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14.E: Bonds and Sinking Funds (Exercises)

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    14.1: Determining the Value of a Bond

    For all questions, assume all interest rates or yields and payment frequencies are compounded semi-annually. Also assume that the redemption price equals the face value.

    Mechanics

    For each of the following bonds and the indicated selling date, calculate the cash price, accrued interest, market price, and determine the amount of the bond premium or discount.

    Face Value Coupon Rate Issue Date Selling Date Maturity Date Market Rate on Selling Date
    1. $1,000 7.16% January 15, 1994 January 15, 1997 January 15, 2024 7.16%
    2. $10,000 9.4% April 28, 1987 October 28, 1990 April 28, 2022 10.71%
    3. $5,000 7.64% November 3, 1995 May 3, 2009 November 3, 2015 3.96%
    4. $100,000 5.81% February 20, 2000 February 20, 2010 February 20, 2015 4.07%
    5. $250,000 6.27% July 5, 1997 March 8, 2007 July 5, 2017 4.21%
    6. $50,000 16.33% January 12, 1982 May 2, 2009 January 12, 2032 4.19%
    7. $2,500 10.41% November 19, 1986 September 13, 1990 November 19, 2036 11.49%
    8. $30,000 8.99% January 30, 1992 February 12, 1995 January 30, 2042 8.99%

    Applications

    For each of questions 9–14, calculate the cash price, accrued interest, market price, and the amount of the premium or discount.

    1. With 17 years until maturity, Julio purchased an $8,000 Government of Saskatchewan bond with a coupon rate of 5.55%. The market yield was 8.65%.
    2. A $5,000 Vancouver Internal Airport bond issued on June 7, 2004, with 14 years to maturity has a coupon rate of 4.42%. It was sold on December 7, 2009, when market rates were 4.07%.
    3. A $25,000 City of Kingston bond issued on July 17, 2007, with five years to maturity has a coupon rate of 5.12%. It was sold on January 10, 2010, at a market rate of 4.18%.
    4. On January 2, 1990, when market rates were 10.1%, a $50,000 Province of Prince Edward Island bond maturing on December 17, 2012, with a coupon rate of 9.75% was sold.
    5. A $100,000 Nova Scotia Power Corporation bond with a coupon rate of 11.25% matures on April 27, 2014. It was sold on February 27, 2006, when market rates were 4.09%.
    6. A $75,000 Government of Canada bond due to mature on September 5, 2020, was sold on September 5, 2009, at a market rate of 3.85%. It carries a coupon rate of 3.84%.
    7. The original holder of a $10,000 Province of Manitoba bond issued December 1, 2006, with a 2% coupon and 30 years to maturity sells her bond on June 1, 2010, when market rates were 5.25%. By what amount did the market price increase or decrease for this investor?

    Challenge, Critical Thinking, & Other Applications

    1. The Alberta Capital Finance Authority issued a 20-year $100,000 bond on December 15, 2005, with a coupon rate of 4.45%. If Mirabelle purchased the bond on June 15, 2007, at a market rate of 4.56% and subsequently sold the bond on March 31, 2009, at a market rate of 3.74%, determine the amount by which the market price increased or decreased for Mirabelle.
    2. A $125,000 Province of Ontario 50-year bond issued on March 1, 1995, carries at 9.5% coupon. Amy purchased the bond on September 1, 1999, at a market rate of 5.91% and later sold the bond on September 30, 2008, when posted rates were 6.13%. Based solely on the market price, determine the gain or loss that Amy experienced.
    3. On August 16, 2012, a bond had a market price of $8,240.66 and accrued interest of $157.95 when the market rate was 8%. What is the bond's face value if it matures on May 15, 2033?
    4. A 30-year maturity $10,000 face value Government of Canada bond with an 8% coupon was issued on June 1, 1997. Calculate the market price and cash price in the year 2006 on each of June 1, July 1, August 1, September 1, October 1, November 1, and December 1 if the market rate remains constant at 4.5%. Comment on the pattern evident in both the cash price and market price.
    5. Assume a $10,000 bond has 20 years until maturity with a coupon rate of 5%.
      1. Determine its market price at rates of 3%, 4%, 5%, 6%, and 7%.
      2. Do the market prices of the bond equally change for each 1% change in the market rate? Why or why not?
      3. Does a market rate that is 1% higher than the coupon rate result in the same premium or discount as a rate that is 1% lower than the coupon rate? Why or why not?
      4. Assume the bond now only has 10 years until maturity and repeat part (a). e. Compare your answers to parts (a) and (d). What impact does the time until maturity have on the change in the bond price?

