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lower value as a price paid for maintaining total control.

From Cost of Equity to Cost of Capital
While equity is undoubtedly an important and indispensable ingredient of the
financing mix for every business, it is but one ingredient. Most businesses finance some
or much of their operations using debt or some hybrid of equity and debt. The costs of
these sources of financing are generally very different from the cost of equity, and the
minimum acceptable hurdle rate for a project will reflect their costs as well, in proportion
to their use in the financing mix. Intuitively, the cost of capital is the weighted average of
the costs of the different components of financing -- including debt, equity and hybrid
securities -- used by a firm to fund its financial requirements.

˜ 4.9: Interest Rates and the Relative Costs of Debt and Equity
It is often argued that debt becomes a more attractive mode of financing than equity as
interest rates go down and a less attractive mode when interest rates go up. Is this
a. Yes
b. No
Why or why not?

The Costs of Non-Equity Financing
To estimate the cost of the funding that a firm raises, we have to estimate the
costs of all of the non-equity components. In this section, we will consider the cost of
debt first and then extend the analysis to consider hybrids such as preferred stock and
convertible bonds.

The Cost of Debt
The cost of debt measures the current cost to the firm of borrowing funds to
finance projects. In general terms, it is determined by the following variables:
(1) The current level of interest rates: As interest rates rise, the cost of debt for firms will
also increase.
(2) The default risk of the company: As the default risk of a firm increases, the cost of
borrowing money will also increase.
Default Risk: This is the risk that
(3) The tax advantage associated with debt: Since a firm will fail to make obligated
interest is tax deductible, the after-tax cost of debt is a debt payments, such as interest
expenses or principal payments.
function of the tax rate. The tax benefit that accrues from
paying interest makes the after-tax cost of debt lower than
the pre-tax cost. Furthermore, this benefit increases as the tax rate increases.
After-tax cost of debt = Pre-tax cost of debt (1 “ marginal tax rate)

˜ 4.10: Costs of Debt and Equity
Can the cost of equity ever be lower than the cost of debt for any firm at any stage in its
life cycle?
a. Yes
b. No

Estimating the Default Risk and Default Spread of a firm
The simplest scenario for estimating the cost of debt occurs when a firm has long-
term bonds outstanding that are widely traded. The market price of the bond, in
conjunction with its coupon and maturity can serve to compute a yield we use as the cost
of debt. For instance, this approach works for firms that have dozens of outstanding
bonds that are liquid and trade frequently.

Many firms have bonds outstanding that do not trade on a regular basis. Since these
firms are usually rated, we can estimate their costs of debt by using their ratings and
associated default spreads. Thus, Disney with a BBB+ rating can be expected to have a
cost of debt approximately 1.25% higher than the treasury bond rate, since this is the
spread typically paid by BBB+ rated firms.
Some companies choose not to get rated. Many smaller firms and most private
businesses fall into this category. While ratings agencies have sprung up in many
emerging markets, there are still a number of markets where companies are not rated on
the basis of default risk. When there is no rating available to estimate the cost of debt,
there are two alternatives:
Recent Borrowing History: Many firms that are not rated still borrow money from

banks and other financial institutions. By looking at the most recent borrowings
made by a firm, we can get a sense of the types of default spreads being charged
the firm and use these spreads to come up with a cost of debt.
Estimate a synthetic rating and default spread: An alternative is to play the role of

a ratings agency and assign a rating to a firm based upon its financial ratios; this
rating is called a synthetic rating. To make this assessment, we begin with rated
firms and examine the financial characteristics shared by firms within each ratings
class. Consider a very simpler version, where the ratio of operating income to
interest expense, i.e., the interest coverage ratio, is computed for each rated firm.
In table 4.12, we list the range of interest coverage ratios for small manufacturing
firms in each S&P ratings class48. We also report the typical default spreads for
bonds in each ratings class.49
Table 4.12: Interest Coverage Ratios and Ratings
Interest Coverage Ratio Rating Typical
> 12.5 AAA 0.35%

48 This table was developed in early 2000, by listing out all rated firms, with market capitalization lower
than $ 2 billion, and their interest coverage ratios, and then sorting firms based upon their bond ratings. The
ranges were adjusted to eliminate outliers and to prevent overlapping ranges.
49 These default spreads are obtained from an online site: http://www.bondsonline.com. You can find
default spreads for industrial and financial service firms; these spreads are for industrial firms.

