choosing the optimal capital structure-example chapter 16

7/22/2019 Choosing the Optimal Capital Structure-Example Chapter 16

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Choosing the Optimal CapitalStructure: Example

Company is all-equity financed.

Expected EBIT = $500,000.

Firm expects zero growth. 100,000 shares outstanding; Re = 12%;

P0 = $25; T = 40%;

b = 1.0; RRF = 6%;

RPM = 6%.


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Choosing the Optimal Capital Structure

Company has decided to recapitalizeits capital structure by borrowing and

repurchasing its shares


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Estimates of Cost of Debt

% financed with debt, wd Rd

0% -

20% 8.0%30% 8.5%

40% 10.0%

50% 12.0%Debt would be issued to repurchase stock, butthe cost of debt will increase as the financialrisk increases


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Question 1

(1.) For each capital structure underconsideration, calculate the levered beta, the

cost of equity, and the WACC.

Hamada developed his equation by merging

the CAPM with the Modigliani-Miller model.We use the model to determine beta at

different amount of financial leverage, and

then use the betas associated with different

debt ratios to find the cost of equityassociated with those debt ratios. Here is the

Hamada equation: bL = bU [1 + (1 - T)(D/E)]


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The Cost of Equity at Different Levels

of Debt: Hamadas Equation

MM theory implies that beta changes withleverage.

bU

is the beta of a firm when it has no debt(the unlevered beta)

bL = bU [1 + (1 - T)(D/E)]


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The Cost of Equity for wd = 20%

Use Hamadas equation to find beta:

bL= bU [1 + (1 - T)(D/E)]

= 1.0 [1 + (1-0.4) (20% / 80%) ]= 1.15

Use CAPM to find the cost of equity:

Re= RRF + bL (RPM)= 6% + 1.15 (6%) = 12.9%


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Cost of Equity vs. Leverage

wd D/E bL Re

0% 0.00 1.000 12.00%

20% 0.25 1.150 12.90%

30% 0.43 1.257 13.54%

40% 0.67 1.400 14.40%50% 1.00 1.600 15.60%


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The WACC for wd = 20%

WACC = wd (1-T) Rd + we Re WACC = 0.2 (1 0.4) (8%) + 0.8 (12.9%)

WACC = 11.28%

Repeating this procedure for all capital

structures, then:


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WACC vs. Leverage

wd Rd Re WACC

0% 0.0% 12.00% 12.00%

20% 8.0% 12.90% 11.28%

30% 8.5% 13.54% 11.01%

40% 10.0% 14.40% 11.04%50% 12.0% 15.60% 11.40%


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Cost of Equity vs. Leverage

Cost of Equity and Leverage

0%5%

10%15%20%25%30%35%40%45%

50%55%60%65%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Debt-to- Value

Return

s

RL RU

LeverageEffect


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Effects of Leverage on Cost of Equityand WACC

Effects of Leverage on WACC and cost of Equity

0%5%

10%15%20%25%30%35%40%45%50%55%60%65%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Debt-to Value

Returns

RL WACC


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Question 2

(2.) What is the corporate value, the valueof the debt that will be issued, and theresulting market value of equity.


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Calculating Corporate Value andEquity

As the table shows, beta rises with financialleverage. With beta specified, we can determinethe effects of leverage on the cost of equity andthen on the WACC.

We know the EBIT for each capital structure, sowe can calculate the free cash flow. Sincegrowth is zero, there will be no requiredinvestment in capital, and the FCF is equal toNOPAT.

Free cash flow (FCF) =$300,000 With the estimated FCF and WACC, we can find

the corporate value, V. Since growth is zero, V:


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Corporate Value at Different WACC

wd r

d r

s WACC V

0% 0.0% 12.00% 12.00% 2,500,000

20% 8.0% 12.90% 11.28% 2,659,574

30% 8.5% 13.54% 11.01% 2,724,796

40% 10.0% 14.40% 11.04% 2,717,391

50% 12.0% 15.60% 11.40% 2,631,579


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Corporate Value for wd = 20%

Vop = FCF(1+g) / (WACC-g)

g=0, so investment in capital is zero; so

FCF = NOPAT = EBIT (1-T). NOPAT = ($500,000)(1-0.40) = $300,000.

Vop = $300,000 / 0.1128 = $2,659,574.


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Effects of Leverage: The Trade-Off Models

Effects of Leverage: The Trade-Off Models

$0

$1,000,000

$2,000,000

$3,000,000

D/V

FrimValu

e

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

WACC

w d Value WACC


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Debt for wd = 20%

D = wd V

= 0.2 ($2,659,574) = $531,915.

