# after-tax yield question in qbank

Hi guys, i have a question from qbank which i like to seek some clarification. ====================================================== A municipal bond selling at 12% above par offers a yield of 3.2%. A taxable Treasury note selling at an 8% discount offers a yield of 4.6%. An investor in the 32.5% tax bracket wishes to purchase an equal dollar amount of both bonds. The after-tax yield of the two-bond portfolio is closest to: A) 4.67%. B) 2.63%. C) 3.15%. Your answer: B was incorrect. The correct answer was C) 3.15%. The after-tax yield of the Treasury note is the stated yield times one minus the tax rate, or 4.6% times 67.5%, or 3.1%. To calculate the portfolio yield, take the average after-tax yields of both bonds, which is 3.15%. ===================================================== My calculations are: municipal bond = 0.0032 * (1-0.325) * 0.5 = 1.55 Treasury note = 0.0046 * (1-0.325) * 0.5 = 1.08 1.05 + 1.08 = 2.63% The answer from qbank seems like it never include the municipal bond in the calculation. Is it because it is tax exempt? thanks

Muni trading at 112 (12 above par), income from muni is 3.584 (112*0.032, tax-free) Treasury trading at 92 (8 discount to par), income from treasury 2.8566 (92*(0.046)(1-0.325)) Total income=3.584+2.8566=6.4406 Total portfolio value=92+112=204 Portfolio Yield=6.4406/204=3.15%

The muni is not taxable - you dont need to multiply the muni yield by (1-t).