Bond calculations- multiple choice and math

4. Which of the following is true about the face value of a bond?

       It is the notional amount we use to compute coupon payments.
       It is the amount that is repaid at maturity.
       It is usually denominated in standard increments, such as $1,000.
       All of the above are true.

5. What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9600 when released? (percentage)

6. Why is the yield to maturity of a zero-coupon, risk-free bond that matures at the end of a given period the risk-free interest rate for that period?

       Since such a bond provides a risk-free return over that period, the Law of One Price guarantees the risk-free interest rate be equal to this yield.
       Since a bond’s price will converge on its face value as the bond approaches the maturity date, the Law of One Price dictates that the risk-free interest rate will reflect this convergence.
       Since interest rates will rise and fall in response to the movement in bond prices.
       Since there is, by definition, no risk in investing in such bonds, the return from such bonds is the best that can be expected from any investment over the period.

7. A risk-free, zero-coupon bond with a face value of $1,000 has 15 years to maturity. If the YTM is 5.8%, which of the following would be closest to the price this bond will trade at?

8. A risk-free, zero-coupon bond with a $5000 face value has ten years to maturity. The bond currently trades at $3650. What is the yield to maturity of this bond? (percentage)

9. Which of the following statements is FALSE?

       The amount of each coupon payment is determined by the coupon rate of the bond.
       Prior to its maturity date, the price of a zero-coupon bond is always greater than its face value.
       The simplest type of bond is a zero-coupon bond.
       Treasury bills are U.S. government bonds with a maturity of up to one year.

10. Which of the following statements is FALSE?

       The internal rate of return (IRR) of an investment in a zero-coupon bond is the rate of return that investors will earn on their money if they buy a default free bond at its current price and hold it to maturity.
       The yield to maturity of a bond is the discount rate that sets the future value (FV) of the promised bond payments equal to the current market price of the bond.
       Financial professionals also use the term spot interest rates to refer to the default-free zero-coupon yields.
       When we calculate a bond’s yield to maturity by solving the formula,
Price of an n-period bond =  +  + … + , 1 + YTM)
the yield we compute will be a rate per coupon interval.

11. Consider a zero-coupon bond with a $1000 face value and ten years left until maturity. If the YTM of this bond is 10.4%, then the price of this bond?

12. Consider a zero-coupon bond with a $1000 face value and ten years left until maturity. If the bond is currently trading for $459, then the yield to maturity on this bond is?

13

. What is the yield to maturity of a five-year, $5000 bond with a 4.5% coupon rate and semiannual coupons if this bond is currently trading for a price of $4876?

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14

. What must be the price of a $10,000 bond with a 6.5% coupon rate, semiannual coupons, and two years to maturity if it has a yield to maturity of 8% APR?

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15. A $1000 bond with a coupon rate of 5.4% paid semiannually has five years to maturity and a yield to maturity of 7.5%. If interest rates rise and the yield to maturity increases to 7.8%, what will happen to the price of the bond?

       fall by $9.82
       fall by $11.59
       rise by $12.16
       The price of the bond will not change.

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16. What is the coupon rate of a two-year, $10,000 bond with semiannual coupons and a price of $9543.45, if it has a yield to maturity of 6.8%?

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17

. Which of the following bonds will be most sensitive to a change in interest rates?

       a ten-year bond with a $2000 face value whose yield to maturity is 5.8% and coupon rate is 5.8% APR paid semiannually
       a 15-year bond with a $5000 face value whose yield to maturity is 7.4% and coupon rate is 6.2% APR paid annually
       a 20-year bond with a $3000 face value whose yield to maturity is 6.0% and coupon rate is 5.4% APR paid semiannually
       a 30-year bond with a $1000 face value whose yield to maturity is 5.5% and coupon rate is 6.4% APR paid annually

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18

. Which of the following bonds is trading at par?

       a bond with a $2000 face value trading at $

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       a bond with a $1000 face value trading at $999
       a bond with a $1000 face value trading at $1000
       a bond with a $2000 face value trading at $2012

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19. Which of the following bonds is trading at a premium?

       a five-year bond with a $2000 face value whose yield to maturity is 7.0% and coupon rate is 7.2% APR paid semiannually
       a ten-year bond with a $4000 face value whose yield to maturity is 6.0% and coupon rate is 5.9% APR paid semiannually
       a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 7.8% APR paid semiannually
       a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% APR paid monthly

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20. Which of the following statements are true?

       A fall in bond prices causes interest rates to fall.
       A fall in interest rates causes a fall in bond prices.
       A rise in interest rates causes bond prices to fall.
       Bond prices and interest rates are not connected.

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21

. A bond has a $1000 face value, ten years to maturity, and 7% semiannual coupon payments. What would be the expected difference in this bond’s price immediately before and immediately after the next coupon payment?

       $18
       $35
       $70
       $84

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22

. Which of the following bonds will be most sensitive to a change in interest rates?

       a ten-year bond with a $2000 face value whose yield to maturity is 5.8% and coupon rate is 5.8% APR paid semiannually
       a 15-year bond with a $5000 face value whose yield to maturity is 7.4% and coupon rate is 6.2% APR paid annually
       a 20-year bond with a $3000 face value whose yield to maturity is 6.0% and coupon rate is 5.4% APR paid semiannually
       a 30-year bond with a $1000 face value whose yield to maturity is 5.5% and coupon rate is 6.4% APR paid annually

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23. A company issues a ten-year bond at par with a coupon rate of 6% paid semi-annually. The YTM at the beginning of the third year of the bond (8 years left to maturity) is 7.8%. What is the new price of the bond?

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24

. A company issues a ten-year bond at par with a coupon rate of 6% paid semi-annually. The YTM at the beginning of the third year of the bond (8 years left to maturity) is 7.8%. What was the percentage change in the price of the bond over the past two years?

       11.81%
       -43.04%
       -10.56%
       75.55%
 
 
Use the information for the question(s) below.
 
Luther Industries needs to raise $

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million to fund a new office complex. The company plans on issuing ten-year bonds with a face value of $1000 and a coupon rate of 7.0% (annual payments). The following table summarizes the YTM for similar ten-year corporate bonds of various credit ratings:
 

Rating

AAA

AA

A

BBB

BB

YTM

6.70%

6.80%

7.00%

7.40%

8.00%

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25. Assuming that Luther’s bonds receive a AAA rating, the price of the bonds will be closest to: (Points : 1)

       $1021
       $1014
       $1000
       $937

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26. Suppose that when these bonds were issued, Luther received a price of $972.42 for each bond. What is the likely rating that Luther’s bonds received? (Points : 1)

       AA
       BBB
       B
       A