Tax-Equivalent Yield Calculator

Tax-free income can look smaller than taxable income and still be more valuable after tax. The tax-equivalent yield calculator converts a tax-free bond yield into the taxable yield that would be needed to match it after applying your marginal tax rate. This is especially common when comparing municipal bonds with taxable bonds, brokered CDs, Treasury securities, savings products, or bond funds. The calculation is simple, but the interpretation is personal because tax rates, exemptions, and bond features vary.

The calculator has three inputs. Tax-free bond yield is the annual yield on the municipal or other tax-exempt bond you are evaluating. Marginal tax rate is the tax rate that would apply to the next dollar of taxable interest. Taxable yield to compare is optional; it lets the results show the after-tax yield of a taxable alternative and whether the tax-free yield is ahead or behind. The calculation does not apply a separate federal, state, and local stack. It uses the one marginal tax rate you enter, so combine rates only when that is appropriate for the comparison.

Why tax-equivalent yield matters

Suppose one bond pays 4% tax-free and another pays 5% taxable. The 5% figure is not automatically better. At a 24% marginal tax rate, you keep 76% of taxable interest, so the after-tax yield on a 5% taxable investment is 3.8%. The 4% tax-free bond is ahead on after-tax yield before considering fees, risk, maturity, and liquidity. Tax-equivalent yield expresses the same comparison from the other direction: a taxable investment would need to yield about 5.26% to match a 4% tax-free yield at that tax rate.

This page pairs well with the APY calculator when you need to understand a deposit product’s quoted yield, the compound interest calculator when you want to project a yield difference over time, and the CD rate calculator when comparing a taxable CD with a municipal bond. For cash reserves rather than bond income, compare with the savings calculator or money market account calculator.

Formula used by the calculator

The marginal tax rate is converted from a percent to a decimal:

$\text{tax rate} = \frac{\text{marginal tax rate}}{100}$

Tax-equivalent yield divides the tax-free yield by the portion of taxable interest you keep:

$\text{taxable-equivalent yield} = \frac{\text{tax-free bond yield}}{1 - \text{tax rate}}$

The taxable comparison yield is also converted to an after-tax yield:

$\text{taxable after-tax yield} = \text{taxable yield to compare} \times \left(1 - \text{tax rate}\right)$

The advantage shown in the results is:

$\text{advantage} = \text{tax-free bond yield} - \text{taxable after-tax yield}$

If advantage is positive or zero, the calculator labels it as a tax-free yield advantage. If advantage is negative, it labels the absolute value as a taxable yield advantage. The calculator rejects marginal tax rates of 100% or more because the denominator would be zero or negative.

Checking the primary result

Use the defaults: 4% tax-free bond yield, 24% marginal tax rate, and 5% taxable yield to compare. The tax rate decimal is 24 divided by 100, or 0.24. The share of taxable interest kept after tax is 1 minus 0.24, or 0.76.

The taxable-equivalent yield is 4 divided by 0.76, which equals 5.2631578947%. Rounded for display, the taxable yield needed to match is 5.26%. The taxable comparison’s after-tax yield is 5 multiplied by 0.76, or 3.80%. The advantage is the 4.00% tax-free yield minus the 3.80% after-tax taxable yield, or 0.20%. The results therefore shows a tax-free yield advantage of 0.20%.

Those numbers are deliberately yield-only. They do not say the municipal bond is safer, more liquid, or better priced. They say that, before considering those other features, a taxable investment yielding 5% leaves less after-tax yield than a 4% tax-free investment for someone using a 24% marginal tax rate in this simplified comparison.

Choosing the tax rate input

The marginal rate should match the taxable income being compared. If taxable bond interest would be subject to federal income tax and state income tax, while the municipal bond is exempt from both for your situation, you may want a combined marginal rate. If the bond is exempt federally but taxable by your state, a federal-only rate may be closer. If a Treasury security is exempt from state income tax but taxable federally, the comparison may require a different rate than a corporate bond. The calculator cannot infer those rules from the bond name; you provide the tax assumption.

Be careful with average tax rates. A household’s average tax rate across all income is often lower than the marginal rate on the next dollar of interest. Tax-equivalent yield is normally a marginal comparison because it asks what happens to one more dollar of taxable interest. For large investments, alternative minimum tax exposure, Social Security taxation, Medicare surtaxes, state-specific rules, and fund expense ratios may matter. For tax advice, use IRS guidance as a starting point and consult a qualified professional.

Caveats and common mistakes

• Do not compare only the taxable-equivalent yield and ignore credit risk, maturity, duration, or call risk.
• Do not assume every municipal bond is exempt from every tax you pay.
• Do not use a stale tax bracket after income, filing status, or law changes.
• Do not forget fund expenses when comparing a municipal bond fund with an individual taxable bond.
• Do not treat the optional taxable yield comparison as a total-return forecast; it is an after-tax yield snapshot.

Sources

• IRS, Topic no. 403, Interest Received — overview of taxable and tax-exempt interest.
• IRS, Publication 550, Investment Income and Expenses — detailed tax discussion for investment income, including interest.
• CFPB, What is an annual percentage yield? — consumer definition of APY for comparing yield quotes.
• FDIC, Deposit insurance resources — context for insured deposit products that may be compared with bond yields.