The following table gives the prices and # of shares outstanding for 4 stocks in
ID: 2810268 • Letter: T
Question
The following table gives the prices and # of shares outstanding for 4 stocks in a representative stock market. Assume that the prices are as of May 10, 2018 Table 1: Stock prices on May 10, 2018 Company Price # of shares Market Value (In $1.000) $150 S34 $42 $15 20,000 150,000 800,000 450,000 $3,000 $5,100 $33,600 6,750 48,450 Total Market Value as of May 10 1. Compile a price weighted average for May 10, 2018 similar.to the Dow Jones Industrial Average using the above four companies (use a divisor of 2.7). For convenience we will call the average the DJIA Suppose that by July 11, 2018 the price of company A increases by 10% but the price of allof the other companies remain the same. On July 11 the prices of the companies in the market are as given in Table 2 Table 2: Stock prices on July 11, 2018 Company Price # of shares Market Value In $1,000) $165 $34 S42 S15 20,000 150,000 800,000 450,000 $3,300 $5,100 $33,600 6,750 48,750 Total Market Value as of July 11 a. What is the DJIA on July 11 (again divisor is 2.7)? b, what is the % change in the DJIA from May 10 to July 1 1? c, what is the % change in the total market value of the four companies? 3. Using the information in Table 1, assume that company A splits 2 for I If there is no adjustment made to the divisor, what is the DJIA after the split? Suggest a new divisor for use after the stock split so that there is no jump in the DJIA. a. b.Explanation / Answer
1) The price weighted average is calculated by adding all the prices of the stocks in the index and dividing by a common divisor. This ensures that a higher price stock is given more weightage in the index and a percent change in it will have a higher impact on index than a percent change in lower price stock.
As per the definition,
DJIA for May 10, 2018
= (Sum of prices of A, B, C, D on May 10, 2018)/Common Divisor
= ( 150 + 34 + 42 + 15 ) / 2.7
= 241 / 2.7
Therefore, DJIA for May 10, 2018 = 89.2592
2) (a) Similarly, DJIA on July 11, 2018
= (Sum of prices of A, B, C, D on July 11, 2018)/Common Divisor
= ( 165 + 34 + 42 + 15 ) / 2.7
= 256 / 2.7
Therefore, DJIA for May 10, 2018 = 94.8148
(b) % Change in DJIA from May 10 to July 11
= ( 94.8148 - 89.2592) / (89.2592) * 100
= 6.2241 %
(c) % Change in Market Values
= (Market value on July 11, 2018 - Market value on May 10, 2018) / Market value on May 10, 2018
= ( 48750 - 48450) / (48450) * 100
= 0.6192 %
3) For a stock split of 2 for 1 as of May 10, 2018, the stock price of A will become $ 75 and the Number of shares will become 40,000
Therefore, New DJIA of May 10, 2018
= (Sum of new prices of A, B, C, D on May 10, 2018)/Common Divisor
= ( 75 + 34 + 42 + 15 ) / 2.7
= 166 / 2.7
Therefore, New DJIA of May 10, 2018 = 61. 4815
The index value should be unchanged for any kind of corporate action as a corporate action like stock split shouldn't affect the performance of the stock and is just a functional change with no financial impact ( total market value remains same)
(b) The new divisor should be such that the index value for May 10, 2018 should remain unchanged
That means, 89.2592 / x = 61.4815
where, x is the new divisor
Therefore, x = 1.4518
Hence, for any price changes due to demand supply relation going further, Divisor of 1.4518 should be used instead of 2.7 in case of a stock split of 2 for 1 for stock A
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.