Question

Assume the DJIA having 30 companies closed at 10,675 one day recently, and the divisor was 0.1249313.

a) What is the sum of the prices of the 30 stocks in the index, given this information?
b) Now assume that one of the 30 stocks had a 2-for 1 stock split that day, declining from $47.5 to $23.75. What would the new divisor have to be to keep the index unchanged at 10,675?

Answer 1

The sum of the 30 stocks in the DJIA is approximately 1,333.28. After a 2-for-1 stock split, the new divisor needed to maintain the index value at 10,675 is approximately 0.1225740.

Step-by-step explanation:

To answer part a) of the question, the sum of the prices of the 30 stocks in the Dow Jones Industrial Average (DJIA) can be calculated using the given index value and divisor. The formula for the DJIA is:

Index Value = (Sum of the Prices of the Stocks) / Divisor

We rearrange this formula to find the sum of the prices:

Sum of the Prices of the Stocks = Index Value * Divisor

So, using the given figures:

Sum of the Prices of the Stocks = 10,675 * 0.1249313

Sum of the Prices of the Stocks = 1,333.28 (approximately)

For part b), to calculate the new divisor after a 2-for-1 stock split, we first note that the price of the stock decreased from $47.5 to $23.75, effectively keeping the overall capitalization of the company unchanged. However, since the DJIA is a price-weighted index, the divisor must be adjusted to keep the index value the same.

Since the overall sum of the stock prices decreased by $23.75 (from $47.5 to $23.75), the new sum of the stock prices = 1,333.28 - 23.75 = 1,309.53. Now we need to solve for the new divisor which keeps the index value at 10,675:

10,675 = 1,309.53 / New Divisor

New Divisor = 1,309.53 / 10,675

New Divisor = 0.1225740 (approximately)