Capital Structure. IntroductionCapital Structure. IntroductionHow are projects and firms financed? This How are projects and firms financed? This choice determines the choice determines the capital structurecapital structureCapital structure Capital structure isis mix of types of securities issued by the firmmix of types of securities issued by the firm mix of claims that investors have on the firm’s cash mix of claims that investors have on the firm’s cash

flowsflows

Why is it important?Why is it important? Capital structure affects the Capital structure affects the cost of capitalcost of capital, i.e. the , i.e. the

discount rate which we use in valuationdiscount rate which we use in valuation

What are the determinants of the optimal What are the determinants of the optimal (“target”) capital structure?(“target”) capital structure? Optimal c.s. should minimize the cost of capital (i.e. Optimal c.s. should minimize the cost of capital (i.e.

maximize the market value of the firm)maximize the market value of the firm)

Modigliani and Miller proposition: in the absence of Modigliani and Miller proposition: in the absence of taxes, costs of financial distress and capital market taxes, costs of financial distress and capital market imperfections capital structure is irrelevant!imperfections capital structure is irrelevant!Why does the irrelevance result not hold in the real Why does the irrelevance result not hold in the real world? MM proposition is obtained under several strong world? MM proposition is obtained under several strong assumptions. Any of the following factors can kill the assumptions. Any of the following factors can kill the irrelevance result:irrelevance result:

Taxes (corporate and personal) – Modified MM theoryTaxes (corporate and personal) – Modified MM theory Costs of financial distressCosts of financial distress Transaction costsTransaction costs Agency costsAgency costs Asymmetric informationAsymmetric information

We will discuss themWe will discuss them

Sources of Long Term financeSources of Long Term finance

Internal financing (retained earnings)Internal financing (retained earnings) But firms often spend more than they But firms often spend more than they

generate internally. The deficit is financed by generate internally. The deficit is financed by new sales of debt & equitynew sales of debt & equity

Types of instrumentsTypes of instruments EquityEquity DebtDebt LeasesLeases

EquityEquity

Can be publicly traded or notCan be publicly traded or notTypes:Types: Common Stock - claim on the share of profits (after Common Stock - claim on the share of profits (after

tax and payments to creditors)tax and payments to creditors)may have different voting rightsmay have different voting rights

Preferred Stock – paid after tax and payment to Preferred Stock – paid after tax and payment to creditors too, but is normally a fixed claim (similarity to creditors too, but is normally a fixed claim (similarity to debt)debt)

No voting rights in normal timesNo voting rights in normal timesDividend is paid before dividend on common stockDividend is paid before dividend on common stock

WarrantsWarrantsCall options on a firm’s shares Call options on a firm’s shares

Can be publicly traded or notCan be publicly traded or notFixed claim (not a share of profits!)Fixed claim (not a share of profits!)Interest payments occur before payments Interest payments occur before payments to preferred and common stockholders to preferred and common stockholders and and beforebefore taxes, i.e. tax deductible taxes, i.e. tax deductibleNo control (voting) rights in normal timesNo control (voting) rights in normal timesControl rights in case of defaultControl rights in case of defaultCan be Can be convertibleconvertible into stock upon into stock upon realization of some conditionsrealization of some conditions

DebtDebt

Debt differs byDebt differs by MaturityMaturity LiquidityLiquidity

public bonds - liquidpublic bonds - liquid bank loans or private placements - illiquidbank loans or private placements - illiquid

Security (for bonds)Security (for bonds) secured (by an asset)secured (by an asset)

Mortgage bonds, collateral bondsMortgage bonds, collateral bonds

unsecured ordinaryunsecured ordinary Debentures, notes (“backed” by the earning power of the Debentures, notes (“backed” by the earning power of the

firm, no collateral)firm, no collateral)

unsecured subordinatedunsecured subordinated Subordinated debentures (Least protected. Holders of Subordinated debentures (Least protected. Holders of

such bonds are paid after all other creditors)such bonds are paid after all other creditors)

LeasesLeases

Borrowing an asset in exchange for future Borrowing an asset in exchange for future fixed repayments (similar to debt) fixed repayments (similar to debt)

Types of leasesTypes of leases Operating leaseOperating lease

Usually short term and the asset is returnedUsually short term and the asset is returned Capital (investment) leaseCapital (investment) lease