    14.2: Calculating a Bond’s Yield

    For all questions, assume that all interest rates or yields and payment frequencies are compounded semi-annually. Also assume that the redemption price equals the face value.

    Mechanics

    For each of the following bonds, calculate the yield to maturity.

    Face Value Purchase Price Coupon Rate Years Remaining until Maturity
    1. $1,000 $1,546.16 6% 25
    2. $5,000 $3,824.41 5,75% 18.5
    Face Value Purchase Date Purchase Price Maturity Date Coupon Rate
    3. $2,500 January 2, 2009 $1,671.47 January 2, 2025 6.18%
    4. $10,000 April 13, 2003 $14,480.91 October 13, 2017 7.15%

    For each of the following bonds, calculate the investor's yield.

    Purchase Price Selling Price Years Held Coupon Rate Face Value
    5. $23,123.77 $21,440.13 6 7.25% $25,000
    6. $106,590.00 $109,687.75 11 years, 6 months 8.65% $100,000
    Purchase Date Market Rate at Time of Purchase Selling Date Market Rate at Time of Sale Maturity Date Coupon Rate Face Value
    7. September 29, 2005 9% March 29, 2010 7% March 29, 2022 8.65% $500,000
    8. May 21, 1998 6.355% November 21, 2008 6.955% May 21, 2033 7.165% $50,000

    Applications

    1. A $495,000 face value Province of Ontario bond issued with a coupon rate of 7.5% is sold for $714,557.14. If 20 years remain until maturity, what was the yield to maturity?
    2. A $100,000 face value bond is issued with a 5% coupon and 22 years until maturity. If it sells for $76,566.88 9½ years later, what was the yield to maturity?
    3. A $15,000 face value bond matures on August 3, 2024, and carries a coupon of 6.85%. It is sold on February 3, 2009, for $20,557.32. Determine the yield to maturity.
    4. A $50,000 face value Government of Canada bond is purchased for $48,336.48 and sold nine years later for $51,223.23. If the coupon rate is 4.985%, calculate the investor's yield.
    5. Usama acquired a $30,000 face value City of Hamilton bond carrying a 4.95% coupon for $32,330.08 when market rates were 4%. Six years later, market rates are posted at 4.25% and he can sell his bond for $30,765.05. If he doesn't want his investor’s yield to be less than his original yield to maturity, should he sell his bond? Provide calculations to support your answer.
    6. Great-West Life (GWL) issued a $100,000 face value bond carrying a coupon rate of 6.14% and 20 years to maturity. Eight years later, GWL decides to buy back some of its outstanding bonds when current market rates are 7.29%. If the bond was held from the issue date until the selling date, what yield did the bondholder realize on her investment?
    7. Island Telephone Corporation issued a $250,000 face value bond on March 1, 1988, carrying a 9.77% coupon and 30 years to maturity. Global Financial Services purchased the bond on March 1, 1995, at which point the market rate was 8.76%, and sold it on September 1, 2007, for $359,289.44 when market rates were 4.5%. What yield did Global Financial Services realize on its investment?
    8. Briar Rose is considering selling her bond but will do so only if she can realize an investor's yield of no less than 3.75%. She purchased the $20,000 face value bond carrying a 6.35% coupon with 25 years to maturity when market rates were 4.85%. Today, 11 years and 6 months later, the market rate is 6.88%. Should Briar Rose sell her bond? Provide calculations to support your answer.

