The formula with every layer of tax, the comparison with Treasuries and corporates, and the bracket at which munis stop winning.
Tax-equivalent yield is the tax-exempt yield divided by one minus the marginal tax rate the taxable alternative would bear: TEY = muni yield ÷ (1 − t). For an illustrative top-bracket family in a state with a 6.0 per cent income tax, an in-state municipal bond yielding 3.40 per cent is worth the same as a corporate bond yielding 6.39 per cent, because the corporate's interest bears 37 per cent federal tax, the 3.8 per cent net investment income tax and the state tax, 46.8 per cent in all. Against a Treasury, which is free of state tax, the hurdle is 5.74 per cent.
Worked in full in The Family Office Professional by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
For a family office running the bond sleeve of a taxable family, this is the first calculation behind almost every fixed income decision, and it is usually done with only the federal rate. That understates the muni's advantage for exactly the families who own most of them. The formula is one line; the work is in choosing the right rate for the comparison.
| Input | Value |
|---|---|
| In-state municipal bond yield (exempt from federal tax, and from tax in the home state, as most states allow) | 3.40% |
| Corporate bond yield (fully taxable) | 5.10% |
| Treasury yield (exempt from state tax) | 4.30% |
| Federal marginal rate | 37% |
| Net investment income tax | 3.8% |
| State income tax | 6.0% |
| Size of the bond sleeve | $50,000,000 |
State tax is assumed to give no federal deduction, the usual position for a high-income family whose state and local taxes already exceed the deduction cap. Where it is deductible, the combined rate is lower and the formula needs the interaction term.
Against a corporate: t = 37% + 3.8% + 6.0% = 46.8%
Against a Treasury: t = 37% + 3.8% = 40.8% (no state tax on Treasury interest)
TEY vs corporate = 3.40% ÷ (1 − 46.8%) = 6.39%
TEY vs Treasury = 3.40% ÷ (1 − 40.8%) = 5.74%
In Excel, with the muni yield in B1 and the combined rate in B2: =B1/(1-B2). Or, equivalently, take every bond to an after-tax yield with =Yield*(1-Rate) and compare those.
| Bond | Yield | Tax rate | After-tax yield | After-tax income |
|---|---|---|---|---|
| In-state muni | 3.40% | 0.0% | 3.40% | 1,700,000 |
| Corporate | 5.10% | 46.8% | 2.71% | 1,356,600 |
| Treasury | 4.30% | 40.8% | 2.55% | 1,272,800 |
The corporate pays 2,550,000 before tax and 1,193,400 of it goes in tax. The muni keeps 343,400 a year more than the corporate and 427,200 more than the Treasury. Both readings say the same thing: the muni wins as long as its yield exceeds the taxable yield times one minus the tax rate.
| Profile | Combined rate | TEY | Corporate after tax | Better choice |
|---|---|---|---|---|
| 24% federal, no NIIT, 6.0% state | 30.0% | 4.86% | 3.57% | corporate |
| 32% federal, NIIT, 6.0% state | 41.8% | 5.84% | 2.97% | muni |
| 35% federal, NIIT, 6.0% state | 44.8% | 6.16% | 2.82% | muni |
| 37% federal, NIIT, 6.0% state | 46.8% | 6.39% | 2.71% | muni |
| 37% federal, NIIT, no state tax | 40.8% | 5.74% | 3.02% | muni |
| 37% federal, NIIT, 13.3% state | 54.1% | 7.41% | 2.34% | muni |
The break-even combined rate is 1 − 3.40 ÷ 5.10 = 33.3 per cent. Below it, the corporate is worth more after tax; above it, the muni. At a 13.3 per cent state rate the muni is worth as much as a 7.41 per cent corporate, which is why families in high-tax states pay up for in-state paper.
Out-of-state munis. Interest on state and local bonds is excluded from federal income under section 103 of the Internal Revenue Code, but the state exemption is a matter of each state's law: most states exempt their own bonds and tax those of other states, and a few tax some of their own. A muni issued in another state is usually taxed by the family's home state. At 6.0 per cent, the 3.40 per cent becomes 3.20 per cent after tax, a tax-equivalent yield of 6.01 per cent against the corporate. Still ahead here, but a national muni fund is not the same instrument as an in-state bond for a resident of a high-tax state.
Illustrative, not tax advice. The rates are simplified federal and state rates for one illustrative family, with no state deduction against federal tax. Actual brackets, the NIIT thresholds, the state's treatment of its own and other states' bonds, the alternative minimum tax and market discount should be checked with a qualified US tax adviser before any allocation decision.
Divide the muni yield by one minus every tax the alternative would pay. For a top-bracket family in a 6.0 per cent state, 3.40 per cent tax-free equals 6.39 per cent taxable, and the muni wins whenever the combined rate exceeds 33.3 per cent. Taxes on the rest of the portfolio compound in the same way, as in how to calculate tax drag on a taxable portfolio. The Family Office Professional describes how single-family and multi-family offices invest for taxable families, and the free workbook for this case sets out what running such an office costs.
No. Tax-exempt interest is not net investment income, so the 3.8 per cent tax falls on the taxable alternative only and belongs in the tax-equivalent rate. Leaving it out lowers the illustrative tax-equivalent yield from 6.39 to 5.96 per cent against a corporate bond, when state tax is still included, and understates the case for the muni.
When the combined marginal rate on the corporate's interest exceeds one minus the ratio of the two yields. With a muni at 3.40 per cent and a corporate at 5.10 per cent, the break-even rate is 33.3 per cent. A family in the 24 per cent bracket with a 6.0 per cent state tax, 30.0 per cent in all, should own the corporate, before any difference in credit risk.
With whichever the family would actually buy, at the same maturity and similar credit quality, and with the right tax layers. Treasuries are exempt from state income tax, so the hurdle against them is lower: 5.74 per cent in the example, against 6.39 per cent for a fully taxable corporate.
This article is one calculation from The Family Office Professional. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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