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51 The default spreads for bonds issued by banks can be very different from the spreads for industrial
companies. The default spread for an AA- rated financial service company was much higher at the time of
this analysis than the default spread for an AA- rated manufacturing company.
52 With Araacruz, one troublesome aspect of the pre-tax cost of debt is that it is lower than the rate at which
the Brazilian government can borrow. While there are some cases where we would add the default spread
of the country to that of the firm to get to a pre-tax cost of debt, Aracruz may be in a stronger position to
borrow in U.S. dollars than the Brazilian government because it sells its products in a global market and
gets paid in dollars.
53 To estimate the interest coverage ratio here, we added the operating lease expense back to both the
numerator and the denominator:
Interest coverage ratio = (EBIT + Operating lease expense)/ (Interest expense + Operating lease expense)
This is a conservative estimate of the rating. In reality, only a portion of the operating lease expense should
be considered as interest expense. This, in turn, will increase the rating and improve the rating. In fact, the
synthetic rating with this approach will be A.

Disagreement between ratings agencies: While the ratings are consistent across

ratings agencies for many firms, there are a few firms where the ratings agencies
disagree with one agency assigning a much higher or lower rating to the firm than the
Multiple bond ratings for same firm: Since ratings agencies rate bonds, rather than

firms, the same firm can have many bond issues with different ratings depending
upon how the bond is structured and secured.
Lags or Errors in the Rating Process: Ratings agencies make mistakes and there is

evidence that ratings changes occur after the bond market has already recognized the
change in the default risk.
It is a good idea to estimate synthetic ratings even for firms that have actual ratings. If
there is disagreement between ratings agencies or a firm has multiple bond ratings, the
synthetic rating can operate as a tie-breaker. If there is a significant difference between
actual and synthetic ratings and there is no fundamental reason that can be pinpointed for
the difference, the synthetic rating may be providing an early signal of a ratings agency
We computed the synthetic ratings for Disney and Aracruz using the interest
coverage ratios:
Disney: Interest coverage ratio = 2,805/758 = 3.70 Synthetic rating = A-
Aracruz: Interest coverage ratio = 888/339= 2.62 Synthetic rating = BBB
While Disney™s synthetic rating is close to it™s actual rating of BBB+, the synthetic rating
for Aracruz is much higher than it™s rating of B-. The reason for the discrepancy lies in
the fact that Aracruz has two ratings “ one for its local currency borrowings of BBB- and
one for its dollar borrowings of B+. We used the latter to estimate the cost of debt
because almost all of Aracruz™s debt is dollar debt. You can also consider the difference
to be a reflection of the riskiness of Brazil as a country and the penalty that Aracruz pays
for being a Brazilian company. In fact, we can quantify this difference by measuring the
difference in interest rates (in US dollar terms) of Aracruz with the synthetic and actual
Cost of debt with actual rating of B- : 4% + 3.25% = 7.25%
Cost of debt with synthetic rating of BBB: 4% + 1.50% = 5.50%

Country default penalty attached to Aracruz debt = 7.25% - 5.50% = 1.75%

Calculating the Cost of Preferred Stock
Preferred stock shares some of the characteristics of debt - the preferred dividend
is pre-specified at the time of the issue and is paid out before common dividend -- and
some of the characteristics of equity - the payments of preferred dividend are not tax
deductible. If preferred stock is viewed as perpetual, the cost of preferred stock can be
written as follows:
kps = Preferred Dividend per share/ Market Price per preferred share
This approach assumes that the dividend is constant in dollar terms forever and that the
preferred stock has no special features (convertibility, callability etc.). If such special
features exist, they will have to be valued separately to come up with a good estimate of
the cost of preferred stock. In terms of risk, preferred stock is safer than common equity
but riskier than debt. Consequently, it should, on a pre-tax basis, command a higher cost
than debt and a lower cost than equity.

