Question

Stone 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 $27 to $24.70 ($27 is the "rights-on" price; $24.70 is the ex-rights price, also known as the when-issued price). The company is seeking $20 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 the nearest whole number, e.g., 32.)

Number of old shares

Answer 1

As we know that the Theoretical Ex-Right price is given by:

Theoretical Ex-Rights price = New Shares × Issue Price + Old Shares × Market Price / New Shares + Old Shares

Now we know that the Ex Rights price is known to us and we require to find the no of exisitng shares. So we will have following values:

New Shares can be found from the given information that the Company is seeking $20 million for subscription price of $20 Thus it will issue $20 million/$20 = 1 million shares

Issue Price = $20

Old Shares = x

Ex-Rights Price = $24.7

Market Price = $27

Now putting all this values in formula

24.7 = ((1,000,000*20)+(x*27))/(1,000,000+x)

24.7 * (1,000,000 + x) = (20,000,000 + 27x)

24,700,000 + 24.7x = 20,000,000 + 27x

27x - 24.7x = 4,700,000

2.3x = 4,700,000

x = 4,700,000/2.3

x = 2,043,478.26

x = 2,043,478

No of Old Shares = 2,043,478