The Tax Equivalent Yield (TEY) is a crucial metric for investors comparing the returns of taxable investments versus tax-advantaged investments. It helps answer the question: "What yield does a taxable bond need to offer to be equivalent in after-tax return to a tax-exempt bond?"
For instance, a municipal bond might offer a lower stated yield than a corporate bond, but because its interest is exempt from federal (and often state and local) income taxes, its actual after-tax return could be higher. The TEY calculation standardizes this comparison by calculating the hypothetical yield a taxable bond would need to provide to match the after-tax return of a tax-exempt bond.
The Formula
The general formula for calculating the Tax Equivalent Yield (TEY) for a taxable investment is:
Tax-Exempt Yield: The stated yield on a municipal bond or other tax-advantaged investment.
Marginal Tax Rate: The investor's highest income tax rate, including federal, state, and local taxes, that applies to the investment income.
In our calculator, we simplify the input to provide the equivalent taxable yield given a specific taxable yield and the investor's combined tax rate. The calculator essentially performs the reverse logic to show what a tax-free yield would need to be to match a given taxable yield.
Specifically, the calculation performed by this tool is:
This represents the yield you would need from a fully taxable investment to match the net return of an investment yielding Taxable Yield that is tax-exempt.
Use Cases
Investment Comparisons: Investors can use TEY to compare the attractiveness of municipal bonds (tax-exempt) versus corporate bonds or other taxable securities.
Portfolio Allocation: Helps determine the optimal asset allocation between taxable and tax-exempt income streams based on an individual's tax bracket.
Financial Planning: Essential for financial advisors and individuals planning for retirement or managing income during their working years.
Example Calculation
Let's say you are considering an investment with a Taxable Yield of 4.5%. Your combined Federal Tax Rate is 22% and your State Tax Rate is 5%.
First, we calculate the combined marginal tax rate: 22% + 5% = 27%.
Then, we calculate the equivalent taxable yield needed to match a tax-free yield of 4.5%:
Equivalent Taxable Yield = 4.5% / (1 - 0.27)
Equivalent Taxable Yield = 4.5% / 0.73
Equivalent Taxable Yield ≈ 6.16%
This means a taxable investment would need to yield approximately 6.16% to provide the same after-tax return as a tax-exempt investment yielding 4.5% for someone in your tax bracket.
function calculateTaxEquivalentYield() {
var taxableYieldInput = document.getElementById("taxableYield");
var federalTaxRateInput = document.getElementById("federalTaxRate");
var stateTaxRateInput = document.getElementById("stateTaxRate");
var taxableYield = parseFloat(taxableYieldInput.value);
var federalTaxRate = parseFloat(federalTaxRateInput.value);
var stateTaxRate = parseFloat(stateTaxRateInput.value);
var resultValueElement = document.getElementById("resultValue");
// Clear previous results
resultValueElement.innerHTML = "–";
// Input validation
if (isNaN(taxableYield) || isNaN(federalTaxRate) || isNaN(stateTaxRate)) {
resultValueElement.innerHTML = "Please enter valid numbers.";
return;
}
if (taxableYield < 0 || federalTaxRate < 0 || stateTaxRate 100 || stateTaxRate > 100) {
resultValueElement.innerHTML = "Tax rates cannot exceed 100%.";
return;
}
// Calculate combined tax rate (as a decimal)
var combinedTaxRateDecimal = (federalTaxRate / 100) + (stateTaxRate / 100);
// Ensure denominator is not zero or negative
if (1 – combinedTaxRateDecimal <= 0) {
resultValueElement.innerHTML = "Combined tax rate too high to calculate meaningfully.";
return;
}
// Calculate Tax Equivalent Yield
// This formula calculates what a taxable bond's yield would need to be
// to match the after-tax return of a tax-exempt bond with the input 'taxableYield'
// as its tax-exempt yield.
var taxEquivalentYield = taxableYield / (1 – combinedTaxRateDecimal);
// Format and display the result
resultValueElement.innerHTML = taxEquivalentYield.toFixed(2) + "%";
}