OF UNIVERSITY TORONTO Joseph L. Rotman School of Management Nov. 14, 2006 MGT337Y Brean/Kan Pomorski/Xu
MID-TERM EXAMINATION #1
DURATION - 2 hours Aid Allowed: Silent electronic calculator and one 1-sided 8 1 11 crib sheet 2 Name: Circle the section that you are registered in: Brean (911a.m.) Kan (Tue.) Pomorski (Fri. 12p.m.2p.m.) Brean (11a.m.1p.m.) Pomorski (Mon.) Xu (Tue.) Kan (Mon.) Pomorski (Fri. 10a.m.12p.m.) Xu (Wed.) Student Number:
Instructions
1. Answer all questions on the examination paper. 2. Answer ve out of six questions. Each question is worth 20 marks. Do not answer all six questions! In the table below, cross out the question that you choose not to answer. Question 1 2 3 4 5 6 Marks
Total
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1. Assume that you have $118,125 today and there is an investment opportunity which is described by the following production function
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W1 = 25I04 , where I0 is the amount you invest today, and W1 is the output tomorrow. Your utility function of consumption at today and tomorrow is U (C0 , C1 ) = ln(C0 C1 ) = ln(C0 ) + ln(C1 ) where C0 is todays consumption and C1 is tomorrows consumption. (Note: d ln(x)/dx = 1/x.) (a) Suppose capital markets do not exist and you cannot borrow, lend, or save the money you have today. How much should you invest today? What is your optimal consumption plan? (10 marks) (b) If capital markets exist and the interest rate is 25%, what will be your optimal investment and consumption plan? (10 marks) 2. (a) Someone oers you a security which pays $n at the end of the nth year for 100 years (i.e., it pays $1 at the end of the rst year, $2 at the end of the second year, and so on until the last payment is $100 at the end of the 100th year). If the annually compounded interest rate is 8% per year, what is the fair price of such security? (7 marks) Consider a perpetuity that pays $100 every year. The rst payment will be paid out in a moment. The interest rate is 8% per year. (This information applies to parts (b)(d).) (b) Suppose the stated annual interest rate is compounded annually. What is the present value of the perpetuity? (3 marks) (c) Suppose the stated annual interest rate is compounded monthly. What is the present value of the perpetuity? (3 marks) (d) Suppose the stated annual interest rate is continuously compounded. What is the present value of the perpetuity? (3 marks) (e) You want to borrow money for a year at the continuously compounded rate of 8% per year. You will need to pay the overall interest after 1 year. What amount do you need to borrow to ensure that your interest payment will be exactly $100? (4 marks) 3. Today is July 1, 2006. Consider three zero-coupon Treasury bonds with face values of $1,000 and maturities of 6, 12, and 18 months. (These bonds mature on December 31, 2006, June 30, 2007, and December 31, 2007.) The bonds are priced as follows: the 6-month bond sells for $970.87, the 12-month bond sells for $924.56, and the 18-month bond sells for $863.84. Suppose a new coupon-paying Treasury bond with 18 months to maturity is issued today and its coupon rate of 10%/year (but with semi-annual coupon payments). 2
(a) Calculate the theoretical price of the new coupon bond that has a face value of $1,000. (3 marks) (b) Is the bond selling at a premium or at a discount? Why? Is the yield-to-maturity of this bond greater than or less than the coupon rate? (3 marks) (c) Suppose the coupon bond instead sells at par. Describe how you can exploit this arbitrage opportunity to make money. What are the cash-ows of your strategy? (5 marks) (d) Suppose the expectations theory of the term structure holds. What is the markets expectation of the price of the 18-month zero coupon bond (maturing December 31, 2007) on June 30, 2007? (5 marks) (e) If the liquidity preference theory holds instead, is the expected price of bond the lower or higher than what you derived above? Why? (4 marks) 4. Consider a coupon bond issued by the Government of Canada. This bond has 2 years to maturity, annual coupon of $200, and face value of $1000. For parts (a)(c), no calculations are necessary. For these questions, limit your answers to two sentences. We will not grade anything longer than two sentences. (a) If the interest rates go up, will the price of the bond increase or decrease? Why? (3 marks) (b) If the interest rates go up, will the yield-to-maturity of the bond increase or decrease? Why? (3 marks) (c) If the bond were issued by Research in Motion instead, would its price be lower or higher? Why? (3 marks) (d) ABC Corporation has 1 million shares of stock outstanding. It just paid a dividend of $2 per share. The dividend growth rate is expected to be 25% over the next three years, 15% for the two subsequent years, and then 5% per year forever. The required rate of return is 20%. What is the price for one share of ABC? (5 marks) (e) Suppose ABC Corporation in part (d) has found an opportunity to buy a machine at the end of year 2. The machine will cost 50% of ABCs second years total dividend. This investment will increase the dividend per year in the subsequent years by 30% (so the dividend from year 3 onward is equal the original dividend from part (d) multiplied by 1.3). Should the rm buy the machine? What is the price per share of ABCs stock with this opportunity? (6 marks) 5. (a) Consider the following two independent projects: Project A requires an initial investment of $4,500 and delivers cash ows of $4,000 at the end of the rst year and $1,000 at the end of the second year. Project B requires an initial investment of $4,500 and delivers cash ows of $1,000 at the end of the rst year and $4,000 at the end of the second year. 3
Calculate the IRR for each project. (Do not just provide an answer, you need to show the intermediate steps.) If the discount rate is 5%, determine which project(s) you will invest. What if the discount rates are 8% and 10%? (10 marks) (b) You are doing a part-time job and deliver pizza for some of the large chains in the area. To make your deliveries, you have two choices. The rst choice is to purchase a cheaper car whose price is $20,000 and which costs $2,000 per year in gas and $2,000 per year in repairs (assume the costs happen at the end of the year). It will last for 4 years. The alternative is to purchase a more expensive car whose price is $30,000 and which costs $1,500 per year in gas and $1,000 per year in repairs. It will last for 8 years. The discount rate is 10%. Which one should you choose? (Assuming the job will last for a long time and both cars can be replaced.) (10 marks) 6. BloorCo is a high-end boutique in Yorkville. BloorCo estimates that it generates $1,200 in sales per year per square foot of retail oor space. BloorCos pre-tax gross prot margin on sales is 25%. BloorCo built a storage room last year at a cost of $400/square foot last year. The storage room is currently unused but it can be rented out for an annual rent of $20 per square foot. With an additional investment in renovations, the storage room could be turned into retail space. The expected useful life of the renovations for retail is 3 years with zero salvage value. Buildings (the store room) are in CCA Class 3 (5% CCA rate) whereas renovations for retail purposes are in CCA Class 8 (50% CCA rate). Assume the company has many other assets in these two classes and the half-year rule applies. The corporate tax rate is 30%. The appropriate discount rate is 10%. What is the maximum amount of expenditure per square foot that BloorCo should be willing to pay for renovations? For simplicity, assume revenues and expenses are received and paid at the end of each year. (20 marks)
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