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.