Final answer:
After Baker's 3-for-2 stock split, the price of Baker's stock becomes $266.67. The sum of the adjusted stock prices is $426.67. The new divisor is determined by dividing this sum by the original index value to ensure the index's consistency pre- and post-split.
Step-by-step explanation:
The question pertains to the calculation of a new divisor in a price-weighted index after one of the stocks in the index, Baker, undergoes a 3-for-2 stock split. To find the new divisor, we first need to adjust the stock price of Baker post-split, and then recalculate the index using the new prices. After the split, the number of Baker shares will increase, but the price per share will decrease so that the overall value of a shareholder's investment remains the same.
Originally, the price of Baker stock is $400. After a 3-for-2 stock split, each old share is replaced with 1.5 shares of new stock, so the price of each new share will be $400 divided by 1.5, which equals $266.67. The sum of the adjusted stock prices is $56 (Able) + $266.67 (Baker) + $104 (Charlie) = $426.67. The original sum of stock prices was $56 + $400 + $104 = $560. To maintain the same index value after the stock split, we need to find a new divisor such that the pre-split index value is equal to the post-split index value.
The original divisor is computed by dividing the total pre-split stock prices by the index value. Assuming the original index value was set with a divisor that makes the index equal to the sum of the stock prices (which is a common initial setting), the original divisor would be $560 / index value. If the index value was $560 then the divisor would be 1. Now, we keep the index value the same but we have new total stock prices of $426.67. So, the new divisor is $426.67 / index value. If the index value remained at $560, the new divisor would be $426.67 / $560.