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# Multiple choice questions on bonds

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1. One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price.

a. longer; smaller.
b. shorter; larger.
c. longer; greater.
d. shorter; smaller.
e. Statements c and d are correct.

2. Assume that a 10-year Treasury bond has a 12 percent annual coupon, while a 15-year Treasury bond has an 8 percent annual coupon. The yield curve is flat; all Treasury securities have a 10 percent yield to maturity. Which of the following statements is most correct?

a. The 10-year bond is selling at a discount, while the 15-year bond is selling at a premium.
b. The 10-year bond is selling at a premium, while the 15-year bond is selling at par.
c. If interest rates decline, the price of both bonds will increase, but the 15-year bond will have a larger percentage increase in price.
d. If the yield to maturity on both bonds remains at 10 percent over the next year, the price of the 10-year bond will increase, but the price of the 15-year bond will fall.
e. Statements c and d are correct.

3. Assume that a 15-year, \$1,000 face value bond pays interest of \$37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)

a. \$ 821.92 b. \$1,207.57 c. \$ 986.43 d. \$1,120.71 e. \$1,358.24

4. You just purchased a 15-year bond with an 11 percent annual coupon. The bond has a face value of \$1,000 and a current yield of 10 percent. Assuming that the yield to maturity of 9.7072 percent remains constant, what will be the price of the bond one year from now?

a. \$1,000 b. \$1,064 c. \$1,097 d. \$1,100 \$1,150

5. Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest paid semiannually. The required nominal rate on this debt has now risen to 16 percent. What is the current value of this bond?

a. \$1,273
b. \$1,000
c. \$7,783
d. \$ 550
e. \$ 450

6. A corporate bond with 12 years to maturity has a 9 percent semiannual coupon and a face value of \$1,000. (That is, the semiannual coupon payments are \$45.) The bond has a nominal yield to maturity of 7 percent. The bond can be called in three years at a call price of \$1,045. What is the bond's nominal yield to call?

a. 4.62%
b. 10.32%
c. 17.22%
d. 5.16%
e. 2.31%

7. A 10-year bond has a face value of \$1,000. The bond has a 7 percent semiannual coupon. The bond is callable in 7 years at a call price of \$1,040. The bond has a nominal yield to call of 6.5 percent. What is the bond's nominal yield to maturity?

a. 3.14%
b. 6.05%
c. 7.62%
d. 6.27%
e. 6.55%

8. Meade Corporation bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par value of the bonds is \$1,000. The bonds have a 10 percent coupon rate and pay interest on a semiannual basis. What are the current yield and capital gains yield on the bonds for this year? (Assume that interest rates do not change over the course of the year).

a. Current yield = 8.50%; capital gains yield = 1.50%
b. Current yield = 9.35%; capital gains yield = 0.65%
c. Current yield = 9.35%; capital gains yield = -0.85%
d. Current yield = 10.00%; capital gains yield = 0.00%
e. Current yield = 10.50%; capital gains yield = -1.50%

9. A 16-year bond with a 10 percent annual coupon has a current yield of 8 percent. What is the bond's yield to maturity (YTM)?

a. 6.9%
b. 7.1%
c. 7.3%
d. 7.5%
e. 7.7%

10. Which of the following statements is most correct?

a. Other things held constant, a callable bond would have a lower required rate of return than a noncallable bond.
b. Other things held constant, a corporation would rather issue noncallable bonds than callable bonds.
c. Reinvestment rate risk is worse from a typical investor's standpoint than interest rate risk.
d. If a 10-year, \$1,000 par, zero coupon bond were issued at a price that gave investors a 10 percent rate of return, and if interest rates then dropped to the point where kd = YTM = 5%, we could be sure that the bond would sell at a premium over its \$1,000 par value.
e. If a 10-year, \$1,000 par, zero coupon bond were issued at a price that gave investors a 10 percent rate of return, and if interest rates then dropped to the point where kd = YTM = 5%, we could be sure that the bond would sell at a discount below its \$1,000 par value.

#### Solution Preview

1. One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price.

a. longer; smaller.
b. shorter; larger.
c. longer; greater.
d. shorter; smaller.
e. Statements c and d are correct.

The longer the time to maturity the more the volatility in price. Hence c and d are correct. (Answer e)

2. Assume that a 10-year Treasury bond has a 12 percent annual coupon, while a 15-year Treasury bond has an 8 percent annual coupon. The yield curve is flat; all Treasury securities have a 10 percent yield to maturity. Which of the following statements is most correct?

a. The 10-year bond is selling at a discount, while the 15-year bond is selling at a premium.
b. The 10-year bond is selling at a premium, while the 15-year bond is selling at par.
c. If interest rates decline, the price of both bonds will increase, but the 15-year bond will have a larger percentage increase in price.
d. If the yield to maturity on both bonds remains at 10 percent over the next year, the price of the 10-year bond will increase, but the price of the 15-year bond will fall.
e. Statements c and d are correct.

The 10 year bond will sell at a premium because the coupon payment is more than the yield on treasury securities.
The 15 year bond will sell at a discount because the coupon payment is less than the yield on treasury securities.
Hence a and b are incorrect.

C is correct (Explanation in answer 1 above)
D is incorrect (As the time to maturity approaches the value will move towards the face value. Hence the price of 10 yr bond which is selling at a premium will decline and the price of 15 yr bond which is selling at a discount will rise.)