Question

XYZ stock price and dividend history are as follows: Dividend Paid at Year-End $ 5 Year 2015 2016 2017 2018 Beginning-of-Year Price $114 120 100 105 An investor buys four shares of XYZ at the beginning of 2015, buys another two shares at the beginning of 2016, sells one share at the beginning of 2017, and sells all five remaining shares at the beginning of 2018. a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Arithmetic mean Geometric mean b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018. (Negative amounts should be indicated by a minus sign.) Cash Flow Date 01/01/2015 01/01/2016 01/01/2017 01/01/2018

Answer 1

solution: a) year Price return calculation 2015 2016 2017 2018 Dividend 1145 120 100 105 5 9.65% (120+5-114)/114 5 -12.50% (100+5-120/120 5 10.00% (105+5-100)/100 *return = (curren year Price - previous year price+Dividend)/Previous year price arithmatic average rate of return = (0.0965-0.125+0.1)/3 Geometric mean = -1+((1+0.0965)*(1-0.125)*(1+0.1))^(1/3) 2.38% 1.81% b) date net cash flow 01/01/2015 01/01/2016 01/01/2017 01/01/2018 Calculation -456-114*4 -220 -120*2+4*5 130 100*1+6*5 550 105*5+5*5 B-2.dollar weighted average rate of return = IRR 0.2378%