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Yield on "Tax-Free"
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 tax-free status that the yield-to-maturity (YTM) on muni bonds is a proper measure of the after-tax 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 short-term 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 tax-free 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 after-tax 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 tax-free coupon earnings, plus the after-tax compound interest earned on the reinvested coupons, minus the capital gains tax on discounted bonds.  The five-year 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 yield-to-maturity.  The results are shown in the table.

** For 5 years to maturity

Note that the 4% coupon bond has a bond-equivalent yield less than the 4.0% one would expect for a bond sold at par.  This is because the after-tax 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 tax-deductible, the bond-equivalent yield would be 4.127% which is above the YTM on a fully tax-free 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 "tax-free" muni bond is disallowed.

Two lessons can be learned from these results: 

(1)  The return on a muni is not entirely tax-free.  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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