Lecture Note 1 Valuation under MM

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Lecture Note 1Valuation under MM
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What is in This Note?

• Overview of Modigliani-Miller Proposition I and
  II (No Tax)
• Overview of Modigliani-Miller Proposition I and
  II (with Corporate Tax)
• Overview of Modigliani-Miller Proposition I and
  II (with Corporate and Personal Tax)
• Overview of Modigliani-Miller Proposition I and
  II (with Asymmetric Information) Reference
  Chapters 14, 15, and 16 of RWJJ, Chapters 17, and
  18 of BMA

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Roadmap

• Overview of Modigliani-Miller Propositions I and
  II (No Taxes)
• Overview of Modigliani-Miller Propositions I and
  II (with corporate Taxes)
• Overview of Modigliani-Miller Propositions I and
  II (with both corporate and personal Taxes)
• Overview of Modigliani-Miller Propositions I and
  II (with asymmetric information)

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MM Proposition I (No Taxes)
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Roadmap

• Overview of Modigliani-Miller Propositions I
• Homemade Leverage and Leveraged Equity
• Assumption of Modigliani-Miller Propositions I
• Modigliani-Miller Propositions I

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Capital Structure and the Pie

• The value of a firm is defined to be the sum of
  the value of the firms debt and the firms
  equity.
• V D E

• If the goal of the firms management is to make
  the firm as valuable as possible, then could the
  firm pick the debt-equity ratio that makes the
  pie as big as possible?

S
D
E
Value of the Firm
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MM Proposition I (No Taxes) Debt Policy is
Irrelevant

• MM Proposition I (No Taxes)
• Assumption
• Intuition
• capital structure is irrelevant

S
E
S
E
D
B
B
D

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Modigliani-Miller Proposition I (No Taxes)

• The total value of the securities issued by a
  firm is independent of the firms choice of
  capital structure.
• The firms value is determined by its real
  assets and growth opportunities, not by the types
  of securities it issues.
• This is the very step Modigliani-Miller results,
  and it holds in an idealized world.

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Assumptions under Modigliani-Miller Proposition I

• 1. Capital structure does not affect investment
  policy
• 2. No taxes (corporate taxes, personal taxes,
  etc)
• 3 Bankruptcy is costless
• 4. Managers maximized shareholders (E) value,
  not total firm value (the Pie, ED).
• 5. Perfect and complete capital markets
• 6. Symmetric information (No black box)

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Intuition

• We can create a levered or (un)levered position
  by adjusting the trading in our own account.
• This homemade leverage suggests that capital
  structure is irrelevant in determining the value
  of the firmVL VU

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Homemade Leverage An Example
Recession Expected Expansion EPS of Unlevered
Firm 2.50 5.00 7.50 Earnings for 40
shares 100 200 300 Less interest on 800
(8) 64 64 64 Net Profits 36 136 236 ROE
(Net Profits / 1,200) 3.0 11.3 19.7 We are
buying 40 shares of a 50 stock, using 800 in
margin. We get the same ROE as if we bought into
a levered firm. Our personal debt-equity ratio
is
12

• ????????/???,
• ????????/???

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Homemade (Un)Leverage An Example

• Recession Expected Expansion
• EPS of Levered Firm 1.50 5.67 9.83
• Earnings for 24 shares 36 136 236
• Plus interest on 800 (8) 64 64 64
• Net Profits 100 200 300
• ROE (Net Profits / 2,000) 5 10 15
• Buying 24 shares of an otherwise identical
  levered firm along with some of the firms debt
  gets us to the ROE of the unlevered firm.
• This is the fundamental insight of MM

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• ????????/???,
• ????????/???

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In-Class Exercise

• Ross, Westerfield, and Jaffe Question 1 (pp. 449)
• Firm has a total market value of 150,000 under
  no debt. EBIT (Earnings before interest and
  taxes) is 14,000 under normal case and is 40
  higher if in expansion and is 70 lower when it
  is recession. There are currently 2,500 shares
  outstanding.
• 1. Calculate EPS (Earnings per share)
• 2.Repeat 1 when the firms issues 60,000 to
  buyback the shares in the open market.

