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The market value of debt is usually more difficult to obtain directly since very
few firms have all of their debt in the form of bonds outstanding trading in the market.
Many firms have non-traded debt, such as bank debt, which is specified in book value
terms but not market value terms. To get around the problem, many analysts make the
simplifying assumptions that the book value of debt is equal to its market value. While
this is not a bad assumption for mature companies in developed markets, it can be a
mistake when interest rates and default spreads are volatile.
A simple way to convert book value debt into market value debt is to treat the
entire debt on the books as a coupon bond, with a coupon set equal to the interest
expenses on all of the debt and the maturity set equal to the face-value weighted average
maturity of the debt, and to then value this coupon bond at the current cost of debt for the
company. Thus, the market value of \$ 1billion in debt, with interest expenses of \$ 60
million and a maturity of 6 years, when the current cost of debt is 7.5% can be estimated
as follows:
# 1&
(1"
% (1.075) 6 ( 1,000
Estimated Market Value of Debt = 60% = \$930
(+
(1.075) 6
.075
% (
\$ '
This is an approximation and that a more accurate computation would require valuing
each debt issue separately, using this process. As a final point, we should add the present
!
75

value of operating lease commitments to this market value of debt to arrive at an
aggregate value for debt in computing the cost of capital.
Can financing weights change over time?
Using the current market values to obtain weights will yield a cost of capital for
the current year. But can the weights attached to debt and equity, and the resulting cost of
capital, change from year to year? Absolutely, and especially in the following scenarios:
Young firms: Young firms often are all equity funded largely because they do not
â€¢
have the cash flows (or earnings) to sustain debt. As they become larger, increasing
earnings and cashflow usually allow for more borrowing. When analyzing firms early
in the life cycle, we should allow for the fact that the debt ratio of the firm will
probably increase over time towards the industry average.
Target Debt Ratios and Changing financing mix: Mature firms sometimes decide to
â€¢
change their financing strategies, pushing towards target debt ratios that are much
higher or lower than current levels. When analyzing these firms, we should consider
the expected changes as the firm moves from the current to the target debt ratio.
As a general rule, we should view the cost of capital as a year-specific number, and
change the inputs each year. Not only will the weights attached to debt and equity change
over time, but so will the estimates of beta and the cost of debt. In fact, one of the
advantages of using bottom-up betas is that the beta each year can be estimated as a
function of the expected debt to equity ratio that year.

Illustration 4.15: Market value and book value debt ratios: Disney and Aracruz
Disney has a number of debt issues on its books, with varying coupon rates and
maturities. Table 4.15 summarizes Disneyâ€™s outstanding debt:
Table 4.15: Debt at Disney: September 2003
Stated
Debt Face Value Interest rate Maturity Wtd Maturity
Commercial Paper \$0 2.00% 0.5 0.0000
Medium term paper \$8,114 6.10% 15 9.2908
Senior Convertibles \$1,323 2.13% 10 1.0099
Other U.S. dollar denominated debt \$597 4.80% 15 0.6836
Privately Placed Debt \$343 7.00% 4 0.1047
Euro medium-term debt \$1,519 3.30% 2 0.2319
76

Preferred Stock59 \$485 7.40% 1 0.0370
Cap Cities Debt \$191 9.30% 9 0.1312
Other \$528 3.00% 1 0.0403
Total \$13,100 5.60% 11.5295

To convert the book value of debt to market value, we use the current pre-tax cost of debt
for Disney of 5.25% as the discount rate, \$13,100 as the book value of debt and the
current yearâ€™s interest expenses of \$ 666 million as the coupon:

# &
1
(1"
% (1.0525)11.53 ( 13,100
Estimated MV of Disney Debt = 666% = \$12,915 million
(+
(1.0525)11.53
.0525
% (
\$ '
To this amount, we add the present value of Disneyâ€™s operating lease commitments. This
present value is computed by discounting the lease commitment each year at the pre-tax
!
cost of debt for Disney (5.25%):60
Year Commitment Present Value
1 \$ 271.00 \$ 257.48
2 \$ 242.00 \$ 218.46
3 \$ 221.00 \$ 189.55
4 \$ 208.00 \$ 169.50
5 \$ 275.00 \$ 212.92
6 â€“9 \$ 258.25 \$ 704.93
Debt Value of leases = \$ 1,752.85