9.50 - 12.50 AA 0.50%
7.50 “ 9.50 A+ 0.70%
6.00 “ 7.50 A 0.85%
4.50 “ 6.00 A- 1.00%
4.00 “ 4.50 BBB 1.50%
3.50 - 4.00 BB+ 2.00%
3.00 “ 3.50 BB 2.50%
2.50 “ 3.00 B+ 3.25%
2.00 - 2.50 B 4.00%
1.50 “ 2.00 B- 6.00%
1.25 “ 1.50 CCC 8.00%
0.80 “ 1.25 CC 10.00%
0.50 “ 0.80 C 12.00%
< 0.65 D 20.00%
Source: Compustat and Bondsonline.com
Now consider a private firm with $ 10 million in earnings before interest and taxes and
$3 million in interest expenses; it has an interest coverage ratio of 3.33. Based on this
ratio, we would assess a “synthetic rating” of BB for the firm and attach a default spread
of 2.50% to the riskfree rate to come up with a pre-tax cost of debt.
By basing the synthetic rating on the interest coverage ratio alone, we run the risk
of missing the information that is available in the other financial ratios used by ratings
agencies. The approach described above can be extended to incorporate other ratios. The
first step would be to develop a score based upon multiple ratios. For instance, the
Altman Z score, which is used as a proxy for default risk, is a function of five financial
ratios, which are weighted to generate a Z score. The ratios used and their relative
weights are usually based upon past history on defaulted firms. The second step is to
relate the level of the score to a bond rating, much as we have done in table 4.12 with
interest coverage ratios. In making this extension, though, note that complexity comes at
a cost. While credit or Z scores may, in fact, yield better estimates of synthetic ratings
than those based only upon interest coverage ratios, changes in ratings arising from these
scores are much more difficult to explain than those based upon interest coverage ratios.
That is the reason we prefer the flawed but simpler ratings that we get from interest
coverage ratios.

Short Term and Long Term Debt
Most publicly traded firms have multiple borrowings “ short term and long term
bonds and bank debt with different terms and interest rates. While there are some analysts
who create separate categories for each type of debt and attach a different cost to each
category, this approach is both tedious and dangerous. Using it, we can conclude that
short-term debt is cheaper than long term debt and that secured debt is cheaper than
unsecured debt, even though neither of these conclusions is justified.
The solution is simple. Combine all debt “ short and long term, bank debt and
bonds- and attach the long term cost of debt to it. In other words, add the default spread
to the long term riskfree rate and use that rate as the pre-tax cost of debt. Firms will
undoubtedly complain, arguing that their effective cost of debt can be lowered by using
short-term debt. This is technically true, largely because short-term rates tend to be lower
than long-term rates in most developed markets, but it misses the point of computing the
cost of debt and capital. If this is the hurdle rate we want our long-term investments to
beat, we want the rate to reflect the cost of long-term borrowing and not short-term
borrowing. After all, a firm that funds long term projects with short-term debt will have
to return to the market to roll over this debt.

Operating Leases and Other Fixed Commitments
The essential characteristic of debt is that it gives rise to a tax-deductible
obligation that firms have to meet in both good times and bad and the failure to meet this
obligation can result in bankruptcy or loss of equity control over the firm. If we use this
definition of debt, it is quite clear that what we see reported on the balance sheet as debt
may not reflect the true borrowings of the firm. In particular, a firm that leases substantial
assets and categorizes them as operating leases owes substantially more than is reported
in the financial statements.50 After all, a firm that signs a lease commits to making the

50 In an operating lease, the lessor (or owner) transfers only the right to use the property to the lessee. At
the end of the lease period, the lessee returns the property to the lessor. Since the lessee does not assume
the risk of ownership, the lease expense is treated as an operating expense in the income statement and the
lease does not affect the balance sheet. In a capital lease, the lessee assumes some of the risks of ownership
and enjoys some of the benefits. Consequently, the lease, when signed, is recognized both as an asset and
as a liability (for the lease payments) on the balance sheet. The firm gets to claim depreciation each year on
the asset and also deducts the interest expense component of the lease payment each year. In general,
capital leases recognize expenses sooner than equivalent operating leases.

lease payment in future periods and risks the loss of assets if it fails to make the
For corporate financial analysis, we should treat all lease payments as financial
expenses and convert future lease commitments into debt by discounting them back the
present, using the current pre-tax cost of borrowing for the firm as the discount rate. The
resulting present value can be considered the debt value of operating leases and can be
added on to the value of conventional debt to arrive at a total debt figure. To complete the
adjustment, the operating income of the firm will also have to be restated:
Adjusted Operating income = Stated Operating income + Operating lease expense
for the current year “ Depreciation on leased asset
In fact, this process can be used to convert any set of financial commitments into debt.

