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(as in the leveraged buyout of RJR Nabisco) if debt ratios are increased.
15 This will have the effect of reducing interest cost, when debt is increased, and thus interest coverage
ratios. This will lead to higher ratings, at least in the short term, and a higher optimal debt ratio.

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8.8. The cost of capital, which is 9.15%, when the firm is unlevered, decreases as the firm
initially adds debt, reaches a minimum of 8.50% at 30% debt and then starts to increase
again.
Table 8.8: Cost of Equity, Debt and Capital, Disney
Cost of Debt (after-
Debt Ratio Cost of Equity tax) Cost of Capital
0% 9.15% 2.73% 9.15%
10% 9.50% 2.73% 8.83%
20% 9.95% 3.14% 8.59%
30% 10.53% 3.76% 8.50%
40% 11.50% 8.25% 10.20%
50% 13.33% 13.00% 13.16%
60% 15.66% 13.50% 14.36%
70% 19.54% 13.86% 15.56%
80% 27.31% 14.13% 16.76%
90% 50.63% 14.33% 17.96%

The optimal debt ratio is shown graphically in Figure 8.3.




To illustrate the robustness of this solution to alternative measures of levered betas, we
re-estimate the costs of debt, equity and capital under the assumption that debt bears
some market risk, and the results are summarized in Table 8.9.
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Table 8.9: Costs of Equity, Debt and Capital with Debt carrying Market Risk- Disney
Debt Beta of Cost of Interest rate Tax Cost of Debt Beta of Cost of
Ratio equity Equity on debt Rate (after-tax) debt Capital
0% 1.07 9.15% 4.35% 37.30% 2.73% 0.02 9.15%
10% 1.14 9.50% 4.35% 37.30% 2.73% 0.02 8.82%
20% 1.23 9.91% 5.00% 37.30% 3.14% 0.05 8.56%
30% 1.33 10.39% 6.00% 37.30% 3.76% 0.10 8.40%
40% 1.37 10.59% 12.00% 31.24% 8.25% 0.41 9.65%
50% 1.43 10.89% 16.00% 18.75% 13.00% 0.62 11.94%
60% 1.63 11.86% 16.00% 15.62% 13.50% 0.62 12.84%
70% 1.97 13.48% 16.00% 13.39% 13.86% 0.62 13.74%
80% 2.64 16.72% 16.00% 11.72% 14.13% 0.62 14.64%
90% 4.66 26.44% 16.00% 10.41% 14.33% 0.62 15.54%

If the debt holders bear some market risk16, the cost of equity is lower at higher levels of
debt and Disney™s optimal debt ratio is still 30%, which is unchanged from the optimal
calculated under the conventional calculation of the levered beta.

IV. Firm Value and Cost of Capital
The reason for minimizing the cost of capital is that it maximizes the value of the
firm. To illustrate the effects of moving to the optimal on Disney™s firm value, we start
off with a simple valuation model, designed to value a firm in stable growth.
Firm Value = Cashflow to Firm (1 + g) / (Cost of Capital -g)
where
g = Growth rate in the cashflow to the firm (in perpetuity)
We begin by computing Disney™s current free cash flow using its current earnings before
interest and taxes of $2,805 million, its tax rate of 37.30%, and its reinvestment in 1998
in working capital and net fixed assets:
EBIT (1- tax rate) = 2805 (1 “ 0.373) = $ 1,759
+ Depreciation & Amortization = $ 1,077



16 To estimate the beta of debt, we used the default spread at each level of debt, and assumed that 25% this
risk is market risk. Thus, at a C rating, the default spread is 12%. Based upon the market risk premium of
4.82% that we used elsewhere, we estimated the beta at a C rating to be:
Imputed Debt Beta at a C rating =(12%/4.82%)*0.25 = 0.62
The assumption that 25% of the default risk is market risk is made to ensure that at a D rating, the beta of
debt (1.02) is roughly equal to the unlevered beta of Disney (1.09).

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- Capital Expenditures = $ 1,049
- Change in Non-cash Working Capital $ 64
Free Cash Flow to the Firm = $ 1,722
The market value of the firm at the time of this analysis was obtained by adding up the
estimated market values of debt and equity:
Market Value of Equity = $ 55,101
+ Market Value of Debt = $ 14,668
= Value of the Firm $ 69,769
Based upon the current cost of capital of 8.59%, we solve for the implied growth rate:
Growth rate = (Firm Value * Cost of Capital- CF to Firm)/(Firm Value + CF to Firm)
= (69,769*.0859-1,722)/(69,769+1,722) = .0598 or 5.98%
Now assume that Disney shifts to 30% Debt and a WACC of 8.50%. The firm can now
be valued using the following parameters:
Cash flow to Firm = $1,722 million
WACC = 8.50%
Growth rate in Cash flows to Firm = 5.98%
Firm Value = 1,722 *1.0598/(.0850-.0598) = $ 72,419 million
The value of the firm will increase from $69,769 million to $72,419 million if the firm
moves to the optimal debt ratio:
Increase in firm value = $ 72,419 mil - $ 69,769 mil = $ 2,650 million
With 2047.6 million shares outstanding, assuming that stockholders can evaluate the
effect of this refinancing, we can calculate the increase in the stock price:
Increase in stock price = Increase in Firm Value / Number of shares outstanding
= $ 2,650/2,047.6 = $ 1.29 /share
Since the current stock price is $ 26.91, the stock price can be expected to increase to
$28.20, which translates into about a 5% increase in the price.
The limitation of this approach is that the growth rate that we have assumed in
perpetuity may be too high; a good rule of thumb for stable growth is that it should not




