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Homework3_Solutions - ISOM 111 L7-L8 Fall 2010 1 Homework 3...

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ISOM 111 L7-L8, Fall 2010 1 Homework 3 Solutions I. Company A is considering the acquisition of two separate but large companies, Company B and Company C, having sales and assets equal to its own. The following table gives the probabilities of returns for each of the three companies under various economic conditions. The table also gives the probabilities of returns for each possible combination: Company A plus Company B, and Company A plus Company C. Return Distribution for Companies A, B, and C and for Two Possible Acquisitions Economic Condition Probability Company A Returns Company B Returns Company C Returns Company A+B Returns Company A+C Returns 1 .2 17% 19% 13% 18% 15% 2 .2 15% 17% 11% 16% 13% 3 .2 13% 15% 15% 14% 14% 4 .2 11% 13% 17% 12% 14% 5 .2 9% 11% 19% 10% 14% (a) For each of Companies A, B and C, find the mean return and the standard deviation of returns. (b) Find the mean return and the standard deviation of returns for the combination of Company A plus Company B. (c) Find the mean return and the standard deviation of returns for the combination of Company A plus Company C. (d) Compare the mean returns for each of the two possible combinations - Company A plus Com- pany B and Company A plus Company C. Is either mean higher? How do they compare to Company A’s mean return? (e) Compare the standard deviation of the returns for each of the two possible combinations - Company A plus Company B and Company A plus Company C. Which stand deviation is smaller? Which possible combination involves less risk? How does the risk carried by this combination compare to the risk carried by Company A alone? (f) Which acquisition would you recommend - Company A plus Company B or Company A plus Company C? Solution : (a) For Company A, the mean return equals μ A = 17% × 0 . 2 + 15% × 0 . 2 + 13% × 0 . 2 + 11% × 0 . 2 + 9% × 0 . 2 = 13% ,
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ISOM 111 L7-L8, Fall 2010 2 and the standard deviation equals σ A = p (17% - 13%) 2 × 0 . 2 + (15% - 13%) 2 × 0 . 2 + . . . + (9% - 13%) 2 × 0 . 2 2 . 83% . For Company B, note that its return is just that of Company A + 2%, hence μ B = μ A + 2% = 15%, and σ B = σ A 2 . 83%. As to Company C, if you compare the returns of Companies B and C, you find they have the same distribution – they have the same set of possible values, and for each value, the corresponding probabilities are the same – hence, μ C = μ B = 15% , σ C = σ B 2 . 83% . (b) The return of the combination of Companies A and B is just that of Company A + 1%, hence μ A & B = μ A + 1% = 14%, and σ A & B = σ A 2 . 83%.
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