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In-Class Exercise
Shares repurchased 1,000 shares ?
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Summary MM Proposition I (No Taxes)

• We can create a levered or unlevered position by
  adjusting the trading in our own account.
• This homemade leverage suggests that capital
  structure is irrelevant in determining the value
  of the firm
• VL VU

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MM Proposition II (No Taxes)
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Roadmap

• MM Proposition I (No Taxes)
• Equity risk increases wit the level of debt
• Proof
• Economic Intuition

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Modigliani-Miller Proposition II (No Taxes)

• We denote the expected returns on assets, debt
  and equity by RA, RD , and RE , respectively.
  Then
• Where D and E are the market values of debt and
  equity and

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Modigliani-Miller Proposition II (No Taxes)

• Proof
• Let total market value of the assets, debt, and
  equity as A, D, and E, respectively

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MM Proposition II (No Taxes)
Cost of capital R ()
RA
RA
RD
RD
Debt-to-equity Ratio
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MM Proposition II (No Taxes)

• 1. Increasing the debt level does not affect the
  riskiness of the assets, but it does increase the
  riskiness of the equity
• In the same firm, RD is always less than RE,
• This is because the debt has a higher priority
  and this is less risky. But the weighted sum of
  the returns of debt and equity is always a
  constant, and is equal to the return on assets, RA

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In-Class Exercise

• Please evaluate the following argument
• Equity is cheap because the firm does not have
  to pay investors any dividends if it does not
  want to.

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In-Class Exercise P/E ratio

• Firm X has expected revenues (or EBIT) of 5
  million per year. It has a capital structure with
  10 million in risk-free debt paying 4 and 4
  million shares which sell at 10/share. This
  implies that firm value is 50 million.
• 1. What are the RA, RD , and RE, and EPS
• 2. What is the P/E ratio?

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In-Class Exercise P/E ratio

• RA 5 /(4010)10

• EPS(5-100.04)/41.15/share
• P/E10/1.158.7

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Continued

• The CEO decides to boost the P/E ratio in order
  to increase shareholder value. The firm issues
  1 million new shares at 10/share and uses the
  proceeds to buy back all its debt.
• What are the EPS and P/E ratio?
• Can you evaluate the firms based on the P/E ratio
  and EPS?

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In-Class Exercise P/E ratio

• EPS(5-)/51/share
• P/E10/110
• In evaluating firms, we must focus on expected
  cash flows and risk, not P-E ratios and earnings
  per share

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In-Class Exercise Share repurchase
Profit Shares EPS P/E ratio Share price (per share)
500 100 5 8 40

• The firm now repurchases 20 shares.

Profit Shares EPS P/E ratio Share price (per share)
500 80 6.25 6.4 40

• Can you evaluate the firms based on the P/E ratio
  and EPS?

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Corporate Taxes and Firm Value MM Propositions I
and II (with Corporate Taxes)
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Roadmap

• Corporate Tax Shield
• MM Propositions I and II (with Taxes)
• The implication of optimal debt level under MM
  Propositions I and II (with Taxes)

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Capital Structure Corporate Taxes
The tax deductibility of interest increases the
total distributed income to both bondholders and
shareholders.
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Corporate Taxes and Value

• Interest Tax Shield
• Corporate Taxes Shied Tax savings resulting from
  deductibility of interest payments.
• More interest payments, more tax savings.
• What is the optimal level of debt?

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MM Proposition I (With Taxes)
The present value of this stream of cash flows is
VL
The present value of the first term is VU The
present value of the second term is TCD
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MM Proposition I (With Taxes)
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All equity-firm and levered firm
Taxes
Equity
TAXES
Equity
Debt
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MM Proposition II (With Taxes)

• We denote the expected returns on assets, debt
  and equity by RA, RD , and RE, respectively.
  Then
• Where D and E are the market values of debt and
  equity and

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MM Proposition II (With Taxes)

• Proof
• Let total market value of the assets, debt, and
  equity as A, D, and E, respectively

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MM Proposition II (with Taxes)

• 1. Increasing the debt level does not affect the
  riskiness of the assets, but it does increase the
  riskiness of the equity
• In the same firm, RD is always less than RE,
• This is because the debt has a higher priority
  and this is less risky. But the weighted sum of
  the returns of debt and equity is always a
  constant, and is equal to the return on assets, RA

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MM Proposition I and II (With Taxes)

• Firm Value
• Value of All Equity Firm PV Tax Shield

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Tax Shield Effect
Value of firm underMM with corporatetaxes and
debt
Value of firm (V)
Present value of taxshield on debt
VL VU TCD
Maximumfirm value
VU Value of firm with no debt
0
Debt (D)
D
Optimal amount of debt
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In-Class Exercise

• Ross, Westerfield, and Jaffe Question 2 (pp. 449)
• Firm has a total market value of 150,000 under
  no debt. EBIT (Earnings before interest and
  taxes) is 14,000 under normal case and is 40
  higher if in expansion and is 70 lower when it
  is recession. The corporate tax rate is 40.
  There are currently 2,500 shares outstanding.
• 1. Calculate EPS (Earnings per share)
• 2.Repeat 1 when the firms issues 60,000 to
  buyback the shares in the open market. Debt pays
  5 interest.

