Suppose that you are trying to value an IPO of stock in a st

Suppose that you are trying to value an IPO of stock in a start-up in the RFID industry. Suppose its current liquidation value is estimated to be $6,000,000 and its debt worth $5,000,000. Based upon industry experience, you derive an average estimate of u=3 and d=0.25, and the risk-free rate is 4.5%.

(a) Using a one period binomial option pricing model, estimate its offer price assuming that 1,000,000 shares will be outstanding after the offer.

(b) What will the company get if the underwriter spread on this issue is 18% and it sells 500,000 shares in the offering?

(c) What would the price of a warrant on such stock be worth if it promised two shares of stock for every warrant with an exercise price of $5?

Solution

In this context, the equity value of the firm is determined in a fashion similar to a call option valuation using the binomial pricing model. This is so because the payoff matrix for a firm\'s equity holders upon the firm\'s liquidation is similar to that of a call option payoff.

Risk Free Rate = r = 4.5 %, u = 3 and d = 0.25

Risk Neutral Probability of Upward movement = [1.045 - 0.25/3-0.25] = 0.2891 approximately.

If u occurs, then liquidation value = 3 x 6 = $ 18 million and if d occurs, then liquidation value = 0.25 x 6 = $ 1.5 million

Debt Value = $ 5 million

If u occurs equity payoff = 18 - 5 = $ 13 million and if d occurs, equity payoff = 0 as debt is greater than the firm\'s total liquidation value of $ 1.5 million.

Hence, Equity Value = PV of Expected Equity Payoff = [13 x 0.2891 + 0 x (1-0.2891)] / 1,045 = $ 3.5966 million approximately.

(a) Number of Shares outstanding = 1 million

Therefore, offer price = 3.5966 / 1 = $ 3.5966 per share

(b) Underwriting Spread = 18 % and number of shares sold = 500000

Let the price per share accruing to the firm be $ K per share.

Therefore, K = (1-0.18) x 3.5966 = $ 2.949212

Total Proceeds accruing to the firm = 500000 x 2.949212 = $ 1474606

(c) Exercise Price of Warrant = $ 5 which is less than the offer price of $ 3.5966. Hence, the warrant initially will have zero value. Warrant Price accrues only when the share price goes above the warrant exercise price.