The following table gives the prices and # of shares outstanding for 4 stocks in

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. A price-weighted index simply takes the price of each stock as the weight given to stock.

Price Weighted average of DJIA on May 10' 2018 = Sum of the Prices per shares of all the 4 firms / divisor

Given Divisor = 2.7

= ($150 + $34 + $42+ $15) / 2.7

= $89.26

DJIA Index on May 10' 2018 = $89.26

2a) Given price of A changed to $165

-> DJIA on July 11 = (165+34+42+15) / 2.7

-> DJIA on July 11 = $94.81

2b) % change in DJIA from May 10 to July 11 = ((Final - Initial) / Initial) * 100

= ((94.81-89.26)/89.26)*100

= 6.22%

% change in DJIA from May 10 to July 11 = 6.22%

2c) Total Market Value of Companies on May 10 = $48,450,000

Total Market Value of Companies on July 11 = $48,750,000

% Change in Market Value = Final Market Value - ((Initial Market Value) / Initial Market Value) * 100

= ((48,750,000-48,450,000)/48,450,000)*100

= 0.62%

% Change in Market Value = 0.62%

3. Companies A splits in to 2-for-1.

This implies that for every one stock, 2 new stocks are issued -> The number of stocks in A now gets multiplied by 2; this results in a reduction in the price per share of stock but the total market value of the Company A remains the same. A stock split just increases the no.of shares outstanding and simultaneously reducing the stock price such that the total market value of the firm remains the same.

Therefore, the new outstanding shares of company A = 20,000*2 = 40,000

New price per share of Company A = 150/2 = $75 (Information from Table 1 is asked to be considered)

3a) When the divisor is not adjusted for the stock split; DJIA after the split = (75+34+42+15)/2.7

DJIA after the split = $61.48

3b) When a stock split occurs, as we know that the total market value of the firm remains unchanged. So, a stock split cannot affect the total value of DJIA even though there is a change in price per share. For DJIA to remain the same during the stock split, the divisor is adjusted for the changed price of the stock such that the end value of DJIA remains unchanged.

->Actual DJIA before stock split = Sum of prices after stock split / New Divisor

-> 89.26 = (75+34+42+15) / New Divisor

-> New Divisor = 166/89.26

-> New Divisor = 1.86

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