2010 2011 2012 2013 S 116 $ 123 $ 105 $ 110 $ 4 $4 An investor buys four shares

ID: 2784572 • Letter: 2

Question

2010 2011 2012 2013 S 116 $ 123 $ 105 $ 110 $ 4 $4 An investor buys four 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 five remaining shares at the beginning of 2013 a. What are the a average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Geometric mean 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.) 1/1/2010 S 1/1/2011 1/1/2012 1/1/2013 b-2. What is the dollar-weighted rate of return? (Hint If your calcufator 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.)

Explanation / Answer

a. What are the arithmetic and geometric average time-weighted rates of return for the investor?

Time-weighted average returns are based on year-by-year rates of return and can be calculated with the help of following formula

Yearly Return = {(capital gains + dividend)/price}*100

Return from 2010-2011 = {(123 - 116) + 4} /116 *100 = 9.48%

Return from 2011-2012 = {(105 - 123) + 4} /123 *100 = -11.82%

Return from 2011-2012 = {(110 - 105) + 4} /105 *100 = 8.57%

Arithmetic mean = (9.48% -11.82% +8.57%)/3 = 6.67%/3 = 2.224%

Geometric mean = (1.0948 *0.8818 * 1.0857) ^1/3 – 1 = 0.0158 = 1.58%

The arithmetic average time-weighted rates of return for the investor is 2.224%

The geometric average time-weighted rates of return for the investor is 1.58%

b. 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

Time

Year

Cash flow

1/1/2010

4* -$116 = -$464

1/1/2011

2 *-$123 = - $246

1/1/2012

1* $ 105 = $105

1/1/2013

5* $110 = $550

Note: Negative sign for cash outflow

c. The dollar-weighted return is the internal rate of return (IRR) that can be calculated by discounting from the rate which makes the sum of the present value of each net cash flow to zero.

0 = -$464/ (1+IRR) ^0 - $246/ (1+IRR) ^1 + $105/ (1+IRR) ^2 + $ 550/ (1+IRR) ^3

From trial and error method, we can calculate the value of IRR, which is

IRR = -3.18%