Deck 15: Bonds and Sinking Funds

Question 1

Name four variables that affect a bond's price. Which ones, if any, have an inverse effect on the bond's price? That is, for which variables does a lower value of the variable result in a higher bond price?

Answer 1

Four variables affecting a bond's price are:
-the time remaining until maturity of the bond
-the prevailing market rate of return on bonds
-the bond's coupon rate
-the face value of the bond
Only the prevailing market rate of return always has an inverse effect on the bond's price.

Question 2

Under what circumstance can you realize a capital gain on a bond investment?

Answer 2

The usual circumstance is where the prevailing market rate of return on bonds is lower when you sell the bond than when you purchased it.

Question 3

Assuming that the bond issuer does not default on any payments, is it possible to lose money on a bond investment? Discuss briefly.

Answer 3

Yes. If, during the holding period, the capital loss (due to a rise in the prevailing market rate of return) exceeds the coupon interest paid on the bond, you will suffer a net loss on the bond investment.

Question 4

On a recent interest payment date, a bond's price exceeded its face value. If the prevailing market rate of return does not change thereafter, will the bond's premium be different on later interest payment dates? Explain.

Question 5

If you are firmly convinced that prevailing interest rates will decline, what adjustment should you make to the average maturity of bonds in your bond portfolio?

Question 6

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 7

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 8

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 9

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 10

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 11

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 12

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 13

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 14

Denis purchased a $10,000 face value Ontario Hydro Energy bond maturing in five years. The coupon rate was 6.5% payable semiannually. If the prevailing market rate at the time of purchase was 5.8% compounded semiannually, what price did Denis pay for the bond? (Taken from CIFP course materials.)

Question 15

Bernard purchased a $50,000 bond carrying a 4.5% coupon rate when it had 8 years remaining until maturity. What price did he pay if the prevailing rate of return on the purchase date was 5.2% compounded semiannually? (Taken from CIFP course materials.)

Question 16

A $1000, 6.5% coupon bond has 13½ years remaining until maturity. Calculate the bond premium if the required return in the bond market is 5.5% compounded semiannually.

Question 17

A $1000, 5.5% coupon bond has 8½ years remaining until maturity. Calculate the bond premium if the required return in the bond market is 6.3% compounded semiannually.

Question 18

A $5000, 5.75% coupon bond has 16 years remaining until maturity. Calculate the bond discount if the required return in the bond market is 6.5% compounded semiannually.

Question 19

A $25,000, 6.25% coupon bond has 21½ years remaining until maturity. Calculate the bond discount if the required return in the bond market is 5.2% compounded semiannually.

Question 20

Eight years ago, Yan purchased a $20,000 face value, 6% coupon bond with 15 years remaining to maturity. The prevailing market rate of return at the time was 7.2% compounded semiannually; now it is 4.9% compounded semiannually. How much more or less is the bond worth today?

Question 21

Bond A and Bond B both have a face value of $1000, each carries a 5% coupon, and both are currently priced at par in the bond market. Bond A matures in 2 years and Bond B matures in 10 years. If the prevailing required rate of return in the bond market suddenly drops to 4.7% compounded semiannually, how much will the market price of each bond change? What general rules does this outcome demonstrate?

Question 22

Bond C and Bond D both have a face value of $1000, and each carries a 4.2% coupon. Bond C matures in 3 years and Bond B matures in 23 years. If the prevailing required rate of return in the bond market suddenly rises from the current 4.5% to 4.8% compounded semiannually, how much will the market price of each bond change? What general rules does this outcome demonstrate?

Question 23

Using the 'Market Value of Bonds' Chart This student textbook's Online learning centre (OLC) provides an interactive chart for comparing the response of the prices of two bonds to a given change in the bond market's required rate of return. Go to the OLC's Student Edition. In the navigation bar, select "Chapter 15" in the drop-down box. In the list of resources for Chapter 15, select "Links in Student textbook" and then click on the link named "Market Value of Bonds. "Follow the instructions with this chart to solve:
Bond A and Bond B both have a face value of $1000, each carries a 5% coupon, and both are currently priced at par in the bond market. Bond A matures in 2 years and Bond B matures in 10 years. If the prevailing required rate of return in the bond market suddenly drops to 4.7% compounded semiannually, how much will the market price of each bond change? What general rules does this outcome demonstrate?

