To calculate the number of shares Carbon8 must sell, we need to consider the underwriter's fee, the underpricing, and the additional costs.
First, let's calculate the underwriter's fee:
Underwriter's fee per share = $1.25
Total underwriter's fee = $1.25 * Number of shares
Next, let's calculate the underpricing:
Underpricing percentage = 7.5%
Underpriced amount per share = $28.00 * 7.5%
Underpriced amount per share = $28.00 * 0.075
Now, let's calculate the total additional costs:
Total additional costs = $785,000
To raise the desired amount of capital, the total amount raised must be $120 million. Let's denote the number of shares as "x".
Total amount raised = (Number of shares * Stock price per share) - Underpriced amount per share - Total underwriter's fee - Total additional costs
$120,000,000 = (x * $28.00) - ($28.00 * 0.075 * x) - ($1.25 * x) - $785,000
Now, we can solve for "x" to find the number of shares Carbon8 must sell.