An investor buys six shares of XYZ at the beginning of 2010, buys another two sh

ID: 2612379 • Letter: A

Question

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.

What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.)

To compute dollar-weighted return, 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. (Enter your answer as an integer. Negative amounts should be indicated by a minus sign.)

XYZ stock price and dividend history are as follows:

Explanation / Answer

a).

Year Return [(capital gains + dividend)/price]

2010-11 [(132 – 122) + 5]/122 = 12.30%

2011-12 [(110- 132) + 5]/132 = – 12.88%

2012-13 [(115 – 110) + 5]/110 = 9.09%

Arithmetic mean: (12.30 – 12.88 + 9.09)/3 = 2.84%

Geometric mean: (1.123× .8722 × 1.0909)1/3 – 1 = .022358= 2.24%

Date

Cash Flow (for the investor)

1/1/2010

-732 (Purchase of 6 shares at $122 each)

1/1/2011

-234 ( Purchase of 2 shares at $132 less dividend income on 6 shares held

1/1/2012

145 (Dividends on 7 shares plus sale of one share at price of $110 each

1/1/2013

840 (Dividends on 7 shares plus sale of 7 shares at price of $115 each

IRR Function in excel

= 0.75%