Tax-equivalent yield formula: comparing a muni with a taxable bond

The tax-equivalent yield formula

TEY = tax-free yield ÷ (1 − marginal tax rate)

Interest on most US municipal bonds is exempt from federal income tax, so their quoted yields are lower than those of taxable bonds with similar risk. The TEY turns the muni yield into the taxable yield that would leave you with the same income after tax. In Excel: =B2/(1-B3), which returns 4.71% for a 3.20% muni and a 32% rate.

Use your marginal rate, the rate on the next dollar of income, because the bond's interest is taxed at that rate. Your average tax rate is lower and makes the muni look worse than it is.

Adding state tax

A muni from your own state is usually exempt from state income tax as well. Add the state rate to the federal rate: 32% + 5% = 37%, and the TEY becomes 3.20% ÷ 0.63 = 5.08%. An out-of-state muni is normally taxed by your state, so only the federal rate applies.

The simple sum slightly overstates the combined rate if you itemize and can deduct state tax on your federal return. The precise combined rate is then federal + state × (1 − federal) = 35.4%, and the TEY 4.95%. With the cap on the federal deduction for state and local taxes, many investors use the simple sum. High earners who pay the 3.8% net investment income tax on taxable interest can add it to the federal rate, because muni interest is not subject to it.

Worked example: TEY, break-even rate and a bracket table

The yellow cells hold the muni yield, the two tax rates and the corporate yield. Rows 7 to 14 calculate the TEY with and without state tax, the after-tax corporate yield and the break-even rate. Rows 17 to 23 repeat the TEY for every federal bracket, and row 25 finds the lowest bracket where the muni comes out ahead.

Worked example: TEY, break-even rate and a bracket table

	A	B	C
1	Input or result	Value
2	Muni yield (tax-exempt)	3.20%
3	Federal marginal tax rate	32%
4	State marginal tax rate	5.0%
5	Taxable corporate bond yield	4.60%
6
7	TEY, federal tax only	4.71%
8	Combined rate, federal + state (simple sum)	37.0%
9	TEY, in-state muni (federal + state)	5.08%
10	Combined rate if state tax is deductible	35.4%
11	TEY with the deductible combined rate	4.95%
12	Corporate yield after federal + state tax	2.90%
13	Higher after tax (in-state investor)	Muni
14	Break-even tax rate: 1 − muni ÷ taxable	30.4%
15
16	Federal bracket	TEY of the 3.20% muni	Higher after tax
17	10%	3.56%	Taxable
18	12%	3.64%	Taxable
19	22%	4.10%	Taxable
20	24%	4.21%	Taxable
21	32%	4.71%	Muni
22	35%	4.92%	Muni
23	37%	5.08%	Muni
24
25	Lowest bracket where the muni wins (MINIFS)		32%

Illustrative yields and tax rates, simplified US tax rules. Educational only, not investment or tax advice.

The break-even tax rate

Turn the formula around to find the tax rate at which the two bonds pay the same after tax: t* = 1 − muni yield ÷ taxable yield. For a 3.20% muni and a 4.60% corporate bond, t* = 1 − 3.20 ÷ 4.60 = 30.4%. Above that rate the muni wins, below it the taxable bond does. The ratio 3.20 ÷ 4.60 = 69.6% is the muni-to-taxable yield ratio that bond desks quote, usually against Treasuries of the same maturity.

TEY by tax bracket

A small table answers the question for every investor at once. The federal income tax brackets are 10%, 12%, 22%, 24%, 32%, 35% and 37%, so the TEY formula is filled down next to each rate, and IF compares it with the corporate yield. The muni wins only from the 32% bracket upwards, which =MINIFS(A17:A23,C17:C23,"Muni") returns. For an investor in the 22% bracket the 3.20% muni is worth only 4.10% taxable, less than the 4.60% bond.

After-tax yield: the same comparison the other way

Instead of grossing up the muni, you can tax the corporate bond: after-tax yield = taxable yield × (1 − tax rate). At the combined 37% rate the 4.60% corporate bond keeps 4.60% × 0.63 = 2.90%, against 3.20% for the muni. Both methods always pick the same bond. The after-tax version is handy when you compare several bond types at once: Treasury interest is taxed federally but not by the states, corporate interest by both, an in-state muni by neither.

What the TEY does not tell you

• Credit and call risk: compare bonds of similar rating and maturity, and use the yield to worst for callable munis. Revenue bonds depend on the coverage of their pledged revenues (see the debt service coverage ratio).
• AMT: interest on some private activity bonds is subject to the alternative minimum tax.
• Discount bonds: a muni bought below the de minimis threshold can produce taxable market discount at maturity.
• Account type: in a tax-deferred account such as an IRA the exemption is wasted, so the TEY comparison does not apply.

Common mistakes

• Multiplying instead of dividing. 3.20% × 1.32 = 4.22% understates the TEY. The correct gross-up is 3.20% ÷ (1 − 0.32) = 4.71%.
• Using the average tax rate. The bond's interest is taxed at your marginal rate. The average rate is lower and makes the muni look worse.
• Adding state tax for an out-of-state muni. Only bonds from your own state (and some territories) are usually free of your state's tax.
• Comparing different bonds. A 20-year BBB revenue bond and a 5-year AA corporate bond differ in more than tax. Match maturity and credit quality first.
• Ignoring AMT and market discount. Some munis are not fully tax-free, which lowers their real TEY.
• Holding munis in a tax-deferred account. In an IRA or 401(k) the exemption is worth nothing, and the lower muni yield is a pure loss.