XYZ stock price and dividend history are as follows Year 2010 2011 2012 2013 Beg

ID: 2820246 • Letter: X

Question

XYZ stock price and dividend history are as follows Year 2010 2011 2012 2013 Beginning-of-Year Price Dividend Paid at Year-End $2 $130 $153 $128 $ 133 An investor buys five shares of XYZ at the beginning of 2010, buys another two shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all six 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. Enter your answer as a percentage rounded to two decimal places.) Arithmetic average return Geometric average return To compute dollar-weighted return, 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. (Enter your answer as an integer. Negative amounts should be indicated by a minus sign.) b. Date 1/1/2010 1/1/2011 1/1/2012 1/1/2013 Cash Flow (for the investor)

Explanation / Answer

a. Yearly Return = {(capital gains + dividend)/price}*100

Return from 2010-2011 = {(153 - 130) + 2} /130 *100 = 19.23%

Return from 2011-2012 = {(128 - 153) + 2} /153 *100 = -15.03%

Return from 2012-2013 = {(133 - 128) + 2} /128 *100 = 5.47%

Arithmetic mean = (19.23% -15.03% +5.47%)/3 = 9.67%/3 = 3.22%

Geometric mean = [(1+19.23%)*(1-15.03%) *(1+5.47%)] ^ (1/3) -1

= (1.1923 *0.8497 * 1.0547) ^1/3 – 1 = 0.0223 = 2.23%

The arithmetic average time-weighted rates of return for the investor is 3.22%

The geometric average time-weighted rates of return for the investor is 2.23%

(Note: the answer can slightly vary because of rounding off)

Time

Year

Cash flow form stock buying/selling

Cash flow from Dividend

Total Cash Flow

1/1/2010

5* -$130 = -$650

-$650.00

1/1/2011

2 *-$153= -$306

5*2 =10

-$296.00

1/1/2012

1* $ 128 = $128

7*2 =14

$142.00

1/1/2013

6* $133 = $798

6*2 = 12

$810.00

Note: Negative sign for cash outflow