Tax-equivalent yield: drag the band
Drag the handle to set the federal marginal rate. The tax-exempt yield is held still, so the headline equivalent moves only because more or less tax is being undone. At a 32 percent band the identity is divide by 0.68. At 0 percent the two quotes already match.
Tax-equivalent yield
5.15%
Federal band
32%
The exempt yield is a fixed 3.50 percent. Multiply the equivalent by one minus the tax rate and you must get 3.50 back. Illustrative arithmetic, federal only, not a bond pick or advice.
Tax-exempt yield
3.50 percent, held still so only the band moves the equivalent.
In short
- Drag the handle right for a higher federal band.
- Read the tax-equivalent yield. Check it: times one minus the tax rate must return the exempt yield.
- Stop at 0 percent, where the equivalent equals the exempt quote.
- Stop at 32 percent, the default teaching-sheet band.
Undo the tax, then compare
A tax-exempt yield and a taxable yield cannot be compared as printed. Tax-equivalent yield puts them on the same after-tax footing: exempt yield over one minus the marginal tax rate.
The tax-equivalent yield calculator is the working tool. Taxable against tax-exempt yield is the pair in a table. How tax-equivalent yield works is the long form.
Federal only, on purpose
State tax, the federal exemption for some Treasuries, and the alternative minimum tax are local adjustments. Folding a guessed state rate into the one-line identity is how an equivalent becomes a number nobody can audit.
Credit risk is also outside it. Matching tax treatment does not match issuers. A municipal quote is not the same object as a Treasury quote just because made the yields meet.
Three conversions, not one
APR against APY is compounding. Tax-equivalent yield is tax. Real return is inflation. After-tax, after-inflation, after-compounding is three identities. How APR and APY work is the compounding step. How real returns work is the inflation step. Tax-exempt is the wrapper this identity is built for.
Common questions
Why does a higher tax band raise the equivalent?
Because more tax is being undone. The same exempt coupon is worth more, in taxable-yield terms, to a holder in a higher band.
Does this include state tax?
No. Federal only. A state that taxes Treasuries and exempts its own municipals widens the gap; a state that taxes both narrows it.
Should I buy the municipal?
The picture will not say. It equalises tax treatment. It is educational material, not advice.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.