Question

Fishwick Enterprises has 207,500 shares outstanding, half of which are owned by Jennifer Fishwick and half by her cousin. The two cousins have decided to sell 105,000 shares in an IPO. Half of these shares would be issued by the company to raise new cash, and half would be shares that are currently held by Jennifer Fishwick. Suppose that the shares are sold at an issue price of $50 but rise to $80 by the end of the first day’s trading. Suppose also that investors would have been prepared to buy the issue at $80.

a. What percentage of the company will Jennifer own after the issue? (Round your answer to the nearest whole percentage.)

b. What will her holding be worth at the end of the first day’s trading?

c. Suppose the issue had been priced at $80. How many shares would the company have needed to sell to raise the same gross proceeds from the IPO?

d. What in this case would be Jennifer’s wealth (cash plus the value of her remaining holding)? (Enter your answer in millions rounded to 1 decimal place.)

e. What is the cost of underpricing to Jennifer in dollars? (Enter your answer in millions rounded to 1 decimal place.)

Answer 1

There are 207,500 shares outstanding. Half shares are owned by Jennifer Fishwick while the rest of the other half of the shares are owned by her cousin.

Shares owned by Jennifer = 207,500/2 = 103,750

Shares owned by her cousin = 207,500/2 = 103,750

Number of shares sold in an initial public offering (IPO) = 105,000 shares

Half shares shall be used to raise cash and the remaining half shall be held by Jennifer.

Shares used to raise cash = 105,000/2 = 52,500
The issue price is $50, and the price rises to $80 at the end of the trading day. The investors are ready to buy shares at $80.

Solution a) Shares held by Jennifer before the issue = 103,750

Shares sold by Jennifer during the issue = 52,500

Shares held by Jennifer after the issue = 103,750 - 52,500 = 51,250

Total number of shares after the issue = 207,500 + 52500 (new issue) = 260,000
% of shares owned by Jennifer after the issue = (Shares of Jennifer/Total shares)x100
= (51,250/260,000)x100

= 19.71%

= 20% (approx.)

Solution b) Number of shares held by Jennifer at the end of the first trading day = 51,250

Share Price at the end of first trading day = 80

Value of shares held by Jennifer = 80*51,250 = $4,100,000

Solution c) Amount raised by IPO (Gross Proceeds) = Number of shares sold * Issue Price

Original issue price = $50

Number of shares sold in an initial public offering (IPO) = 105,000 shares

Thus, Amount raised through IPO = 105000*50 = $5,250,000

If the issue price was $80, then, the number of shares to be issued for same gross proceeds are calculated as:

= Gross Proceeds/New issue price

= 5,250,000/80 = 65,625 shares

Solution d) Continuation in part (c), total number of shares to be issued = 65,625

Number of shares sold by Jennifer in this case = 65,625/2 = 32812.5 = 32813

Cash generated by selling the shares = 32813*80 = $2,625,040

Shares held after the issue = 103,750 - 32813 = 70937

Value of the shares held = 70937*80 = $5,674,960

Total value = 5,674,960 + 2,625,040 = $8,300,000 = $8.3 million

Solution e) Shares sold by Jennifer =  52,500

Underpricing = Number of shares*(Market price - Issue price)

= 52,500*(80- 50)

= 52,500*30 = $1,575,000

= $1.575 million

= $1.6 million (approx)

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