XYZ stock price and dividend history are as follows: An investor buys six shares
ID: 2817982 • Letter: X
Question
XYZ stock price and dividend history are as follows:
An investor buys six shares of XYZ at the beginning of 2010, buys another two shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all seven remaining shares at the beginning of 2013.
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.)
b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2010, to January 1, 2013. (Negative amounts should be indicated by a minus sign.)
b-2. What is the dollar-weighted rate of return? (Hint: If your calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and error.) (Negative value should be indicated by a minus sign. Round your answer to 4 decimal places.)
Rate of return %
Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 120 $ 2 2011 $ 129 $ 2 2012 $ 115 $ 2 2013 $ 120 $ 2Explanation / Answer
a What are the arithmetic and geometric average time-weighted rates of return for the investor Return = (Capital Gain + Dividends/Price) Year Return 2010-11 (129-120+2)/120 0.091666667 0.091667 2011-12 (115-129+2)/129 -0.093023256 0.093023 2012-13 (120-115+2)/115 0.060869565 0.06087 0.080365 Arithmetic mean = (0.091666667+(-0.093023256)+0.060869565)/3 0.019837659 1.98% Geometric Mean ((1+0.91666667)*(1+-0.093023256)*(1+0.06086965))^1/3 - 1 1.02% b - 1 Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2010 to January 1, 2013 Date Cash flow Explanation 1/1/2010 -720 Purchase of 6 shares at 120 1/1/2011 -246 Purchase of 2 shares at 129 and receipt of dividend for 6 shares at 2 1/1/2012 131 Sale of one share and dividend on 8 shares 1/1/2013 854 Sale of seven share and dividend on 7 shares b-2 What is the dollar-weighted rate of return Dollar weighted return is the internal rate of return Therefore, $0 = -$ 720 + -$ 246*/(1+IRR) + $131/(1+IRR)^2 + $ 854/(1+IRR)^3 We would calculate IRR using the trial and error method Assuming IRR is 18%, we get Year Cash flow Discount factor @ 18% Present Value 0 -720 1.0000 -720.000 1 -246 0.8475 -208.475 2 131 0.7182 94.082 3 854 0.6086 519.771 -314.622 Assuming IRR is 1%, we get Year Cash flow Discount factor @ 10% Present Value 0 -720 1.0000 -720.000 1 -246 0.9901 -243.564 2 131 0.9803 128.419 3 854 0.9706 828.884 -6.262 Assuming IRR is 0.75%, we get Year Cash flow Discount factor @ 0.75% Present Value 0 -720 1.0000 -720.000 1 -246 0.9926 -244.169 2 131 0.9852 129.057 3 854 0.9778 835.070 -0.042 Assuming IRR is 0.7483%, we get Year Cash flow Discount factor @ 0.75% Present Value 0 -720 1.0000 -720.000 1 -246 0.9926 -244.173 2 131 0.9852 129.061 3 854 0.9779 835.112 0.000 Dollar weighted return = 0.7483%
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