assignment2 fundamentals of corporate finance, 4th edition brealey

AK/ADMS3530 3.0 Assignment #1 Winter 2007 Instructions: (1) (2) (3) (4) (5) (6) (7) (8) This assignment is to be done individually You must sign and submit the standard cover page supplied as the last page of this assignment Before you start, please read the note “Writing Style Required for ADMS3530 Assignments” posted in the “Assignments” folder on the course web site Please stick to the writing guidelines suggested in the note This assignment is due at the start of class, the week of February 5, 2007 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, February 6, 2007, midnight This assignment is to be either handwritten or printed out 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 Late assignments will not be accepted whether for technical or any other reason Decimal places: please keep at least in your calculations and in your final answers Question (12 marks) You became incredibly wealthy one day and a huge contributing factor to your success was the education that you’d received at York/Atkinson As a way to thank the school you set up an endowment today in the amount of $5,000,000 But you don’t just hand over $5,000,000 just like that!!! You stipulate that York use the funds to provide scholarships to ADMS3530 students totaling $250,000 annually The scholarships are to commence one year from today and are to continue for as long as ADMS3530 is around (in effect for ever!!!) The market interest rate for the foreseeable future is expected to be 5% per annum compounded annually (a) Based on the above information will York be able to meet your stipulation by providing ADMS3530 students with annual scholarships totaling $250,000 for ever? Provide supporting analysis (2 marks) ADMS3530 3.0 Assignment #1 (b) What if your endowment was $4,000,000 instead of $5,000,000 would York still be able to meet your stipulation? If not what would be the maximum annual scholarship payout? Provide supporting analysis (3 marks) (c) As we all know the cost of education keeps going up and up To accommodate these inflationary pressures you ask that the $250,000 scholarship grow at a constant rate of 1% annually Would York be able to fund this scholarship for ever with your $5,000,000 endowment? If not what would be the maximum annual scholarship? Provide supporting analysis (4 marks) (d) What would your endowment have to be to accommodate annual scholarships of $300,000 with a constant growth rate of 1% annually? Provide supporting analysis (3 marks) Question (9 marks) You have finally decided that this is the year that you purchase that exotic car (Aston Martin Vanquish (007’s car), Porsche Carrerra GT, Bentley Continental etc…etc.) But your spouse (Salma Hayak or Brad Pitt depending on who you are) insists that you must decide on the maximum purchase price you can afford before you ever look at your first car Assume that the only source of money to finance your purchase is based on your family income The details of which follow… Your annual income is $50,000 before taxes which is taxed at a flat rate of 30% Of the after tax income you can commit 25% annually towards the purchase of the car for the next years (starting year from today) Your spouse’s annual income is $5,000,000!!! (remember it’s Salma or Brad) before taxes which is taxed at a flat rate of 50% Of the after tax income your spouse will only commit 0.5% annually to the purchase of your car for the next years (starting year from today) The prevailing rate of interest on auto loans in the market place is 7% compounded annually Assuming you can get an auto loan, can you afford one of the luxury cars which are priced today at over $250,000? Or will you have to buy a Honda Odyssey (which costs approx $50,000) mini van which is that much more practical as you have small children Show your calculations to support your decision Question (15 marks) Page ADMS3530 3.0 Assignment #1 RRSP season is coming up and Canadians will be faced with many investment opportunities Assume that you are a Canadian resident with a marginal tax rate of 40% You have decided to invest in a $1,000 RRSP Since this is tax deductible and you will receive a $400 tax refund given your marginal tax rate (40% of $1,000) You have two options available to you The first is presented here and the second appears in part (c) below In order to buy the RRSP you may borrow $1,000 and then pay down your $1,000 loan with the $400 immediate tax refund Throughout this question interest rate is assumed to be 9% compounded monthly (a) What is the monthly payment required to pay down the loan in one year? (2 marks) (b) To what will the single $1,000 contribution grow over the next 20 years? (2 marks) (c) Let’s say that you opted rather than borrow the $1,000 and immediately pay down the $400 and then pay out the loan over a one year period (as in part (a) above) that you agreed last year to make monthly contributions to a savings plan in order to realize a $600 payout by the end of the 12th month (i.e today) and then borrow the remaining $400 to purchase the $1,000 RRSP now, how much would you need to save on a monthly basis? You will immediately pay down the $400 by the end of the first month that it is due (3 marks) (d) Assuming that you would like to continue your RRSP investment in part (a) or part (c) annually for the next 20 years until your retirement Compare the two RRSP plans by calculating the PV of both options (4 marks) (e) What is the benefit