5. XYZ stock price and dividend history are as follows:

Year Beginning-of-Year Price Dividend Paid at Year-End 2005 $100 $4 2006 120 4 2007 90 4 2008 100 4 An investor buys three shares of XYZ at the beginning of 2005, buys another two shares at the beginning of 2006, sells one share at the beginning of 2007, and sells all four remaining shares at the beginning of 2008.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor?

b. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2005, to January 1, 2008. If your calculator cannot calculate internal rate of return, you will have to use trial and error.)