Usually lasts for the entire life of the asset and the Usually lasts for the entire life of the asset and the asset can sometimes be acquired at the end by the asset can sometimes be acquired at the end by the lessee at low pricelessee at low price

Financing patternsFinancing patterns

In the US, on average, 60-80% of the investment In the US, on average, 60-80% of the investment expenditures is financed with internal funds. In other expenditures is financed with internal funds. In other countries reliance on internal funds is generally lower but countries reliance on internal funds is generally lower but still 40-60%.still 40-60%.NewNew sales of debt strongly prevail over sales of debt strongly prevail over newnew equity equity issuesissuesLarge variations between types of firms and industries Large variations between types of firms and industries (e.g. for startups equity financing strongly prevails)(e.g. for startups equity financing strongly prevails)Capital structure: in the US, average market value debt-Capital structure: in the US, average market value debt-equity ratio is 0.5 (very roughly). Large variations equity ratio is 0.5 (very roughly). Large variations between industries: from 0.08 in biotech to 3 in financial between industries: from 0.08 in biotech to 3 in financial sector.sector.

Pie model of the firmPie model of the firm

As long as D is fixed, maximizing E is equivalent As long as D is fixed, maximizing E is equivalent to maximizing the whole pie (i.e. the total firm to maximizing the whole pie (i.e. the total firm value). But D is not fixed if debt is riskyvalue). But D is not fixed if debt is risky

DE

F D

E

Vdefault

Modigliani – Miller Modigliani – Miller without taxeswithout taxes

Irrelevance of capital structure (MM I)Irrelevance of capital structure (MM I)

Cost of levered equity as a function of Cost of levered equity as a function of capital structure (MM II)capital structure (MM II)

Financing a firm with equityFinancing a firm with equityEntrepreneur has an investment opportunityEntrepreneur has an investment opportunityInvestment needed: $800Investment needed: $800The project cash flows:The project cash flows:

Prob(strong)=Prob(weak)=1/2Prob(strong)=Prob(weak)=1/2Suppose:Suppose:

Risk free interest rate = 5%Risk free interest rate = 5% The appropriate risk premium for this investment = 10%The appropriate risk premium for this investment = 10% Hence, the cost of capital (return investors require) is 15%Hence, the cost of capital (return investors require) is 15%

NPV = -800 + (½*1400 + ½*900)/1.15 = $200 > 0NPV = -800 + (½*1400 + ½*900)/1.15 = $200 > 0

Imagine, in order to finance the project entrepreneur Imagine, in order to finance the project entrepreneur sells 100% of shares of this project to outside investors – sells 100% of shares of this project to outside investors – the project will be all-equity financedthe project will be all-equity financedHow much would he raise?How much would he raise?

Fair price for 100% of shares isFair price for 100% of shares is(½*1400 + ½*900)/1.15 = 1000(½*1400 + ½*900)/1.15 = 1000He would invest 800 and keep 200. Hence, his gain is He would invest 800 and keep 200. Hence, his gain is exactly NPVexactly NPVIn fact he could sell 80% of shares and keep 20% for In fact he could sell 80% of shares and keep 20% for himself. Then investors would provide 800 and he would himself. Then investors would provide 800 and he would get 0.2*1000 = 200, i.e. the sameget 0.2*1000 = 200, i.e. the same

Imagine, entrepreneur had invested 400 from his Imagine, entrepreneur had invested 400 from his own money and had raised only 400 as outside own money and had raised only 400 as outside equity.equity.He had to sell exactly 40% to outside investors He had to sell exactly 40% to outside investors and would keep 60%. His payoff would be and would keep 60%. His payoff would be 0.6*1000 – 400 = 200, e.g. as before0.6*1000 – 400 = 200, e.g. as beforeHence, observation: in a perfect market (no Hence, observation: in a perfect market (no transaction cost, asymmetric info problems, transaction cost, asymmetric info problems, moral hazard) it does not matter whether to moral hazard) it does not matter whether to finance a firm internally or by raising external finance a firm internally or by raising external fundsfunds

Adding DebtAdding Debt

Modigliani – Miller Proposition IModigliani – Miller Proposition IIn a perfect capital market a firm’s total market value is In a perfect capital market a firm’s total market value is equal to the market value of the total cash flows equal to the market value of the total cash flows generated by its assets and is generated by its assets and is independent of its capital independent of its capital structure:structure:

U = A = E + DU = A = E + D A – A – market value of assets, market value of assets, UU – market value of unlevered – market value of unlevered

equity, equity, EE – market value of levered equity, – market value of levered equity, DD – market value of – market value of debt.debt.