Illustration 4.13: Calculating the Cost Of Preferred Stock: Disney and Deutsche Bank
Both Disney and Deutsche Bank have preferred stock outstanding. THe preferred
dividend yields on the issues are computed in March 2004 in table 4.14:
Table 4.14: Cost of Preferred Stock
Company Preferred Stock Price Annual Dividend Yield
Disney $ 26.74 $ 1.75 1.75/26.74 = 6.54%
Deutsche Bank 103.75 Euros 6.60 Euros 6.6/103.75 = 6.36%

Notice that the cost of preferred stock for Disney is higher than its pre-tax cost of debt of
5.25% and is lower than its cost of equity of 10%. For Deutsche Bank as well, the cost of
preferred stock is higher than its pre-tax cost of debt (5.05%) and is lower than its cost of
equity of 8.76%. For both firms, the market value of preferred stock is so small relative to
the market values of debt and equity that it makes almost no impact on the overall cost of

˜ 4.11: Why do companies issue preferred stock?

Which of the following are “good” reasons for a company issuing preferred stock?
a. Preferred stock is cheaper than equity
b. Preferred stock is treated as equity by the ratings agencies and regulators
c. Preferred stock is cheaper than debt
d. Other:

Calculating the Cost of Other Hybrid Securities
In general terms, hybrid securities share some of the characteristics of debt and
some of the characteristics of equity. A good example is a convertible bond, which can be
viewed as a combination of a straight bond (debt) and a conversion option (equity).
Instead of trying to calculate the cost of these hybrid securities individually, they can be
broken down into their debt and equity components and treated separately.
In general, it is not difficult to decompose a hybrid security that is publicly traded
(and has a market price) into debt and equity components. In the case of a convertible
bond, this can be accomplished in two ways:
An option pricing model can be used to value the conversion option and the

remaining value of the bond can be attributed to debt.
The convertible bond can be valued as if it were a straight bond, using the rate at

which the firm can borrow in the market, given its default risk (pre-tax cost of
debt) as the interest rate on the bond. The difference between the price of the
convertible bond and the value of the straight bond can be viewed as the value of
the conversion option.
If the convertible security is not traded, we have to value both the straight bond and the
conversion options separately.

Illustration 4.14: Breaking down a convertible bond into debt and equity components:
Convertible Debt: This is debt that can be
In March 2004, Disney had convertible
converted into stock at a specified rate, called
bonds outstanding with 19 years left to maturity the conversion ratio.
and a coupon rate of 2.125%, trading at $1,064
a bond. Holders of this bond have the right to convert the bond into 33.9444 shares of

stock anytime over the bond™s remaining life.54 To break the convertible bond into
straight bond and conversion option components, we will value the bond using Disney™s
pre-tax cost of debt of 5.25%:55
Straight Bond component
= Value of a 2.125% coupon bond due in 19 years with a market interest rate of 5.25%
= PV of $21.25 in coupons each year for 19 years56 + PV of $1000 at end of year 19
#1" (1.0525)"19 & 1000
= 21.25% = $629.91
$ '
Conversion Option = Market value of convertible “ Value of straight bond
= 1064 - $629.91 = $434.09
The straight bond component of $630 is treated as debt, while the conversion option of
$434 is treated as equity.

˜ 4.12: Increases in Stock Prices and Convertible Bonds
As stock prices go up, which of the following is likely to happen to the convertible bond
(you can choose more than one)
a. The convertible bond will increase in value
b. The straight bond component of the convertible bond will decrease in value
c. The equity component of the convertible bond will increase as a percentage of the
total value
d. The straight bond component of the convertible bond will increase as a percentage of
the total value

Calculating the Weights of Debt and Equity Components
Once we have costs for each of the different components of financing, all we need
are weights on each component to arrive at a cost of capital. In this section, we will

54 At this conversion ratio, the price that investors would be paying for Disney shares would be $29.46,
much higher than the stock price of $20.46 prevailing at the time of the analysis.
55 This rate was based upon a 10-year treasury bond rate. If the 5-year treasury bond rate had been
substantially different, we would have recomputed a pre-tax cost of debt by adding the default spread to the
5-year rate.
56 The coupons are assumed to be annual. With semi-annual coupons, you would divide the coupon by 2
and apply a semi-annual rate to calculate the present value.

consider the choices for weighting, the argument for using market value weights and
whether the weights can change over time.

