Question

XYZ stock price and dividend history are as follows:

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2015		$	120			$	2
2016			129				2
2017			115				2
2018			120				2

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

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.)

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.)

Answer 1

Answer A

Arithmetic Average return; The Arithmetic average return is simple average returns.

Formula: Sum of Returns/ No of Year

Calculation of returns:

1. Year 2015 = [{129(price on 2016) - 120(price on 2015)} + 2 ( dividend)/120(price on 2015)*100

= 9.17%

2. Year 2016 = [115-129] + 2/ 129

=(-9.30%)

2. Year 2017 = [120-115] + 2/ 115

= 6.07%

Arithmetic mean = 9.17+ (-9.30%)+6.07%/3

=1.98%

Geometric average return =

where,

gn= Geometric Average Return
rc = cumulative return over the entire period
n = number of equal subset periods to average the return

= [(1+9.17%)*(1-9.30%)*(1+6.07%)]^(1/3) - 1

=[(1 + 0.0917) * (1 + (-0.093)) * (1 + 0.0607)] ^1/3 − 1 = 1.65%

Answer B

Year	Cash Flow(buy/sell)	Dividend	Total Cash Flow
0	6*(-$120) = -$720	0	-$720
1	2*(-$129) = -$258	6*$2 = $12	-$246
2	1*$115= $115	8*2 = $16	$131
3	7*$120 =$840	7*2=$14	$854

Answer B2

Dollar-weighted rate of return =

Here:

• DWR is the dollar-weighted return we require.
• CFn is the cash flow for each period

as per Chart B

0= -$720(CF0) + -$246(CF1)/(1+DWR) + $131(CF2)/(1+DWR)^2 +  $854(CF3)/(1+DWR)^3

Calculation of IRR