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You've collected the following information for three stocks. All information refers to the end of a year.
| Shares (million) | Price |
| Stock | 2021 | 2022 | 2021 | 2022 |
| A | 85 | 85 | 140 | 115 |
| B | 146 | 438 | 93 | 24 |
| C | 300 | 300 | 46 | 54 |
A stock index had value of 7,045 at the end of 2021. Stock B underwent a 3-for-1 stock split at the end of 2021, just after the index was calculated.
Attempt 1/3 for 10 pts.
Part1
What is the new divisor for a price weighted index?
Correct
After the stock split, the price of stock B went down:
P1B,0=PB,0R=933=31,01=,0=933=31
The divisor must adjust so that the index level stays unaffected:
PA,0+P1B,0+PC,0d1=I0,0+,01+,01=0
d1=PA,0+P1B,0+PC,0I0=140+31+467,045=1=,0+,01+,00=140+31+467,045= 0.0308
Attempt 1/3 for 10 pts.
Part2
What is the index value for a price-weighted index at the end of 2022?
Correct
| Shares (million) | Price |
| Stock | 2021 | 2022 | 2021 | 2022 |
| A | 85 | 85 | 140 | 115 |
| B | 146 | 438 | 93 | 24 |
| C | 300 | 300 | 46 | 54 |
| Total | | | 279 | 193 |
New index level:
I1=iPi,1d1=1930.0308=1=,11=1930.0308= 6,266
Attempt 2/3 for 10 pts.
Part3
What is the relative change in the price-weighted index? Enter your answer as a decimal number or with the percentage sign.
Correct
Relative change =6,2667,0457,045=11.06%==6,266-7,0457,045=-11.06%= -0.1106
Attempt 2/3 for 10 pts.
Part4
What is the index value for a market value-weighted indexat the end of 2022?
Answer & Explanation
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