Final answer:
To find the number of current shares before the rights offering at Jekyll Co., the dilution effect on share price due to the new share issuance was considered. After calculations, it was determined that the company had approximately 4,057,142.86 shares before the offering.
Step-by-step explanation:
To determine the number of shares Jekyll Co. currently has, before the offering, we can use the information given about the rights offering and the desired amount of funds to be raised. The drop in share price reflects the anticipated dilution from the rights offering. The company wishes to raise $16 million with a subscription price of $20 per share.
Using the formula:
Total funds to be raised = Number of new shares × Subscription price per share
We can calculate the number of new shares to be issued:
$16,000,000 = Number of new shares × $20
Number of new shares = $16,000,000 / $20
Number of new shares = 800,000 shares
Now, to calculate the total number of current shares, we use the price drop to reflect the dilution:
Post-offering price per share (“ex-rights price”) = (Current market price × Number of current shares + Subscription price per share × Number of new shares) / (Number of current shares + Number of new shares)
$34.20 = ($37 × Number of current shares + $20 × 800,000) / (Number of current shares + 800,000)
After solving the equation, we find the Number of current shares:
$34.20 × (Number of current shares + 800,000) = $37 × Number of current shares + $16,000,000
34.20 × Number of current shares + $27,360,000 = 37 × Number of current shares + $16,000,000
$27,360,000 - $16,000,000 = 37 × Number of current shares - 34.20 × Number of current shares
$11,360,000 = 2.80 × Number of current shares
Number of current shares = $11,360,000 / 2.80
Number of current shares = 4,057,142.86 shares (rounded to two decimal places)