Question

XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 130 $ 5 2011 $ 144 $ 5 2012 $ 120 $ 5 2013 $ 125 $ 5 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.) Arithmetic mean % Geometric mean % 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 $ 1/1/2011 1/1/2012 1/1/2013 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 %

Answer 1

Here Given are below details.
YearBeginning-of-Year PriceDividend Paid at Year-End2010$130$ 52011$144$ 52012$120$ 52013$125$ 5
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	$1,040	Dividends on eight shares, plus sale of eight shares at $125 per share

The dollar weighted return is affected by the period of cash contribution and cash withdrwals. contributing cash in periods when the cost of share was high and withdrawing them in the periods of low stock prices resulted in decrease in the dollar weighted return.

In time-weighted return, this effect of cash contribution/ withdrawl is removed and only the actual return on the stock is calculted, resulting in a higher return than dollar weighted return.