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exceed the riskfree rate17. We can use an alternate and more conservative approach to
estimate the change in firm value. Consider first the change in the cost of capital from
8.59% to 8.50%, a drop of 0.09%. This change in the cost of capital should result in the
firm saving on its annual cost of financing its business:
Cost of financing Disney at existing debt ratio = 69,769 * .0859 = $5,993 million
Cost of financing Disney at optimal debt ratio = 69,769 * .0850 = $5,930 million
Annual savings in cost of financing =$5,993 million - $5,930 million = $ 63 million
Note that most of these savings are implicit rather than explicit. 18 The present value of
these savings over time can now be estimated using the new cost of capital of 8.50% and
the capped growth rate of 4% (set equal to the riskfree rate);
Present value of savings in perpetuity = Expected savings next year / (Cost of capital “ g)
= 63 /(.085-.04) = $ 1,400 million
Since this increase in value accrues entirely to stockholders, we can estimate the increase
in value per share by dividing by the total number of shares outstanding:
Increase in value per share = $ 1,400/2047.6 = $ 0.68
New stock price = $26.91+ $0.68 = $ 27.59
Using this approach, we estimated the firm value and cost of capital at different debt
ratios in Figure 8.4.




17 No company can grow at a rate higher than the long term nominal growth rate of the economy. The
riskfree rate is a reasonable proxy for the long term nominal growth rate in the economy because it is
composed of two components “ the expected inflation rate and the expected real rate of return. The latter
has to equate to real growth in the long term.
18 The cost of equity is an implicit cost and does not show up in the income statement of the firm. The
savings in the cost of capital are therefore unlikely to show up as higher aggregate earnings. In fact, as the
firm™s debt ratio increases the earnings will decrease but the per share earnings will increase.

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Figure 8.4: Disney Firm Value at Different Debt Ratios

$100,000



$80,000



$60,000



$40,000
Value (millions $)




$20,000



$-
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

$(20,000)



$(40,000)



$(60,000)
Debt Ratio

Firm Value Change due to shift in leverage


Since the asset side of the balance sheet is kept fixed and changes in capital
structure are made by borrowing funds and repurchasing stock, this analysis implies that
the stock price would increase to $27.59 on the announcement of the repurchase. Implicit
in this analysis is the assumption that the increase in firm value will be spread evenly
across both the stockholders who sell their stock back to the firm and those who do not.
To the extent that stock can be bought back at the current price of $ 26.91 or some value
lower than $ 27.59, the change in stock price will be larger. For instance, if Disney could
have bought stock back at the existing price of $ 26.91, the increase19 in value per share
would be $ 0.77.


8.3. ˜: Rationality and Stock Price Effects
Assume that Disney does make a tender offer for it™s shares but pays $28 per share. What
will happen to the value per share for the shareholders who do not sell back?



19 To compute this change in value per share, we first compute how many shares we would buy back with
the additional debt taken on of $ 6,263 billion (Debt at 30% optimal “ Current Debt) and the stock price of
$ 26.91. We then divide the increase in firm value of $ 1,400 million by the remaining shares outstanding:
Change in stock price = $ 1400 million / (2047.6 “ (6263/26.91)) = $ 0.77 per share

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a. The share price will drop below the pre-announcement price of $26.91
b. The share price will be between $26.91 and the estimated value (above) or $27.59
c. The share price will be higher than $27.59



This spreadsheet allows you to compute the optimal debt ratio firm value for any
firm, using the same information used for Disney. It has updated interest coverage ratios
and spreads built in.




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Table 8.10: Cost of Capital Worksheet for Disney

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00%
D/(D+E)
0.00% 11.11% 25.00% 42.86% 66.67% 100.00% 150.00% 233.33% 400.00% 900.00%
D/E
$0 $6,977 $13,954 $20,931 $27,908 $34,885 $41,861 $48,838 $55,815 $62,792
$ Debt
1.07 1.14 1.23 1.35 1.56 1.93 2.42 3.22 4.84 9.67
Beta


$3,882 $3,882 $3,882 $3,882 $3,882 $3,882 $3,882 $3,882 $3,882 $3,882
EBITDA
$1,077 $1,077 $1,077 $1,077 $1,077 $1,077 $1,077 $1,077 $1,077 $1,077
Depreciation
$2,805 $2,805 $2,805 $2,805 $2,805 $2,805 $2,805 $2,805 $2,805 $2,805
EBIT
∞ 9.24 4.02 2.23 0.84 0.50 0.42 0.36 0.31 0.28
Interest
∞ 0.38 0.17 0.10 0.03 -0.02 -0.03 -0.04 -0.05 -0.06
Pre-tax Int. cov
AAA AAA A- BB+ CCC C C C C C
Likely Rating
4.35% 4.35% 5.00% 6.00% 12.00% 16.00% 16.00% 16.00% 16.00% 16.00%
Pre-tax cost of debt
37.30% 37.30% 37.30% 37.30% 31.24% 18.75% 15.62% 13.39% 11.72% 10.41%
Adj Marginal Tax Rate


9.15% 9.50% 9.95% 10.53% 11.50% 13.33% 15.66% 19.54% 27.31% 50.63%
Cost of equity
2.73% 2.73% 3.14% 3.76% 8.25% 13.00% 13.50% 13.86% 14.13% 14.33%

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