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	$22		108,000,000		$33		108,000,000
Stock M	74		2,100,000		43		4,200,000a
Stock R	40		20,000,000		43		20,000,000
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

a.

Price Weighted Index

PWI Year 1 = (22+74+40)/3 = $45.33

Base value of Index for Year 1 as a base period is 100.

PWI Year 2 = (33+43+43)/3 = $39.67

Value of Index for Year 2 shall be = (PWI Year 2) / (PWI Base year)*100 = 39.67 / 45.33 *100

= 87.51

Market Value Weighted Index

Firstly, need to calculate total market value of each company for Year 1:

Stock K - $22*108,000,000 shares outstanding = $2,376,000,000

Stock M - $74*2,100,000 shares outstanding = $155,400,000

Stock R - $40*20,000,000 shares outstanding = 800,000,000

Entire market value of Index component equals to sum of market value of each company for Year 1

=3,331,400,000

Index value for Year 1 as a base year shall be 100.

Afterwards, we need to calculate total market value of each company for Year 2:

Stock K - $33*108,000,000 shares outstanding = $3,564,000,000

Stock M - $43*4,200,000 shares outstanding = $180,600,000

Stock R - $43*20,000,000 shares outstanding = 860,000,000

Entire market value of Index component equals to sum of market value of each company for Year 2

=$4,604,600,000

Index value for Year 2 = Market Captialisation for year 2 / Market Capitalisation for base year *100

= 4,604,600,000 / 3,331,400,000 * 100 = 138.22

b.

Computation of change in value of each index during each year:

- Percentage change in PWI = (Index value for year 2 - index value for year 1) / Index value for year 1 * 100

= (87.51 - 100) / 100 * 100 = -12.49%

- Percentage change in VWI = (Index value for year 2 - index value for year 1) / Index value for year 1 * 100

= (138.22 - 100) / 100 * 100 = 38.22%

c.

Total value of investment during year 1 by investing $1,000 in each of the 3 stock = $3,000

Total value of investment during year 2 = (1000 * 33 / 22) + (1000 * 43 / (74/2) ) + (1000 * 43 / 40)

= $1,500 + $1,162.16 + $1,075

= $3,737.16

Percentage change in value = (3,737.16 - 3000) / 3000 *100

= 24.57%