Question

You are given the following information concerning two stocks that make up an index.  

					Price per Share
	Shares Outstanding				Beginning of Year				End of Year
Kirk, Inc.		38,000			$	46			$	51
Picard Co.		34,000				76				82

a. Assume that you want to build a price-weighted index including the two stocks. Please calculate the beginning index and the end index.  (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Beginning Index:

End Index:

b. What is the return for the price-weighted index? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Index Return: %

c. Assume that you want to rebuild a value-weighted index with the index value at the beginning of the year equal to 100. What is the index level at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.

Index Level at the end:

d. What is the return of the value-weighted index? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Index Return: %

e. Assume the value-weighted index has been existing for 10 years and the index level happened to be 311.05 at the beginning of the year. What is the index level at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.

Index Level at the end:

f. What is the return of this existing value-weighted index? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Index Return: %

Answer 1

a. price weighted index = sum of all share prices of index/number of companies
price weighted index at beginning = ($46 + $76 ) / 2 = 61
Price weighted index at end = ($51 + $82) / 2 = 66.5

b. Change in price wieghted index = 66.5 - 61 = 5.5
% return on index = 5.5/61 = 0.0902 = 9.02%

c. Market capitalization of Kirk, inc at Beginning = $ 46 * 38,000 = $1,748,000
Market capitalization of Picard Co at Beginning = $ 76 * 34,000 = $2,584,000
Weight of Kirk. inc at Beginning = $1,748,000 / ($1,748,000 + $2,584,000 ) = 40.35%
Weight of Picard C oat Beginning = $2,584,000 / ($1,748,000 + $2,584,000 ) = 59.65%
Index level at Beginning = [($46 * 40.35%) + ($76 * 59.65%)] * Factor
100 = 63.895 * Factor
Factor = 100/63.895 = 1.565

Market capitalization of Kirk, inc at End = $ 51 * 38,000 = $1,938,000
Market capitalization of Picard Co at End = $ 82 * 34,000 = $2,788,000
Weight of Kirk. inc at End = $1,938,000 / ($1,938,000 + $2,788,000 ) = 41.01%
Weight of Picard C oat End = $2,788,000 / ($1,938,000 + $2,788,000 ) = 58.99%
Index level at End = [($51 * 41.01%) + ($82 * 58.99%)] * 1.565 = 108.43

d. %return of the value weighted index = (108.43 - 100)/100 = .0843 = 8.43%