Question

Consider the following stock price and shares outstanding information.

	DECEMBER 31, Year 1				DECEMBER 31, Year 2
	Price		Shares Outstanding		Price		Shares Outstanding
Stock K	$23		110,000,000		$34		110,000,000
Stock M	82		2,100,000		50		4,200,000a
Stock R	36		29,000,000		38		29,000,000
aStock split two-for-one during the year.

1. Compute the beginning and ending values for a price-weighted index and a market-value-weighted index. Assume a base value of 100 and Year 1 as the base period. Do not round intermediate calculations. Round your answers to two decimal places.

             PWI_{Year 1}:

             PWI_{Year 2}:

             VWI_{Year 1}:

             VWI_{Year 2}:

2. Compute the percentage change in the value of each index during the year. Do not round intermediate calculations. Round your answers to two decimal places.

   Percentage change in PWI:   %

   Percentage change in VWI:   %

3. Compute the percentage change for an unweighted index assuming $1,000 is invested in each stock. Do not round intermediate calculations. Round your answer to two decimal places.

     %

Answer 1

QUESTION a)

The Price Weighted Index for Year 1 is:

PWI1 = (23+82+36)/3 =47.

Because Stock M has a stock split, now at the end of year 1, stock of 82 would become stock of 41, the divisor must change appropriately so that PWI1 remains same even after stock split. So new divisor is:

D = (23+41+36)/47 = 2.13

The Price Weighted Index for Year 2 is:

PWI2 = (34+50+38)/2.13 =57.34

Therefore if PWI1 = 100 (base), then PWI2 = 100*57.34/47 = 122

The Market Capitalization weighted Index values can be determined by:

Year 1:

Price	Shares Outstanding	Market Capitalization	% Weight
23	110,000,000	2,530,000,000	67.54%
82	2,100,000	172,200,000	4.60%
36	29,000,000	1,044,000,000	27.87%

VWI1 = (67.54%)(23) + (4.60%)(82) + (27.87%)(36) = 29.33

Year 2:

Price	Shares Outstanding	Market Capitalization	% Weight
34	110,000,000	3,740,000,000	74.03%
50	4,200,000	210,000,000	4.16%
38	29,000,000	1,102,000,000	21.81%

VWI2 = (74.03%)(34) + (4.16%)(50) + (21.81%)(38) = 35.54

Therefore, if VWI1 = 100 (base), then VWI2 = 100*35.54/29.33 = 121.14

QUESTION b)

%change in PWI = (122 - 100)/100 = 22%

%change in VWI = (121.14 - 100)/100 = 21.14%

QUESTION c)

For an unweighted index, individual return is to be computed:

	Year 1	Year 2	Return
Stock K	23	34	48%
Stock M	82	100	22%
Stock R	36	38	6%

Therefore, return would be 48%+22%+6% = 75%