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

An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaining shares at the beginning of 2021.

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, 2018, to January 1, 2021. If your calculator cannot calculate internal rate of return, you will have to use trial and error.)