Question

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.

Answer #1

**(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

= $3,700

New Index Value = New sum of price / Divisior

= 3,700 / 30

= 123.33

*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

= 37

*New divisor must be 37 to keep index value
unchanged.*

You construct a price-weighted index of 33 stocks. At the
beginning of the day, the index is 9,241.90. During the day, 32
stock prices remain the same, and 1 stock price increases $4.10. At
the end of the day, your index value is 9,267.86. What is the
divisor on your index? (Do not round intermediate calculations.
Round your answer to 8 decimal places.)

The price-weighted Dow Jones Industrial Average Index closed at
12,500 today and the divisor was 0.14. One of the 30 constituent
stocks had a 5-for-1 stock split right declining from $100 to $20
per share right after the market close (immediately after the index
value and divisor above were observed). What would the new divisor
have to be to keep the index value unchanged at
12,500?
Group of answer choices
1) 0.1320
2) 0.1424
3) 0.1416
4) 0.1336

5. A price-weighted index has 3 stocks: A, B and C. Their price
at the start of the index was $35, $48 and $90.
What is the initial divisor if the index start with a value of
100?
By the end of the first year, the price of the 3 stocks is $40,
$52 and $83 respectively. How much has the index gone up?
If stock C has a 3-for-1 split, what would be the new index
value after one...

A price-weighted index consists of stocks A, B, and C which are
priced at $38, $24, and $26 a share, respectively. The current
index divisor is 2.7. What will the new index divisor be if stock B
undergoes a 3-for-1 stock split? (Round your final answer to four
decimal points.)

The Hydro Index is a price weighted stock index based on the 4
largest boat manufacturers in the nation. Consider the four stocks
in the following table. Pt represents price at time t,
and Qt represents shares outstanding at time t. (Please pay close
attention to stock split)
P0
Q0
P1
Q1
P2
Q2
A
80
200
90
200
98
200
B
50
300
40
300
50
300
C
90
200
110
200
115
200
D
100
100
90
100...

A price-weighted index consists of stocks A, B, and C which are
priced at $50, $35, and $15 a share, respectively. The current
index divisor is 2.75. What will the new index advisor be if stock
A undergoes a 5-for-1 stock split?
A. 0.40
B. 0.65
C. 1.00
D. 1.65

A price-weighted index consists of stocks A, B, and C which are
priced at $50, $35, and $15 a share, respectively. The current
index divisor is 2.75. What will the new index advisor be if stock
A undergoes a 5-for-1 stock split?
Multiple Choice
A. 0.40
B. 0.65
C. 1.00
D. 1.65
1.85

Problem 5-1 Price-Weighted Divisor (LO4, CFA2)
Able, Baker, and Charlie are the only three stocks in an index.
The stocks sell for $38, $200, and $106, respectively. If Baker
undergoes a 3-for-2 stock split, what is the new divisor for the
price-weighted index? (Do not round intermediate
calculations. Round your answer to 5 decimal places.)

1. Three stocks have share prices of $25, $50, and $30 with
total market values of $400 million, $250 million, and $150
million, respectively. If you were to construct a market
value-weighted index of the three stocks, what would be the index
value? ① 8,500 ② 9,000 ③ 9,250 ④ 9,500
1)-1 With the above benchmark index, today the prices of three
stocks changed to $30, $45 and $35. What would be the new index
value? ① 9,250 ② 9,500...

Match the description to the correct index.
1. An price-weighted average of 30 stocks.
2. The best measure of overall market performance.
3. A market-value weighted index heavily weighted in technology
stocks.
Dow Jones Industrial Average
S&P 500
Nasdaq

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