AFF 502, Problem Set Number Two November 8th, 2023

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Toronto Metropolitan University *

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502

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Finance

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Jan 9, 2024

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AFF 502 P ROBLEM S ET T WO S TUDENT N AME ____________________S TUDENT N UMBER ________________________ S TUDENT N AME ____________________S TUDENT N UMBER ________________________ S TUDENT N AME ____________________S TUDENT N UMBER ________________________ P LEASE NOTE THE FOLLOWING :  If you make any assumptions to solve the problem, clearly state them at the beginning of the solution and explain the reason.  The problem set is to be done individually or in a group of no more than 3 students.  You are to hand in an electronic copy of the assignment on the D2L Class page. Only one member of the group needs to submit the hard copy however the first worksheet in your workbook must clearly state the names, student numbers and section number of all of the group members.  REMINDER: This assignment is due at the start of the final exam on December 11 th at 8:00 am. 1

Q UESTION O NE : YOUR SISTERS ’ M ORTGAGES (30 MARKS ) Your sisters Rebecca and Debra each just bought a house. Rebecca paid $1,000,000 for the house. Rebecca had a down payment of $200,000. Rebecca got a mortgage with a 2-year term and a 25-year amortization period. Rebecca’s mortgage rate was 7.2% compounded semi-annually. Rebecca will make monthly mortgage payments. Debra bought a smaller house. She paid $850,000 for the house. Debra had a down payment of $250,000. Debra got a mortgage with a 2-year term and a 20-year amortization period. Debra’s mortgage rate was 6.4% compounded semi-annually. Debra will make monthly mortgage payments. 1) What is the amount of the Rebecca’s monthly payment? 2) How much will Rebecca pay in interest during the 1 st month of the mortgage? 3) Rebecca plans on making her required monthly payment during the life of the mortgage. How much will she owe on the mortgage at the end of the term? 4) How much will Rebecca pay in interest over the life of the mortgage? 5) What is the amount of the Debra’s monthly payment? 6) How much will Debra pay in interest during the 1 st month of the mortgage? 7) Debra plans on making her required monthly payment during the life of the mortgage. How much will she owe on the mortgage at the end of the term? 8) How much will Debra pay in interest over the life of the mortgage? 2

P ROBLEM 2: R ETIREMENT P LANNING FOR YOUR O THER S IBLINGS ’ R ETIREMENT (30 MARKS ) Your 4 siblings Maya, Kadeisha, Samuel and Tesho are all 22 years old. Each of them plans on retiring in 40 years. They have already determined the amount of money they need at retirement. These amounts are shown in the table below: Maya Kadeisha Samuel Tesho Amount Needed $5,500,000 $5,500,000 $5,500,000 $5,500,000 Maya has decided to start saving for retirement immediately. She will make an annual contribution into her retirement account. The contribution will be made at the end of each year. She expects to earn 7.2% compounded annually prior to retirement. What is amount of her annual contribution? Samuel has decided to start saving for retirement immediately. He will make an annual contribution into his retirement account. The contributions will be made at the end of each year. He expects to earn 7.2% compounded annually prior to retirement. After the initial contribution Samuel plans on increasing his annual contributions by 4% each year. What is the amount of his initial contribution? Kadiesha has decided to postpone saving for her retirement. Her plan is to make her first contribution to her retirement account when she turns 33, eleven years from now. She will make a total of 30 annual contributions to the account. The contributions will be made at the end of the year. She expects to earn 7.2% compounded annually prior to retirement. What is amount of her annual contribution? Tesho has decided to postpone saving for his retirement. His plan is to mark his first contribution to his retirement account when he turns 43, which will be 21 years from today. He will make a total of 20 annual contributions to the account. The contribution will be made at the end of each year. He expects to earn 7.2% compounded annually prior to retirement. The first contribution to his retirement account will be made 21 years from today. 3

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P ROBLEM 3: D EFINED B ENEFIT P ENSION PLANS (30 MARKS ) You have 2 sisters, Chrystia and Melanie. Your sisters are 32 years old. Your sisters wish to retire when they are 57 years old. Each of your sisters expect to live for 30 years after they retire. Each sister will receive a total of 30 annual payments from their pension. Chrystia and Melanie belong to a defined benefit pension plan. Chrystia’s defined benefit pension plan will pay her 2% for each year she has worked at her company. Chrystia has worked for her current employer for 10 years. She expects to work for her current employer until she retires in 25 years. Her annual pension will be based on her average annual salary during her last 5 years of work. The calculation is the number of years worked * 2% * average annual salary during her last 5 years of work. She currently is being paid $70,000 per year. For simplicity you may assume that the salary is being paid at the beginning of the year. She expects her salary to increase by 3% per year. There will be a total of 24 salary increases. During retirement she will receive an annual income from her pension plan. The annual pension payments will be made at the beginning of each year. Her annual pension payments will increase by the rate of inflation. Chrystia expects inflation to be 3% per year during retirement. Melanie’s defined benefit pension plan will pay her 2% for each year she has worked at her company. Melanie has worked for her current employer for 5 years. She expects to work for her current employer until she retires in 25 years. Her annual pension will be based on her average annual salary during her last 5 years of work. The calculation is the number of years worked * 2% * average annual salary during her last 5 years of work. She currently is being paid $70,000 per year. For simplicity you may assume that the salary is being paid at the beginning of the year. She expects her salary to increase by 2% per year. There will be a total of 24 salary increases. During retirement she will receive an annual income from her pension plan. The annual payments will be made at the beginning of each year. Melanie’s pension plan is not indexed, her annual payments will not change. Chrystia and Melanie’s employers believe that after retirement the pension plans will earn an effective annual rate of return of 6%. Prior to retirement the pension plans will earn an effective annual rate of return of 8%. Part A: 1) What is the amount of Chrystia’s first pension payment? 2) What is the amount of Melanie’s first pension payment? 3) How much money will Chrystia’s employer need to have when Chrystia retires to make the annual pension payments to Chrystia? 4

4) How much money will Melanie’s employer need to have when Melanie retires to make the annual pension payments to Melanie? . P ROBLEM 4: M ORTGAGE S TRESS T EST (10 MARKS ) Your brother is applying for mortgage. Your brother earns $120,000 per year. He is going to purchase a house which costs $900,000. The property taxes will be $450 per month. The heating costs are $200 per month. You brother has a car loan and the payments are $420 per month and he a student loan payment of $250 per month. The lender is prepared to lend your brother money at a rate of 5.8% compounded semi-annually. The term will be 5 years and the amortization period will be 25 years. Your brother will make monthly payments on his mortgage. The lender’s requirements are that the GDS ratio cannot be greater than 0.39 and TDS ratio cannot be greater than 0.44. The lender is required to stress all new mortgages. What is the maximum size of the mortgage that the lender can give your brother? Assuming your brother is granted the maximum mortgage amount what will be the amount of your brother’s monthly mortgage payments? 5