Business Math: A Step-by-Step Handbook 2021 Revision A
Chapter 14 Review Exercises
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 earn 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.
