Newdex has a net income of $4,000,600 (including the effect of out of pocket cost) and 1,000,000 shares outstanding. It needs to raise $6,600,000 in funds for a new asset. Its investment banker plans to sell an issue of common stock to the public for $50, less a spread of 10%. How much must Newdex's after-tax income increase by to prevent dilution of earnings per share? (round "EPS" to one decimal place)

To solve this problem, we need to calculate the earnings per share (EPS) and determine the amount by which Newdex's after-tax income must increase to prevent dilution.

First, let's calculate the current EPS:
EPS = Net Income / Number of Shares Outstanding

EPS = $4,000,600 / 1,000,000
EPS = $4.00

Next, let's calculate the number of shares that will be issued:
Amount to be raised / (Issue price per share - Spread)
Shares = $6,600,000 / ($50 - $5)
Shares = $6,600,000 / $45
Shares = 146,667

Now, let's calculate the potential dilution in EPS:
Potential Dilution = Shares Issued / Number of Shares Outstanding

Potential Dilution = 146,667 / 1,000,000
Potential Dilution = 0.1467

Finally, let's calculate the amount by which Newdex's after-tax income must increase to prevent dilution:
Required Increase in After-tax Income = Current EPS * Potential Dilution

Required Increase in After-tax Income = $4.00 * 0.1467
Required Increase in After-tax Income = $0.5868

Therefore, Newdex's after-tax income must increase by $0.5868 million (or $586,800) to prevent dilution of earnings per share.