XYZ stock price and dividend history are as follows: An investor buys six shares

Question

XYZ stock price and dividend history are as follows:

An investor buys six shares of XYZ at the beginning of 2010, buys another three shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all eigth remaining shares at the beginning of 2013.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2010, to January 1, 2013. (Negative amounts should be indicated by a minus sign.)

Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 130 $ 5 2011 $ 144 $ 5 2012 $ 120 $ 5 2013 $ 125 $ 5

Explanation / Answer

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Year Beginning of Year Price Dividend Paid at Year-End 2010 130 $5 2011 144 $5 2012 120 $5 2013 125 $5 Year Return = (Capital gain+Dividend)/Price] 2010-2011 (144-130+5)/130 14.61% 2011-2012 (120-144+4)/144 -13.19% 2012-2013 (125-120+5)/120 8.33% Arithmetic mean = (14.61-13.19+8.33)/3 3.25% Geometric mean= cubic root((1+14.61%)*(1-13.19%)*(1+8.33%))-1 2.53% Date Cash Flow Explanation 1/1/2010 ($780) Purchase of six shares at $130 per share 1/1/2011 ($402) Purchase of three shares at $144, plus dividend income on six shares held 1/1/2012 $165 Dividends on nine shares, plus sale of one share at $120 1/1/2013 $1040 Dividends on eight shares, plus sale of eight shares at $125 per share

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