Question

Magenta Corporation wants to raise $51.1 million in a seasoned equity offering, net of all fees. Magenta stock currently sells for $12 per share. The underwriters will require a spread of $0.4 per share, and indicate that the issue must be underpriced by 4 percent. In addition to the underwriter’s fee, the firm will incur $2,100,000 in legal, accounting, and other costs. How many shares must Magenta sell? (Enter your answer in millions rounded to 3 decimal places.)

Answer 1

Magenta Corporation must sell approximately 4.783 million shares at a net proceeds of $11.12 per share to raise $51.1 million, considering underwriters' spread and the cost for legal and accounting fees.

Step-by-step explanation:

To calculate how many shares Magenta Corporation must sell, we first need to determine the net proceeds per share that Magenta will receive after accounting for the fees and underpricing. Magenta's stock is currently sold at $12 per share. The underwriters' spread is $0.4 per share. Additionally, the underwriting is underpriced by 4 percent, meaning the shares will sell for 4 percent less than the current market value.First, we calculate the selling price after the underpricing:Selling price after underpricing = Current price - (Current price × underpricing rate) = $12 - ($12 × 0.04) = $11.52.

Now, we subtract the underwriters' spread:Net proceeds per share = Selling price after underpricing - underwriters' spread = $11.52 - $0.4 = $11.12.To find out the total amount of money Magenta will receive from the offering, we add the additional incurred costs to the amount they want to raise:Total amount Magenta needs = Desired proceeds + additional costs = $51.1 million + $2.1 million = $53.2 million.Finally, we calculate how many shares they need to sell:Number of shares to be sold = Total amount needed / Net proceeds per share = $53.2 million / $11.12 ≈ 4.783 million shares.Therefore, Magenta Corporation must sell approximately 4.783 million shares to raise the desired $51.1 million, net of all fees.