    Challenge, Critical Thinking, & Other Applications

    1. A $50,000 face value TransCanada Corporation bond carrying a 5.1% coupon matures on January 11, 2017. The bond is purchased on July 11, 2008, for $53,336.24 and later sold on January 11, 2010, for $53,109.69.
      1. Calculate the yield to maturity on the purchase date.
      2. Calculate the yield to maturity on the selling date.
      3. Calculate the investor's yield and express it as a percent change from yield to maturity on the purchase date.
    2. A $75,000 face value Canada Post Corporation bond carrying a 4.08% coupon will mature on July 16, 2025. The bond was purchased on January 16, 2006, when market rates were 4.2% and later sold on July 16, 2009, when market rates were 4.05%.
      1. Calculate the purchase price of the bond along with the amount of the premium or discount.
      2. Calculate the selling price of the bond along with the amount of the premium or discount.
      3. Calculate the investor's yield on the bond and express it as a percent change of the market rate on the purchase date.
      4. Convert the purchase date market rate and the investor's yield to their effective rates. Express the investor's yield as a percent change of the original effective rate.
    3. The finance manager for Global Holdings Corporation has some funds to invest in bonds. The following three $50,000 face value bond options are available:
      1. A bond carrying a coupon rate of 5.07% with 13 years until maturity and selling for $51,051.79.
      2. A bond carrying a coupon rate of 4.99% with 8.5 years until maturity and selling for $50,552.33.
      3. A bond carrying a coupon rate of 3.96% with 20 years and 6 months until maturity and selling for $44,022.81. Based solely on each bond's yield to maturity, rank the bonds and recommend the one in which the manager should invest the money.
    4. Thirty years ago the Mario Brothers invested in a $100,000 face value bond carrying a 7.55% coupon. They have held onto the bond the whole time until today, when the bond matures. In looking at historical bond prices, they wonder what yield they might have realized by selling the bond somewhere along the way. At five-year intervals, the selling price of the bond would have been $105,230.26, $108,133.36, $120,755.53, $141,716.98, and $130,443.72. Calculate the investor's yield throughout the history of the bond and rank the five-year intervals from highest to lowest.

    14.3: Sinking Fund Schedules

    Mechanics

    Create complete sinking fund schedules for each of the following sinking funds.

    Future Value Payment Timing Payment Frequency Nominal Interest Rate Term (Years)
    1. $50,000 End Annually 8.2% annually 5
    2. $75,000 Beginning Semi-annually 4.25% semi-annually 4
    3. $10,000 End Quarterly 6.2% annually 2
    4. $30,000 Beginning Monthly 3.8% quarterly 7 months

    Create partial sinking fund schedules for the indicated payments for each of the following sinking funds.

    Future Value Payment Timing Payment Frequency Nominal Interest Rate Term (Years) Payment #
    5. $5,000,000 End Semi-annually 7% semi-annually 6 7 to 10
    6. $250,000 Beginning Annually 10% annually 10 4 to 7
    7. $800,000 End Monthly 5% quarterly 8 Fifth year
    8. $2,000,000 Beginning Quarterly 6% monthly 5 Third year

    Applications

    For questions 9–12, create a complete sinking fund (due) schedule. Calculate the total payments and the total interest earned.

    1. A $500,000 face value bond with semi-annual interest payments is issued with four years until maturity. The bond comes with a sinking fund provision that requires a sinking fund deposit timed to match the interest payments. The sinking fund will earn 4% compounded semi-annually.
    2. A $125,000 face value bond is issued with two years until maturity. The ordinary sinking fund provision requires quarterly deposits and can earn an interest rate of 7.4% compounded semi-annually.
    3. Jamie and Athena want to take their children to Disney World one year from today. The estimated cost of their stay is $8,600, for which they will save up the funds in advance. Their savings plan can earn 5% compounded quarterly and they will make their first quarterly deposit today.
    4. Because of rising demand, a manufacturer predicts that in three years’ time it will need to acquire land on which to build a new production plant. It estimates the value of the land at $5 million. The company makes its first semi-annual deposit today into a sinking fund earning 7.35% compounded monthly. For questions 13–15, create a partial sinking fund schedule.

