Question

XYZ's stock price and dividend history are as follows:

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2016	$	100			$	4
2017		120				4
2018		90				4
2019		100				4

An investor buys three shares of XYZ at the beginning of 2016, buys another two shares at the beginning of 2017, sells one share at the beginning of 2018, and sells all four remaining shares at the beginning of 2019.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Round your year-by-year rates of return and final answer to 2 decimal places. Do not round other calculations.)

b. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2016, to January 1, 2019. If your calculator cannot calculate internal rate of return, you will have to use trial and error.) (Round your answers to 4 decimal places. Negative amount should be indicated by a minus sign.)

Answer 1

For time weighted return, we use the simple formula

R = [(1+R1) * (1+R2)* ....*(1+RN)]^1/N - 1

Where R1 is the HPY of period 1 and N is the number of periods.

HPY 2016 = 4/100 *100 = 4%

HPY 2017 = 120-100+4/100 *100 =24%

And so on,

We calculated the HPY for all the 4 time periods and then put them into this formula. Number of period is 4. So, 1/N = 0.25. Hence we get the Geometric avg time weighted return of 3.94% and taking a arithmetic mean of the 4 HPY We get an arithmetic mean of 10.22%.

For the dollar weighted return.

We prepare the cash flows for each year.

1st = (-100*3) + (4*3) = -288

As 3 shares were purchased and we received dividend on them.

2nd = -120*2 + 5*4 = -220

2 shares were purchased for 120$ each and we received total dividends of 20$ on all the 5 shares.

And so on. After we compute the cash flows for 4 years. We use IRR function to calculate money weighted return.

Which is =IRR(Value1:Value4)