of one plan over the other assuming that the interest rate remains at 9% monthly compounded throughout the next 20 years? (4 marks) Question (13 marks) Another Canadian investor is planning his retirement information please help him with his calculations (a) Given the following What will be the amount in an RRSP after 25 years, at which time he will retire and live off the proceeds, if contributions of $3,000 are made at each year-end for its first seven years and month-end contributions of $500 are made for the subsequent 18 years? Assume that the plan earns 8% compounded quarterly for the first 12 years, and 7% compounded semiannually for the subsequent 13 years (4 marks) Page ADMS3530 3.0 Assignment #1 (b) Your investor would like to set up a Scholarship Fund in his name at Atkinson College with a $500 annual award to a deserving applicant The first award will be made at the end of the 15th year of his retirement Subsequent awards will be made at the end of each year perpetually Given the RRSP amount in part (a) above, how much can your investor expect to withdraw at the end of each month, starting the first month after his retirement, and still be able to set up the Scholarship Fund? (Assume the interest rate is 10% compounded monthly throughout his retirement.) (6 marks) (c) What complications might occur in achieving the plan in part (b)? (3 marks) Question (14 marks) Throughout this question consider the following bond: face value of $1,000, coupon rate is 8%, semi-annual coupon payments, years of maturity, and a purchase price of $1,055.69 (a) Calculate the current yield and yield to maturity on the bond as of the date of purchase (3 marks) (b) Calculate the current yield and bond price on each anniversary date of the bond purchase until maturity Suppose on each of these dates the yield to maturity on the bond is 7%, 6.6%, 6.2%, and 6.36%, respectively (6 marks) (c) Assume instead of holding the bond until maturity, you sell the bond on the second anniversary of its purchase (right after you receive the last coupon) Based on your results in part (b) above, what is your total rate of return over this 2-year holding period? What is your annual rate of return over the same period? Assume you can reinvest the previous coupons at an APR of 10% quarterly compounded (5 marks) Question (8 marks) This question has two parts, (a) and (b) (a) Do you think it is necessary for bond prices to fluctuate in response to changing interest rates? Why? Please limit your answer to one paragraph (4 marks) (b) Why should investors be cautious when replying on yield to maturity as Page ADMS3530 3.0 Assignment #1 a measure of the return on their bond investment? Please limit your answer to one paragraph (4 marks) Question (15 marks) Rite Bite Enterprises historically has not been a dividend paying company but in its latest board meeting the company decided to start paying a fixed dividend of $1.5 for the next year After the first dividend, they expect that the dividend will grow at 5% over the following three years and it will maintain a constant 6% annual growth rate thereafter (Please draw a timeline to show your work.) (a) What are the expected dividends in years and 10? (2 marks) (b) If the discount rate for the stock is 10%, at what price will the stock sell today? (5 marks) (c) What is the expected stock price three years from now? (3 marks) (d) If your annual required rate of return is 12% for the next years and 8% thereafter how much will you pay for a share of Rite Bite’s stocks today? (5 marks) Question (14 marks) This question has two parts, (a) and (b) (a) The common stock of Veritas Ltd is currently trading at $ 48 on the TSX You also know the following information about the Veritas stock: its P/E ratio is 16, Veritas Ltd has a required rate of return of 10% on its common equity, and the company’s dividends are expected to grow at 6% forever What is Veritas’ payout ratio today? What is Veritas’ plowback ratio today? (6 marks) (b) Butterfly Tractors Corp has experienced an outstanding growth in recent years, which is expected to continue in the future In particular, earnings and dividends are forecasted to grow at a rate of 5% during the next years, and at a constant rate of 6% thereafter Butterfly just paid a dividend of $2 and the required rate of return on its stock is 12% Suppose that you buy one share of Butterfly stock today and sell it at the end of Year Compute the 1-year dividend yield, 1-year capital gains yield, and 1-year total rate of return on your investment for each of Years 1, 2, 3, and Assume that previous dividends are not reinvested (8 Marks) Page ADMS3530 3.0 Assignment #1 Atkinson Faculty of Liberal and Professional Studies YORK UNIVERSITY Toronto, Ontario, Canada ADMS3530 3.0 Finance Professor Section Assignment #1 Due Date: Start of class, week of February 5, 2007 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 ... stock today and sell it at the end of Year Compute the 1-year dividend yield, 1-year capital gains yield, and 1-year total rate of return on your investment for each of Years 1, 2, 3, and Assume that... value of $1,000, coupon rate is 8%, semi-annual coupon payments, years of maturity, and a purchase price of $1,055.69 (a) Calculate the current yield and yield to maturity on the bond as of the... rate of 5% during the next years, and at a constant rate of 6% thereafter Butterfly just paid a dividend of $2 and the required rate of return on its stock is 12% Suppose that you buy one share of