IIIB 2CapitalStructure

Lecture IIIB-2: Capital Structure (Ch. 16 & 17) : 

Lecture IIIB-2: Capital Structure (Ch. 16 & 17) Overview 1. Does leverage affect firm value in a perfect capital market? 1.1 An example 1.2 Home-made leverage 1.3 MM proposition I 1.4 Effect of leverage on return (MM II) and risk (1) MM II (2) Risk-return trade off 2. MM with corporate taxes 3. MM with bankruptcy costs 3.1 Bankruptcy costs 3.2 MM with bankruptcy costs

Overview: 

Overview For the discussion of cost of capital, we take the capital structure of a firm as given. Now we look at the effect of capital structure on the firm’s value. Capital structure policy refers to a decision on the mix of debt and equity for a given asset size. Our goal is to find out an optimal capital structure of a firm. Major results are Modigliani and Miller (MM) propositions I and II.

1. Does leverage affect firm value in a perfect capital market?: 

1. Does leverage affect firm value in a perfect capital market? 1.1 An Example The ABC (Amazing Brew Coffee) Company is reviewing its capital structure. Assume no taxes and a perfect capital market. The company has no debt. All operating income is paid out as dividends. Its current position is as follows:

1.1 An example..: Table 1 current structure: 

1.1 An example..: Table 1 current structure Mr. Modigliani, the firm's president, proposes to issue $1,000 of debt at 10% and use the proceeds to repurchase 50 shares. His analysis follows.

1.1 An example..: Table 2 Proposed structure: 

1.1 An example..: Table 2 Proposed structure

1.1 An example..Figure 1: Financial leverage, EPS and EBIT: 

1.1 An example..Figure 1: Financial leverage, EPS and EBIT

1.1 An example..: some conclusions from Figure 1: 

1.1 An example..: some conclusions from Figure 1 Let us draw some conclusions from Figure 1. The effect of financial leverage depends on ABC’s EBIT. At a high level of EBIT, leverage is beneficial. Under the expected scenario (i.e., state 2), leverage increases ROE and EPS. Shareholders, however, are exposed to more risk under the proposed capital structure since the ROE and EPS are more variable and sensitive to changes in EBIT.

1.1 An example..: Mr. Modigliani’s argument: 

1.1 An example..: Mr. Modigliani’s argument Mr. Jack Modigliani’s argument: “Since we expect operating income to be $250 which is above the critical level of $200, the shareholders will be better off with levered capital structure.” Indifference EBIT: Note from Figure 1 that EPS (earnings per share) is $2 under current and proposed capital structure when EBIT equals to $200. How do we find out the “indifference” EBIT? Let $X denote EBIT. Under current structure, EPS is simply $X/100. Under the proposed structure, you pay interest of $100, and there are a total of 50 shares, so EPS is ($X$100)/50. Equate these two EPS’s and solve for $X gives $X=$200. ■

1.2 Home-made leverage: 

1.2 Home-made leverage Ms. Jane Miller’s counter-argument: “Leverage will help the shareholders as long as operating income is above $200. But you ignore the possibility of investors’ borrowing on their own account. Suppose that a person borrows $20 and puts up $20 of her own money. She then invests a total of $40 in two unlevered ABC shares.” To see Ms. Jane Miller’s view, let’s consider two cases: Case 1: Proposed capital structure. Buy 1 levered share at $20 Case 2: No change in capital structure. Borrow $20 & use $20 of her own to buy 2 un-levered shares

1.2 Home-made leverage: 

1.2 Home-made leverage Payoff from case 1 and case 2 are identical. Payoffs of 1 levered share is equal to the payoff of the home-made portfolio of stock and borrowing. Value of 1 levered share = Value of the portfolio The portfolio has 2 un-levered shares purchased with $20 borrowing and $20 of your own money. Value of 1 levered share = ($20*2 - $20 borrowing) =$20  Levered share price = $20.

1.3 MM proposition I: 

1.3 MM proposition I With perfect capital markets and no taxes, a change in capital structure does not add any value to the shareholders. Formally, this is MM proposition I: VU = VL = B + S , where,VU  value of the unlevered firm VL  value of the levered firm S  market value of equity B  market value of debt.

1.3 MM proposition I..: Unlevering the stock: 

1.3 MM proposition I..: Unlevering the stock One more thing before we leave MM I. Example: Unlevering the stock Suppose ABC adopts the proposed capital structure. Suppose that our investor prefers the original (unlevered) capital structure. How can this investor “unlever” the stock to re-create the original payoffs? Suppose she buys one levered share at $20 and lends $20 at 10%. She receives earnings for 1 share and interest from her $20 lending. Her total payoffs are exactly same as the original payoffs of two unlevered shares. (See Table 5).

