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Assignment1_solutions_Winter2007

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Unformatted text preview: AK/ADMS3530 3.0 Assignment #1 Solutions Winter 2007 Question 1 (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) Answer This is a perpetuity question. The formula should be of the form PV perpetuity = Annual Payment / Annual Int. Rate OR Endowment = Annual Scholarship / Annual Int. Rate Endowment = \$250,000 / 5% = \$250,000 / 0.05 = \$5,000,000 Therefore your \$5,000,000 endowment is sufficient to fund annual scholarships of \$250,000 forever based on a prevailing annual interest rate of 5%. (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) Answer Based on the answer above York would NOT be able to meet you stipulation as there would be a shortfall in the endowment of \$5,000,000 - \$4,000,000 = \$1,000,000. ADMS3530 3.0 Assignment #1 Solutions With a \$4,000,000 endowment the Annual Scholarship = Endowment * Annual Int. Rate Annual Scholarship = \$4,000,000 * 0.05 = \$200,000 Therefore with a \$4,000,000 endowment York would be able to fund a maximum annual scholarship of \$200,000 with prevailing annual interest rates of 5%. (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) Answer PV perpetuity = Annual Payment / (Annual Int. Rate – Growth Rate of Payment) OR Endowment = Annual Scholarship / (Annual Int. Rate – Growth Rate of Scholarship) Endowment = \$250,000 / (0.05 – 0.01) = \$6,250,000 Therefore with an endowment of \$5,000,000 there would be shortfall of \$6,250,000 – \$5,000,000 = \$1,250,000. Annual Scholarship = Endowment * (Annual Int. Rate – Constant Growth Rate of Scholarship) Annual Scholarship = \$5,000,000 * (0.05 – 0.01) = \$200,000 With an endowment of \$5,000,000 York would be able to fund an annual scholarship of \$200,000 that would grow at a constant annual rate of 1%....
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