Question

1. XYZ stock price and dividends history are as follows Year Beginning-of-year price Dividend paid at year- $100 $110 $90 $95 end $4 $4 $4 $4 2005 2006 2007 2008 An investor buys three shares of XYZ at the beginning of 2005, buys another two shares at the beginning of 2006, sells one share at the beginning of 2007, and sells all four remaining shares at the beginning of 2008. Hint: When the investor buys three shares at the beginning of 2005, she cannot receive dividends paid at the end of 2004. She can receive dividend payments on these three shares at the end of 2005 A. Computer HPR for each period (05-06, 06-07, and 07-08) (6pts) B. Compute the arithmetic return. (3pts) C. Compute the geometric return. (3pts) D. Computer the dollar-weighted rate of return. Draw the time line to show cash flows. Write down the formula and calculate the dollar-weighted rate of return. The time line includes four dates corresponding to the turns of the year for January 1, 2005 to January 1, 2008. (8pts)

Answer 1

A.

Holding Period Return (HPR) is the return during a period. It is summation of Capital appreciation and dividend.

$HPR = \frac{(P_{1}-P_{0})+D}{P_{0}}$

Where,

P1 = Price at end of period

P0 = Price at beginning

D = Dividends

Please refer below spreadsheet for calculation and answer.

Formula reference -

B .

Arithmetic Return(AR) is the simple average return of holding period.

$AR = \frac{\sum Return}{n}$

n is number of period.

Please refer above spreadsheet for calculation.

AR = 3.15%

C.

Geometric return calculation consider the compounding from period to period. To calculate Geometric Average us follow step

Step1= Add 1 to each holding period return

Step2=Multiple each return(step1)

Step3 = raise to power inverse of total period to Step2 ,

Step4 = (Step3-1) = Geometric Return

In excel, use =GEOMEAN-1 formula to calculate the geometric return.

Please refer to above spreadsheet for calculations

Geometric return = 2.33%

D.

Dollar- weighted Rate of Return (DWRR) is the rate at which present value of all cash out flows equals to present value of all cash inflows.

$Initial Capital Cash out flow = \sum_{n=1}^{n}\frac{Cash flow_{n}}{(1+r_{dw})^n}$

Where,

r_dw = Dollar-weighted rate of return

n = period

In excel, use =irr to series of cash flows to calculate DWRR.

Please refer to above spreadsheet for calculation of DWRR and Time Line of cash flows.

DWRR = -0.17%