after-tax yield question in qbank purchase, investor, question, discount, like

hardwork24

Hi guys,
i have a question from qbank which i like to seek some clarification.

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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%.
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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

siavosh

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

Penny-wenny

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%