Question 24

Bond C and Bond D both have a face value of $1000, and each carries a 4.2% coupon. Bond C matures in 3 years and Bond B matures in 23 years. If the prevailing required rate of return in the bond market suddenly rises from the current 4.5% to 4.8% compounded semiannually, how much will the market price of each bond change? What general rules does this outcome demonstrate?

Question 25

Bonds A, B, C, and D all have a face value of $1000 and carry a 7% coupon. The time remaining until maturity is 5, 10, 15, and 25 years for A, B, C, and D, respectively. Calculate their market prices if the rate of return required by the market on these bonds is 6% compounded semiannually. Summarize the observed pattern or trend in a brief statement.

Question 26

Bonds E, F, G, and H all have a face value of $1000 and carry a 7% coupon. The time remaining until maturity is 5, 10, 15, and 25 years for E, F, G, and H, respectively. Calculate their market prices if the rate of return required by the market on these bonds is 8% compounded semiannually. Summarize the observed pattern or trend in a brief statement.

Question 27

Bonds J, K, and L all have a face value of $1000 and all have 20 years remaining until maturity. Their respective coupon rates are 6%, 7%, and 8% compounded semiannually. Calculate their market prices if the rate of return required by the market on these bonds is 5% compounded semiannually. Summarize the observed pattern or trend in a brief statement.

Question 28

Bonds M, N, and Q all have a face value of $1000 and all have 20 years remaining until maturity. Their respective coupon rates are 7%, 6%, and 5%. Calculate their market prices if the rate of return required by the market on these bonds is 8% compounded semiannually. Summarize the observed pattern or trend in a brief statement.

Question 29

A $1000, 7% coupon bond has 15 years remaining until maturity. The rate of return required by the market on these bonds has recently been 7% (compounded semiannually). Calculate the price change if the required return abruptly:
a) Rises to 8%.
b) Rises to 9%.
c) Falls to 6%.
d) Falls to 5%.
e) Is the price change caused by a 2% interest rate increase twice the price change caused by a 1% interest rate increase?
f) Compare the magnitude of the price change caused by a 1% interest rate increase to the price change caused by a 1% interest rate decrease.

Question 30

This problem investigates the sensitivity of the prices of bonds carrying differing coupon rates to interest rate changes. Bonds K and L both have a face value of $1000 and 15 years remaining until maturity. Their coupon rates are 6% and 8%, respectively. If the prevailing market rate decreases from 7.5% to 6.5% compounded semiannually, calculate the price change of each bond:
a) In dollars.
b) As a percentage of the initial price.
c) Are high-coupon or low-coupon bonds more sensitive to a given interest rate change? Justify your response using the results from part b.

Question 31

Three years after the issue of a $10,000, 6.5% coupon, 25-year bond, the rate of return required in the bond market on long-term bonds is 5.6% compounded semiannually.
a) At what price would the bond sell?
b) What capital gain or loss (expressed as a percentage of the original investment) would the owner realize by selling the bond at that price?

Question 32

Four and one-half years ago Gavin purchased a $25,000 bond in a new Province of Ontario issue with a 20-year maturity and a 6.1% coupon. If the prevailing market rate is now 7.1% compounded semiannually:
a) What would be the proceeds from the sale of Gavin's bonds?
b) What would be the capital gain or loss (expressed as a percentage of the original investment)?

Question 33

Three years ago Quebec Hydro sold an issue of 20-year, 6.5% coupon bonds. Calculate an investor's percent capital gain for the entire three-year holding period if the current semiannually compounded return required in the bond market is:
a) 5.5%.
b) 6.5%.
c) 7.5%.

Question 34

Two and one-half years ago the Province of Saskatchewan sold an issue of 25-year, 6% coupon bonds. Calculate an investor's percent capital gain for the entire 2½ -year holding period if the current rate of return required in the bond market is:
a) 6.5%.
b) 6%.
c) 5.5%.