Adding the debt value of operating leases to the market value of debt of \$12,915 million
yields a total market value for debt of \$14,668 million at Disney.
Aracruz has debt with a book value of 3,946 million BR, interest expenses of 339
million BR in the current year and an average maturity for the debt of 3.20 years. Since
most of the debt is dollar debt, we used the nominal dollar pre-tax cost of debt for the
firm of 7.25% (from illustration 4.12)61. The market value of Aracruz debt is:

59 Preferred stock should really not be treated as debt. In this case, though, the amount of preferred stock is
small that we have included it as part of debt for Disney.
60 Disney reports total commitments of \$715 million beyond year 6. Using the average commitment from
year one through five as an indicator, we assumed that this total commitment would take the form of an
annuity of \$178.75 million a year for four years.
61 If the debt had been predominantly nominal BR debt, we would have used a nominal BR cost of debt.
77

# &
1
(1"
% (1.0725) 3.20 ( 3,946
MV of Aracruz Debt = 339% = 4,094 million BR
(+ 3.20
.0725 ( (1.0725)
%
\$ '

There are no lease commitments reported in Aracruzâ€™s financial statements.62
!
In table 4.16 we contrast the book values of debt and equity with the market
values for Disney and Aracruz. The market value of equity is estimated using the current
market price and the number of shares outstanding.
Table 4.16: Book value versus Market Value: Debt Ratios
BV: Debt BV: Equity BV: D/(D+E) MV: Debt MV: Equity MV: D/E
Disney \$13,100 \$24,219 35.10% \$14,668 \$55,101 21.02%
Aracruz \$3,946 \$5,205 43.12% \$4,094 \$9,189 30.82%

For Disney, the market value debt ratio of 21.02% is much lower than the book value
debt ratio of 35.10%. For Aracruz, the market debt ratio is 30.82%, lower than the book
debt ratio of 43.12%.
Bookscapeâ€™s only debt takes the form of operating lease commitments. The
bookstore has a 25 years remaining on a real estate leases, requiring the payment of
\$500,000 a year. The present value of these operating lease commitments, using a 5.50%
pre-tax cost of borrowing, is:
Present value of operating lease commitments = 500 (PV of annuity, 5.5%, 25 years)
= \$6.707 million
Bookscape does not have a market value of equity, since it is a private firm. The book
value of equity for the firm at the end of 2003 was \$ 5 million.

Estimating and using the cost of capital
With the estimates of the costs of the individual components â€“ debt, equity and
preferred stock (if any) â€“ and the market value weights of each of the components, the
cost of capital can be computed. Thus if E, D and PS are the market values of equity, debt
and preferred stock respectively, the cost of capital can be written as follows:

62While many companies outside the United States do no provide details on lease commitments in future
years, Aracruz publishes financial statements that use US accounting standards for its ADR listing.
78

Cost of Capital = ke ( E/ (D+E+PS)) + kd ( D/ (D+E+PS)) + kps ( PS/ (D+E+PS))
The cost of capital is a measure of the composite cost of raising money that a firm faces.
It will generally be lower than the cost of equity, which is the cost of just equity funding.
It is a source of confusion to many analysts that both the cost of equity and the
cost of capital are used as hurdle rates in investment analysis. The way to resolve this
confusion is to recognize when it is appropriate to use each one.
If we want to adopt the perspective of just the equity investors in a business or a
â€¢
project and measure the returns earned just by these investors on their investment,
the cost of equity is the correct hurdle rate to use. In measuring the returns to
equity investors then, we have to consider only the income or cashflows left over
after all other claimholders needs (interest payments on debt and preferred
dividends, for instance) have been met.
If the returns that we are measuring are composite returns to all claimholders,
â€¢
based upon earnings before payments to debt and preferred stockholders, the
comparison should be to the cost of capital.
While these principles are abstract, we will consider them in more detail in the next
chapter when we look at examples of projects.

