
Yield
on "TaxFree"
Muni Bonds

Coupon earnings on municipal
bonds are free of
federal income tax. For residents of the state where issued, they
are also free of state income tax. One would expect with their
taxfree
status that the yieldtomaturity (YTM) on muni bonds is a proper
measure of the aftertax
return. But this is not the case.
YTM is computed on the assumption
that all coupon
earnings are reinvested at the YTM rate. In practice this is not
possible. Usually the earnings are held in a shortterm
investment
like a money market fund. We assume here that they accumulate at
compound interest in a taxable fund, paying 2.5% per annum.
Because of their taxfree status,
muni bonds normally
offer lower YTMs than do taxable bonds. Their main benefits come
into play only for those in the higher tax brackets. We therefore
assume a relatively high combined state and federal tax rate of 40% on
ordinary income, and 24% on capital gains.
A muni purchased at a discount has
a capital gain
at maturity that is subject to tax. On the other hand, a muni
purchased
at a premium suffers a capital loss at maturity, but
that loss is exactly compensated by the higher coupon earnings, and
thus
cannot be claimed as a capital loss for tax purposes.
We will examine three muni bonds,
each with a
YTM of 4%, and maturity of 5 years. They differ only in the
coupon
rates which are 6%, 4%, and 2.5%, respectively. The first sells
at
a premium, the second at par, and the third at a discount. Even
though
they have the same YTM, their aftertax returns will differ.
In computing the return on each of
the muni bonds,
we first determine the value of the investment at maturity. This
comprises the face value of the bonds, plus the taxfree coupon
earnings,
plus the aftertax compound interest earned on the reinvested coupons,
minus the capital gains tax on discounted bonds. The fiveyear
gain
relative to the purchase price is then converted into an equivalent
annualized
return. This can also be converted into a bond equivalent yield
for
comparison against the quoted yieldtomaturity. The results are
shown in the table.
Coupon

YTM

Price**

Annualized
Return

BondEquiv
Yield

6.0%

4.0%

108.983

3.754%

3.719%

4.0%

4.0%

100.000

3.832%

3.796%

2.5%

4.0%

93.263

3.545%

3.514%

** For 5 years to maturity
Note that the 4% coupon bond
has a bondequivalent
yield less than the 4.0% one would expect for a bond sold at par.
This is because the aftertax return on the reinvested coupons is below
the YTM rate.
Also note that the 4% coupon
has a better return
than either the 6% coupon or the 2.5% coupon. The 2.5% coupon
suffers
mainly from the capital gains tax bite. The 6% coupon suffers
because
a higher fraction of the total return comes from the interest on the
reinvested
coupons which are taxed as ordinary income at the combined state and
federal
tax rate.
If the
capital loss on
the 6% coupon were taxdeductible, the bondequivalent yield would be
4.127%
which is above the YTM on a fully taxfree bond bought at par.
This
would represent a tax loophole favoring high coupons sold at a
premium,
and explains why such a tax loss on a "taxfree" muni bond is
disallowed.
Two lessons can be learned from
these results:
(1) The return on a muni is
not entirely
taxfree. The effective yield is normally less than the YTM
quoted
at time of purchase, even for those bought at par.
(2) For a given YTM, munis
bought at either
a large premium or discount return less than those bought at or near
par.
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