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sued is in the form of short-term tax anticipation notes that raise funds to pay for expenses be-
fore actual collection of taxes. Other municipal debt may be long term and used to fund large
capital investments. Maturities range up to 30 years.
The key feature of municipal bonds is their tax-exempt status. Because investors pay neither
federal nor state taxes on the interest proceeds, they are willing to accept lower yields on these
securities. This represents a huge savings to state and local governments. Correspondingly,
Bodie’Kane’Marcus: I. Elements of Investments 2. Global Financial © The McGraw’Hill
Essentials of Investments, Instruments Companies, 2003
Fifth Edition

34 Part ONE Elements of Investments



$ billion



Industrial revenue bonds General obligation

F I G U R E 2.5
Outstanding tax-exempt debt
Source: Flow of Funds Accounts of the U.S., Board of Governors of the Federal Reserve System, 2001.

exempting interest earned on these bonds from taxes results in a huge drain of potential tax rev-
enue from the federal government, which has shown some dismay over the explosive increase
in the use of industrial development bonds.
Because of concern that these bonds were being used to take advantage of the tax-exempt
feature of municipal bonds rather than as a source of funds for publicly desirable investments,
the Tax Reform Act of 1986 restricted their use. A state is now allowed to issue mortgage rev-
enue and private purpose tax-exempt bonds only up to a limit of $50 per capita or $150 mil-
lion, whichever is larger. In fact, the outstanding amount of industrial revenue bonds stopped
growing after 1986, as evidenced in Figure 2.5.
An investor choosing between taxable and tax-exempt bonds needs to compare after-tax re-
turns on each bond. An exact comparison requires the computation of after-tax rates of return
with explicit recognition of taxes on income and realized capital gains. In practice, there is a
simpler rule of thumb. If we let t denote the investor™s federal plus local marginal tax rate and
r denote the total before-tax rate of return available on taxable bonds, then r (1 t) is the
after-tax rate available on those securities. If this value exceeds the rate on municipal bonds,
rm, the investor does better holding the taxable bonds. Otherwise, the tax-exempt municipals
provide higher after-tax returns.
One way of comparing bonds is to determine the interest rate on taxable bonds that would
be necessary to provide an after-tax return equal to that of municipals. To derive this value, we
set after-tax yields equal and solve for the equivalent taxable yield of the tax-exempt bond.
This is the rate a taxable bond would need to offer in order to match the after-tax yield on the
tax-free municipal.
Bodie’Kane’Marcus: I. Elements of Investments 2. Global Financial © The McGraw’Hill
Essentials of Investments, Instruments Companies, 2003
Fifth Edition

2 Global Financial Instruments

Tax-Exempt Yield
TA B L E 2.3
Marginal Tax Rate 2% 4% 6% 8% 10%
Equivalent taxable
yields corresponding
20% 2.5 5.0 7.5 10.0 12.5
to various tax-exempt
30 2.9 5.7 8.6 11.4 14.3
40 3.3 6.7 10.0 13.3 16.7
50 4.0 8.0 12.0 16.0 20.0

r(1 t) rm (2.1)
r (2.2)
1 t
Thus, the equivalent taxable yield is simply the tax-free rate divided by 1 t. Table 2.3 pres-
ents equivalent taxable yields for several municipal yields and tax rates.
This table frequently appears in the marketing literature for tax-exempt mutual bond funds
because it demonstrates to high tax-bracket investors that municipal bonds offer highly at-
tractive equivalent taxable yields. Each entry is calculated from Equation 2.2. If the equiva-
lent taxable yield exceeds the actual yields offered on taxable bonds, after taxes the investor
is better off holding municipal bonds. The equivalent taxable interest rate increases with the
investor™s tax bracket; the higher the bracket, the more valuable the tax-exempt feature of mu-
nicipals. Thus, high-bracket individuals tend to hold municipals.
We also can use Equation 2.1 or 2.2 to find the tax bracket at which investors are indiffer-
ent between taxable and tax-exempt bonds. The cutoff tax bracket is given by solving Equa-
tion 2.1 for the tax bracket at which after-tax yields are equal. Doing so, we find
t 1 (2.3)
Thus, the yield ratio rm /r is a key determinant of the attractiveness of municipal bonds. The
higher the yield ratio, the lower the cutoff tax bracket, and the more individuals will prefer to
hold municipal debt. Figure 2.6 graphs the yield ratio since 1955.

