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 $42 to $39.20 ($42 is the rights-on price; $39.20 is the ex-rights price, also known as the when-issued price). The company is seeking $12 million in additional funds with a per-share subscription price equal to $30.

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

Let the initial market value be $ V million and the original number of shares (pre-rights issue) be N

Current Stock Price = V/ N = $ 42 - (A)

Gross Proceeds from Rights Issue = $ 12 million and Subscription Price = $ 30

Number of Shares Issued = 12000000 / 30 = 400000 or 0.4 million

Stock Price post Rights Issue = $ 39.2

Therefore, (V + 12) / (N+0.4) = $ 39,2 - (B)

Substituting Equation (A) in Equation (B), we get:

(42N + 12) / (N + 0.4) = 39.2

42N + 12 = 39.2N + 15.68

2.8N = 3.68

N = 3.68 / 2.8 = 1.31428571 million or 1314285.71 ~ 1314286