Illustration 4.16: Estimating Cost of Capital
Culminating the analysis in this chapter, we first estimate the costs of capital for
each of Disneyâ€™s divisions, In making these estimates, we use the costs of equity that we
obtained for the divisions in illustration 4.11 and Disneyâ€™s cost of debt from illustration
4.12. We also assume that all of the divisions are funded with the same mix of debt and
equity as the parent company. Table 4.17 provides estimates of the costs of capital for the
divisions:
Table 4.17: Cost of capital for Disneyâ€™s divisions
After-tax cost
Business Cost of Equity of debt E/(D+E) D/(D+E) Cost of capital
Media Networks 10.10% 3.29% 78.98% 21.02% 8.67%
Parks and Resorts 9.12% 3.29% 78.98% 21.02% 7.90%
Studio Entertainment 10.43% 3.29% 78.98% 21.02% 8.93%
Consumer Products 10.39% 3.29% 78.98% 21.02% 8.89%
Disney 10.00% 3.29% 78.98% 21.02% 8.59%
79

The cost of capital for Disney as a company is 8.59% but the costs of capitals vary across
divisions with a low of 7.90% for the parks and resorts division to a high or 8.93% for
studio entertainment.
To estimate the cost of capital in both real and nominal US dollar terms for
Aracruz in real terms, we use the cost of equity (from illustration 4.11) and the after-tax
cost of debt (from illustration 4.12) and the estimates are reported in table 4.18:
Table 4.18: Cost of Capital for Aracruz: Real and US Dollars
After-tax Cost
Levered Beta Cost of Equity of Debt D/(D+E) Cost of Capital
In Real Terms
Paper & Pulp 0.7576 11.46% 3.47% 30.82% 9.00%
Cash 0 2.00% 2.00%
Aracruz 0.7040 10.79% 3.47% 30.82% 8.53%
In US Dollar Terms
Paper & Pulp 0.7576 13.46% 4.79% 30.82% 10.79%
Cash 0 4.00% 4.00%
Aracruz 0.7040 12.79% 4.79% 30.82% 10.33%

The nominal dollar costs of capital can be converted into nominal BR costs of capital
using the differential inflation rates in the two countries, just as the cost of equity was
earlier in the chapter.
When estimating the cost of equity for Bookscape, we assumed that the company
would be funded using the same market debt to equity ratio as the book/publishing
industry. Staying consistent, we will use the market debt to capital ratio to compute the
cost of capital for the firm. We will also present two estimates of the cost of capital â€“ one
using the market beta and the other using the total beta:
Beta Cost of After-tax Cost Cost of
Equity of debt D/(D+E) Capital
Market Beta 0.82 7.97% 3.30% 16.90% 7.18%
Total Beta 2.06 13.93% 3.30% 16.90% 12.14%

The cost of capital estimated using the total beta is a more realistic estimate, given that
this is a private company, and we will use it as the cost of capital for Bookscape in the
coming chapters.
Equity, Debt and Cost of Capital for Banks
80

Note that we did not estimate a cost of capital for Deutsche Bank even though we
have estimates of the costs of equity and debt for the firm. The reason is simple and goes
to the heart of how firms view debt. For non-financial service firms, debt is a source of
capital and is used to fund real projects â€“ building a factory or making a movie. For
banks, debt is raw material that is used to generate profits. Boiled down to its simplest
elements, it is a bankâ€™s job to borrow money (debt) at a low rate and lend it out at a
higher rate. It should come as no surprise that when banks (and their regulators) talk
about capital, they mean equity capital.63
There is also a practical problem in computing the cost of capital for a bank. If we
define debt as any fixed commitment where failure to meet the commitment can lead to
loss of equity control, the deposits made by customers at bank branches would qualify
and the debt ratio of a bank will very quickly converge on 100%. If we define it more
narrowly, we still are faced with a problem of where to draw the line. A pragmatic
compromise is to view only long term bonds issued by a bank as debt, but it is an
artificial one. Deutsche Bank, for instance, had long-term debt in December 2003 was 82
billion Euros, common equity with a market value of 40.96 billion Euros and preferred
stock with a market value of 4.1 billion Euros. Using the cost of equity of 8.76% (from
illustration 4.11), the after-tax cost of debt of 3.13% from illustration 4.12 and the cost of
preferred stock (6.36%) from illustration 4.13:
Cost of capital = 3.13% (82/127.06) + 8.47% (40.96/127.06) + 6.36%(4.1/127.06)
= 5.05%
With Deutsche Bank, we will do almost all of our analyses using the cost of equity rather
than the cost of capital.

Conclusion
This chapter explains the process of estimating discount rates, by relating them to
the risk and return models described in the previous chapter â€“
The cost of equity can be estimated using risk and return models -- the capital asset
â€¢
pricing model, where risk is measured relative to a single market factor, the arbitrage

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