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

Year	Beginning-of-Year Price	Dividend Paid at Year-End
2019	$ 195	$ 7
2020	225	7
2021	185	7
2022	195	7

An investor buys three shares of XYZ at the beginning of 2019, buys another two shares at the beginning of 2020, sells one share at the beginning of 2021, and sells all four remaining shares at the beginning of 2022.

Required:

a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Round your year-by-year rates of return and final answers to 2 decimal places. Do not round other calculations.)

Arithmetic:

Geometric:

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, 2019, to January 1, 2022. If your calculator cannot calculate IRR, you will have to use trial and error or a spreadsheet program.) (Round your answer to 4 decimal places. Negative amount should be indicated by a minus sign.)

Dollar-Weighted Rate of Return: