Hassan Mustafa has recently started his new job as a financial manager in a firm called ScanSoft. ScanSoft is developing a new process to manufacture optical disks. The development costs were higher than expected, so ScanSoft requires an immediate cash inflow of $5,200,000. To raise the required capital, the company decided to issue bonds. Since ScanSoft had no expertise in issuing and selling bonds, Hassan suggested that the company work with an investment dealer. The investment dealer bought the company's entire bond issue at a discount, and then planned to sell the bonds to the public at face value or the current market value. To ensure it would raise the $5,200,000 it required, ScanSoft plans to issue 5200 bonds with a face value of $1000 each, on January 20, 2021. Interest is paid semi-annually on July 20 and January 20, beginning July 20, 2021. The bonds pay interest at 5.5% compounded semiannually. Hassan Mustafa realized that when the bonds mature on January 20, 2041, there must be $5,200,000 available to repay the bondholders. To have enough money on hand to meet this obligation, He suggested that ScanSoft set up a sinking fund (an interest-bearing account into which payments are made at regular intervals to provide a desired sum of money at a specified future time) using a specially designated savings account. The company earns interest of 1.6% compounded semi-annually on this sinking fund account. ScanSoft began making semi-annual payments to the sinking fund on July 20, 2021. ScanSoft issued the bonds, sold them all to the investment dealer, and used the money raised to continue its research and development. 1. How much would an investor have to pay for one of these bonds to earn 4.4% compounded semi-annually? 2. a. What is the size of the sinking fund payments? b. What will be the total amount deposited into the sinking fund account would be by January 2041? c. How much of the sinking fund will be interest? 3. Suppose ScanSoft discovers on January 20, 2031, that it can earn 2.5% interest compounded semi-annually on its sinking fund account. a. What is the balance in the sinking fund after the January 20, 2031, sinking fund payment? b. What is the new sinking fund payment if the fund begins to earn 2.5% on January 21, 2031? c. What will be the total amount deposited into the sinking fund account the life of the bonds? d. How much of the sinking fund will then be interest? To travel to his new job, Hassan is shopping for a new vehicle, and has noticed that many vehicle manufacturers are offering special deals to sell off the current year's vehicles before the models arrive. Hassan's local Ford dealership is advertising 3.9% financing for a full 48 months (i.e., 3.9% compounded monthly) or up to $4000 cash back on selected vehicles. The vehicle that Hassan wants to purchase costs $24,600 including taxes, delivery, licence, and dealer preparation. This vehicle qualifies for $1800 cash back if Hassan pays cash for the vehicle. Hassan has a good credit rating and knows that he could arrange a vehicle loan at his bank for the full price of any vehicle he chooses. His other option is to take the dealer financing offered at 3.9% for 48 months. Hassan wants to know which option requires the lower monthly payment. 4. Suppose Hassan buys the vehicle on July 1. What monthly payment must Hassan make if he chooses the dealer's 3.9% financing option and pays off the loan over 48 months? (Assume he makes each monthly payment at the end of the month and his first payment is due on July 31.) 5. Suppose the bank offers Hassan a 48-month loan with the interest compounded monthly and the payments due at the end of each month. If Hassan accepts the bank loan, he can get $1800 cash back on this vehicle. Help Hassan work out a method to calculate the bank rate of interest required to make bank financing the same cost as dealer financing. First, calculate the monthly rate of interest that would make the monthly bank payments equal to the monthly dealer payments. Then calculate the effective rate of interest represented by the monthly compounded rate. If the financing from the bank is at a lower rate of interest compounded monthly, choose the bank financing. The reason is that the monthly payments for the bank's financing would be lower than the monthly payments for the dealer's 3.9% financing a. How much money would Hassan have to borrow from the bank to pay cash for this vehicle? b. Using the method above, calculate the effective annual rate of interest and the nominal annual rate of interest required to make the monthly payments for bank financing exactly the same as for dealer financing 6. Suppose Hassan decides to explore the costs of financing a more expensive vehicle. The more expensive vehicle costs $34,900 in total and qualifies for the 3.9% dealer financing for 48 months or $2500 cash back. What is the highest effective annual rate of interest at which Hassan should borrow from the bank instead of using the dealer's 3.9% financing? Hassans wife Dana also needs a car. While reading the newspaper, she notices an ad for an Acura TSX She thinks that it is her ideal vehicle. The ad quotes both a cash purchase price of $37,500 and a monthly lease payment option. Since she does not have enough money to pay cash for a car, she would have to finance it from Honda by paying interest of 5.9% compounded monthly on a loan. The lease option requires payments of $594 a month for 48 months with a $1,330 down payment or equivalent trade. Freight and air tax are included. Dana does not have a vehicle to offer as a trade-in. If the vehicle is leased, then after 48 months it could be purchased for $16,155. The lease purchase would be based on an interest rate of 3.89%. During the term of the lease, kilometres are limited to 24,000 per year, with an additional charge of $0.08 per kilometre for excess kilometres. The costs include freight and air tax, but exclude taxes, registration. licence, and dealer administration charges. Dana is particularly impressed with the four years or 100,000 kilometre" warranty on the engine and transmission. The manufacturer also offers 24-hour roadside assistance. Dana must decide whether to buy or lease this car. She lives in a province with a 13% HST tax rate. She realizes that the costs of licence and insurance must be paid. but she will ignore these in her calculations. 7. If Dana buys the car, what is the total purchase price, including taxes? 8. Since Dana has no down payment, she must finance the car if she purchases it. (a) Is it cheaper to borrow the money from Honda or to lease? (b) The bank is offering a vehicle loan rate of 8% compounded annually. Is it better to buy or to lease the car at this rate? 9. Suppose Dana has a $4000 down payment for this car. a. What is the purchase price of the car if she pays cash for it? Assume the down payment is subtracted from the price of the car including tax. b. If the monthly lease payment is $594, is it cheaper to lease or buy the car if Dana can get the special dealer rate of 3.8%? Before starting the new job, Hassan Mustafa and his wife, Dana, were discussing how to plan for their three young sons university education. Stephen turned 12 years old in April, Jack turned 9 in January. and Danny turned 7 in March. Although university was still a long way off for the boys. Hassan and Dana wanted to ensure enough funds were available for their studies. Hassan and Dana decided to provide each son with a monthly allowance that would cover tuition and some living expenses. Because they were uncertain about the boys' finding summer jobs in the future, Hassan and Dana decided their sons would receive the allowance at the beginning of each month for four years. The parents also assumed that the costs of education would continue to increase. Stephen would receive an allowance of $1000 per month, starting September 1 of the year he turns 18. Jack would receive an allowance that is 8% more than Stephen's allowance. He would also receive it at the beginning of September 1 of the year he turns 18. Danny would receive an allowance that is 10% more than Jack's at the beginning of September of the year he turns 18. Hassan and Dana visited their local bank manager to fund the investment that would pay for the boys' allowances for university. The bank manager suggested an investment paying interest of 4.0% compounded monthly, from the day of the investment until the three boys had each completed their four years of education. Hassan and Dana thought this sounded reasonable. So, on June 1, they deposited the sum of money necessary to finance their sons' post-secondary educations. 10. How much allowance will each of the boys receive per month based on their parents' assumptions of price increases? 11. a. How much money must Hassan and Dana invest for each son on June 1 to provide them the desired allowance? b. Create a timeline of events for each of the sons. c. What is the total amount invested on June 1?