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Recession Normal Expansion
EBIT 4,200 14,000 19,600
Interest 0 0 0
Taxes 1,680 5,600 7,840
NI 2,520 8,400 11,760
EPS 1.01 3.36 4.70
?EPS 70 40
Recession Normal Expansion
EBIT 4,200 14,000 19,600
Interest 3,000 3,000 3,000
Taxes 480 4,400 6,640
NI 720 6,600 9,960
EPS .48 4.40 6.64
?EPS 89.09 50.91
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Corporate Taxes and Firm Value under the Presence
of Financial Distress Costs
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Roadmap

• What are the costs of financial distress?
• What are the direct and indirect costs of
  financial distress
• The implication of optimal debt level under MM
  Propositions I and II with significant costs of
  financial distress

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Corporate Taxes and Firm Value

• Interest Tax Shield
• Financial Distress Ccosts

• Costs of Financial Distress - Costs arising from
  bankruptcy or distorted business decisions before
  bankruptcy.
• Direct Costs Legal and administrative costs
• Indirect Costs Impaired ability to conduct
  business (e.g., lost sales)

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Financial Distress

• Costs of Financial Distress - Costs arising from
  bankruptcy or distorted business decisions before
  bankruptcy.
• Market Value Value if all Equity Financed
• PV Tax Shield
• - PV Costs of Financial Distress

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Tax Savings and Financial Distress Costs
Value of firm underMM with corporatetaxes and
debt
Value of firm (V)
Present value of taxshield on debt
VL VU TCD
Maximumfirm value
Present value offinancial distress costs

V Actual value of firm
VU Value of firm with no debt
0
Debt (D)
D
Optimal amount of debt
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Capital Structure and the Pie Model Revisited

• Taxes and bankruptcy costs can be viewed as just
  another claim on the cash flows of the firm.
• Let G and L stand for payments to the government
  and bankruptcy lawyers, respectively.
• VT E D G L
• The essence of the MM intuition is that VT
  depends on the cash flow of the firm capital
  structure just slices the pie.

E
D
G
L
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Taxes and Firm Value MM Proposition I (with
Corporate Taxes and Personal Taxes)
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Personal Taxes and Firm Value

• Interest payments are only taxed at the
  individual level since they are tax deductible by
  the corporation, so the bondholder receives
  (1-TB)
• Dividends face double taxation (firm and
  shareholder), which suggests a stockholder
  receives the net amount (1-TC) x (1-TS)

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Personal Taxes

• If TS TB then the firm should be financed
  primarily by debt (avoiding double tax).
• The firm is indifferent between debt and equity
  when
• (1-TC) x (1-TS) (1-TB)

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Asymmetric Information and Firm Value

Stock price falls
Stock-for-debt exchange offers
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New Equity Issues

• Background information
• There are two equally probable states of nature.
  The true state is revealed to management at t0
  and to investors at t1.
• The firm has no cash and the firms want to issue
  stock to raise 100.

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New Equity Issues
No New Equity Issue New Equity Good
250 350 Bad 130 230
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New Equity Issues

• Questions
• What is the firms expected value, with or
  without new equity issue?
• With new equity issue, what is the firms
  expected value that the old shareholders get, if
  the state is Good and if the state is Bad?
• If the managers have superior information about
  the firms prospect, should they issue new equity
  when the state is Good?

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New Equity Issues

• Firm Value (Issue no new equity)
• (0.5)(250 130) 190
• Firm Value (New equity)
• (0.5)(350 230) 290
• Note that old shareholders have a claim to the
  portion (190/290), or 65.5 of the value of the
  firm if it issues new equity.

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New Equity Issues

• Thus, if the firm issues equity and the state is
  good, old shareholders are worth
• (190/290)(350) 229.31
• And, if the firm issues equity and the state is
  bad, old shareholders are worth
• (190/290)(230) 150.69

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New Equity Issues

• Lets pull these numbers together, and see what
  happens if the management knows that the state is
  likely to be good or bad, and they are acting on
  behalf of the old shareholders
• Old shareholder payoffs
• Do Nothing Issue Equity
• Good news 250.00 229.31
• Bad news 130.00 150.69

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New Equity Issues

• The equilibrium payoffs
• Do Nothing Issue Equity
• Good news 250.00
• Bad news 230

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New Equity Issues

• The optimal strategy for old equity is to not
  issue equity if they know state will be good, and
  issue equity if the state will be bad!
• But, markets can figure this out too As a
  result, they will knock down the value of the
  firm when a new equity is announced!

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Conclusion

• What are the Modigliani-Miller Propositions I and
  II under perfect world?
• What are the implications of optimal debt level
  under Modigliani-Miller Propositions I and II?
• What are the Modigliani-Miller Propositions I and
  II with corporate taxes?
• What are the implications of optimal debt level
  under Modigliani-Miller Propositions I and II
  with corporate taxes?
• Why the stock price drops when there is an
  Stock-for-debt exchange offer?