please show paper calculations.

if you are trying to value an IPO of a start-up in corporate information security industry called Alpha Inc. The firms current book value is $32 million. The company also has bank debt with face value of $30 million that is due in ten years. Bonds with similar risk profile currently yield 15% per year while the risk-free rate is 3% per year. Your investigation of the information security industry indicates that the industry is highly competitive and quickly evolving. Thus, most firms that attempt a public offering either never complete the offering or have a very brief life after the offering. A few successful businesses, however, have managed to generate a sustainable profit stream after a few years of operations. You summarize your findings as follows. The average IPO firm in the industry has market value of equity of $100 million, book value of assets of 24 million, and debt to equity ratio (calculated using book values) of 0.5. Most firms file for bankruptcy in less than five years. Within ten years after the IPO, 70% of firms are liquidated, with the average liquidation value of $21 million. The average market capitalization (i.e., market value of equity) for firms still on the market ten years after the IPO is $830 million.

• Using a binomial option pricing model, estimate alphas offer price assuming that 7 million shares will be outstanding after the offer.
• How much money will the company raise if the underwriter spread on this issue is 8% and its sells 5 million shares in the offering?