Solution

To determine whether the options will be treated as dilutive or not, we need to calculate the potential impact of the options on the company's earnings per share (EPS).

The basic EPS formula is:

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Number of Common Shares Outstanding

To calculate the potential impact of the options on EPS, we need to consider the number of additional shares that would be issued if all the options were exercised at the exercise price. If the options would result in a decrease in EPS, they would not be dilutive, and if they would result in an increase in EPS, they would be dilutive.

Step 1: Determine the number of additional shares that would be issued if all options were exercised

The number of additional shares that would be issued if all options were exercised is calculated as follows:

Number of options issued x Exercise price / Average market price

= 500 x $40 / $50

= 400

Therefore, if all the options were exercised, 400 additional shares would be issued.

Step 2: Calculate the impact on EPS

To calculate the impact on EPS, we need to recalculate EPS assuming that all the options were exercised and the additional shares were issued.

Weighted average number of shares outstanding after the exercise of options

= Weighted average number of shares outstanding + Number of additional shares that would be issued if all options were exercised

Assuming that the weighted average number of shares outstanding before the exercise of options was 1,000,000, the weighted average number of shares outstanding after the exercise of options would be:

= 1,000,000 + 400

= 1,000,400

Now we can calculate the potential impact on EPS:

Basic EPS without options = Net Income / Weighted average number of shares outstanding

Basic EPS with options = Net Income / (Weighted average number of shares outstanding + Number of additional shares that would be issued if all options were exercised)

If the Basic EPS with options is lower than the Basic EPS without options, the options are not dilutive. If the Basic EPS with options is higher than the Basic EPS without options, the options are dilutive.

Assuming that the net income for the period is $1,000,000 and there are no preferred dividends, the Basic EPS without options would be:

= $1,000,000 / 1,000,000

= $1.00

The Basic EPS with options would be:

= $1,000,000 / (1,000,400)

= $0.999

Since the Basic EPS with options is slightly lower than the Basic EPS without options, the options are not dilutive.

Therefore, in this scenario, the options will not be treated as dilutive.