Question

Your firm has 8 million shares​ outstanding, and you are about to issue 5 million new shares in an IPO. The IPO price has been set at $ 18 per​ share, and the underwriting spread is 7 %. The IPO is a big success with​ investors, and the share price rises to $ 53 the first day of trading.

a. How much did your firm raise from the​ IPO?

b. What is the market value of the firm after the​ IPO?

c. Assume that the post IPO value of the firm is the fair market value. Suppose your firm could have issued shares directly to investors at their fair market​ value, in a perfect market with no underwriting spread and no underpricing. What would the share price have been in this​ case, if you raise the same amount as in part ​(a​)?

d. Comparing part ​(b​) and part ​(c​), what is the total cost to the​ firm's original investors due to market imperfections from the​ IPO

Answer 1

Solution:

Part A )

Share issue price = $18, Number of share issued = 5 million , Underwriting spread = 7%

Amount raised = [Issued Price – Issued price * Underwriting spread] * Number of shares issued

Amount raised = [$18 – $18*0.07] * 5 million = 83,700,000

Part B )

Market value of the firm = Number of shares * market price of the share = (10+5 ) million * $53 = 795,000,000

Part C )

Since we are raising 83,700,000 from the IPO and Market value of the firm is 795,000,000 after IPO. If the market is perfect then the market value of the firm before IPO should be

Market value of the firm = Market value after IPO - Market value of IPO = 795,000,000 - 83,700,000 = 711,300,000

Share price = 711,300,000 / 10 million = $71.13

Part D )

Total cost due to market imperfection = ($71.13 - $53) * 10 million = $181.3 million