Ross5eChap10sm - Chapter 10 Risk and Return Lessons from...

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Chapter 10: Risk and Return: Lessons from Market History 10.1 a. Capital gains = $56 – $52 = $4 per share; Total capital gains is $2000 ( $4 x 500) b. Total dollar returns = Dividends + Capital Gains = $1,000 + ($4 x 500) = $3,000 On a per share basis, this calculation is $2 + $4 = $6 per share c. On a per share basis, $6/$52 = 0.1153 or 11.53% On a total dollar basis, $3,000/(500*$52) = 0.1153 or 11.53% d. No, you do not need to sell the shares to include the capital gains in the computation of the returns. The capital gain is included whether or not you realize the gain. Since you could realize the gain if you choose, you should include it. (Note that for tax purposes, you must sell the stock.) 10.2 a. The capital gain is the appreciation of the stock price. Find the amount that Seth paid for the stock one year ago by dividing his total investment by the number of shares he purchased ($62.50 = $12,500 / 200). Because the price of the stock increased from $62.50 per share to $69.75 per share, he earned a capital gain of $7.25 per share (=$69.75 – $62.50). Capital Gain = (P t+1 – P t ) (Number of Shares) = ($69.75 – $62.50) (200) = $1,450 Seth’s capital gain is $1,450 . b. The total dollar return is equal to the dividend income plus the capital gain. He received $750 in dividend income, as stated in the problem, and received $1,450 in capital gains, as found in part (a). Total Dollar Gain = Dividend income + Capital gain = $750 + $1,450 = $2,200 Seth’s total dollar return is $2,200 . c. The percentage return is the total dollar gain on the investment as of the end of year 1 divided by the initial investment of $12,500. R t+1 = [Div t+1 + (P t+1 – P t )] / P t = [$750 + $1,450] / $12,500 = 0.176 The percentage return is 17.60%. b. The dividend yield is equal to the dividend payment divided by the purchase price of the stock. Dividend Yield = Div 1 / P t Answers to End–of–Chapter Problems B–121
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= $750 / $12,500 = 0.06 The stock’s dividend yield is 6.00%. 10.3Apply the percentage return formula. Note that the stock price declined during the period. Since the stock price decline was greater than the dividend, your return was negative. R t+1 = [Div t+1 + (P t+1 – P t )] / P t = [$1.75 + ($33 – $40)] / $40 = –0.13125 The percentage return is –0.13125 10.4 To find the real return we need to use the Fisher equation. Re–writing the Fisher equation to solve for the real return, r, in terms of the nominal return, R, and the expected inflation, π , we get: r = [(1 + R) / (1 + π )] – 1 Year T–bill return Inflation Real return Year T–bill Return Inflation Real Return 1973 9.36 4.78 4.37 1974 12.3 7.68 4.29 1975 9.52 7.05 2.31 1976 5.87 9.10 –2.96 1977 9.45 7.64 1.68 1978 8.44 7.90 0.50 1979 9.69 11.01 –1.19 1980 11.2 12.23 –0.92 Sum 75.81 67.39 5.04 a. The average return for T–bills over this period was: Average return = 75.81 / 8 Average return = 9.47% And the average inflation rate was: Average inflation = 67.39 / 8 Average inflation = 8.42% b. Using the equation for variance, we find the variance for T–bills over this period was: Variance = 1/7[(.0936 – .0947) 2 + (.01233 – .0947) 2 + (.0952 – .0947) 2 + (.0587– .0947) 2 + (.0945 – .0947) 2 + (.0844 – .0947) 2 + (.0969 – .0947) 2 + (.112 – .0947) 2 ] Variance = 0.00035721 And the standard deviation for T–bills was: Answers to End–of–Chapter Problems B–122
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Standard deviation = (0.00035721) 1/2 Standard deviation = 0.0189 or 1.89% The variance of inflation over this period was: Variance = 1/7[(.0478 – .0842) 2 + (.0768 – .0842) 2 + (.0705 – .0842) 2 + (.091 – .0842) 2 + (.0764 – .0842) 2 + (.079 – .0842) 2 + (.1101 – .0842) 2 + (.1223 – .0842) 2 ] Variance = 0.00054289
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