In recent years, the ratio of tax-exempt to taxable yields has hovered around .75. What does
this imply about the cutoff tax bracket above which tax-exempt bonds provide higher after-
tax yields? Equation 2.3 shows that an investor whose tax bracket (federal plus local) ex-
ceeds 1 .75 .25, or 25%, will derive a greater after-tax yield from municipals. Note, Taxable versus
however, that it is difficult to control precisely for differences in the risks of these bonds, so Tax-Exempt
the cutoff tax bracket must be taken as approximate. Yields

2. Suppose your tax bracket is 28%. Would you prefer to earn a 6% taxable return or Concept
a 4% tax-free yield? What is the equivalent taxable yield of the 4% tax-free yield?

Corporate Bonds
Corporate bonds are the means by which private firms borrow money directly from the pub-
lic. These bonds are structured much like Treasury issues in that they typically pay semiannual
Bodie’Kane’Marcus: I. Elements of Investments 2. Global Financial © The McGraw’Hill
Essentials of Investments, Instruments Companies, 2003
Fifth Edition

36 Part ONE Elements of Investments










1955 1960 1965 1970 1975 1980 1995 2000

F I G U R E 2.6
Ratio of yields on tax-exempt to taxable bonds

coupons over their lives and return the face value to the bondholder at maturity. Where they
corporate bonds
differ most importantly from Treasury bonds is in risk.
Long-term debt issued
Default risk is a real consideration in the purchase of corporate bonds. We treat this issue
by private
in considerable detail in Chapter 9. For now, we distinguish only among secured bonds, which
corporations typically
paying semiannual have specific collateral backing them in the event of firm bankruptcy; unsecured bonds, called
coupons and debentures, which have no collateral; and subordinated debentures, which have a lower prior-
returning the face
ity claim to the firm™s assets in the event of bankruptcy.
value of the bond at
Corporate bonds sometimes come with options attached. Callable bonds give the firm the
option to repurchase the bond from the holder at a stipulated call price. Convertible bonds give
the bondholder the option to convert each bond into a stipulated number of shares of stock.
These options are treated in more detail in Part Three.
Figure 2.7 is a partial listing of corporate bond prices from The Wall Street Journal. The
listings are similar to those for Treasury bonds. The highlighted AT&T bond has a coupon
rate of 6 1„2% and a maturity date of 2029. Only 37 AT&T bonds traded on this day. The clos-
ing price of the bond was 90 1„2% of par, or $905, which was up 1„4 of a point from the previ-
ous day™s close. In contrast to Treasury bonds, price quotes on corporate bonds use explicit
The current yield on a bond is annual coupon income per dollar invested in the bond. For
this bond, the current yield is calculated as
Annual coupon income 65
Current yield .072, or 7.2%
Price 905
Bodie’Kane’Marcus: I. Elements of Investments 2. Global Financial © The McGraw’Hill
Essentials of Investments, Instruments Companies, 2003
Fifth Edition

2 Global Financial Instruments

F I G U R E 2.7
Listing of corporate
bond prices
Source: From The Wall
Street Journal, October 19,
2001. Reprinted by
permission of Dow Jones &
Company, Inc. via
Copyright Clearance Center,
Inc. © 2001 Dow Jones &
Company, Inc. All Rights
Reserved Worldwide.

Note that current yield ignores the difference between the price of a bond and its eventual


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