Tax-equivalent yield

Muni interest is free of federal income tax

Why would anyone take a lower yield on purpose? A muni is a bond from a state or a city. Most muni interest is free of federal income tax. A corporate bond's interest is taxed. Part of every interest dollar goes to the IRS.

Your tax bracket is the rate you pay on your top dollars of income. In the 24 percent bracket, you lose 24 cents of each extra dollar. Picture two neighbors. Ana is in the 37 percent bracket. Ben is in the 12 percent bracket.

Ana loses 37 cents of every taxable interest dollar. Ben loses 12 cents. So skipping the tax saves Ana far more. The common mistake is putting munis in an IRA or a pension fund. Those accounts don't pay tax on interest as it's earned. So the muni's tax break goes to waste.

Most muni interest is free of federal income tax. That break is worth the most to people in high brackets, in taxable accounts.

Tax-equivalent yield: divide by what you keep

How do you compare a tax-free muni with a taxable bond? You find the muni's tax-equivalent yield. That's the taxable yield that leaves you the same money after tax. A muni is a bond from a state or a city, and most of its interest is free of federal income tax. A corporate bond's interest is taxed.

Say Dana is in the 24 percent bracket. Her bracket is the tax on her top dollars. She keeps 76 cents of each taxable dollar. Dana's muni pays 3 percent. To find what a taxable bond must pay, divide 3 by 0.76, the part she keeps.

That comes to 3.95 percent. A taxable bond has to pay 3.95 percent to leave Dana with 3 percent after tax. The rule is the muni yield divided by one minus the bracket. One minus the bracket is the part you keep.

The common mistake is multiplying. 3 times 0.76 is 2.28, which is lower than the muni. The answer has to come out higher, so divide. Tax-equivalent yield is the muni yield divided by what you keep. It's always higher than the muni yield.

After-tax yield: the same math, the other way

How much of a taxable bond's yield do you actually keep? That's its after-tax yield: the yield left after federal income tax. Tax-equivalent yield turns a tax-free muni yield into a taxable one, so you divide. After-tax yield goes the other way, so you multiply.

Say Lee is in the 35 percent bracket. Her bracket is the tax on her top dollars. She buys a 6 percent corporate bond. She keeps 1 minus 0.35, which is 0.65 of every interest dollar.

6 percent times 0.65 is 3.9 percent. That's her after-tax yield. The common mistake is multiplying by 0.35. That 2.1 percent is the part the IRS takes, not the part she keeps.

So a comparable muni paying more than 3.9 percent leaves Lee with more money. After-tax yield is the taxable yield times what you keep. Tax-equivalent yield divides, and after-tax yield multiplies.

Worked example: a 3.6% muni in the 37% bracket

1. A 3.6 percent muni, for an investor in the 37 percent bracket. What's its tax-equivalent yield, the taxable yield that matches it after tax?
2. Step one, what she keeps. 1 minus 0.37 is 0.63, so she keeps 63 cents of each taxable dollar.
3. Step two, divide the muni yield by what she keeps. 3.6 over 0.63 is 5.71 percent.
4. Step three, check it. 5.71 is higher than 3.6, and a tax-equivalent yield always comes out higher than the muni.
5. So a taxable bond would have to pay 5.71 percent to match this muni.

Common mistakes

divide by (1 − bracket), don't multiply

You multiplied. Tax-equivalent yield divides by what you keep. Take a 4 percent muni in the 32 percent bracket. 4 times 0.68 is 2.72, lower than the muni itself. Divide instead. 4 over 0.68 is 5.88 percent. The tax-equivalent yield always beats the muni yield.