    For the specified time frame, calculate the total payments and the total interest earned.

    1. A $10 million face value bond is issued with 20 years until maturity. The sinking fund provision requires semi-annual deposits, and the fund can earn an interest rate of 8.5% compounded semi-annually. The company would like detailed information on the sixth through eighth years.
    2. A sinking fund is set up for a newly issued $750,000 face value bond with 25 years until maturity. Quarterly deposits will be made into a fund earning 10% compounded annually. Interest and principal information is needed for the third year.
    3. Revisit the opening situation discussed in this section. Recall that you had your eye on a home with a list price of $325,000 that requires a 5% down payment. At the end of every month for the past four years, you have been contributing an amount rounded up to the nearest dollar into a five-year savings plan earning 5% compounded monthly. You have found a new home for $250,000 and wonder if you have enough to meet the 5% down payment requirement.
      1. Create a schedule for the 45th through 51st payments into your savings plan.
      2. Can you buy the $250,000 home today? Justify your answer.

    Challenge, Critical Thinking, & Other Applications

    1. Gillette (a division of Procter and Gamble) projects it will need $500 million today to fund the research and development for a new product line. This money will be charged interest at 6.5% compounded annually. Financing is arranged such that the first end-of-month payment to the sinking fund will start three years and one month from today with the aim of repaying the debt in total after seven years from today. The fund can earn 7.8% compounded monthly. For the fund itself, create a sinking fund schedule for the first six months of its third year.
    2. Yogi is saving up for a $10,000 down payment on his new car, which he plans to purchase one year from now. He will make deposits at the end of every three months into a fund earning 4% compounded quarterly. He already has saved $3,000 today. Create a complete sinking fund schedule and calculate the total payments and interest earned.
    3. In total, $10 million in bonds carrying a coupon rate of 5% semi-annually with 10 years until maturity was issued seven years ago. The denomination of each bond is $10,000. A sinking fund provision has required semi-annual deposits into a fund earning 6.6% compounded semi-annually. Today, the market rate on bonds has risen to 7% compounded semiannually. The company decides to use the money in its sinking fund to purchase its bonds on the open market.
      1. If it uses the maximum funds available, how many bonds can it purchase today?
      2. Assuming it purchased the bonds, revise and create a complete sinking fund schedule for the last three years.
    4. Every year, a National Car Rental retail outlet needs to purchase its rental fleet of vehicles to reflect current year models. The estimated purchase price of its fleet is $500,000. However, it does not need to save up this entire amount since it sells the previous fleet to automotive dealerships for 45% of the purchase price. Create a complete annual sinking fund schedule for the retail outlet, assuming its sinking fund earns 3.6% compounded monthly and it makes end-of-month deposits. Determine the total payments made along with the total interest earned.
    5. 20. A $100 million face value bond is issued with 30 years until maturity. The sinking fund provision requires semi-annual payments into a fund earning 8% compounded semi-annually.
      1. Calculate the total interest earned and total payments.
      2. For the 10th through 15th year inclusive, calculate the total interest earned.

    14.4: Debt Retirement and Amortization

    For all questions, assume that all interest rates or yields and payment frequencies are compounded semi-annually and that the redemption price equals the face value.

    Mechanics

    For questions 1–4, assume the bond has a sinking fund requirement. Calculate the following for each question:

    1. The annual cost of the bond debt
    2. The book value of the bond debt after the payment number specified in the last column
    Bond Face Value Coupon Rate Years to Maturity Sinking Fund Rate Find Book Value after Payment #
    1. $500,000 8% 5 5.5% 6
    2. $2,500,000 4.4% 25 5% 20
    3. $1,000,000 6.5% 15 7.25% 25
    4. $750,000 5.25% 10 4% 9

    For questions 5–6, create a complete bond premium amortization table.