Perfect capital market:Perfect capital market: No taxesNo taxes No costs of financial distressNo costs of financial distress No transaction and issuance costsNo transaction and issuance costs No asymmetric informationNo asymmetric information The firms' financing and operating decisions are independent. In The firms' financing and operating decisions are independent. In

particular, no agency costs (managers maximize firm value)particular, no agency costs (managers maximize firm value) Individuals can undertake the same financial transactions as the Individuals can undertake the same financial transactions as the

firms and at the same prices (e.g. borrow at the same interest firms and at the same prices (e.g. borrow at the same interest rate)rate)

IntuitionIntuition

If the way we divide cash flows from an asset If the way we divide cash flows from an asset among different claims (securities) does not among different claims (securities) does not affect these cash flows, the total market value of affect these cash flows, the total market value of these claims must be independent of the way we these claims must be independent of the way we divide the cash flowsdivide the cash flows (We need some more for this result to hold: any (We need some more for this result to hold: any

division is costless, all investors know the same as division is costless, all investors know the same as insiders, i.e. do not treat a particular division as any insiders, i.e. do not treat a particular division as any signal of firm value, investors can freely trade at the signal of firm value, investors can freely trade at the same terms as firms)same terms as firms)

MM I holds not only for a split into debt and MM I holds not only for a split into debt and equity, but for any combination of any securitiesequity, but for any combination of any securities

Proof by arbitrage argumentProof by arbitrage argumentConsider firm 1 and firm 2.Consider firm 1 and firm 2.At t=1,2,...., both firms generate the same (random) At t=1,2,...., both firms generate the same (random) earnings (EBIT) X > 0.earnings (EBIT) X > 0.But they differ in their cap. structure:But they differ in their cap. structure:

Firm 1 has equity and debt (risk free and perpetual for simplicity)Firm 1 has equity and debt (risk free and perpetual for simplicity) Firm 2 has no debtFirm 2 has no debt

Firm 1 pays annual interest Firm 1 pays annual interest rrff, which is equal to the , which is equal to the return on safe debt in the marketreturn on safe debt in the marketmarket value of firm i's debt: market value of firm i's debt: DDii

market value of firm i's equity: market value of firm i's equity: EEii

total market value of firm i: total market value of firm i: UUii = = EEii + + DDii

Hence, at t:Hence, at t: firm 1's debtholders receive: firm 1's debtholders receive: rrf f DD11 firm 1's equityholders receive: X- firm 1's equityholders receive: X- rrf f DD11 firm 2's equityholders receive: Xfirm 2's equityholders receive: X

Step 1: It cannot be that Step 1: It cannot be that U₂U₂>>U₁U₁..Proof:Proof:Suppose Suppose U₂U₂>>U₁U₁ and consider an investor and consider an investor holding a fraction holding a fraction αα of firm 2's shares. At t, he of firm 2's shares. At t, he would receive would receive αXαX. Instead, he could:. Instead, he could: Sell the shares for Sell the shares for αU₂αU₂ Buy in a fraction Buy in a fraction αU₂αU₂//U₁U₁ of firm 1's debt and equity of firm 1's debt and equity

as: as: αU₂ αU₂ = (= (αU₂αU₂//UU₁)⋅₁)⋅D₁D₁+(+(αU₂αU₂//U₁U₁)⋅)⋅E₁E₁ At t, the investor would receive:At t, the investor would receive:

((αU₂αU₂//U₁U₁) ) rrf f DD11 + ( + (αU₂αU₂//U₁U₁) (X- ⋅) (X- ⋅ rrf f DD11) = () = (αU₂αU₂//U₁U₁))X X > > αXαX for all X for all X

Hence, there is an arbitrage opportunity. Intuition: Hence, there is an arbitrage opportunity. Intuition: Arbitrageurs can "undo firm 1's leverage" by buying its Arbitrageurs can "undo firm 1's leverage" by buying its debt and equity in proportions such that interest paid debt and equity in proportions such that interest paid and received cancel. and received cancel.

