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ADMS3530 3.0 Assignment #1 Page 1 AK/ADMS3530 3.0 Fall 2006 Assignment #1 Solutions Instructions: (1) This assignment is to be done individually. You must sign and submit the standard cover page supplied as the last page of this assignment. (2) This assignment is due in class on the week of October 9 , 2006. (3) This assignment is to be 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. (4) This assignment carries a total mark of 100 points . (5) 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 10, midnight . (6) Late assignments will not be accepted whether for technical or any other reason. Notations We will denote the PV and FV annuity factors respectively by PVIFA(r,n) and FVIFA(r,n), i.e.: r r n r FVIFA r r n r PVIFA n n 1 ) 1 ( ) , ( ; ) 1 ( 1 ) , ( + + Question 1 (16 marks) Consider the following stream of cash flows: Where the payments of C start one year from and last for 20 years; and the payments of X start in 21 years and last forever. The interest rate is 5%. (a) If C = \$200 and X = \$150, what is the present value of this stream? (5 marks) (b) If the present value of the stream is \$5,000 and X = \$100, what is the value of C? (5 marks) 0 1 2 3 20 21 22 C C C C X X

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ADMS3530 3.0 Assignment #1 Page 2 (c) Assume now that the value of the stream at year 20 is \$10,000 and that X = 2C. What is the value of C? (6 marks) Solution (a) One simple way to compute the PV is by considering the following equivalent stream: a perpetuity of \$150 starting in one year and a 20-year annuity of \$50. The PV is then given by: PV = \$150 / 5% + \$50 x PVIFA(5%,20) = \$3,000 + \$623.11 = \$3,623.11 (b) Following part (a), we can consider a perpetuity of \$100 and a 20-year annuity of (C – 100): PV = \$5,0000 = \$100 / 5% + (C - 100) x PVIFA(5%,20) = \$2,000 + (C - 100) x PVIFA(5%,20) Or \$3,000 = (C - 100) x PVIFA(5%,20) C – 100 = \$240.73 C = \$340.73 (c) Value at 20 = \$10,000 = C x FVIFA(5%,20) + 2C / 5% \$10,000 = C x [ FVIFA(5%,20) + 2 / 5%] \$10,000 = C x [ 33.07 + 40] = 73.07 x C Or C = 10,000 / 73.07 = \$136.86 Question 2 (16 marks) You are thinking of buying a used car that costs \$6,000 and has an expected zero resale value at the end of 4 years. Both Bank of Montreal (BMO) and Toronto-Dominion Bank (TD) are offering special low-rate car loans to York students. BMO will loan you the \$6,000 and charge you a 6% EAR and want the loan repaid in 48 equal monthly payments, with the first payment due at the end
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