    Bond Face Value Coupon Rate Years to Maturity Market Interest Rate at Time of Purchase
    5. $50,000 8% 2 5%
    6. $100,000 7% 4 4.5%

    For questions 7–8, create a complete bond discount accrual table.

    Bond Face Value Coupon Rate Years to Maturity Market Interest Rate at Time of Purchase
    7. $20,000 5% 3 6.75%
    8. $250,000 6.6% 3.5 7.8%

    Applications

    1. The City of Toronto has an outstanding $5 million face value bond carrying a 7% coupon. It makes payments of $436,150 to its sinking fund every six months. Calculate the annual cost of the bond debt.
    2. The Province of Nova Scotia issued a $50 million face value bond on June 1, 2007, carrying a coupon rate of 6.6% with 20 years until maturity. A sinking fund earning 4.3% compounded semi-annually with payments at the end of every six months was established. Calculate the book value of the bond debt on December 1, 2012.
    3. Newfoundland and Labrador Hydro issued a $100 million face value bond on February 27, 1996, carrying an 8.4% coupon with 30 years until maturity. A matching sinking fund earning 5.1% compounded semi-annually was set up to retire the debt in full upon maturity.
      1. Calculate the annual cost of the bond debt.
      2. Calculate the book value of the bond debt on August 27, 2011.
    4. The Province of Ontario issued a $175 million face value bond on March 1, 1995, carrying a 9.5% coupon with 50 years until maturity. The matching sinking fund, with the payment rounded up to the next $100, is expected to earn 6.3% compounded semi-annually and will retire the debt in full upon maturity.
      1. Calculate the annual cost of the bond debt.
      2. Calculate the book value of the debt on September 1, 2015.
    5. Three years before maturity, a $55,000 face value bond carrying a 5.5% coupon is acquired when posted market rates are 4.77% compounded semi-annually. Create a complete bond premium amortization table. How much total interest is received? What is the amortized bond premium total, and what nominal net income was realized?
    6. Jaycee works in the finance department. His company just acquired 12 $5,000 face value bonds carrying a 6.1% coupon with four years remaining until maturity. Current market yields are 7.65% compounded semi-annually. Construct a complete bond discount accrual table. How much interest does the company receive on its investment? What is the accrued bond discount total, and what nominal net income was realized?
    7. When the current bond market is yielding 5.89% compounded semi-annually, Jennifer purchases six $10,000 face value bonds carrying a 4.2% coupon with three years until maturity for her RRSP. Construct a complete table for the premium or discount. What total capital gain or capital loss will she record for the second year?
    8. On March 20, 2011, Hussein decides to invest in a $15,000 face value Ville de Gatineau bond carrying a 4.1% coupon when current market yields are 3.76%. The bond matures on March 20, 2014. Construct a complete table for the premium or discount. What total capital gain or capital loss will be recorded in 2013?

