What this calculator does
A tax-free bond paying 4 per cent is not competing with a taxable bond paying 4 per cent. It is competing with whatever taxable yield would leave 4 per cent after tax, and that depends entirely on your marginal rate.
The effect is larger than most people expect at higher rates. At a 32 per cent marginal rate, a 4 per cent tax-free yield is equivalent to 5.88 per cent taxable. At 45 per cent it takes 7.27 per cent taxable to match the same 4 per cent.
The formula
Divide the tax-free yield by one minus the marginal tax rate. The result is the pre-tax yield a taxable investment would need to offer to leave the same amount after tax.
| Term | Meaning |
|---|---|
| Taxable equivalent yield | The pre-tax yield a taxable bond must pay to match the tax-free one. |
| Marginal tax rate | The rate applied to your next dollar of income, which is what matters here. |
| Tax-free yield | The stated yield on the exempt investment. |
The inputs explained
| Field | What to enter |
|---|---|
| Tax-free yield (%) | The yield on the tax-free investment. |
| Marginal tax rate (%) | Your marginal tax rate, meaning the rate on your highest dollar of income, not your average rate. |
When to use it
Comparing a municipal bond with a corporate one
The exemption is only worth having if the equivalent yield beats what taxable bonds offer.
Assessing a tax-advantaged account
The same arithmetic shows what a sheltered return is worth against a taxed one.
Understanding why exempt bonds pay less
They can offer lower yields precisely because the after-tax result still competes.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What taxable yield matches 4 per cent tax-free?
The equivalent taxable yield at four marginal rates.
| Marginal tax rate | Taxable equivalent yield | Extra yield a taxable bond must offer |
|---|---|---|
| 15% | 4.71% | 0.706% |
| 24% | 5.26% | 1.26% |
| 32% | 5.88% | 1.88% |
| 45% | 7.27% | 3.27% |
Questions
Should I use my marginal or average tax rate?
Marginal, because the investment income sits on top of your other income and is taxed at the highest rate that applies. Using the average rate understates the benefit of the exemption.
Why do tax-free bonds offer lower yields?
Because the market prices in the exemption. Issuers can pay less and still attract buyers whose after-tax return remains competitive, which is precisely the benefit the exemption is meant to deliver to them.
Does this apply outside the United States?
The arithmetic applies anywhere an investment is exempt while alternatives are taxed, though the specific instruments differ. Municipal bonds are the classic American example; other countries have their own exempt vehicles.
Is a tax-free bond always better at a high rate?
Not automatically. Credit quality, liquidity and duration still matter, and an exempt bond with worse credit is not a bargain simply because of its tax treatment. The equivalent yield is one input among several, and tax advice should come from a qualified professional.
For a discount instrument's yield, see the bond equivalent yield calculator. For the effect of inflation on a return, see the real interest rate calculator.