Stock Price-Weighted and Value-Weighted Index Calculation

Explanation

Price weight = [(4) + (10)] / 2 = 7

To calculate the price-weighted index, we need to multiply the price of each stock by its respective weight and sum them up. In this case, we have two stocks: Company A and Company B.

Initially, the price of Company A's stock was $8, and the price of Company B's stock was $2. The weights of the stocks in a price-weighted index are determined by their prices relative to the total index price. Since the initial total index price was $10 ($8 + $2), the weight of Company A was 80% ($8 / $10) and the weight of Company B was 20% ($2 / $10).

Now, the price of Company A's stock has changed to $4, and the price of Company B's stock remains the same at $2. We need to recalculate the weights based on the new prices. The new total index price is $6 ($4 + $2), and the weight of Company A is 66.67% ($4 / $6), while the weight of Company B is 33.33% ($2 / $6).

To calculate the price-weighted index, we multiply the price of each stock by its weight and sum them up:

Price-weighted index = (Price of Company A × Weight of Company A) + (Price of Company B × Weight of Company B) = ($4 × 66.67%) + ($2 × 33.33%) = $2.67 + $0.67 = $3.34

Therefore, the price-weighted index is $3.34.

To calculate the value-weighted index, we need to multiply the market value of each stock by its respective weight and sum them up. The market value of a stock is calculated by multiplying its price by the number of shares outstanding.

Initially, the market value of Company A's stock was $8 ($8 price × 1 share) and the market value of Company B's stock was $2 ($2 price × 1 share). Using the same weights as before (80% for Company A and 20% for Company B), we can calculate the value-weighted index:

Value-weighted index = (Market value of Company A × Weight of Company A) + (Market value of Company B × Weight of Company B) = ($8 × 80%) + ($2 × 20%) = $6.40 + $0.40 = $6.80

Now, after the price change, the market value of Company A's stock is $4 ($4 price × 1 share), and the market value of Company B's stock remains at $2. We need to recalculate the weights based on the new market values. The new total market value is $6 ($4 + $2), and the weight of Company A is 66.67% ($4 / $6), while the weight of Company B is 33.33% ($2 / $6).

Calculating the value-weighted index using the updated weights and market values:

Value-weighted index = (Market value of Company A × Weight of Company A) + (Market value of Company B × Weight of Company B) = ($4 × 66.67%) + ($2 × 33.33%) = $2.67 + $0.67 = $3.34

Therefore, the value-weighted index is $3.34.

Based on the calculations above, none of the answer choices provided match the correct values for both the price-weighted and value-weighted indices.