    Challenge, Critical Thinking, & Other Applications

    1. For a large project, New Flyer Industries considers issuing a $15 million face value bond with a 10-year maturity date. When issued, the finance manager estimates it will have a coupon rate of 6.2%. The matching sinking fund provision will require the full repayment of the amount upon maturity and is estimated to earn 5.45% compounded semi-annually. In examining future cash flows, the manager estimates that the company will be able to afford no more than $2 million per year toward the financing of this project. Based on financial calculations, should the company proceed with the project as planned? Provide appropriate calculations to support your answer.
    2. In Canada, 50% of an individual's capital gains are taxed at the person's current tax rate. Sylvester has a tax rate of 24%. He considers purchasing a $100,000 face value bond carrying a 7.15% coupon with five years remaining until maturity. Current market yields are posted at 8.55% compounded semi-annually. He will purchase the bond only if, in any given year, the capital gains tax amount remains under $150. Should he purchase the bond? Provide the necessary calculations to support your answer.
    3. The annual cost of bond debt depends on many factors, including the time to maturity and the interest rate achieved by the sinking fund. Assume a $10 million face value bond carrying a coupon rate of 7% with 10 years until maturity.
      1. Calculate the annual cost of the bond debt if the matching sinking fund can earn semi-annually compounded rates of 4% and 7%. What percentage more is the annual cost of the debt at 4% than 7%?
      2. Leaving the sinking fund rate at 5%, calculate the annual cost of the bond debt if the time to maturity is either 8 years or 12 years. What percentage more is the annual cost of the debt at 8 years than 12 years?
    4. The current market rate is 5% compounded semi-annually. Two bonds with four years until maturity are acquired. The first bond has a $50,000 face value and carries a coupon rate of 6.4%. The second bond has a $30,000 face value and carries a coupon rate of 4.6%.
      1. Construct the appropriate premium or discount table for each bond.
      2. For each year, determine the net capital gain or net capital loss recorded for both bonds combined.

    Review Exercises

    For all questions, assume that all interest rates or yields and payment frequencies are compounded semi-annually and that the redemption price equals the face value.

    Mechanics

    1. A Province of Alberta $100,000 face value bond carrying a 5.03% coupon was issued on December 17, 1998, with 20 years until maturity. What was its purchase price on June 17, 2005, when market yields were 4.29%?
    2. A Government of Canada $50,000 face value bond carrying a 5.75% coupon was issued on June 1, 2008, with 25 years until maturity. What was its market price on November 21, 2009, when market rates were 3.85%?
    3. A $35,000 face value bond carrying a 7% coupon will mature on October 3, 2019. If it is purchased on April 3, 2006, for $46,522.28, what is its yield to maturity?
    4. A $55,000 face value bond carrying a 4% coupon is purchased for $33,227.95 on March 29, 1997. The bond is later sold on September 29, 2007, for $60,231.63. Calculate the semi-annual investor's yield.
    5. A Province of Manitoba $250,000 face value bond carrying a 2% coupon was issued on December 1, 2006, with 30 years until maturity. On January 10, 2010, when market yields were 4.19%, what were its market price, accrued interest, cash price, and premium or discount?
    6. Carlyle needs to save up $20,000 to meet the down payment requirement on his new home. He wants to make semiannual deposits at the beginning of each six months for the next four years, putting them into a fund earning 6.12% compounded semi-annually. Construct a complete sinking fund due schedule.
    7. A $15 million face bond carrying an 8.5% coupon has nine years until maturity. The bond issue has a sinking fund provision requiring semi-annual payments, and the full bond value must be saved by its maturity date. If the fund can earn 7.35% compounded semi-annually, calculate the annual cost of the bond debt.
    8. When market yields are 16%, a $65,000 face value bond carrying a 6.75% coupon is purchased three years before maturity. Construct a complete bond discount accrual table for the bondholder.

