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Reading 67: Introduction to the Valuation of Fixed Income

1.What is the present value of a 7 percent semi-annual pay corporate bond with a $1,000 face value and 20 years to maturity if it is yielding 6.375 percent?  If a municipal bond is yielding 4.16 percent and an investors marginal tax rate is 35 percent, would the investor prefer the corporate bond or the municipal bond?

       Value            Investor preference

A)                 $1,121.23        municipal bond

B)                 $1,070.09        corporate bond

C)                 $1,121.23        corporate bond

D)                 $1,070.09        municipal bond

2What is the present value of a three-year security that pays a fixed annual coupon of 6 percent using a discount rate of 7 percent?

A)   92.48.

B)   100.00.

C)   101.75.

D)   97.38.

3An investor has the following options available to them:

§ They can buy a 10% semi annual coupon, 10-year bond for $1,000.

§ The coupons can be reinvested at 12%.

§ They estimate the bond will be sold in 3 years $1,050.

Based on this information, what would be the average annual rate of return over the 3 years?

A)   11.5%.

B)   13.5%.

C)   10.0%.

D)   9.5%.

4If an investor purchases a 8 1/2s 2001 Feb. $10,000 par Treasury Note at 105:16 and holds it for exactly one year, what is the rate of return if the selling price is 105:16?

A)   8.00%.

B)   8.06%.

C)   8.22%.

D)   8.50%.

5Assuming the risk-free rate is 5 percent and the appropriate risk premium for a AAA-rated issuer is 4 percent, the appropriate discount rate for a 10-year Treasury note is:

A)   4%.

B)   9%.

C)   5%.

D)   1%.

答案和详解如下:

1.What is the present value of a 7 percent semi-annual pay corporate bond with a $1,000 face value and 20 years to maturity if it is yielding 6.375 percent?  If a municipal bond is yielding 4.16 percent and an investors marginal tax rate is 35 percent, would the investor prefer the corporate bond or the municipal bond?

       Value            Investor preference

A)                 $1,121.23        municipal bond

B)                 $1,070.09        corporate bond

C)                 $1,121.23        corporate bond

D)                 $1,070.09        municipal bond

The correct answer was D)

N = 20 * 2 = 40; I/Y = 6.375/2 = 3.1875; PMT = 70/2 = 35; and FV = 1,000.

Compute PV = $1,070.09.

The taxable-equivalent yield on the municipal bond is:

4.16% / (1 - 0.35) = 6.4%

The investor would prefer the municipal bond because the taxable-equivalent yield is greater than the yield on the corporate bond:

6.4% > 6.375%

2What is the present value of a three-year security that pays a fixed annual coupon of 6 percent using a discount rate of 7 percent?

A)   92.48.

B)   100.00.

C)   101.75.

D)   97.38.

The correct answer was D)

This value is computed as follows:

Present Value = 6/1.07 + 6/1.072 + 106/1.073 = 97.38

The value 92.48 results if the coupon payment at maturity of the bond is neglected. The coupon rate and the discount rate are not equal so 100.00 cannot be the correct answer.

3An investor has the following options available to them:

§ They can buy a 10% semi annual coupon, 10-year bond for $1,000.

§ The coupons can be reinvested at 12%.

§ They estimate the bond will be sold in 3 years $1,050.

Based on this information, what would be the average annual rate of return over the 3 years?

A)   11.5%.

B)   13.5%.

C)   10.0%.

D)   9.5%.

The correct answer was A)

1.  Find the FV of the coupons and interest on interest:

        n = 3(2) = 6; i = 12/2 = 6; PMT = 50;  compute           FV =       348.77

2.  Determine the value of the bond at the end of 3 years:  given =   1,050.00

                                                           1,398.77

3.  Equate FV (1398.77) with PV (1000)  over 3 years (n = 6); compute i = 5.75(2) = 11.5%

4If an investor purchases a 8 1/2s 2001 Feb. $10,000 par Treasury Note at 105:16 and holds it for exactly one year, what is the rate of return if the selling price is 105:16?

A)   8.00%.

B)   8.06%.

C)   8.22%.

D)   8.50%.

The correct answer was B)

Purchase Price = [(105 + 16/32)/100] x 10,000 = $10,550.00

Selling price = [(105 + 16/32)/100] x 10,000 = $10,550.00

Interest = 8 1/2% of 10,000 = $850.00

Return = (P end - P beg + Interest)/P beg = (10,550.00 - 10,550.00 + 850.00)/10,550.00 = 8.06%

5Assuming the risk-free rate is 5 percent and the appropriate risk premium for a AAA-rated issuer is 4 percent, the appropriate discount rate for a 10-year Treasury note is:

A)   4%.

B)   9%.

C)   5%.

D)   1%.

The correct answer was C)

For a 10-year treasury the relevant discount rate is the risk free rate.

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