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mid06-1 - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Nov. 14, 2006 Brean/Kan MGT337Y MID-TERM EXAMINATION #1 Pomorski/Xu DURATION - 2 hours Aid Allowed: Silent electronic calculator and one 1-sided 8 1 2 × 11” crib sheet Name: Student Number: Circle the section that you are registered in: Brean (9–11a.m.) Brean (11a.m.–1p.m.) Kan (Mon.) Kan (Tue.) Pomorski (Mon.) Pomorski (Fri. 10a.m.–12p.m.) Pomorski (Fri. 12p.m.–2p.m.) Xu (Tue.) Xu (Wed.) Instructions 1. Answer all questions on the examination paper. 2. Answer five 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 Marks 1 2 3 4 5 6 Total 1
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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 W 1 = 25 I 3 4 0 , where I 0 is the amount you invest today, and W 1 is the output tomorrow. Your utility function of consumption at today and tomorrow is U ( C 0 , C 1 ) = ln( C 0 C 1 ) = ln( C 0 ) + ln( C 1 ) where C 0 is today’s consumption and C 1 is tomorrow’s 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 offers you a security which pays $ n at the end of the n th year for 100 years (i.e., it pays $1 at the end of the first 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 first payment will be paid out in a moment. The interest rate is 8% per year.
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