Question 35

During periods of declining interest rates, long-term bonds can provide investors with impressive capital gains. The best example in recent times occurred in the early 1980s. In September 1981 the bond market was pricing long-term bonds to provide a rate of return of over 18.5% compounded semiannually. Suppose you had purchased 10% coupon bonds in September 1981 with 20 years remaining until maturity. Four and one-half years later (in March 1986) the bonds could have been sold at a prevailing market rate of 9.7% compounded semiannually. What would have been your semiannually compounded rate of total return on the bonds during the 4½-year period?

Question 36

The downside of the long-term bond investment story occurs during periods of rising long-term interest rates, when bond prices fall. During the two years preceding September 1981, the market rate of return on long-term bonds rose from 11% to 18.5%, compounded semiannually. Suppose you had purchased 10% coupon bonds with 22 years remaining until maturity in September 1979 and sold them in September 1981. What would have been your semiannually compounded rate of total return on the bonds during the two-year period?

Question 37

A bond with a face value of $1000 and 15 years remaining until maturity pays a coupon rate of 5%. Calculate its yield to maturity if it is priced at $900.

Question 38

A bond with a face value of $1000 and 15 years remaining until maturity pays a coupon rate of 10%. Calculate its yield to maturity if it is priced at $1250.

Question 39

Manuel bought a $100,000 bond with a 4% coupon for $92,300 when it had five years remaining to maturity. What was the prevailing market rate at the time Manuel purchased the bond? (Taken from CIFP course materials.)

Question 40

Pina bought a 6% coupon, $20,000 face value corporate bond for $21,000 when it had 10 years remaining until maturity. What are her nominal and effective yields to maturity on the bond? (Taken from CIFP course materials.)

Question 41

Bonds A and C both have a face value of $1000 and pay a coupon rate of 6.5%. They have 5 and 20 years, respectively, remaining until maturity. Calculate the yield to maturity of each bond if it is purchased for $950.

Question 42

Bonds D and E both have a face value of $1000 and pay a coupon rate of 7%. They have 5 and 20 years, respectively, remaining until maturity. Calculate the yield to maturity of each bond if it is purchased for $1050.

Question 43

A $5000 Government of Canada bond carrying a 6% coupon is currently priced to yield 6% compounded semiannually until maturity. If the bond price abruptly rises by $100, what is the change in the yield to maturity if the bond has:
a) three years remaining to maturity?
b) 15 years remaining to maturity?

Question 44

A $10,000 Nova Chemicals Corp bond carrying an 8% coupon is currently priced to yield 7% compounded semiannually until maturity. If the bond price abruptly falls by $250, what is the change in the yield to maturity if the bond has:
a) two years remaining to maturity?
b) 12 years remaining to maturity?

Question 45

In the spring of 1992 it became apparent that Olympia & York (O&Y) would have serious difficulty in servicing its debt. Because of this risk, investors were heavily discounting O&Y's bond issues. On April 30, 1992 an Olympia & York bond issue, paying an 11.25% coupon rate and maturing on October 31, 1998, traded at $761.50 (per $1000 of face value). (This was at a time when Government of Canada bonds with a similar coupon and maturity date were trading at a premium of about 10% above par.) If O&Y had managed to make the contractual payments on these bonds, what yield to maturity would investors who purchased those bonds on April 30, 1992, have realized? (P.S.: They didn't!)

Question 46

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face alue is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 47

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 48

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 49

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 50

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 51

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 52

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 53

Calculate the purchase price of the $1000 face value of the bond. (Assume that the face value is $1000, that bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 54

A $1000, 6.5% coupon bond issued by Bell Canada matures on October 15, 2029. What was its flat price on June 11, 2010 if its yield to maturity was 4.75% compounded semiannually?

Question 55

A $1000, 6% coupon, 25year Government of Canada bond was issued on June 1, 2005. At what flat price did it sell on April 27, 2009 if the market's required return was 4.6% compounded semiannually?

Question 56

A $1000, 10% coupon bond issued by Ontario Hydro on July 15, 1994 matures on July 15, 2019. What was its flat price on June 1, 2003 when the required yield to maturity was 5.5% compounded semiannually?

