### CFA Practice Question

A price-weighted index has a value of 226 at the close of the day, with the denominator equal to 17.45. After the close of the day's trading, one of the stocks splits 2:1, and the index value changes to 221.5 before adjustment for the split. The new denominator should be ______.
A. 8.73
B. 17.10
C. 17.80
Explanation: Before adjusting the denominator for the split, the index value of 221.5 implies a numerator = 221.5 x 17.45 = 3,865.175 = sum of the product of price and number of shares across all securities in the index.

New denominator = 3,865.175 / 226 = 17.10

User Comment
smillis Why is this not C? At close index is 226 w/ demon of 17.45 implying numer of 226x17.45 =3943.70. After close the index *changes* to 221.5 (new demon assoc with 221.5??) = demon of 17.8 (3943.7 / 221.5)??
egghead couse after split the 3943.7 is updated as well.
So both nominatir and denominator have changed. but their ratio should remain the same.
In formulas that is: s1/17,45 = 226. s2/17.45=221.5. s2/x=226. thus x=s2/226=17.45 * 221.5 / 226
vitt 226/17,45 = 221,5/x
mlaci Wrong text in the question:

226 is "at the close", the split is "after the close" and 221.5 is "before the adjustment" due to split. So BOTH 226 and 221.5 is before the slit.
charliedba No mlaci. After the split, 226 becomes 221.5 so you need to change the denominator from 17.45 to be?
Rob09 i used vitt's method, it seemed to be the most logical
NickPash Simply make 2 equations if 226=17.45 & then 221=x. Using cross multiplication you have 226*x=17.45*221. It's similar to Vitt's and more straight forward.
sgspotts A normal split in a price-weighted index will always decrease the denominator. Therefore you can immediately rule out 17.80. Because the split was relatively small (2 for 1), the denominator won't change dramatically and you can determine that 17.10 is correct. A reverse split will have the opposite effect, ie increase the denominator.
shiva5555 this is backwards.