mm proposition

Corporate Finance Lecture Note 1 1

Valuation under MM


MM Proposition I (No Taxes)


Roadmap

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

Assumption of Modigliani-Miller Propositions I Modigliani-Miller Propositions I


Capital Structure and the Pie

• The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity.

V = D + E

• If the goal of the firm’s 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?

Value of the Firm

S DE


MM Proposition I (No Taxes) Debt Policy is Irrelevant

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

SE DS

BE

B D=


Modigliani-Miller Proposition I (No Taxes)

• The total value of the securities issued by a firm is independent of the firm’s choice of capital structure.

• The firm’s 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.


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, E+D).

• 5. Perfect and complete capital markets• 6. Symmetric information (No black box)


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 firm:VL = VU


Homemade Leverage: An ExampleRecessionExpected 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: 32

200,1$

800$

E

D


Homemade (Un)Leverage: An Example

RecessionExpected ExpansionEPS of Levered Firm $1.50 $5.67 $9.83Earnings for 24 shares $36 $136 $236Plus interest on $800 (8%)$64 $64 $64Net Profits $100 $200 $300ROE (Net Profits / $2,000) 5% 10% 15%Buying 24 shares of an otherwise identical levered firm along with some of the firm’s debt gets us to the ROE of the unlevered firm.This is the fundamental insight of M&M


In-Class Exercise

• 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.


In-Class Exercise

Shares repurchased = 1,000 shares ?


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


MM Proposition II (No Taxes)


Roadmap

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


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

E A A DR = R + (R R )D

E

A

EBIT EBITR =

Market value of total assets Market value of debt+equity


Modigliani-Miller Proposition II (No Taxes)

• Proof:• Let total market value of the assets, debt, and

equity as A, D, and E, respectively

A D E

A D E D E

A D E

CF CF CF

A A Aby MMI, A=D+E, so

CF CF CF CF CFD E( ) ( ),

A D+E D+E D+ED E

Thus, R = R ( )+R ( )D+E D+E

Algebraic rearrangement gives the result

EBIT

D E



Debt-to-equity Ratio

Cos

t of

capi

tal:

R (

%)

( )E A A D

DR R R R

E

D

E

RA

RD

RA

RD



• 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


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.”


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?



• RA= $5 /(40+10)=10%

E A A DR = R + (R R ) 10% 10 / 40*(10% 4%) 11.5%D

E

EPS=(5-10*0.04)/4=$1.15/shareP/E=10/1.15=8.7


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?



• EPS=(5-)/5=$1/shareP/E=10/1=10

• In evaluating firms, we must focus on expected cash flows and risk, not P-E ratios and earnings per share


In-Class Exercise: Share repurchase

• The firm now repurchases 20 shares.

Profit Shares EPS P/E ratio Share price (per share)

500 100 5 8 40

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?


Corporate Taxes and Firm Value

MM Propositions I and II (with Corporate Taxes)


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)


Capital Structure & Corporate Taxes

Income Statement of

Firm U

Income Statement of

Firm L

Earnings before interest and taxes $1,000 $1,000Interest paid to bondholders - 80 Pretax income 1,000 920 Tax at 35% 350 322 Net income to stockholders 650 598

Total income to both bondholders and stockholders $0+650=$650 $80+598=$678

Interest tax shield (.35 x interest) $0 $28

The tax deductibility of interest increases the total distributed income to both bondholders and shareholders.


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?


MM Proposition I (With Taxes)

L U CV V T D

The total cash flow to debt holders, and equity holders

( ) (1 )D C DEBIT R D T R D

The present value of this stream of cash flows is VL

Clearly ( ) (1 )D C DEBIT R D T R D

The present value of the first term is VU

The present value of the second term is TCD

(1 ) (1 )C D C DEBIT T R D T R D

(1 )C D D C DEBIT T R D R DT R D


MM Proposition I (With Taxes)The present value of this stream of cash flows is

Assuming that: (1) the the positive tax bracket is perpetual and

(2) assume that the it has the same risk as the interest on the debt

D c c

D c

D

R DT DT

R DT

R cDT

The present value of this stream of cash flows (1 ) is

Assuming that: (1) the the EBIT is perpetual and

(2) : The cost of capital to an all-equity firm.

