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