Question

# Consider the three stocks in the following table. Pt represents price at time t, and Qt...

Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period. P0 Q0 P1 Q1 P2 Q2 A 93 100 98 100 98 100 B 53 200 48 200 48 200 C 106 200 116 200 58 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What will be the divisor for the price-weighted index in year 2? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Calculate the rate of return of the price-weighted index for the second period (t = 1 to t = 2).

Solution :-

(A) The rate of return on a price-weighted index of the three stocks for the first period = ( 87.33 / 84 ) - 1 = 3.97%

Yr 1 = ( 93 + 53 + 106 ) / 3 = 84

Yr 2 = ( 98 + 48 + 116 ) / 3 = 87.33

(B) The divisor for the price-weighted index in year 2

In the absence of a split, stock C would sell for 110, and the value of the index would be :-

( 98 + 48 + 116 ) / 3 = 87.33

After the split, stock C sells at 55. Therefore, we need to set the divisor (d) such that:

83.33 = ( 98 + 48 + 58 ) / d

d = 2.45

(C)

Calculate the rate of return of the price-weighted index for the second period (t=1 to t=2).

The rate of return is zero.

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