1.3 MM proposition I..: Unlevering the stock..: 

1.3 MM proposition I..: Unlevering the stock.. “unlever” the stock by buying one share and lending $20:

1.4 Effect of leverage on return (MM II) and risk: 

1.4 Effect of leverage on return (MM II) and risk (1) Leverage and equity returns: MM II For our discussion of the cost of capital, we have taken the firm’s capital structure as given. We now look at how the cost of capital changes with a change in capital structure. Our goal: to find out an optimal or target capital structure, which maximizes the firm value or equivalently minimizes the cost of capital. We take the cost of debt as constant, at least, initially. In order to find out the WACC, we need to find out the relation between return on equity and capital structure.

1.4 (1) MM II: 

1.4 (1) MM II Consider ABC’s expected returns in two cases (Table 6). Intuitively, what is happening here? In all-equity case, Jane earns 12.5% on her $2,000 equity. In levered case, she earns 12.5% on $1,000 equity, and additional 2.5% (i.e., 12.5% - 10%). Her total return on $1,000 equity is 15%: $1,000*12.5% + $1,000*(12.5% - 10%) = $1,000 [ 12.5% + (1,000/1,000)*(12.5% - 10%) ]

1.4 (1) MM II..: 

1.4 (1) MM II.. Suppose Jane puts only $500 equity and borrows $1,500 at 10%. From her $500 equity, she earns 12.5% return. From her $1,500 borrowings, she earns 2.5% (i.e., 12.5% - 10%). Total payoff on her $500 equity is $500*12.5% + $1,500*(12.5% - 10%) = $500 * [ 12.5% + ($1,500/$500) * (12.5% - 10%) ] Total rate of return on her $500 equity is [ 12.5% + ($1,500/$500) * (12.5% - 10%) ] or more generally rS = r0 + (B/S)*(r0 - rB ), where r0 = return on asset.

1.4 (1) MM II.. : 

1.4 (1) MM II.. Leverage and equity returns (another derivation: formal) r0 = Expected operating income / Market value of a firm MM I says that capital structure does not affect a firm’s value. So, r0 is independent of its debt decision. A firm is a portfolio of debt (D) and equity (E). So, rwacc is an weighted average of returns on debt and equity.   Rearranging, we have MM II:

1.4 (1) MM II..: 

1.4 (1) MM II.. cost of capital B/S rB WACC = r0

1.4 (1) MM II..: Another look at indifferece EBIT: 

1.4 (1) MM II..: Another look at indifferece EBIT What if Jane does not get any extra earnings from debt? Then, in levered case, her return on equity is equal to that in all-equity case. It is her return on equity at indifference EBIT.

1.4 (1) MM II..: Another look at indifferece EBIT..: 

1.4 (1) MM II..: Another look at indifferece EBIT.. In out ABC example, borrowing rate is 10%. Total size of asset is $2,000. When RA=10%, ABC makes $2,000*10% = $200, which must be the indifference EBIT. 

1.4 (1) MM II..: Another look at indifferece EBIT..: 

1.4 (1) MM II..: Another look at indifferece EBIT.. Indifference EBIT based on ROE = ROA + (B/S)*(ROA - rB ). At an indifference EBIT, the EPS of the levered and unlevered share is identical. Stock price still remains at $20 in our ABC example. At indifference EBIT, EPS/Price is also identical for levered and unlevered capital structure. Under an unlevered structure, EPS/Price = ROE(All E) = ROA. Under a levered structure, EPS/Price = ROE (Levered). So at an indifference EBIT, ROE (Levered) = ROA, which implies ROA = rB. This makes sense. When ROA = rB, Jane earns only enough operating income to cover her interest payment, and there is no beneficial effect of leverage. Hence ROE (Levered) is same as the ROE of all equity case, which is equal to the ROA.

1.4 (2) Risk-Return trade-off: 

1.4 (2) Risk-Return trade-off MM I: A firm's leverage does not affect its value. MM II: return on equity increases as leverage increases. So, as leverage increases, the rate of return on equity goes up, but the value of the firm stays constant. How can they be reconciled? What is happening is that risk is increasing as leverage increases.

1.4 (2) Risk-Return trade-off..: 

1.4 (2) Risk-Return trade-off.. A firm’s beta is a weighted average of the betas of debt and equity: A = [B/(B+S)]*B + [S/(B+S)]*S. Rearranging, S = A + (A - B )*(B/S). With 50% debt and 50% equity (B/S =1), B =0, we have S= 2*A. Two components of risk in equity beta. Business risk: A measures the riskiness of the firm’s asset primarily arising from the nature of the firm’s operation. Financial risk: A* (B/S) depends on the firm’s financial policy.

