Assume that the DJIA closed at 11,875 one day recently, and the divisor was 0.12493117. a....

Assume that the DJIA closed at 11,875 one day recently, and the divisor was 0.12493117.

a. What is the sum of the prices of the 20 stocks in the index, given this information?

b. Assume that one stock in the index, Pfizer, moved $4.40 that day, while the index itself moved about 105 points (to close at 10,875). What percentage of the total movement in the DJIA that day was accounted for by the movement in Pfizer?

c. Now assume that one of the 20 stocks had an initial price of $47.50 and the same stock had a 4-for-1 stock split that day. What would the new divisor have to be to keep the index unchanged at 11,875?

Expert Solution

Part (a)

Sum of the prices = Index value x Divisor = 11,875 x 0.12493117 = 1,483.56

Part (b)

percentage of the total movement in the DJIA that day was accounted for by the movement in Pfizer = Increase in Price / (Divisor x increase in index points) = 4.40 / (0.12493117 x 105) = 33.54%

Part (c)

4-for-1 stock split will change the price, P1 = 47.50 to a new price = P2 = 47.50 / 4 = 11.875

Hence, let D be the new divisor, hence

11,875 = New sum of the prices / D = (old sum - P1 + P2) / D = (1,483.56 - 47.50 + 11.875) / D

Hence, the new divisor, D = (1,483.56 - 47.50 + 11.875) / 11,875 = 0.12193117

jeff jeffy answered 2 years ago

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