## Figure

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 revenue 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 revenue and private purpose tax-exempt bonds only up to a limit of \$50 per capita or \$150 million, 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 returns 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.

r(1 - t) = rm

Thus, the equivalent taxable yield is simply the tax-free rate divided by 1 - t. Table 2.3 presents 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 attractive equivalent taxable yields. Each entry is calculated from Equation 2.2. If the equivalent 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 municipals. 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 indifferent between taxable and tax-exempt bonds. The cutoff tax bracket is given by solving Equation 2.1 for the tax bracket at which after-tax yields are equal. Doing so, we find t = 1

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 aftertax yields? Equation 2.3 shows that an investor whose tax bracket (federal plus local) exceeds 1 — .75 = .25, or 25%, will derive a greater after-tax yield from municipals. Note, however, that it is difficult to control precisely for differences in the risks of these bonds, so the cutoff tax bracket must be taken as approximate.

## Retirement Planning For The Golden Years

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