Tax-Equivalent Yield (TEY) Calculation in 32% Marginal Bracket
An investor subject to a 32% federal marginal income tax rate is evaluating a 5.10% tax-exempt municipal bond. What is the equivalent corporate taxable yield?
TEY = Municipal Tax-Free Yield ÷ (1 - Marginal Tax Rate) = 5.10% ÷ (1 - 0.32) = 5.10% ÷ 0.68 = 7.50%.
Complete Analysis & Legal Rationale
To produce the same after-tax cash flow as the 5.10% tax-free muni, a taxable corporate bond must pay at least 7.50%. At 7.50%, the investor pays 32% tax ($2.40), keeping exactly $5.10.
Mathematical Step-by-Step Derivation
- Step 1: Formula: TEY = Muni Yield ÷ (1 - Tax Rate)
- Step 2: 1 - 0.32 = 0.68 complement
- Step 3: 5.10% ÷ 0.68 = 7.50%.
Distractor Autopsy (Why Other Options Are Traps)
FINRA exam writers design incorrect distractors using specific calculation mistakes and regulatory misconceptions. Review why each option succeeds or fails:
5.10% ÷ 0.68 = 7.50% exact tax-equivalent yield.
Multiplies by (1 + 0.32) = 5.10% × 1.32 = 6.73%, an incorrect formula.
Calculates corporate after-tax yield (5.10% × 0.68) instead of grossing up.
Divides by 1 - 0.37 (wrong tax bracket).
Official Standard: Federal statutory foundation for tax-equivalent comparison.