Lecture IIIB2: Financial Leverage and Capital Structure Policy Ch. 16

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Lecture IIIB-2 Financial Leverage and Capital
Structure Policy (Ch. 16)

• 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

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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
  firms 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.

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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

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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.

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1.1 An example.. Table 2 Proposed structure
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1.1 An example..Figure 1 Financial leverage,
EPS and EBIT
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1.1 An example.. some conclusions from Figure 1

• Let us draw some conclusions from Figure 1.
• The effect of financial leverage depends on ABCs
  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.

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1.1 An example.. Mr. Modiglianis argument

• Mr. Jack Modiglianis 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 EPSs and solve for X gives
  X200.

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1.2 Home-made leverage

• Ms. Jane Millers 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 Millers view, lets 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

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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 (202 - 20
  borrowing) 20
• ? Levered share price 20.

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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 EL DL ,
• where,VU ? value of the unlevered firm
• VL ? value of the levered firm
• DL ? market value of equity
• EL ? market value of debt.

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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).

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1.3 MM proposition I.. Unlevering the stock..
unlever the stock by buying one share and
lending 20
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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 firms 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.

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1.4 (1) MM II

• Consider ABCs 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 1,00012.5 1,000(12.5 -
10) 1,000 12.5 (1,000/1,000)(12.5
- 10)
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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
• 50012.5 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
• RE RA (D/E)(RA - RD ), where RA return
  on asset.

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1.4 (1) MM II..

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

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1.4 (1) MM II..

• cost of capital

RE RA (RA - RD )(D/E)
WACC RA
RD
D/E
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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.
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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 RA10, ABC
  makes 2,00010 200, which must be the
  indifference EBIT.

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

• Indifference EBIT based on ROE ROA (D/E)(ROA
  - RD ).
• 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 RD.
• This makes sense. When ROA RD, 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.

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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.

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1.4 (2) Risk-Return trade-off..

• A firms beta is a weighted average of the betas
  of debt and equity
• ?A D/(DE)?D E/(DE)?E.
• Rearranging,
• ?E ?A (?A - ?D )(D/E).
• With 50 debt and 50 equity (D/E 1), ?D 0, we
  have ?E 2?A.
• Two components of risk in equity beta.
• Business risk ?A measures the riskiness of the
  firms asset primarily arising from the nature of
  the firms operation.
• Financial risk ?A (D/E) depends on the firms
  financial policy.

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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 Ls taxable income goes down by the interest
  expense.
• Interest expense DRD 20010 20
• Firm Ls tax goes down by 20Tc 2030 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 (DRD) Tc / RD DTc.

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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 DTc 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 D,
• 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 D/E ratio and
  (1?TC ) the rate of increase depends on the
  spread between ? and RD . Formally, (? ? cost
  of capital for unlevered firm),

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2. MM with corporate taxes..
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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.

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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.

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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 firms
  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.

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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.

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3.2 MM with bankruptcy costs

• If firms have a high D/E 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.

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3.2 MM with bankruptcy costs..(Figure 4) D/E and
firm value
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3.2 MM with bankruptcy costs..(Figure 5) D/E and
cost of capital
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3.2 MM with bankruptcy costs..(Figure 6)
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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.

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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.