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debt ratio using this normalized value.
In chapter 4, we noted that Aracruz™s synthetic rating of BBB, based upon the

interest coverage ratio, is much higher than its actual rating of B- and attributed
the difference to Aracruz being a Brazilian company, exposed to country risk.
Since we compute the cost of debt at each level of debt using synthetic ratings, we
run to risk of understating the cost of debt. The difference in interest rates
between the synthetic and actual ratings is 1.75% and we add this to the cost of
debt estimated at each debt ratio from 0% to 90%. You can consider this a
country-risk adjusted cost of debt for Aracruz.
Aracruz has a market value o equity of about $3 billion (9 billion BR). We used

the interest coverage ratio/ rating relationship for smaller companies to estimate
synthetic ratings at each level of debt. In practical terms, the rating that we assign
to Aracruz for any given interest coverage ratio will generally be lower than the
rating that Disney, a much larger company, would have had with the same ratio.

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Using the normalized operating income, we estimated the costs of equity, debt and capital
in table 8.13 for Aracruz at different debt ratios.
Table 8.13: Aracruz Cellulose: Cost of Capital, Firm Value and Debt Ratios
Firm
Debt Cost of Bond Interest rate Tax Cost of Debt Value in
BR
Ratio Beta Equity Rating on debt Rate (after-tax) WACC
0% 0.54 10.80% AAA 6.10% 34.00% 4.03% 10.80% 12,364
10% 0.58 11.29% AAA 6.10% 34.00% 4.03% 10.57% 12,794
20% 0.63 11.92% A 6.60% 34.00% 4.36% 10.40% 13,118
30% 0.70 12.72% BBB 7.25% 34.00% 4.79% 10.34% 13,256
40% 0.78 13.78% CCC 13.75% 34.00% 9.08% 11.90% 10,633
50% 0.93 15.57% CCC 13.75% 29.66% 9.67% 12.62% 9,743
60% 1.20 19.04% C 17.75% 19.15% 14.35% 16.23% 6,872
70% 1.61 24.05% C 17.75% 16.41% 14.84% 17.60% 6,177
80% 2.41 34.07% C 17.75% 14.36% 15.20% 18.98% 5,610
90% 4.82 64.14% C 17.75% 12.77% 15.48% 20.35% 5,138

The optimal debt ratio for Aracruz using the normalized operating income is 30%, a
shade below it™s current debt ratio of 30.82% but the cost of capital at the optimal is
almost identical to it™s current cost of capital. This indicates that Aracruz is at it™s optimal
debt ratio. There are two qualifiers we would add to this conclusion. The first is that the
volatility in paper and pulp prices will undoubtedly cause big swings in operating income
over time, and with it the optimal debt ratio. The second is that as an emerging market
company, Aracruz is particularly exposed to political or economic risk in Brazil in
particular and Latin America in general. . It is perhaps because of this fear of market
crises that Aracruz has a cash balance amounting to more than 7% of the total firm value.
In fact, the net debt ratio for Aracruz is only about 23%.

In Practice: Normalizing Operating Income
In estimating optimal debt ratios, it is always more advisable to use normalized
operating income, rather than current operating income. Most analysts normalize earnings
by taking the average earnings over a period of time (usually 5 years). Since this holds
the scale of the firm fixed, it may not be appropriate for firms that have changed in size
over time. The right way to normalize income will vary across firms:
1. For cyclical firms, whose current operating income may be overstated (if the
economy is booming) or understated (if the economy is in recession), the operating
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income can be estimated using the average operating margin over an entire economic
cycle (usually 5 to 10 years)
Normalized Operating Income = Average Operating Margin (Cycle) * Current Sales
2. For firms which have had a bad year in terms of operating income, due to firm-
specific factors (such as the loss of a contract), the operating margin for the industry
in which the firm operates can be used to calculate the normalized operating income:
Normalized Operating Income = Average Operating Margin (Industry) * Current Sales
The normalized operating income can also be estimated using returns on capital across an
economic cycle (for cyclical firms) or an industry (for firms with firm-specific problems),
but returns on capital are much more likely to be skewed by mismeasurement of capital
than operating margins.



