XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 140 $ 4 2011 $ 159 $ 4 2012 $ 132 $ 4 2013 $ 137 $ 4 An investor buys five 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 seven 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.) Arithmetic mean 2.93 % Geometric mean 2.08 % 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.) Date Cash Flow 1/1/2010 $ -700 1/1/2011 -457 1/1/2012 164 1/1/2013 987 b-2. What is the dollar-weighted rate of return? (Hint: If your calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and error.) (Negative value should be indicated by a minus sign. Round your answer to 4 decimal places.) Rate of return % Solution a) Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $140.00 $4.00 2011 $159.00 $4.00 2012 $132.00 $4.00 2013 $137.00 $4.00 Return = [(Capital Gains + Dividend)/Price] Year 2010-2011 (($159 - $140)+$4)/$140 16.43% Year 2011- 2012 (($132 - $159)+$4)/$132 -14.47% Year 2012-2013 (($137 - $132)+$4)/$132 6.82% Arithmetic mean: = (16.43%+(14.47%)+6.82%)/3 2.93% Geometric Mean Return 1+ return% 16.43% 1.164 -14.47% 0.855 6.82% 1.068 Geometric Mean =( (1.164 x .855 x 1.068)^(1/3 ))-1 2.08% 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. Date 1/1/2010 1/1/2011 1/1/2012 1/1/2013 Cash Flow -$700.00 -$457.00 $164.00 $987.00 Date Cash Flow 1/1/2010 -$700.00 Purchase of 5 shares at $140 per share 1/1/2011 - $457.00 Purchase of 3 shares at $159, plus dividend income on 5 shares held 1/1/2012 $164.00 Sale of 1 share at $132, plus dividend income on 8 shares held 1/1/2013 $987.00 Sale of 7 share at $137, plus dividend income on 7 shares held b-2 Date Cash Flow 1/1/2010 -$700.00 1/1/2011 -$457.00 1/1/2012 $164.00 1/1/2013 $987.00 IRR = Rate of Return 0.21%.

1. XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend
Paid at Year-End 2010 $ 140 $ 4 2011 $ 159 $ 4 2012 $ 132 $ 4 2013 $ 137 $ 4 An investor buys
five 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 seven 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.)
Arithmetic mean 2.93 % Geometric mean 2.08 % 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.) Date Cash Flow 1/1/2010 $ -700 1/1/2011 -457
1/1/2012 164 1/1/2013 987 b-2. What is the dollar-weighted rate of return? (Hint: If your
calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and
error.) (Negative value should be indicated by a minus sign. Round your answer to 4 decimal
places.) Rate of return %
Solution
a) Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $140.00 $4.00
2011 $159.00 $4.00 2012 $132.00 $4.00 2013 $137.00 $4.00 Return = [(Capital
Gains + Dividend)/Price] Year 2010-2011 (($159 - $140)+$4)/$140 16.43% Year 2011-
2012 (($132 - $159)+$4)/$132 -14.47% Year 2012-2013 (($137 - $132)+$4)/$132 6.82%
Arithmetic mean: = (16.43%+(14.47%)+6.82%)/3 2.93% Geometric Mean Return
1+ return% 16.43% 1.164 -14.47% 0.855 6.82% 1.068 Geometric Mean =(
(1.164 x .855 x 1.068)^(1/3 ))-1 2.08% 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.
Date 1/1/2010 1/1/2011 1/1/2012 1/1/2013 Cash Flow -$700.00 -$457.00 $164.00 $987.00
Date Cash Flow 1/1/2010 -$700.00 Purchase of 5 shares at $140 per share 1/1/2011 -
$457.00 Purchase of 3 shares at $159, plus dividend income on 5 shares held 1/1/2012
$164.00 Sale of 1 share at $132, plus dividend income on 8 shares held 1/1/2013 $987.00
Sale of 7 share at $137, plus dividend income on 7 shares held b-2 Date Cash Flow
1/1/2010 -$700.00 1/1/2011 -$457.00 1/1/2012 $164.00 1/1/2013 $987.00
IRR = Rate of Return 0.21%