Taxable-Equivalent Yield Calculator

The comparison question

Suppose one yield is treated as exempt from the tax represented by the entered rate. The question is: what taxable yield would leave the same after-tax percentage? If the tax-exempt yield is E and the tax rate is t, the taxable equivalent is E ÷ (1 − t). The page then subtracts the modeled tax from that equivalent to show the equality check.

At a 3% tax-exempt yield and a 25% tax assumption, the equivalent is 3% ÷ 0.75 = 4%. Tax at 25% is 1 percentage point, leaving 3% after tax. The result is a comparison, not a prediction of a bond’s future return.

Why the denominator matters

The taxable yield is the amount before tax, so the after-tax relationship is taxable yield × (1 − tax rate) = tax-exempt yield. Solving for taxable yield requires division by the retained fraction. Subtracting 25% from 3% would answer a different question and would understate the equivalent taxable yield.

As the tax rate rises, the retained fraction becomes smaller and the grossed-up taxable equivalent becomes larger. The calculator shows the uplift in percentage points so the visitor can see how much of the comparison comes from the assumption rather than from the investment itself.

Yield definitions must match

A coupon rate, current yield, yield to maturity, distribution yield, and total return are not interchangeable. The formula can be applied to any entered yield only if both alternatives use the same definition, period, price basis, and compounding convention.

Before comparing two securities, write down whether the input is a quoted yield, a realized return, or a projected return. Fees, premium or discount, call features, default risk, duration, liquidity, and price volatility may matter more than a small tax-equivalent difference.

Tax exemption is not universal

The label ‘tax-exempt’ can refer to a particular tax, investor, jurisdiction, account, income category, or holding condition. A security may be exempt from one tax but not another, and a resident may face a different rule from a nonresident. The calculator intentionally asks the visitor to supply the tax assumption rather than making that legal determination.

For a worldwide comparison, record the country or region, tax year, investor status, tax type, and source of the exemption. A currency selector can format a separate investment amount, but it does not establish the applicable tax rate or convert a yield into a local legal result.

Negative and high tax rates

A negative entered yield is retained as a mathematical scenario, although it may represent a fee-like or price-based outcome rather than ordinary coupon income. The tax rate must remain below 100% because a 100% rate would make the gross-up denominator zero.

High rates produce large equivalent yields and should prompt a review of the input. A high result does not mean the tax-exempt investment is automatically better; it only says the taxable comparison would need that yield under the selected uniform-rate assumption.

Compare after-tax outcomes

The best use is to place the output next to an actual after-tax estimate that includes the relevant tax treatment, costs, and cash-flow definition. If the alternative taxable yield is above the taxable-equivalent result, it may produce a higher after-tax percentage under the simplified model; if it is below, the opposite is true. Risk and liquidity remain separate decisions.

Do not compare a tax-exempt yield to a taxable total return without adjusting the definitions. A total return can include price change and reinvestment, while a current yield may not. Keep the same horizon and terminology on both sides of the comparison.

A reproducible note

A clear worksheet note states: tax-exempt yield, assumed tax rate, formula, resulting equivalent yield, and which taxes are or are not included. For the default, record 3%, 25%, 3% ÷ (1 − 0.25) = 4%, and a 3% after-tax check.

Round only for display. If the input rate is quoted to two decimals, do not report a six-decimal equivalent as though the underlying investment were known to that precision. Preserve the source and date of the quoted yield outside the calculator.

FAQs

Does this calculate a bond price? No, it compares yield percentages. Does it include state or local tax? No, unless the entered single rate is intended as a combined assumption. Is a higher tax-equivalent yield always better? No; it says nothing about risk, fees, duration, default, or liquidity. Can I use it for another tax-advantaged product? Yes as arithmetic, but only if the entered yield and tax treatment are genuinely comparable.