Question

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 $39 to $34.90 ($39 is the rights-on price; $34.90 is the ex-rights price, also known as the when-issued price). The company is seeking $26 million in additional funds with a per-share subscription price equal to $20.

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 answer to nearest whole number, e.g., 32.)

Answer 1

Subscription price per share = $20,

Additional funds raised = $26 million = 26000000

No of shares issued through rights issue = Additional funds raised / Subscription price per share = 26000000 / 20 = 1300000 shares

Let x = number of shares before the offering

Then market capitalization before rights issue = (No of share before offering)(rights on price) = (x)(39) = 39x

Total shares after rights issue = number of shares before the offering + No of shares issued through rights issue = x + 1300000

Ex rights price = (Market capitalization before rights issue + increment to market capitalization due to rights issue) / Total shares after rights issue

As it is given that increment to market capitalization due to rights issue = additional funds raised, therefore

Ex rights price = (Market capitalization before rights issue + additional funds raised) / Total shares after rights issue

34.90 = (39x + 26000000) / (x + 1300000)

34.90x + 45370000 = 39x + 26000000

39x - 34.90x = 45370000 - 26000000

4.10x = 19370000

x = 19370000 / 4.10= 4724390.24 = 4724390 (rounded to nearest whole number)

Hence current number of shares before offering = 4724390 shares