Step 2: It cannot be that Step 2: It cannot be that U₁>U₂U₁>U₂..Proof:Proof:Suppose Suppose U₁>U₂U₁>U₂ and consider an investor and consider an investor holding a fraction holding a fraction αα of firm 1's shares. At t, he of firm 1's shares. At t, he would receive X- would receive X- rrffDD11. Instead, he could:. Instead, he could: Sell the shares for Sell the shares for αEαE11 Borrow Borrow αDαD11 Invest the total in a fraction Invest the total in a fraction αα((U₁U₁//U₂U₂) of firm 2's ) of firm 2's

shares:shares: αE₁+αD₁ αE₁+αD₁ = = αα((U₁U₁//U₂U₂))U₂U₂ At t, the investor would get At t, the investor would get αα((U₁U₁//U₂U₂)X and pay )X and pay

interests interests rrffDD11: : αα((U₁U₁//U₂U₂)X - )X - rrffDD11 > > αα(X- (X- rrf f DD11) for all X.) for all X.

Hence, there is an arbitrage opportunity. Intuition: Hence, there is an arbitrage opportunity. Intuition: Arbitrageurs can "lever up" firm 2 by borrowing on Arbitrageurs can "lever up" firm 2 by borrowing on individual accounts (homemade leverage).individual accounts (homemade leverage).

Example: arbitrage for our firmExample: arbitrage for our firm

Changing a capital structure Changing a capital structure does does notnot change stock price change stock price

Example: leveraged recapitalizationExample: leveraged recapitalization Harrison Industries is currently all-equity with 50 mln Harrison Industries is currently all-equity with 50 mln

shares traded at $4 per share. Hence, its assets shares traded at $4 per share. Hence, its assets market value = equity value = 200market value = equity value = 200

Harrison plans to borrow $80 mln and use the money Harrison plans to borrow $80 mln and use the money to repurchase stockto repurchase stock

How much would the stock cost after the transaction?How much would the stock cost after the transaction? Imagine after the announcement the stock price Imagine after the announcement the stock price

would be $would be $xx. The firm can repurchase 80 mln/x . The firm can repurchase 80 mln/x shares. The stock price after the transaction must be shares. The stock price after the transaction must be equal $equal $xx too (investors are forward looking) too (investors are forward looking)

50 mln – 80 mln/x has left. Their total value should be 50 mln – 80 mln/x has left. Their total value should be assets market value – debt market value = 200 – 80 assets market value – debt market value = 200 – 80 =120=120

x(50 – 80/x) = 120 x(50 – 80/x) = 120 x = 4 – did not change! x = 4 – did not change!

Market value balance sheet after each stage Market value balance sheet after each stage of Harrison’s leveraged capitalizationof Harrison’s leveraged capitalization

NoteNote: this was a zero-NPV transaction. Non-zero NPV : this was a zero-NPV transaction. Non-zero NPV transaction would change the stock price, but choosing transaction would change the stock price, but choosing whether to use debt or equity for financing does not whether to use debt or equity for financing does not matter for the stock pricematter for the stock price

Returns to equity with and without Returns to equity with and without leverageleverage

Levered equity has higher expected return than Levered equity has higher expected return than levered. Why? Because it’s more levered. Why? Because it’s more riskyrisky..

Leverage increases both return and risk of Leverage increases both return and risk of equityequity

Modigliani – Miller Proposition IIModigliani – Miller Proposition II

In fact, the following relationship is true:In fact, the following relationship is true:

Return (expected) on all firm’s assets Return (expected) on all firm’s assets rrAA = return on = return on unlevered equity unlevered equity rrUU = (E/(E+D)) = (E/(E+D))rrEE + (D/(D+E)) + (D/(D+E))rrDD

Here Here rrEE – return (expected) on equity in a levered firm, – return (expected) on equity in a levered firm, rrDD – return – return (expected) on debt(expected) on debt

Hence, MM II:Hence, MM II:

Firm’s return on equity (cost of equity) increases with Firm’s return on equity (cost of equity) increases with leverageleverage

Cost of capital for a firm:Cost of capital for a firm:

rrWACCWACC – weighted average cost of capital – weighted average cost of capital

(we will use it for valuation of projects and (we will use it for valuation of projects and firms)firms)

As the fraction of the As the fraction of the firm financed with debt firm financed with debt increases, both the increases, both the equity and the debt equity and the debt become riskier and become riskier and their cost of capital their cost of capital rises. Yet, because rises. Yet, because more weight is put on more weight is put on the lower-cost debt, the lower-cost debt, the weighted average the weighted average cost of capital remains cost of capital remains constant.constant.

