{
  "id": "tax-equivalent-yield",
  "version": "2bfa7c409814",
  "status": "published",
  "name": "Tax Equivalent Yield Calculator",
  "question": "What is my tax equivalent yield?",
  "summary": "Works out the taxable yield that matches a tax-free municipal bond yield after your federal and state income tax, and compares it with a taxable bond.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/tax-equivalent-yield-calculator",
  "markdown": "https://www.acalculator.org/finance/tax-equivalent-yield-calculator.md",
  "kind": "function",
  "method": "combined rate t = federal + state; kept = tax-free yield (in-state) or tax-free yield × (1 − state) (out of state); TEY = kept ÷ (1 − t); a taxable yield keeps yield × (1 − t).",
  "assumptions": [
    "The combined rate adds the federal and state rates. It does not subtract a federal deduction for state tax.",
    "The bond’s interest is free of federal income tax and of the alternative minimum tax. Some municipal bonds are taxable or subject to the AMT.",
    "Tax on capital gains, the net investment income tax and effects on the taxation of Social Security benefits are not included."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "muni": {
        "title": "Tax-free yield",
        "description": "The yield of the municipal bond or fund whose interest is free of federal income tax.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      },
      "fed": {
        "title": "Federal tax rate",
        "description": "Your federal income tax bracket: the rate on your last dollar of income.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 99
      },
      "state": {
        "title": "State tax rate",
        "description": "Optional: your state and local income tax rate on interest.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      },
      "instate": {
        "title": "Free of your state tax too?",
        "description": "Yes when the bond is from your own state (or a fund of them), so its interest is not taxed by your state.",
        "type": "string",
        "enum": [
          "yes",
          "no"
        ]
      },
      "taxable": {
        "title": "Compare with a taxable yield",
        "description": "Optional: the yield of a taxable bond or CD to compare with.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      }
    }
  },
  "outputs": {
    "tey": {
      "label": "Tax equivalent yield",
      "description": "The taxable yield that leaves the same after tax as the tax-free yield.",
      "format": "percent"
    },
    "rate": {
      "label": "Combined tax rate",
      "description": "The federal rate plus the state rate.",
      "format": "percent"
    },
    "kept": {
      "label": "Tax-free yield after tax",
      "description": "What the muni keeps: its yield, less your state tax when it is out of state.",
      "format": "percent"
    },
    "taxableAfter": {
      "label": "Taxable yield after tax",
      "description": "The taxable yield × (1 − combined tax rate).",
      "format": "percent"
    },
    "better": {
      "label": "Which pays more after tax",
      "description": "The taxable yield compared with the tax equivalent yield.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "muni": 3,
      "fed": 24,
      "state": 5,
      "instate": "yes"
    },
    "outputs": {
      "tey": 4.225352112676056,
      "rate": 29,
      "kept": 3
    },
    "text": "A tax-free yield of 3% equals a taxable yield of 4.225% at a 29% tax rate."
  },
  "examples": [
    {
      "given": {
        "muni": 3,
        "fed": 37,
        "state": 0,
        "instate": "yes"
      },
      "expect": {
        "tey": 4.761904761904762,
        "rate": 37,
        "kept": 3
      },
      "source": "Municipal Securities Rulemaking Board, Understanding Taxable Municipal Bonds (taxable equivalent yield = tax-exempt yield ÷ (1 − tax bracket); 3% at a 37% bracket is about 4.76%), https://www.msrb.org/Understanding-Taxable-Municipal-Bonds (retrieved 2026-10-03); hand calculation in content.mdx: 3 ÷ 0.63"
    },
    {
      "given": {
        "muni": 3,
        "fed": 24,
        "state": 5,
        "instate": "yes",
        "taxable": 4
      },
      "expect": {
        "tey": 4.225352112676056,
        "rate": 29,
        "taxableAfter": 2.84,
        "better": "The tax-free yield"
      },
      "source": "hand calculation in content.mdx: 3 ÷ (1 − 0.24 − 0.05); FINRA, Bonds (municipal bonds are typically exempt from federal tax and, for residents of the issuing state, from state and local taxes), https://www.finra.org/investors/investing/investment-products/bonds (retrieved 2026-10-03)"
    },
    {
      "given": {
        "muni": 3,
        "fed": 24,
        "state": 5,
        "instate": "no",
        "taxable": 5
      },
      "expect": {
        "kept": 2.85,
        "tey": 4.014084507042254,
        "taxableAfter": 3.55,
        "better": "The taxable yield"
      },
      "source": "hand calculation in content.mdx: 3 × 0.95 ÷ 0.71; Municipal Securities Rulemaking Board, Understanding Taxable Municipal Bonds (taxable equivalent yield = tax-exempt yield ÷ (1 − tax bracket); 3% at a 37% bracket is about 4.76%), https://www.msrb.org/Understanding-Taxable-Municipal-Bonds (retrieved 2026-10-03)"
    },
    {
      "given": {
        "muni": 4.5,
        "fed": 22,
        "instate": "yes"
      },
      "expect": {
        "tey": 5.769230769230769,
        "rate": 22
      },
      "source": "hand calculation in content.mdx: 4.5 ÷ 0.78; Municipal Securities Rulemaking Board, Understanding Taxable Municipal Bonds (taxable equivalent yield = tax-exempt yield ÷ (1 − tax bracket); 3% at a 37% bracket is about 4.76%), https://www.msrb.org/Understanding-Taxable-Municipal-Bonds (retrieved 2026-10-03)"
    }
  ],
  "sources": [
    "Municipal Securities Rulemaking Board, Understanding Taxable Municipal Bonds: taxable equivalent yield = tax-exempt yield ÷ (1 − tax bracket). https://www.msrb.org/Understanding-Taxable-Municipal-Bonds (retrieved 2026-10-03)",
    "FINRA, Bonds: municipal bonds are typically exempt from federal tax and, for residents of the issuing state, from state and local taxes. https://www.finra.org/investors/investing/investment-products/bonds (retrieved 2026-10-03)"
  ],
  "related": [
    "bond",
    "capital-gains-tax",
    "cd"
  ],
  "changelog": []
}