ADMS3530 3.0 Assignment #1 AK/ADMS3530 3.0 Fall 2007 Assignment #1 Instructions: (1) (2) (3) (4) (5) (6) This assignment is to be done individually You must sign and submit the standard cover page supplied as the last page of this assignment This assignment is due in class in the week of October 8, 2007 This assignment can be typed or handwritten Work that is too difficult to read due to messiness and poor handwriting will receive zero credit You must show your work to receive full credit This assignment carries a total mark of 100 points For Internet section students, the assignment must be uploaded to the Centre for Distance Education: http://www.atkinson.yorku.ca/cde/assignmentupload and identified precisely in accordance with the course outline by Tuesday, October 9, midnight Late assignments will not be accepted whether for technical or any other reason Question (TVM) (15 marks) This question consists of the following three independent parts (a) John plans to retire in 15 years, and he wants to have an annuity of $50,000 a year for 20 years after retirement John wants to receive the first annuity payment at the end of the 15th year from today (the same day as his retirement date) How much must John invest today in order to have his retirement annuity if the annual interest rate is 6%? (5 marks) (b) How long would it take to accumulate $1 million if you begin putting $100 in the bank every week starting one week from now at an EAR of 8% with weekly compounding? There are 52 weeks in a year (5 marks) (c) Jen is going to deposit $250 into an account at the beginning of each of the next years starting today The account will then be left to compound for another 10 years (between the end of year and the end of year 15) At the end of year 16, Jen will start receiving a perpetuity from the account If the account pays 7% annually, how much each year will she receive from the perpetuity? (5 marks) Page ADMS3530 3.0 Assignment #1 Question (TVM) (16 marks) A 20-year annuity was purchased with $180,000 that had accumulated in an RRSP The annuity provides a semiannually compounded rate of return of 5% and makes equal month-end payments (a) What is the monthly payment? (4 marks) (b) What will be the principal portion of Payment #134? (4 marks) (c) What will be the interest portion of Payment #210? (4 marks) (d) How much interest will be paid in the 6th year? (4 marks) Question (TVM) (15 marks) Consider the following stream of cash flows: X X X X Y Y 10 11 12 where the payments of X start one year from today and last for 10 years; and the payments of Y start in 11 years from now and last forever The interest rate is 4% (a) If X = $100 and Y = $200, what is the present value of this stream? (4 marks) (b) If the present value of the stream is $4,000 and Y = $100, what is the value of X? (5 marks) (c) Assume now that the value of the stream at year 10 is $8,000 and that Y = 3X What is the value of X? (6 marks) Question (Mortgage) (20 marks) Below is a summary of special mortgage deals from TD Canada Trust as of September 13, 2007: Special Offers – TD Canada Trust Year Closed Variable Interest Rate Mortgage Year Fixed Rate Mortgage Rates 5.750% 6.180% Page ADMS3530 3.0 Assignment #1 As a recent graduate of Atkinson’s BAS finance program, you are trying to decide which mortgage option to choose You need a $300,000 mortgage for your new luxury 500 square foot condo at the corner of King and Bay, downtown Toronto You have chosen a 25 year amortization period for the loan (a) If you assume that rates not change over the five-year term of the mortgage, what is the monthly payment under the 5.75% variable rate option? (4 marks) (b) If you decide to go with the 6.18% fixed mortgage rate, what is the remaining balance of your $300,000 loan at the end of year 5? (4 marks) (c) You have been studying the sub prime market meltdown and are convinced that year variable mortgage interest rates will actually decline to 5.05% beginning in year of your mortgage loan but will then increase to 7.00% for year 3, and If you are correct, which option is best? (6 marks) (d) You have now decided to take the 6.18% fixed rate mortgage but you decide to go with a 20 year amortization period instead of a 25 year period What will be your total interest savings over the entire loan period (assume rates remain at 6.18%) by taking the 20 year amortization period? (6 marks) Question (Bonds) (16 marks) Bonds K and L both have a face value of $1,000, pay semi-annual coupons and have 15 years remaining until maturity Their coupon rates are 6% and 8% respectively If the prevailing market rate decreases from 7.5% to 6.5% compounded semiannually (a) Calculate the price change of each bond in dollars (4 marks) (b) Calculate the price change of each bond as a percentage of the initial price (4 marks) (c) Are high-coupon or low-coupon bonds more sensitive to a given interest rate change? Justify your response using the results from part (b) (4 marks) (d) What would be the coupon rate that would lead to the largest price change as a percentage of the initial price? What would be this percentage change? (4 marks) Page ADMS3530 3.0 Assignment #1 Question (Bonds) (18 marks) Assume that you are an investor and are in the market for corporate debt You run across XYZ Corporation’s bonds which have a 20 year term, a 7.5% coupon (interest paid semi-annually) and were issued five years ago (Sep 1st 2002) at par of $1,000 Over the last five years, interest rates have fluctuated substantially and the following table shows the required returns for XYZ bonds for the last years: Date Sep 1st., 2003 Sep 1st., 2004 Sep 1st., 2005 Sep 1st., 2006 Sep 1st., 2007 Required Return 8.50% 6.75% 5.95% 6.35% ? (a) Calculate the rate of return for each of the last four years since the bonds were issued Assume that the coupons are not reinvested (6 marks) (b) What relationship your results in (a) illustrate? (2 marks) (c) Calculate your current yield and your yield to maturity if you purchase the bond on September 1st, 2007 at a price of $1,070? (4 marks) (d) If you purchase the bond on September 1st, 2007 at a price of $1,070, what are the total rate of return and the effective annual rate of return if you decide to sell the bond after years at a price of $1,030? Assume the coupons are reinvested at 5% semi-annually compounded (6 marks) Page ADMS3530 3.0 Assignment #1 Atkinson Faculty of Liberal and Professional Studies YORK UNIVERSITY Toronto, Ontario ADMS3530 3.0 Finance Professor Section Assignment #1 Due Date: Class of the week of October 8, 2007 (Section H: Tuesday, Oct 9, Upload to the CDE before midnight) Personal Work Statement I, the undersigned: • warrant that the work submitted herein is my work and not the work of others • acknowledge that I have read and understood the Senate Policy on Academic Honesty • acknowledge that it is a breach of the University Regulations to give and receive unauthorized assistance on a graded piece of work Name (typed or printed) York Student # Signature Page ... Calculate the price change of each bond in dollars (4 marks) (b) Calculate the price change of each bond as a percentage of the initial price (4 marks) (c) Are high-coupon or low-coupon bonds more sensitive... is the present value of this stream? (4 marks) (b) If the present value of the stream is $4,000 and Y = $100, what is the value of X? (5 marks) (c) Assume now that the value of the stream at year... = 3X What is the value of X? (6 marks) Question (Mortgage) (20 marks) Below is a summary of special mortgage deals from TD Canada Trust as of September 13, 2007: Special Offers – TD Canada Trust