XYZ’s stock price and dividend history are as follows:

Year Beginning-of-Year Price Dividend Paid at Year-End 2016 $100 $4 2017 120 4 2018 90 4 2019 100 4 An investor buys three shares of XYZ at the beginning of 2016, buys another two shares at the beginning of 2017, sells one share at the beginning of 2018, and sells all four remaining shares at the beginning of 2019.

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, 2016, to January 1, 2019. If your calculator cannot calculate internal rate of return, you will have to use trial and error.)