Extensions of the Cost of Capital Approach

The cost of capital approach, which works so well for manufacturing firms that
are publicly traded, may need to be adjusted when we are called upon to compute optimal
debt ratios for private firms or for financial service firms, such as banks and insurance
companies.

Private Firms
There are three major differences between public and private firms in analyzing
optimal debt ratios. One is that unlike the case for publicly traded firms, we do not have a
direct estimate of the market value of a private firm. Consequently, we have to estimate
firm value before we move to subsequent stages in the analysis. The second difference
relates to the cost of equity and how we arrive at that cost. While we use betas to estimate
the cost of equity for a public firm, that usage might not be appropriate when we are
computing the optimal debt ratio for a private firm, where the owner may not be well
diversified. Finally, while publicly traded firms tend to think of their cost of debt in terms
of bond ratings and default spreads, private firms tend to borrow from banks. Banks
assess default risk and charge the appropriate interest rates.




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To analyze the optimal debt ratio for a private firm, we make the following
adjustments. First, we estimate the value of the private firm, by looking at how publicly
traded firms in the same business are priced by the market. Thus, if publicly traded firms
in the business have market values that are roughly three times revenues, we would
multiply the revenues of the private firm by this number to arrive at an estimated value.
Second, we continue to estimate the costs of debt for a private firm using a bond rating,
but the rating is a synthetic rating, based on interest coverage ratios. We tend to require
much higher interest coverage ratios to arrive at the same rating, to reflect the fact that
banks are likely to be more conservative in assessing default risk at small, private firms.

Illustration 8.6: Applying the Cost of Capital Approach to a Private Firm: Bookscape
Bookscapes as a private firm, has neither a market value for its equity nor a rating
for its debt. In chapter 4, we assumed that Bookscape would have a debt to capital ratio
of 16.90%, similar to that of publicly traded book retailers, and that the tax rate for the
firm is 40%. We computed a cost of capital based on that assumption. We also used a
“total beta”of 2.0606 to measure the additional risk that the owner of Bookscape is
exposed to because of his lack of diversification.
Cost of equity = Risfree Rate + Total Beta * Risk Premium
= 4% + 2.0606 * 4.82% = 13.93%
Pre-tax Cost of debt = 5.5% (based upon synthetic rating of BBB)
Cost of capital = 13.93% (.8310) + 5.5% (1-.40) (.1690) = 12.14%
In order to estimate the optimal capital structure for Bookscape, we made the following
assumptions:
While Bookscapes has no conventional debt outstanding, it does have one large

operating lease commitment. Given that the operating lease has 25 years to run
and that the lease commitment is $500,000 for each year, the present value of the
operating lease commitments is computed using Bookscape™s pre-tax cost of debt
of 5.5%:
Present value of Operating Lease commitments (in thousands) = $500 (PV of
annuity, 5.50%, 20 years) = 6,708




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Note that Bookscape™s pre-tax cost of debt is based upon their synthetic rating of
BBB, which we estimated in chapter 4.
Bookscape had operating income before taxes of $ 2 million in the most recent

financial year, after depreciation charges of $400,000 and operating lease
expenses of $ 600,000. Since we consider the present value of operating lease
expenses to be debt, we add back the imputed interest expense on the present
value of lease expenses to the earnings before interest and taxes to arrive at an
adjusted earnings before interest and taxes. For the rest of the analysis, operating
lease commitments are treated as debt and the interest expense estimated on the
present value of operating leases:
Adjusted EBIT (in ˜000s) = EBIT + Pre-tax cost of debt * PV of operating lease
expenses = $ 2,000+ .055 * $6,7078 = $2,369
To estimate the market value of equity, we looked at publicly traded book retailers

and computed an average price to earnings ratio of 16.31 for these firms. Applying
this multiple of earnings to Bookscape™s net income of $1,320,000 in 2003 yielded an
estimate of Bookscape™s market value of equity.
Estimated Market Value of Equity (in ˜000s) = Net Income for Bookscape * Average
PE for publicly traded book retailers = 1,320 * 16.31 = $21,525
The interest rates at different levels of debt will be estimated based upon a “synthetic”

bond rating. This rating will be assessed using table 8.14, which summarizes ratings
and default spreads over the long-term bond rate as a function of interest coverage
ratios for small firms that are rated by S&P as of January 2004.
Table 8.14: Interest Coverage Ratios, Rating and Default Spreads: Small Firms
Interest Coverage Ratio Rating Spread over T Bond Rate
> 12.5 AAA 0.35%
9.50-12.50 AA 0.50%
7.5 - 9.5 A+ 0.70%
6.0 - 7.5 A 0.85%
4.5 - 6.0 A- 1.00%
4.0 - 4.5 BBB 1.50%
3.5 “ 4.0 BB+ 2.00%
3.0 - 3.5 BB 2.50%
2.5 - 3.0 B+ 3.25%
2.0 - 2.5 B 4.00%