Choices for Weighting
In computing weights for debt, equity and preferred stock, we have two choices.
We can take the accounting estimates of the value of each funding source from the
balance sheet and compute book value weights. Alternatively, we can use or estimate
market values for each component and compute weights based upon relative market
value. As a general rule, the weights used in the cost of capital computation should be
based upon market values. This is because the cost of capital is a forward-looking
measure and captures the cost of raising new funds to finance projects. Since new debt
and equity has to be raised in the market at prevailing prices, the market value weights
are more relevant.
There are some analysts who continue to use book value weights and justify them
using four arguments, none of which are convincing:
Book value is more reliable than market value because it is not as volatile: While

it is true that book value does not change as much as market value, this is more a
reflection of weakness than strength, since the true value of the firm changes over
time as new information comes out about the firm and the overall economy. We
would argue that market value, with its volatility, is a much better reflection of
true value than is book value.57
Using book value rather than market value is a more conservative approach to

estimating debt ratios. The book value of equity in most firms in developed
markets is well below the value attached by the market, whereas the book value of
debt is usually close to the market value of debt. Since the cost of equity is much
higher than the cost of debt, the cost of capital calculated using book value ratios

57 There are some who argue that stock prices are much more volatile than the underlying true value. Even
if this argument is justified (and it has not conclusively been shown to be so), the difference between
market value and true value is likely to be much smaller than the difference between book value and true

will be lower than those calculated using market value ratios, making them less
conservative estimates, not more so.58
Since accounting returns are computed based upon book value, consistency

requires the use of book value in computing cost of capital: While it may seem
consistent to use book values for both accounting return and cost of capital
calculations, it does not make economic sense. The funds invested in these
projects can be invested elsewhere, earning market rates, and the costs should
therefore be computed at market rates and using market value weights.

Estimating Market Values
In a world where all funding was raised in financial markets and are securities
were continuously traded, the market values of debt and equity should be easy to get. In
practice, there are some financing components with no market values available, even for
large publicly traded firms, and none of the financing components are traded in private

The Market Value of Equity
The market value of equity is generally the number of shares outstanding times
the current stock price. Since it measures the cost of raising funds today, it is not good
practice to use average stock prices over time or some other normalized version of the
Multiple Classes of Shares: If there is more than one class of shares outstanding,

the market values of all of these securities should be aggregated and treated as
equity. Even if some of the classes of shares are not traded, market values have to
be estimated for non-traded shares and added to the aggregate equity value.
Equity Options: If there other equity claims in the firm - warrants and conversion

options in other securities - these should also be valued and added on to the value
of the equity in the firm. In the last decade, the use of options as management

58 To illustrate this point, assume that the market value debt ratio is 10%, while the book value debt ratio is
30%, for a firm with a cost of equity of 15% and an after-tax cost of debt of 5%. The cost of capital can be
calculated as follows “
With market value debt ratios: 15% (.9) + 5% (.1) = 14%
With book value debt ratios: 15% (.7) + 5% (.3) = 12%

compensation has created complications, since the value of these options has to be
How do we estimate the value of equity for private businesses? We have two choices.
One is to estimate the market value of equity by looking at the multiples of revenues and
net income at which publicly traded firms trade. The other is to bypass the estimation
process and use the market debt ratio of publicly traded firms as the debt ratio for private
firms in the same business. This is the assumption we made for Bookscape, where we
used the industry average debt to equity ratio for the book/publishing business as the debt
to equity ratio for Bookscape.

The Market Value of Debt


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