Question

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).

Answer 1

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.