Question

XYZ stock price and dividend history are as follows:

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2015		$	104			$	2
2016			115				2
2017			90				2
2018			105				2

An investor buys three shares of XYZ at the beginning of 2015, buys another one shares at the beginning of 2016, sells one share at the beginning of 2017, and sells all three 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.)

Date	Cash Flow
01/01/2015
01/01/2016
01/01/2017
01/01/2018

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

a. Arithmetic mean = (12.50% -20%+ 18.89%) /3 = 3.80%

Geometric mean = [(1+2.5%) *(1-20%) *(1+18.89%) ^1/3] -1 =2.28%

2015-2016	12.50%	[(115-104+2)/104]
2016-2017	-20%	[(90-115+2)/115]
2017-2018	18.89%	[(105-90+2)/90]

b1.

	Net cash flow
1/1/2015	-312
1/1/2016	-109
1/1/2017	98
1/1/2018	321

b2. IRR = -0.1898%

	Purchase	Dividend Income	Sale proceeds	Net cash flow
1/1/2015	-312			-312
1/1/2016	-115	6		-109
1/1/2017	90	8		98
1/1/2018		6	315	321
IRR				-0.1898%