How many shares are there currently, before the offering?

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Red Shoe Co. has concluded that additional equity financing will be needed to expand operations and that the needed funds will be best obtained through a rights offering. It has correctly determined that as a result of the rights offering, the share price will fall from $66 to $61.00 ($66 is the rights-on price; $61.00 is the ex-rights price, also known as the when-issuedprice). The company is seeking $14 million in additional funds with a per-share subscription price equal to $42.
How many shares are there currently, before the offering? (Assume that the increment to the market value of the equity equals the gross proceeds from the offering.) (Do not round intermediate calculations and round your final answer to nearest whole number, e.g., 32.)
  Number of old shares
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Answer : there 1,266,667 shares currently, before the offering

Working notes for the above answer is as under

We have provided with the information that,

the share price will fall from $66 to $61.00

Now make the equation as follow

61=(42+$66N)/(N+1)

Solving this equation as follow

61(N+1) =(42+$66N)

61N+61=42+66N

61-42=66N-61N

19=5N

N=19/5

N=3.8

New shres= 14,000,000 /$ 42 per share

=333,333 share

Old share= New share *3.8

=333,333*3.8

=1,266,667

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