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Reading 67: Introduction to the Valuation of Fixed Income

1.A 5-year bond with a 10 percent coupon has a present yield to maturity of 8 percent. If interest rates remain constant one year from now, the price of the bond will be:

A)   lower.

B)   higher.

C)   the same.

D)   cannot be determined.

2.An investor buys a 20-year, 10 percent semi-annual bond for $900. She wants to sell the bond in 6 years when she estimates yields will be 10 percent. What is the estimate of the future price?

A)   $946.

B)   $1,000.

C)   $1,079.

D)   $1,152.

3.A discount bond (nothing changes except the passage of time):

A)   falls in value as time passes.

B)   has a steady value as time passes.

C)   rises in value as time passes.

D)   price is not related to time passing.

4.If market rates do not change, as time passes the price of a zero-coupon bond will:

A)   approach zero.

B)   approach the purchase price.

C)   approach par.

D)   move randomly about the purchase price.

5.Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Assume the term structure of interest rates is flat at 6%. If the term structure of interest rates does not change over the next twelve-month interval, the bond's price change (as a percentage of par) will be closest to:

A)   -0.84.

B)   -0.56.

C)   0.00.

D)   0.84.

6.If a bond sells at a discount and market rates are expected to stay the same until maturity, the price of the bond will:

A)   increase over time, approaching the par value minus the final interest payment at maturity.

B)   decrease over time.

C)   increase over time, approaching the par value at maturity.

D)   remain constant until maturity.

答案和详解如下:

1.A 5-year bond with a 10 percent coupon has a present yield to maturity of 8 percent. If interest rates remain constant one year from now, the price of the bond will be:

A)   lower.

B)   higher.

C)   the same.

D)   cannot be determined.

The correct answer was A)

A premium bond sells at more than face value, thus as time passes the bond value will converge upon the face value.

2.An investor buys a 20-year, 10 percent semi-annual bond for $900. She wants to sell the bond in 6 years when she estimates yields will be 10 percent. What is the estimate of the future price?

A)   $946.

B)   $1,000.

C)   $1,079.

D)   $1,152.

The correct answer was B)

Since yields are projected to be 10 percent and the coupon rate is 10 percent, we know that the bond will sell at par value.

3.A discount bond (nothing changes except the passage of time):

A)   falls in value as time passes.

B)   has a steady value as time passes.

C)   rises in value as time passes.

D)   price is not related to time passing.

The correct answer was C)

A discount bond sells at less than face value, therefore as time passes the bond value will converge upon the face value.

4.If market rates do not change, as time passes the price of a zero-coupon bond will:

A)   approach zero.

B)   approach the purchase price.

C)   approach par.

D)   move randomly about the purchase price.

The correct answer was C)

A bond's value may differ substantially from it's maturity value prior to maturity.  But as maturity draws nearer the bond's value converges to it's maturity value.  This statement is true for regular bonds as well as zero-coupon bonds. 

5.Consider a bond that pays an annual coupon of 5% and that has three years remaining until maturity. Assume the term structure of interest rates is flat at 6%. If the term structure of interest rates does not change over the next twelve-month interval, the bond's price change (as a percentage of par) will be closest to:

A)   -0.84.

B)   -0.56.

C)   0.00.

D)   0.84.

The correct answer was D)

The bond price change is computed as follows:

Bond Price Change = New Price – Old Price = (5/1.06 + 105/1.062) - (5/1.06 + 5/1.062 + 105/1.063) = 98.17 - 97.33 = 0.84.

The value -0.84 is the correct price change but the sign is wrong. The value 0.00 is incorrect because although the term structure of interest rates does not change the bond price increases since it is selling at a discount relative to par.

6.If a bond sells at a discount and market rates are expected to stay the same until maturity, the price of the bond will:

A)   increase over time, approaching the par value minus the final interest payment at maturity.

B)   decrease over time.

C)   increase over time, approaching the par value at maturity.

D)   remain constant until maturity.

The correct answer was C)

The bond’s price will increase towards the par value over time.

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