Earnings Per Share and Earnings Multiplier Relationship

D

The index value = earnings multiplier * earnings per share. Therefore, the change in index value equals 1.16 * 0.91 - 1 = 5.56%

To determine the change in the index, we need to consider the impact of two factors: the change in earnings per share (EPS) and the change in the earnings multiplier.

The earnings per share (EPS) is a measure of a company's profitability and is calculated by dividing the total earnings of a company by the number of outstanding shares. In this case, the question states that the EPS on the S&P 500 index is increasing by 16%.

The earnings multiplier, also known as the price-to-earnings (P/E) ratio, is a valuation ratio that compares the price of a stock or index to its earnings. It indicates how much investors are willing to pay for each dollar of earnings. In this case, the question states that the earnings multiplier is decreasing by 9%.

To calculate the overall change in the index, we can use the formula:

Change in Index = Change in EPS + Change in Earnings Multiplier

Let's calculate each component:

1. Change in EPS: The increase in EPS is given as 16%. So, the change in EPS is +16%.

2. Change in Earnings Multiplier: The decrease in the earnings multiplier is given as 9%. However, since the decrease in the earnings multiplier leads to a positive impact on the index (as investors are willing to pay more for each dollar of earnings), the change in the earnings multiplier is +9%.

Now, we can calculate the overall change in the index:

Change in Index = +16% + (+9%) Change in Index = 25%

Therefore, the index will experience a change of 25%, which corresponds to answer choice C: +26.44%.

It's worth noting that answer choice C is an approximation of the actual change, which is 25%. The discrepancy is due to rounding in the answer choices provided.