    Applications

    1. When posted market rates are 9.65%, a $75,000 face value bond carrying a 7% coupon is purchased with 23½ years to maturity. With eight years remaining until maturity the bond is then sold, when posted market rates are 3.5%. Calculate the investor's yield.
    2. A $275,000 face value Province of British Columbia bond carrying a 10.6% coupon is issued on September 5, 1990, with 30 years until maturity. The bond is purchased on March 5, 2002, when posted rates are 5.98%. Calculate the purchase price of the bond. What is the amount of its premium or discount?
    3. 11. A $40,000 face value bond carrying a 7.6% coupon is purchased with four years until maturity. Posted rates are then 4.9%. Construct an appropriate complete table for the capital gain or loss. What is the total gain accrued or loss amortized in the third year?
    4. A $50 million face value bond carrying a 4.83% coupon with 25 years until maturity is issued. The bond has a sinking fund requirement with semi-annual payments designed to retire the full face value upon maturity. If the sinking fund is expected to earn 3.89% compounded semi-annually, calculate the annual cost of the bond debt. What is the book value of the debt after 10 years?
    5. A $62,000 face value bond carrying an 8.88% coupon is purchased on July 15, 2011. The bond matures on November 13, 2027. At the time of purchase, the market rate on the bond was 4.44%. Calculate the market price, accrued interest, and cash price of the bond. Determine the amount of the bond premium or discount.
    6. A bond is purchased on September 17, 1997, for $28,557.25 with 14 years until maturity. The 6% coupon pays $967.50 every six months. Calculate the yield to maturity.
    7. A $300,000 face value bond carrying a 4% coupon is issued with four years until maturity. A sinking fund with semiannual payments is set up and is expected to earn 6.35% compounded semi-annually. Construct a complete sinking fund schedule. Calculate the annual cost of the debt. What is the book value of the debt after the fifth payment?
    8. A $500,000 face value bond makes semi-annual payments of $15,900 and will mature on January 2, 2014. The bond is purchased on July 14, 1997, when posted market rates are 7.77%. Calculate the market price, accrued interest, cash price, and the amount of the bond premium or discount.

    Challenge, Critical Thinking, & Other Applications

    1. In Canada, 50% of an individual's capital gains or losses are taxed or deducted respectively at the individual’s current tax rate. Tammy has a tax rate of 12.76%. She just purchased a $120,000 face value bond carrying a 9.89% coupon with six years remaining until maturity. Current market yields are posted at 6.14% compounded semi-annually. Calculate her taxes owing or deducted on the capital gain or loss in the fourth year.
    2. 18. A $75 million face value bond carrying a 4.45% coupon is issued with 35 years until maturity. The sinking fund provision requires 80% of the face value to be saved up by the maturity date. The sinking fund is projected to earn 4.95% compounded semi-annually.
      1. Create a partial sinking fund schedule detailing the first two years, last two years, and the 10th and 11th years.
      2. Calculate the total interest earned by the sinking fund.
      3. Calculate the annual cost of the bond debt.
      4. Determine the book value of the bond debt after the 29th payment.
    3. A $400,000 face value bond carrying a 5.6% coupon is issued on March 23, 2007, and expected to mature on March 23, 2011. The sinking fund provision requires semi-annual payments such that the full amount is saved upon maturity. The fund is expected to earn 3.7% compounded semi-annually.
      1. Create a complete sinking fund schedule for the issuing company. Calculate the total interest earned.
      2. Suppose an investor purchased $50,000 of the bond on September 23, 2007, at a market rate of 5.45% and later sells the bond on March 23, 2009, at a market rate of 3.74%. Calculate the investor's yield.
      3. If an investor purchased $25,000 of the bond on March 23, 2008, for $25,991.24, what would be the yield to maturity?
      4. For each investor in parts (b) and (c), construct a complete table detailing the amortized gain or discount accrued. Assume the investor in part (b) held onto the bond until maturity instead of selling it.
    4. 20. A $650,000 face value bond carrying a 4.59% coupon is issued on March 30, 2005, and expected to mature on March 30, 2010. The sinking fund provision requires semi-annual payments such that the full amount is saved upon maturity. The fund is expected to earn 4.25% compounded semi-annually.
      1. Create a complete sinking fund for the issuing company. Calculate the total interest earned.
      2. Suppose an investor purchased $100,000 of the bond on September 30, 2005, at a market rate of 4.75% and later sells the bond on September 30, 2008, at a market rate of 4.27%. Calculate the investor's yield.
      3. If an investor purchased $34,000 of the bond on September 30, 2007, for $34,167.47, what would be the yield to maturity?
      4. For each investor in parts (b) and (c), construct a complete table detailing the amortized gain or discount accrued. Assume the investor in part (b) held onto the bond until maturity instead of selling it.

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    This page titled 14.E: Bonds and Sinking Funds (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jean-Paul Olivier via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.