Question 57

A $1000, 6.75% coupon, 25-year Government of Canada bond was issued on March 15, 1971. At what flat price did it trade on July 4, 1981, when the market's required return was 17% compounded semiannually?

Question 58

A $1000, 5.2% coupon, 20-year Province of Ontario bond was issued on March 15, 2009. Calculate its flat price on March 15, April 15, May 15, June 15, July 15, August 15, and September 15, 2010, if the yield to maturity on every date was 6% compounded semiannually.

Question 59

A $1000, 7% coupon, 15-year Province of Saskatchewan bond was issued on May 20, 2001. Calculate its (flat) price on May 20, June 20, July 20, August 20, September 20, October 20, and November 20, 2003, if the yield to maturity on every date was 5.9% compounded semiannually.

Question 60

A $5000, 7% coupon, 20-year bond issued on January 21, 2006, was purchased on January 25, 2007, to yield 6.5% to maturity, and then sold on January 13, 2008, to yield 5.2% to maturity. What was the investor's capital gain or loss:
a) In dollars?
b) As a percentage of her original investment?

Question 61

A $10,000, 14% coupon, 25-year bond issued on June 15, 1984, was purchased on March 20, 1987, to yield 9% to maturity, and then sold on April 20, 1990, to yield 11.5% to maturity. What was the investor's capital gain or loss:
a) In dollars?
b) As a percentage of his original investment?

Question 62

A $1000 face value, 7.6% coupon bond pays interest on May 15 and November 15. If its flat price on August 1 was $1065.50, at what price (expressed as a percentage of face value) would the issue have been reported in the financial pages?

Question 63

A $5000 bond was sold for $4860 (flat) on September 17. If the bond pays $200 interest on June 1 and December 1 of each year until maturity, what price (expressed as a percentage of face value) would have been quoted for bonds of this issue on September 17?

Question 64

If a broker quotes a price of 108.50 for a bond on October 23, what amount will a client pay per $1000 face value? The 7.2% coupon rate is payable on March 1 and September 1 of each year. The relevant February has 28 days.

Question 65

Calculate the quoted price on April 15, 2006 of the bond outlined below. (Assume that the face value is $1000, that the purchase price is $958.06, that the bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 66

Calculate the quoted price on June 1, 2001 of the bond outlined below. (Assume that the face value is $1000, that the purchase price is $1239.47, that the bond interest is paid semiannually, that the bond was originally issued at its face value, that the bond is redeemed at their face value maturity and that the market rate of return is compounded semiannually.)

Question 67

Using the bond yield given in the final column of Table 15.2, verify the September 22, 2009 quoted price for the Province of New Brunswick 4.4% coupon bond, maturing June 3, 2019.

Question 68

Using the bond yield given in the final column of Table 15.2, verify the September 22, 2009 quoted price for the Province of Ontario 5.85% coupon bond, maturing March 8, 2033.

Question 69

Using the bond yield given in the final column of Table 15.2, verify the September 22, 2009 quoted price for the Province of British Columbia 5.7% coupon bond, maturing June 18, 2029.

Question 70

Using the bond price given in the second-to-last column of Table 15.2, verify the September 22, 2009 yield (to maturity) for the Newfoundland Municipal Financing Authority 5.1% coupon bond, maturing March 29, 2018.

Question 71

Using the bond price given in the second-to-last column of Table 15.2, verify the September 22, 2009 yield (to maturity) for the City of Toronto 4.375% coupon bond, maturing October 28, 2015.

Question 72

Using the bond price given in the second-to-last column of Table 15.2, verify the September 22, 2009 yield (to maturity) for the TransCanada Pipelines Ltd. 8.29% coupon bond, maturing February 5, 2026.

Question 73

Using the bond price given in the second-to-last column of Table 15.2, verify the September 22, 2009 yield (to maturity) for the ING Canada Inc. 5.41% coupon bond, maturing September 3, 2019.

Question 74

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 75

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 76

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 77

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 78

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 79

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)

Question 80

For the sinking fund calculate (rounded to the nearest dollar) a) the size of the periodic sinking fund payment and b) the balance in the sinking fund at the time indicated in the last column. (Round the sinking fund payment to the nearest dollar before calculating the balance.)