Question 4 (Total 20 marks) Xue just won an American Powerball (lottery) and she
ID: 2551726 • Letter: Q
Question
Question 4 (Total 20 marks) Xue just won an American Powerball (lottery) and she must choose among three Zhang award options. She can elect to receive a lump sum today of $60 million, to receive IQ end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million. (20 marks) a. Ifshe thinks she can earn 7.5% annually, which should she choose? (5 marks) b. Ifshe expects to earn 8.5% an uually, which is he best choice? (5 marks) C. If she expects to earn 9.5% annually, which option would you recommend? (5 marks) d. Explain how interest rates influence the optimal choice. (5 marks) Answers for Question 4Explanation / Answer
4. Higher the interest rate, lower the span of period in which payment should be received.
PV @ 7.5% PV @ 8.5% PV @ 9.5% 10 year end payment 30 year end payment Present Value at 7.5% Present Value at 8.5% Present Value at 9.5% 10 year end payment 30 year end payment 10 year end payment 30 year end payment 10 year end payment 30 year end payment A B C D E D*A E*A D*B E*B D*C E*c 1 0.930232558 0.921658986 0.913242009 9.5 5.5 8.84 5.12 8.76 5.07 8.68 5.02 2 0.865332612 0.849455287 0.834010967 9.5 5.5 8.22 4.76 8.07 4.67 7.92 4.59 3 0.80496057 0.782908098 0.761653851 9.5 5.5 7.65 4.43 7.44 4.31 7.24 4.19 4 0.74880053 0.721574284 0.695574293 9.5 5.5 7.11 4.12 6.85 3.97 6.61 3.83 5 0.696558632 0.665045423 0.635227665 9.5 5.5 6.62 3.83 6.32 3.66 6.03 3.49 6 0.647961518 0.612945091 0.580116589 9.5 5.5 6.16 3.56 5.82 3.37 5.51 3.19 7 0.602754901 0.564926351 0.52978684 9.5 5.5 5.73 3.32 5.37 3.11 5.03 2.91 8 0.560702233 0.520669448 0.483823598 9.5 5.5 5.33 3.08 4.95 2.86 4.60 2.66 9 0.521583473 0.479879675 0.441848034 9.5 5.5 4.96 2.87 4.56 2.64 4.20 2.43 10 0.485193928 0.442285415 0.403514187 9.5 5.5 4.61 2.67 4.20 2.43 3.83 2.22 11 0.451343189 0.407636327 0.368506107 5.5 - 2.48 - 2.24 - 2.03 12 0.419854129 0.375701684 0.336535257 5.5 - 2.31 - 2.07 - 1.85 13 0.390561981 0.346268833 0.307338134 5.5 - 2.15 - 1.90 - 1.69 14 0.363313471 0.319141782 0.280674095 5.5 - 2.00 - 1.76 - 1.54 15 0.337966019 0.294139891 0.256323375 5.5 - 1.86 - 1.62 - 1.41 16 0.314386995 0.271096674 0.234085274 5.5 - 1.73 - 1.49 - 1.29 17 0.292453018 0.249858686 0.213776506 5.5 - 1.61 - 1.37 - 1.18 18 0.272049319 0.230284503 0.195229686 5.5 - 1.50 - 1.27 - 1.07 19 0.253069134 0.212243781 0.17829195 5.5 - 1.39 - 1.17 - 0.98 20 0.235413148 0.195616388 0.162823699 5.5 - 1.29 - 1.08 - 0.90 21 0.218988975 0.180291602 0.148697442 5.5 - 1.20 - 0.99 - 0.82 22 0.203710674 0.166167375 0.135796751 5.5 - 1.12 - 0.91 - 0.75 23 0.189498302 0.153149655 0.124015297 5.5 - 1.04 - 0.84 - 0.68 24 0.17627749 0.141151755 0.113255979 5.5 - 0.97 - 0.78 - 0.62 25 0.16397906 0.130093784 0.103430118 5.5 - 0.90 - 0.72 - 0.57 26 0.152538661 0.119902105 0.094456729 5.5 - 0.84 - 0.66 - 0.52 27 0.141896429 0.110508852 0.086261853 5.5 - 0.78 - 0.61 - 0.47 28 0.131996678 0.101851477 0.078777948 5.5 - 0.73 - 0.56 - 0.43 29 0.122787607 0.093872329 0.071943331 5.5 - 0.68 - 0.52 - 0.40 30 0.11422103 0.086518276 0.065701672 5.5 - 0.63 - 0.48 - 0.36 Total 65.21 64.96 62.33 59.11 59.65 54.09 7.50% 8.50% 9.50% If received today 60 60 60 If receive 10 payment of 9.5 65.21 62.33 59.65 If receive 30 payment of 5.5 64.96 59.11 54.09 Best Option 10 Payment of 9.5 10 Payment of 9.5 Should receive todayRelated Questions
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