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1.5 - 2.0 B- 6.00%
1.25 - 1.5 CCC 8.00%
0.8 - 1.25 CC 10.00%
0.5 - 0.8 C 12.00%
< 0.5 D 20.00%
Note that smaller firms need higher coverage ratios than the larger firms to get the
same rating.
The tax rate used in the analysis is 40% and the long term bond rate at the time of this

analysis was 4%.
Based upon this information and using the same approach that we used for Disney, the
cost of capital and firm value are estimated for Bookscape at different debt ratios. The
information is summarized in Table 8.15.
Table 8.15: Costs of Capital and Firm Value for Bookscape
Interest
Debt Total Cost of Bond rate on Tax Cost of Debt Firm
Ratio Beta Equity Rating debt Rate (after-tax) WACC Value (G)
0% 1.84 12.87% AAA 4.35% 40.00% 2.61% 12.87% $25,020
10% 1.96 13.46% AAA 4.35% 40.00% 2.61% 12.38% $26,495
20% 2.12 14.20% A+ 4.70% 40.00% 2.82% 11.92% $28,005
30% 2.31 15.15% A- 5.00% 40.00% 3.00% 11.51% $29,568
40% 2.58 16.42% BB 6.50% 40.00% 3.90% 11.41% $29,946
50% 2.94 18.19% B 8.00% 40.00% 4.80% 11.50% $29,606
60% 3.50 20.86% CC 14.00% 39.96% 8.41% 13.39% $23,641
70% 4.66 26.48% CC 14.00% 34.25% 9.21% 14.39% $21,365
80% 7.27 39.05% C 16.00% 26.22% 11.80% 17.25% $16,745
90% 14.54 74.09% C 16.00% 23.31% 12.27% 18.45% $15,355

The firm value is maximized (and the cost of capital is minimized) at a debt ratio of 40%,
though the firm value is relatively flat between 30% and 50%. The default risk increases
significantly at the optimal debt ratio, as evidenced by the synthetic bond rating of BB,
and the total beta increases to 2.58.

In Practice: Optimal Debt Ratios for Private Firms
Although the trade off between the costs and benefits of borrowing remain the
same for private and publicly traded firms, there are differences between the two kinds of
firms that may result in private firms borrowing less money.



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Increasing debt increases default risk and expected bankruptcy cost much more

substantially for small private firms than for larger publicly traded firms. This is
partly because the owners of private firms may be exposed to unlimited liability, and
partly because the perception of financial trouble on the part of customers and
suppliers can be much more damaging to small, private firms.
Increasing debt yields a much smaller advantage in terms of disciplining managers in

the case of privately run firms, since the owners of the firm tend to be the top
managers, as well.
Increasing debt generally exposes small private firms to far more restrictive bond

covenants and higher agency costs than it does large publicly traded firms.
The loss of flexibility associated with using excess debt capacity is likely to weigh

much more heavily on small, private firms than on large, publicly traded firms, due to
the former™s lack of access to public markets.
All the factors mentioned above would lead us to expect much lower debt ratios at small
private firms.



8.5. ˜: Going Public: Effect on Optimal Debt Ratio
Assume that Bookscape is planning to make an initial public offering in six months. How
would this information change your assessment of the optimal debt ratio?
a. It will increase the optimal debt ratio because publicly traded firms should be able to
borrow more than private businesses
b. It will reduce the optimal debt ratio because only market risk counts for a publicly
traded firm
c. It may increase or decrease the optimal debt ratio, depending on which effect
dominates




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Banks and Insurance Companies
There are several problems in applying the cost of capital approach to financial
service firms, such as banks and insurance companies20. The first is that the interest
coverage ratio spreads, which are critical in determining the bond ratings, have to be

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