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# XYZ stock price and dividend history are as follows:

### Customer Question

XYZ stock price and dividend history are as follows:
Year             Begining year Prices for the Year 05-08 are:
2005            \$100
2006            \$110
2007            \$90
2008            \$95

Dividend paid at year-End for all the above years are \$4 from 2005-2008.
An investor buys three shares of XYZ at the beginning of 2005, buys another two shares at the beginning of 2006, and one share at the beginning of 2007, and sells all four remainging shares at the beginning of 2008.

Requrement1:
What are the Arithmetic and geometric average time-weighted rates of return for the investor?
Arithmeitc mean _________%
Geometric mean __________%

Requirement 2:
What is the dollar-weighted return?
Rate of return ___________%

Prepare a chart of cash flows for the four dates corresponding to the turns fo the year for January 1, 2005, to January 1, 2008.

Year      Cach flows

2005       \$____________
2006       \$____________
2007       \$____________
2008       \$____________
Submitted: 7 years ago.
Category: Homework
Expert:  David replied 7 years ago.

I assume that at the begining the investor sells one share (otherwise he will not have 4 shares by the end of 2007).

You need to calculate the appreciation, it comes from the appresiation od the stock and from dividends

At the end of the year the appresiation is below:

2005: 330-300+3*4 = 42

2006: 450-550+5*4 = -80

2007: 380-360 +4*4 = 36

return is calculated as appreciation over the initial value of the portfolio:

2005: 42/300 = 14%

2006: -80/550 = -14.545%

2007: 36/260 = 10%

arithmetica average of the nubers above (14%--14.545%+10%)/3=3.15%

geometric average = -1+[(1+0.14)*(1-0.14545)*(1+0.1)]^(1/3) = 2.33%

For Dollar return -0.17% you need to use Excell or other software after you get the cash flow, see below

Cash flow:

2005 : -300

2006: -208

2007: 110

2008 : 396

Now use =IRR() function the answer will be -0.17%

Customer: replied 7 years ago.

Where did you get the 330, 450, 380

Expert:  David replied 7 years ago.