Question

XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End...

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 %

Homework Answers

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%
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