Reading 64: Understanding Yield Spreads-LOS i 习题精选 2011, face, security, carries, center

1215

Session 15: Fixed Income: Basic Concepts
Reading 64: Understanding Yield Spreads

LOS i: Calculate the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security.

 

 

A municipal bond carries a coupon of 6.75% and is traded at par. To a taxpayer in the 28% tax bracket, this bond provides an equivalent taxable yield of:

A) 6.75%.

B) 8.53%.

C) 9.38%.

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ETY = Yield/(1 ? Marginal Tax Rate)

0.0675/(1 ? 0.28) = 9.38%

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What would the marginal tax rate have to be for an investor to be indifferent between a 6% yield on tax exempt municipal bonds and a 10% corporate bond?

A) 60%.

B) 40%.

C) 20%.

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10 = 6 / (1 ? MTR )
0.10 = 0.06 / (1 – MTR); 0.10 – 0.1MTR = 0.06;
MTR = -0.04 / -0.10 = 0.40 or 40%

1215

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%.

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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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A municipal bond carries a coupon of 6% and is traded at par. To a taxpayer in the 34% tax bracket, this bond provides an equivalent taxable yield of:

A) 8.53%.

B) 9.09%.

C) 6.00%.

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ETY = yield/(1 ? marginal tax rate)

0.06/(1 ? 0.34) = 9.09%

1215

Consider a corporate bond with a yield of 6.8% and a municipal bond (with equivalent risk) with a 4.9% yield. Which of the following statements is most accurate?

A) An investor with a marginal tax rate of 40% prefers the corporate bond.

B) An investor with a marginal tax rate of 28% is indifferent between the two bonds.

C) The tax-equivalent yield for an investor with a 35% marginal tax rate is 7.32%.

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An investor with a marginal tax rate of 28% has a tax-equivalent yield on the municipal bond of 6.8% and is, therefore, indifferent between the two bonds (of equivalent risk). As the marginal tax rate increases, the investor will prefer the municipal bond to the corporate bond. Note that with a marginal tax rate of 35%, the tax-equivalent yield for the municipal bond would be 4.9 / (1 ? 0.35), or 7.54%.

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A 6% annual coupon paying bond has two years remaining to maturity and is priced at par. Assuming a 40% tax rate, the after-tax yield for this bond is closest to:

A) 4.8%.

B) 2.4%.

C) 3.6%.

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Since the bond is trading at par, its yield to maturity is equal to its coupon rate of 6.0%. The after-tax yield is (1 ? 0.4)(6.0%) = 3.6%.