity cost of capital for

the levered firm with $500 debt.

• E=500, D=500, rD=5%, rU=15%

• We can calculate rE

WACC under Modigliani - Miller

• Notice, MM proposition II implies that the Weighted Average Cost of Capital (WACC) is not reduced by taking on debt – it equals the assets cost of capital.

Capital Budgeting and WACC

• When evaluating the NPV of a project we discount cash flows using the project cost of capital.

• If the project is in the same line of business of that of the firm we will use the assets cost of capital or the unlevered-equity cost of capital

• This is why we use the weighted average cost of capital

Levered and unlevered betas

• The assets beta measures the risk of cash flows generated from the firm’s investments (equivalently, unlevered equity beta).

• Assets beta is not affected by the choice of capital structure

• Equity beta and debt beta of levered firm satisfy:

Levered and unlevered beta

• Example 14.7 (page 443)

Ticker Name Equity beta

D/E ratio Debt beta

LUV Southwest 1.13 0.15 0.00

ALK Alaska Air 1.80 1.06 0.15

SKYW SkyWest 1.69 1.05 0.15

MESA Mesa 3.27 3.52 0.30

CAL Continental 3.76 5.59 0.40

Levered and unlevered beta

• Example continued

Ticker Name Equity beta

D/E ratio Debt beta

Assets beta

LUV Southwest 1.13 0.15 0.00 0.98

ALK Alaska Air 1.80 1.06 0.15 0.96

SKYW SkyWest 1.69 1.05 0.15 0.9

MESA Mesa 3.27 3.52 0.30 0.95

CAL Continental 3.76 5.59 0.40 0.9

Cash as negative debt

• Cash holdings may distort our estimate of the risk of the firm’s business assets

• We measure leverage in terms of net debt:

Net Debt = Debt – Cash and Risk-Free Securities

Cash and beta

• Example 14.8 (page 445)• In mid-2005 Cisco Systems had no debt, $110

billion market cap, beta of 2.2. It had cash and risk free securities worth $16 billion.

• Lets find the market value and risk of Cisco’s business assets excluding its cash.

Cash and beta

• Example continued

Leverage and EPS

• Can firms increase their earnings per share and stock price by taking on leverage?

• If so…wouldn’t it contradict our conclusion (with the help of MM) that such transactions are zero NPV projects in perfect capital markets?

Leverage and EPS

• Example: • Levitron Industries (LVI) is an all equity firm. This

coming year its EBIT (earnings before interest and tax) will be $10 million. It has 10 million shares outstanding and its stock price is $7.50.

• LVI is considering changing its capital structure by borrowing $15 million at 8% and using the proceeds to repurchase 2 million shares at $7.50.

• Lets calculate LVI’s new Earnings per share (EPS)

Leverage and EPS

• Example continued

Leverage and EPS

• Example continued• LVI’s EPS increased by 10%• How is it that EPS increases but the stock price

remains unchanged?• Remember the discussion earlier on leverage

and levered equity returns….• Earnings are riskier now that LVI is levered –

higher in good states but lower in bad states

Equity issuance and dilution

• Can issuing stock dilute the value of equity for current shareholders?

• After all the pie is divided to more pieces• Lets consider the example of Jet Sky Airlines (JSA) – see

page 448.• JSA currently has no debt and 500 million shares

outstanding trading at price $16. A month ago it announced that it needs $1 billion to purchase new planes and expand and that the expansion will be financed with new equity.

Equity issuance and dilution

• Example continued• How will the share price change when the new

equity is issued today?

Assignments

• Page 453-457, questions 2, 11, 14, 16 and Data Case 1-7