Adms 3530 Solution

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AP/ADMS3530 3.0 Assignment #1 Solution Winter 2010 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. Before you start, please read the note “Writing Style Required for ADMS3530 Assignments” posted on the course web site. Please stick to the writing guidelines suggested in the note. This assignment is due in the class of the week of February 8, 2010. 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 9, 2010, midnight. This assignment must 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. 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 4 in your calculations and 2 in your final answers.

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Notations We may denote the PV and FV annuity factors respectively by PVAF(r,n) and FVAF(r,n), i.e.: 1 − (1 + r ) − n (1 + r ) n − 1 PVAF (r , n) ≡ ; FVAF (r , n) ≡ r r Question 1 – TVM (20 marks) On January 1, 2009 Joe Tall signed a contract to play for the York Dunks that guaranteed him, as a minimum, the annual payments negotiated for the first 5 years of his contract. These contract payments were $875,000 for 2009, $650,000 for 2010, $800,000 for 2011, $1 million for 2012, $1 million for 2013 and $300,000 for 2014; in addition, if by the end of 2014 Joe Tall was still with the York Dunks, the contract called for payments of $240,000 per year from 2015 through 2031 and then $125,000 per annum from 2032 through 2041.

ADMS3530 3.0 Fall 2009

Assignment #1

(a) If the relevant effective annual rate of interest is 9% and all payments are made on July 1 of each year beginning on July 1, 2009, what was the present value of all the contract payments on January 1, 2009? (7 marks) (b) If, in lieu of the first six payments described above, Joe Tall were to receive an equal annual salary at the end of each of the six years from 2009 to 2014, what would this equivalent annual salary be? (5 marks) (c) If by July 1, 2014 Joe Tall is contemplating to sign up with another team, what will be his incentive to remain with the York Dunks at that point in time? (4 marks) (d) What does that tell you about the value of the payments scheduled between 2032 and 2041? (4 marks) Answer (a) PV of 240 k$ payments from 2015 to 2031 at July 1, 2015 PVAD = 240,000 * PVAF(9%, 17) * (1 + 0.09) = $2,235,013.97 PV of 125 k$ payments from 2032 to 2041 at July 1, 2032 PVAD = 125,000 * PVAF(9%, 10) * (1 + 0.09) = $874,405.86 PV of all payments on Jan 1, 2009 875,000/(1.09)0.5 + 650,000/(1.09)1.5 + 800,000/(1.09)2.5 + 1,000,000/(1.09)3.5 + 1,000,000/(1.09)4.5 + 300,000/(1.09)5.5 + 2,235,013.97/(1.09)6.5 + 874,405.86/(1.09)23.5 = $5,051,005.95 (b) PV of first six payments on Jan 1, 2009 875,000/(1.09)0.5 + 650,000/(1.09)1.5 + 800,000/(1.09)2.5 + 1,000,000/(1.09)3.5 + 1,000,000/(1.09)4.5 + 300,000/(1.09)5.5 = $3,659,147.72 PMT = PV / PVAF(9%,6) = 3,659,147.72 / 4.4859 = $815,696.42 (c) His incentive is all the payments scheduled after 2014. Their PV on July 1, 2014 is: 2,235,013.97 / 1.09 + 874,405.86 / (1.09)18 = $2,235,840.10 (d) On July 1, 2014, the payments 2032 and 2041 are worth: 2,235,840.10 – 2,235,013.97/1.09 = $185,368.57 when he is considering to sign up with another team. As expected the PV of these payments (15 to 25 years away) is relatively small. Also, in the

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ADMS3530 3.0 Fall 2009

Assignment #1

context of the total contract payments Joe Tall is to receive, the PV of the 2032 to 2041 payments represents a very minor portion.

Question 2 – TVM (18 marks) Mary Ballard, aged 25,...
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