(1 )

C U

A

CU

A

EBIT T V

R

EBIT TV

R

All equity-firm and levered firm


EquityTAXES Equity

Taxes

Debt


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

E A A DR = R + (1 )(R R )C

DT

E

A

EBIT EBITR =

Market value of total assets Market value of debt+equity


MM Proposition II (With Taxes)• Proof:• Let total market value of the assets, debt, and equity as A, D, and

E, respectively

L U U

D D D

U U U

D E

U U

A D EU U

by MMI with taxes, V =D+E=V + D, soV +(1- )D

EBIT(1 ) CF (EBIT-CF )(1 ) CFD+E D+E( ) ( )

V V D+E V D+E

CF (1 ) CFD+E D D+E E( ) ( ),

V D D+E V E D+E

D EThus, R = (1 )R +R ( )

V V

Algebraic rearrangement g

C C

C C C

C

C

T E T

T T T

T

T

UE A D E A D

U U

U E A A D

ives the result

VE D DR ( ) R (1 )R ,R R (1 )R

V V E E

DPlug in V +(1- )D, R R (1 )(R -R )

E

C C

C C

T T

E T T


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


MM Proposition I and II (With Taxes)

Firm Value =

Value of All Equity Firm + PV Tax Shield

E A A D

Cost of equity capital

R = R + (1 )(R R )C

DT

E


Tax Shield Effect

Debt (D)

Value of firm (V)

0

Present value of taxshield on debt

Value of firm underMM with corporatetaxes and debt

VL = VU + TCD

VU = Value of firm with no debt

D*

Maximumfirm value

Optimal amount of debt


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.


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


Corporate Taxes and Firm Value under the Presence of

Financial Distress Costs


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


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)


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


Tax Savings and Financial Distress Costs

Debt (D)

Value of firm (V)

0

Present value of taxshield on debt

Present value offinancial distress costs

Value of firm underMM with corporatetaxes and debt

VL = VU + TCD

V = Actual value of firm

VU = Value of firm with no debt

D*

Maximumfirm value

Optimal amount of debt


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 M&M intuition is that VT depends on the cash flow of the firm; capital structure just slices the pie.

E

G

D

L


Taxes and Firm Value MM Proposition I (with

Corporate Taxes and Personal Taxes)


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)


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)


Asymmetric Information and Firm Value

Stock-for-debtexchange offers

Stock price falls


New Equity Issues

• Background information:

1. There are two equally probable states of nature. The true state is revealed to management at t=0 and to investors at t=1.

2. The firm has no cash and the firms want to issue stock to raise $100.


New Equity Issues

No New EquityNo New Equity Issue Issue New EquityNew Equity

GoodGood $250$250 $350$350

Bad Bad $130$130 $230$230


New Equity IssuesQuestions:

What is the firm’s expected value, with or without new equity issue?

With new equity issue, what is the firm’s 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 firm’s prospect, should they issue new equity when the state is Good?


New Equity Issues

Firm Value (Issue no new equity) Firm Value (Issue no new equity) = =

(0.5)(250 + 130) = $190(0.5)(250 + 130) = $190

Firm Value (New equity) Firm Value (New equity) = =

(0.5)(350 + 230) = $290(0.5)(350 + 230) = $290

Note that old shareholders have a claim Note that old shareholders have a claim to the portion (190/290), or 65.5% of the to the portion (190/290), or 65.5% of the value of the firm if it issues new equity.value of the firm if it issues new equity.


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


New Equity IssuesLet’s 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:Old shareholder payoffs:

Do NothingDo Nothing Issue Issue EquityEquity

Good newsGood news $250.00$250.00 $229.31$229.31

Bad newsBad news $130.00$130.00 $150.69$150.69


New Equity Issues

• The equilibrium payoffs:

Do Nothing Issue Equity

• Good news $250.00

• Bad news $230 $230


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!


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?

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