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 $49 to $47.60 ($49 is the rights on price $47.60 is the ex rights price also known as the when issued price) the company is seeking 16.5 million in additional funds with a per share subscription price equal to $34. 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)

Answer 1

Subscription Price per share = $34

Amount the company is willing to raise = $16.5 million

Number of shares that the company will have to issue in order to raise the required amount = $16.5 million / $34 shares ( we'll keep it as it is for ease)

Let the number of shares before the offering be equal to x million

So, Market Cap before the offering = Price of Equity before offering * Number of shares = $49 * x = $49x million

Ex- Rights Price = (Market Cap before Offering + Gross Proceeds from offering)/ (Number of shares before offering + Number of shares offered)

We have few figures along with ourselves, let's plug them in:

$47.6 = ($49x million + $16.5 million)/(x million + $16.5/$34 million)

So, cross multiplying we get,

$47.6(x million + $16.5/$34 million) = ($49x million + $16.5 million)

i.e.

$47.6x million + ($47.6*16.5)/$34 million = ($49x million + $16.5 million)

$47.6x million + $23.1 million = ($49x million + $16.5 million)

$23.1 million - $16.5 million = $49x million - $47.6x million

$6.6 million = $1.4x million

So, x = $6.6/$1.4

Therefore, x = 4.71 million

So, the number of shares before offering (rounded off to two decimal places) is 4.71 million