Question

XYZ stock price and dividend history are as follows:

Year	Beginning-of-Year Price		Dividend Paid at Year-End
2010	$	102	$ 3
2011	$	105	$ 3
2012	$	91	$ 3
2013	$	96	$ 3

An investor buys three shares of XYZ at the beginning of 2010, buys another one shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all three 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.)

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, 2010, to January 1, 2013. (Negative amounts should be indicated by a minus sign.)

Date	Cash Flow
1/1/2010	$
1/1/2011
1/1/2012
1/1/2013

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             %

Answer 1

Hello Sir/ Mam

Year	Beginning-of-Year Price		Dividend Paid at Year-End
2010	$	102	$ 3
2011	$	105	$ 3
2012	$	91	$ 3
2013	$	96	$ 3

(a) Arithmetic Mean = 1.40% and Geometric Mean = 1.03%

Using above formula:

Year	Beginning-of-Year Price	Dividend Paid at Year-End	Time-Weighted RoR
2010	102	$3	5.88%
2011	105	$3	-10.48%
2012	91	$3	8.79%
2013	96	$3

Hence, Arithmetic Mean = 1.40%

Geometric Mean = 1.03%

(b-1) Cash Flow Schedule :

Date	Cash Flows
1/1/2010	-$306.00
1/1/2011	-$96.00
1/1/2012	$103.00
1/1/2013	$297.00

(b-2) Dollar - Weighted Rate of Return = -0.1990%

Present Value Schedule using IRR :

Time	Cash Flows	Present Value Factor	Present Value
0	-$306.00	1.0000	-$306.00
1	-$96.00	1.0020	-$96.19
2	$103.00	1.0040	$103.41
3	$297.00	1.0060	$298.78
Total			$0.00

I hope this solves your doubt.

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