a.
First, we need to use Holding period return of every year
Holding period return = (Ending share price + dividend - Beginning share price) / Beginning share price
year 2016 = (200+4 -180) / 180 = 0.133
year 2017 = (170+4 -200) / 200 = -0.13
year 2018 = (180+4 -170) / 170 = 0.082
Arithmetic return = (return1 + return2 + return 3) / No of year = {0.133 + (-0.13) + 0.082 } / 3 = 0.0853 / 3 = 0.0284
Hence Arithmetic return is 2.84%
Geometric Return = { ( 1+R1) + ( 1+R2) + ( 1+R3) }1/n - 1 = { ( 1+0.133) + ( 1-0.13) + ( 1+0.082) }1/3 - 1
= ( 1.133* 0.87 * 1.082)0.333-1
= 1.0665 0.3333- 1
= 1.02168 -1
=0.02168= 2.168%
where,
R = return
n = no of year
Hence Geometric return will be 2.168%
b.
First, we will find cash flow for each year.
Dollar weighted rate of return is the same as internal rate of return
use Irr function in excel
Irr = =Irr (number1, number2....., (guess) ) = irr(-$540,-$338, $190,$736) = -0.09%
or you can use formula by doning trail and error
0= CF0 + [CF1 / (1+IRR1)] + [CF2 / (1+IRR2)] + [CF3/ (1+IRR3)]
0= -$540 + [-$338 / (1+IRR1)] + [$190 / (1+IRR2)] + [$736 / (1+IRR3)]
where,
CF =cash flow
0,1,2,3 = time
IRR = internal rate of return = Dollar rate of return
use Cashflow in the following manner.
Beginning Cash flow in the year 2016.
Investment out flow No of share * share price = $180* 3 = - $540
Cash flow in year 2017
Investment out flow No of share * share price = $200* 2 = -$400
Dividend received = No of share on ending of 2016 * Dividend = 3 * $4 = $12
Total cash flow = -$400+ $12 = -$388
Cash flow in year 2018
cash received from selling of stock = no of share sold * sell price = 1 * $170 = $170
Dividend received = No of share on ending of 2017 * Dividend = 5 * $4 = $20
Total cash flow = $170 + $20 = $190
Cash flow in year 2019
cash received from selling of stock = no of share sold * sell price = 4 * $180 = $720
Dividend received = No of share on ending of 2017 * Dividend = 4 * $4 = $16
Total cash flow = $720 + $16 = $736
so our cash flow at
time 0 = - $540
time 1 = - $338
time 2 = $190
time 3 = $736
Hence the Dollar rate of return is - 0.09%
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