2. MM with corporate taxes: 

2. MM with corporate taxes Interest expenses are tax deductible. Debt financing reduces tax bill, and thus has value. To see this, let us compare two firms U and L. They are identical except for a $200 debt at 10% for levered firm L. Suppose corporate tax rate is 30%. Then relative to firm U, Firm L’s taxable income goes down by the interest expense. Interest expense = B*rB = $200*10% = $20 Firm L’s tax goes down by $20*Tc = $20*30% = $6. The tax saving due to interest expense is called the interest tax shield. Suppose this is a perpetual borrowing. Then PV of the interest tax shield is $60. This is $6/0.1 = (B* rB)* Tc / rB = B*Tc.

2. MM with corporate taxes..: 

2. MM with corporate taxes.. So, the levered firm L is more valuable than unlevered firm U by the PV of interest tax shield, which equals to B*Tc for a perpetual debt. MM proposition I with corporate taxes: VL= VU + PV tax shield.  In the special case of permanent debt: VL = VU + Tc B, where VL  value of levered firm, and VU  value of all-equity firm.  MM's Proposition II with corporate taxes: The expected return on the common stock of a levered firm increases in proportion to the B/S ratio and (1TC ); the rate of increase depends on the spread between r0 and rB . Formally, (r0  cost of capital for unlevered firm),

2. MM with corporate taxes..: 

2. MM with corporate taxes..

3. MM with bankruptcy costs: 

3. MM with bankruptcy costs Given MM results so far, what should firms do? They should borrow as much as possible to gain the maximum possible tax shield. But in fact they do not borrow very much. Some typical debt ratios are given in the table below.   In order to explain why firms do not borrow more, we now turn to bankruptcy costs.

3. MM with bankruptcy costs: 3.1 Bankruptcy costs: 

3. MM with bankruptcy costs: 3.1 Bankruptcy costs Costs of financial distress are:   Direct costs of bankruptcy. Indirect costs of bankruptcy. Agency costs of financial distress. (1) Direct Bankruptcy Costs Legal and administrative costs in bankruptcy and liquidation. Warner (1977, Journal of Finance, pp. 337-347) reported that direct bankruptcy costs were on average 5.3% of the overall market value of his sample firms. These magnitudes are small relative to the tax advantage of debt.

3.1 Bankruptcy costs..: 

3.1 Bankruptcy costs.. (2) Indirect Costs of Bankruptcy Costs involved with the difficulties of running a business while it is going through bankruptcy. These costs are probably fairly substantial, perhaps of the same order of magnitude as a strike. However, they are still small relative to the tax shield on debt. (3) Agency Costs of Financial Distress Costs associated with distortion of firm’s incentives. Suppose a firm has $1,000 in cash the day before its $5,000 debt comes due. If the equity-holders (or the managers acting on their behalf) do nothing then the firm will go bankrupt and they will get nothing. What should they do? The manager might go to a Casino.

3.1 Bankruptcy costs..: 

3.1 Bankruptcy costs.. In another case, the firm might forego good projects, where equity-holders have to share rewards with bondholders. Suppose the firm has no cash and has $10,000 debt. If it does nothing, the firm will go bankrupt. Suppose the firm has the following investment opportunity:  Invest $2,000: Returns $11,000 with certainty This is clearly a very attractive project. Is it worth the firm doing it? If they do it, bondholders get $10,000. Equity-holders will not put up the money for investment since, even though it's a very good project: Return to equity-holders' = - 2,000 + 1,000 = - $1,000.

3.2 MM with bankruptcy costs: 

3.2 MM with bankruptcy costs If firms have a high B/S ratio, they have a high probability of bankruptcy. Incorporate bankruptcy cost into MM: There is a trade-off between the tax advantage of leverage and the disadvantage of leverage caused by the costs of financial distress.

3.2 MM with bankruptcy costs..(Figure 4) B/S and firm value: 

3.2 MM with bankruptcy costs..(Figure 4) B/S and firm value

3.2 MM with bankruptcy costs..(Figure 5) B/S and cost of capital: 

3.2 MM with bankruptcy costs..(Figure 5) B/S and cost of capital

3.2 MM with bankruptcy costs..(Figure 6): 

3.2 MM with bankruptcy costs..(Figure 6)

3.2 MM with bankruptcy costs..: 

3.2 MM with bankruptcy costs.. How can this theory be applied in practice? One can use standard NPV techniques to estimate the value of an all-equity financed firm. One can discount each year's interest tax shields to estimate the PV of the interest tax shields. This leaves the costs of financial distress. Direct measurement of the costs of financial distress is not usually possible.

3.2 MM with bankruptcy costs..: 

3.2 MM with bankruptcy costs.. How can one find the optimal capital structure? Over time a firm's managers are able to get some idea of their firm's costs of financial distress and choose the debt ratio taking this into account. If one capital structure is better than another in one industry, the firms using it will tend to do better. Over time firms will move toward an optimal capital structure.