Vansteelandt Inc. has net income of $4,000,000 and 1,000,000 shares outstanding. Its common stock is currently selling for $50 per share. It needs to raise $2,000,000 in funds for a new asset. Its investment dealer plans to sell an issue of common stock to the public for $48 for a spread of 4%. How much must Vansteelandt's aftertax income increase to prevent dilution of EPS?
A) $41,667
B) $166,668
C) $40,000
D) none of the other answers are correct

Question

Quizplus · Accepted Answer

To prevent dilution of EPS, Vansteelandt needs to ensure that the amount raised through the sale of new shares does not decrease EPS.

Currently, EPS is calculated as follows:

EPS = Net Income / Number of Shares = $4,000,000 / 1,000,000 = $4.00

If Vansteelandt issues new shares at $48 per share, the company will receive $47.04 per share after deducting the 4% spread.

Number of new shares = Funds needed / Price per share = $2,000,000 / $47.04 = 42,424.24

Total number of shares after the new issue = 1,000,000 + 42,424 = 1,042,424

To prevent dilution of EPS, the new EPS after the issue should be the same as the current EPS.

New EPS = Net Income / Total number of shares = $4,000,000 / 1,042,424 = $3.84

To achieve this new EPS, net income needs to increase by:

Additional Net Income = (New EPS - Current EPS) * Number of Shares = ($3.84 - $4.00) * 1,000,000 = -$160,000

But this is not possible, so Vansteelandt needs to earn an additional net income of:

Additional Net Income = (New EPS - Current EPS) * Number of Shares = ($4.00 - $3.84) * 1,042,424 = $166,668.16

Therefore, the aftertax income must increase by $166,668 to prevent dilution of EPS.