Assume that you construct a price weighted index of 30 stocks. The sum of the prices of these stocks is $4000. The divisor for this index is 30, and the value of this index is 100. Now assume that one of the 30 stocks, with an average price of $400, has a four-for-one stock split while the value of other stocks remains unchanged.
a) If you make no adjustments to the index, what will be the new value of the index?
b) What does the new divisor have to be to keep the value of the index unchanged at 100.
(a.) Sum of the prices of the stock = $4,000
Value of the index = 100
Divisior of the index = 30
One stock has 4 for 1 stock split.
New share price = Old share price * ( 1 / ratio )
= $400 * 1 / (4/1)
= 400 * 1/4
= 400 / 4
New Share price = 100
New sum of price = Old sum of price - stock split share old price + stock split share new price
= $4,000 - $400 + $100
New Index Value = New sum of price / Divisior
= 3,700 / 30
New Index value is 123.33
(b.) New Index Value = New sum of price / Divisior
required index value = 100
100 = 3700 / divisor
Divisor = 3700 / 100
New divisor must be 37 to keep index value unchanged.
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