Price Weighted Index (stock splits)

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Znieh15

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Extremely confused, on what should be one of the easier concepts…please help..
Question
A stock index consists of 2 stocks: Company A has 50 shares outstanding at $2 each. Company B has 10 shares outstanding valued at $10 each. THe price-weighted index is 6, and market weighted index is 100.
If the price of Company A’s stock increases to $4 per share, and Company B’s stock splits 2 for 1 and is priced at $5, the value of the price-weighted index and value weighted index are?
Answer: Price weighted = 7, Value Weighed = 150.
The answer states “A price weighted index is not affected by a split (4+10)/2 = 7. The divisor is adjusted to account for the price change”
I don’t understand this whatsoever. First off, if it’s not affected, how is the divisor adjusted. Secondly, If the price weighted index was originally 6, wasn’t that just (2+10)/2 =6. If that is correct, in both cases the divisor is 2?
I’ve spend way too much time trying to figure this out, including looking at definition of price weighted index which states (sum of stock prices)/number of stocks in index. Which if I try to calculate I get [(50x4)+(20x5)]/70 = 4.2?
 
The explanation’s pretty poor.
No stock index – price-weighted, value-weighted, or equal-weighted (unweighted) – is affected by a stock split, reverse stock split, stock dividend, or replacement of one stock with another; that’s just the nature of stock indices.
Their point was (i.e., should have been) that the denominator for the price-weighted index needs to change, while the denominator for the value-weighted index does not. The new denominator (divisor) for the price-weighted index is determined by using the new prices (after the split, reverse split, stock dividend, or replacement), and the index value as if nothing had happened. Here, the index value as if nothing had happened would be (4 + 10)/2 = 7. The new divisor – d – has to satisfy (4 + 5)/d = 7, so d = 1.2857. If you use the old divisor (2) with the old (pre-split) stock price, you get an index value of 7. If you use the new divisor (1.2857) with the new (post-split) stock price, you get an index value of 7. The index value isn’t changed because of the split.
 
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