Question 3- What is the dollar value of debt?


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Value of Debt

wd Debt, D

0% $0

20% $531,91530% $817,439

40% $1,086,957

50% $1,315,789


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Question 4

Calculate the market value of equity, theprice per share, the number of sharesrepurchased, and the remaining shares.

Considering only the capital structuresunder analysis, what is the optimal capitalstructure?


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Anatomy of a Recap: BeforeIssuing Debt

Before Debt

Vop $2,500,000

+ ST Inv. 0

VTotal $2,500,000

Debt 0

S $2,500,000

n 100,000

P $25.00

Total shareholder

wealth: S + Cash $2,500,000


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Issue Debt (wd = 20%), ButBefore Repurchase

WACC decreases to 11.28%.

Vop increases to $2,659,574.

Firm temporarily has short-terminvestments of $531,915 (until it usesthese funds to repurchase stock).

Debt is now $531,915.


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Anatomy of a Recap: AfterDebt, but Before Repurchase

Before DebtAfter Debt,Before Rep.

Vop $2,500,000 $2,659,574

+ ST Inv. 0 531,915

VTotal $2,500,000 $3,191,489

Debt 0 531,915

S $2,500,000 $2,659,574

n 100,000 100,000P $25.00 $26.60

Total shareholder

wealth: S + Cash $2,500,000 $2,659,574


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After Issuing Debt, BeforeRepurchasing Stock

Stock price increases from $25.00 to$26.60.

Wealth of shareholders (due to ownershipof equity) increases from $2,500,000 to$2,659,574.


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The Repurchase: No Effect onStock Price

The announcement of an intended repurchase mightsend a signal that affects stock price, and the previouschange in capital structure affects stock price, but therepurchase itself has no impact on stock price.

If investors thought that the repurchase would increase the stockprice, they would all purchase stock the day before, which woulddrive up its price.

If investors thought that the repurchase would decrease thestock price, they would all sell short the stock the day before,which would drive down the stock price.


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Remaining Number of SharesAfter Repurchase

D0 is amount of debt the firm initially has, D isamount after issuing new debt.

If all new debt is used to repurchase shares,

then total dollars used equals (D D0) = ($531,915 - $0) = $531,915. n0 is number of shares before repurchase, n is

number after. Total shares remaining:

n = n0 (D D0)/P = 100,000 - $531,915/$26.60 n = 80,000


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Anatomy of a Recap: AfterRupurchase

Before DebtAfter Debt,Before Rep. After Rep.

Vop $2,500,000 $2,659,574 $2,659,574

+ ST Inv. 0 531,915 0

VTotal $2,500,000 $3,191,489 $2,659,574

Debt 0 531,915 531,915

S $2,500,000 $2,659,574 $2,127,660

n 100,000 100,000 80,000

P $25.00 $26.60 $26.60

Total shareholder

wealth: S + Cash $2,500,000 $2,659,574 $2,659,574


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Key Points

ST investments fall because they are used torepurchase stock.

Stock price is unchanged. Value of equity falls from $2,659,574 to

$2,127,660 because firm no longer owns the STinvestments.

Wealth of shareholders remains at $2,659,574because shareholders now directly own the

funds that were held by firm in ST investments.


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Shortcuts

The corporate valuation approach willalways give the correct answer, but thereare some shortcuts for finding S, P, and n.

Shortcuts on next slides.


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Calculating S, the Value ofEquity after the Recap

S = (1 wd) Vop

At wd = 20%:

S = (1 0.20) $2,659,574 S = $2,127,660.


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Calculating P, the Stock Priceafter the Recap

P = [S + (D D0)]/n0

P = $2,127,660 + ($531,915 0)

100,000

P = $26.596 per share.


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Number of Shares after aRepurchase, n

# Repurchased = (D - D0) / P

n = n0 - (D - D0) / P

# Rep. = ($531,915 0) / $26.596 # Rep. = 20,000.

n = 100,000 20,000

n = 80,000.


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Price per Share vs. Leverage

wd S P n

0% $2,500,000 $25.00 100,000

20% $2,127,660 $26.60 80,000

30% $1,907,357 $27.25 70,000

40% $1,630,435 $27.17 60,000

50% $1,315,789 $26.32 50,000


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Optimal Capital Structure

wd = 30% gives:

Highest corporate value

Lowest WACC

Highest stock price per share

But wd = 40% is close. Optimal range ispretty flat.

choosing the optimal capital structure-example chapter 16

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