Book and Market Interest Rates
When firms borrow money, they do so often at fixed rates. When they issue bonds
to investors, this rate that is fixed at the time of the issue is called the coupon rate. The
cost of debt is not the coupon rate on outstanding bonds nor is it the rate at which the
company was able to borrow at in the past. While these factors may help determine the
interest cost the company will have to pay in the current year, they do not determine the
pre-tax cost of debt in the cost of capital calculations. Thus, a company that has debt that
it took on when interest rates were low, on the books cannot contend that it has a low cost
of debt.
To see why, consider a firm that has $ 2 billion of debt on its books and assume
that the interest expense on this debt is $ 80 million. The book interest rate on the debt is
4%. Assume also that the current riskfree rate is 6%. If we use the book interest rate of
4% in our cost of capital calculations, we are requiring the projects we fund with the
capital to earn more than 4% to be considered good investments. Since we can invest that
money in treasury bonds and earn 6%, without taking any risk, this is clearly not a high
enough hurdle. To ensure that projects earn more than what we can make on alternative
investments of equivalent risk today, the cost of debt has to be based upon market interest
rates today rather than book interest rates.

Assessing the Tax Advantage of Debt
Interest is tax deductible and the resulting tax savings reduce the cost of
borrowing to firms. In assessing this tax advantage, we should keep in mind that:
Interest expenses offset the marginal dollar of income and the tax advantage has

to be therefore calculated using the marginal tax rate.
After-tax cost of debt = Pre-tax cost of debt (1 “ Marginal Tax Rate)
To obtain the tax advantages of borrowing, firms have to be profitable. In other

words, there is no tax advantage from interest expenses to a firm that has
operating losses. It is true that firms can carry losses forward and can offset them
against profits in future periods. The most prudent assessment of the tax effects of
debt will therefore provide for no tax advantages in the years of operating losses
and will begin adjusting for tax benefits only in future years when the firm is
expected to have operating profits.
After-tax cost of debt = Pre-tax cost of debt If operating income < 0
Pre-tax cost of debt (1-t) If operating income>0

Illustration 4.12: Estimating the Costs of Debt for Disney et al.
Disney, Deutsche Bank and Aracruz are all rated companies and we will estimate
their pre-tax costs of debt based upon their rating. To provide a contrast, we will also
estimate synthetic ratings for Disney and Aracruz. For Bookscape, we will use the
synthetic rating of BBB, estimated from the interest coverage ratio to assess the pre-tax
cost of debt.
Bond Ratings: While S&P, Moody™s and Fitch rate all three companies, the

ratings are consistent and we will use the S&P ratings and the associated default
spreads (from table 3.4 in chapter 3) to estimate the costs of debt in table 4.13:
Table 4.13: Cost of Debt
S&P Riskfree Default Cost of Tax After-
Rating Rate Spread debt Rate tax Cost
of Debt

Disney BBB+ 4% ($) 1.25% 5.25% 37.3% 3.29%
Deutsche AA- 4.05% 1.00% 5.05% 38% 3.13%
Aracruz52 B+ 4% ($) 3.25% 7.25% 34% 4.79%

The marginal tax rates of the US (Disney), Brazil (Aracruz) and Germany
(Deutsche Bank) are used to compute the after-tax cost of debt. We will assume
that all of Disney™s divisions have the same cost of debt and marginal tax rate as
the parent company.
Synthetic Ratings: For Bookscape, there are no recent borrowings on the books,

thus making the synthetic rating for the firm our only choice. In 2003, Bookscape
had no interest expenses and reported operating income of $ 2 million after
operating lease expenses of $ 600,000. If we consider the current year™s operating
operating lease expenses to be the equivalent of interest expenses, the resulting
interest coverage ratio is 4.33, yielding a synthetic rating of A- for the firm.53
Adding the default spread of 1.5% associated with that rating to the riskfree rate
results in a pre-tax cost of debt for 5.50%. The after-tax cost of debt is computed
using a 40% marginal tax rate:
After-tax cost of debt = 5.5% (1- .40) = 3.30%
Actual and Synthetic Ratings
It is usually easy to estimate the cost of debt for firms that have bond ratings
available for them. There are, however, a few potential problems that sometimes arise in


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