Levered and Unlevered BetasLevered and Unlevered Betas

Since , these formulas Since , these formulas are consistent with MM IIare consistent with MM II

)( fmf rrβrr

When debt is risk free its beta = 0, and then

Cash, Net Debt and Enterprise Cash, Net Debt and Enterprise ValueValue

Very often Enterprise Value is used as a market value of Very often Enterprise Value is used as a market value of a businessa businessEV = Equity + Net DebtEV = Equity + Net DebtNet Debt = Debt – Cash and Risk-Free SecuritiesNet Debt = Debt – Cash and Risk-Free SecuritiesEV – market value of assets excluding cashEV – market value of assets excluding cashMM I for EV: In a perfect capital market a firm’s EV is MM I for EV: In a perfect capital market a firm’s EV is equal to the market value of the total cash flows equal to the market value of the total cash flows generated by its assets excluding cash and is generated by its assets excluding cash and is independent of the combination of Equity, Debt and independent of the combination of Equity, Debt and Cash (or of the combination of Equity and Net Debt)Cash (or of the combination of Equity and Net Debt)MM II is the same, but MM II is the same, but rrUU, , rrDD and and DD have slightly different have slightly different meanings meanings

Cash reduces market risk of equity (effect Cash reduces market risk of equity (effect opposite to the one of debt)opposite to the one of debt)

Note: here D is Net Debt and betaNote: here D is Net Debt and betaUU is beta of is beta of assets net of cashassets net of cash

Is the following statement true?:Is the following statement true?:

Leverage can increase expected earnings per share. If it Leverage can increase expected earnings per share. If it does, it should increase stock price.does, it should increase stock price.

Wrong. Stock price does not change as we saw. Even if Wrong. Stock price does not change as we saw. Even if EPS increase they become more volatile with leverage.EPS increase they become more volatile with leverage.

Example:Example: Levitron Industries (LVI) is currently all-equity. Its expected next Levitron Industries (LVI) is currently all-equity. Its expected next

year EBIT = $10 mln.year EBIT = $10 mln. It has 10 mln shares outstanding, traded at $7.50 per shareIt has 10 mln shares outstanding, traded at $7.50 per share LVI wants to do leveraged recapitalization: borrowing $15 million LVI wants to do leveraged recapitalization: borrowing $15 million

at interest rate 8% and using the proceeds to repurchase 2 mln at interest rate 8% and using the proceeds to repurchase 2 mln shares at $7.50 (we know such transaction should not change shares at $7.50 (we know such transaction should not change the stock price)the stock price)

Let’s show that EPS will become more volatileLet’s show that EPS will become more volatile

Currently Net Income = EBIT = $10 mlnCurrently Net Income = EBIT = $10 mln Hence EPS = $10 mln/10 mln = $1Hence EPS = $10 mln/10 mln = $1

With the debt, annual interest payment = $15 With the debt, annual interest payment = $15 mln * 0.08 = $1.2 mlnmln * 0.08 = $1.2 mln Hence, NI = EBIT – i = $8.8 mlnHence, NI = EBIT – i = $8.8 mln Hence EPS = $8.8 mln/8 mln = $1.10 > $1Hence EPS = $8.8 mln/8 mln = $1.10 > $1

But $10 mln is But $10 mln is expectedexpected EBIT. Imagine EBIT = EBIT. Imagine EBIT = either $4 or $16 (each with prob. ½)either $4 or $16 (each with prob. ½) In an unlevered firm EPS would be either $0.4 or $1.6In an unlevered firm EPS would be either $0.4 or $1.6 In a levered firm EPS would be either $0.35 or $1.85. In a levered firm EPS would be either $0.35 or $1.85.

More volatility (hence, more risk)More volatility (hence, more risk)

The sensitivity of The sensitivity of EPS to EBIT is EPS to EBIT is higher for a levered higher for a levered firm than for an firm than for an unlevered firm. Thus, unlevered firm. Thus, given assets with the given assets with the same risk, the EPS same risk, the EPS of a levered firm is of a levered firm is more volatile.more volatile.