### Business Math: A Step-by-Step Handbook 2021 Revision A

For all questions, assume that all interest rates or yields and payment frequencies are compounded semi-armually 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

2. A Government of Canada \$50,000 face value bond carrying a 5.75% coupon was issued on Jtme 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 1250,0000!! 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 semi-annual deposits at the beginning of each six months for the next four years, putting them into a fund earning 6.12% compounded semi-armually. Construct a complete sinlcing fund due schedule.

7. A \$15 million face bond carrying an 8.5% coupon has nine years until maturity. The bond issue has a sinlcing fund provision requiring semi-annual payments, and the full bond value must be saved by its maturity date. If the fund can eam 7.35% compounded semi-armually, 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

9. When posted market rates are 9.65%, a \$75,000 face value bond carrying a 7% coupon is purchased with 23V2 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.

10. A 3275,000 face value Province of British Columbia bond carrying a 10.6% coupon is issued on September 5, 1990, with 30 years tmtil 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?

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?

12. 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 sinlcing fund is expected to eam 3.89% compounded semi-annually, calculate the annual cost of the bond debt. What is the book value of the debt after 10 years?

13. 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.

14. 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.

15. A \$300,000 face value bond carrying a 4% coupon is issued with four years until maturity. A sinking fund with semi-annual 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?

16. 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

17. In Canada, SO% 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.

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. a. Create a partial sinking fund schedule detailing the first two years, last two years, and the 10th and 11th years. b. Calculate the total interest earned by the sinking fund. c. Calculate the annual cost of the bond debt. d. Determine the book value of the bond debt after the 29th payment.

19. 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. a. Create a complete sinking fund schedule for the issuing company. Calculate the total interest earned. b. 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. c. If an investor purchased \$25,000 of the bond on March 23, 2008, for \$25,991.24, what would be the yield to maturity? d. 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.

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. a. Create a complete sinking fund for the issuing company. Calculate the total interest earned. b. 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. c. If an investor purchased \$34,000 of the bond on September 30, 2007, for \$34,167.47, what would be the yield to maturity? d. 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. 