The Whistling Straits Corporation needs to raise $86 million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. The offer price is $40 per share and the company's underwriters charge a spread of 8 percent. If the SEC filing fee and associated administrative expenses of the offering are $975,000, how many shares need to be sold

Number of shares  to be sold =2,363,451.09 units

Explanation:

The gross amount to be raised inclusive of administrative fees

= $86 million + $975,000

= $86, 975,000

Total sum to be raised inclusive of underwriting fees

= 100/(100-8)× 86, 975,000

= $94,538,043.48  

Note the amount to be raised net the underwriting fees(i.e $86,975,000)  represents 92%. So we need to work back to 100%

Total number of shares = Gross sum to be raised   / unit price of share

                                      =$94,538,043.48  /$40

                                       =2,363,451.09 units

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