could you please provide a solution so i can check my work?

Suppose that two firms go public on the same day. Both firms offer 10,000 primary shares for sale. One of these firms is a HOT IPO in the following sense. HOT IPOs have a 70% chance of being worth $35 per share, and 30% chance of being worth $10 per share at the end of the first day of trading. The other firm is a COLD IPO in the following sense. COLD IPOs have a 50% chance of being worth $30 per share and 50% chance of being worth $8 per share at the end of the first day of trading. Informed investors know which of the two firms going public is a HOT IPO. Uninformed investors are unsure. Informed investors bid for 10,000 shares on the HOT IPO and do not bid on any shares in the COLD IPO. Uninformed investors bid for 10,000 shares on each of the HOT and COLD IPOs, Shares for the HOT IPO are therefore over-subscribed. Assume that oversubscribed IPOs are filled on a pro-rata basis. Assume that for each informed investor, there are four uninformed investors. a) Ignoring discounting, what is the expected value of an IPO of unknown type? (2 point) b) If the offer price is the expected value of an IPO of unknown type as in part a), what are the expected profits for uninformed investors from purchasing shares in IPOs? What are the expected profits for informed investors from purchasing shares in IPOs? (4 points) c) At what price could the firm offer their shares that would ensure that uninformed investors break even on their investment? (2 points) d) What are "Winner's Curse" and IPO underpricing respectively? Explain why (or why not) your answers to parts a)-c) imply IPO underpricing. (4 points) e) Suppose one of these firms goes public offering 10,000 shares with an offer price of $20 per share. Its IPO includes an overallotment option of 15%. What is the total expected payoff from the overallotment option if with 50% probability the opening price is $35 per share and with 50% probability the opening price is $15 per share? (2 points) Suppose that two firms go public on the same day. Both firms offer 10,000 primary shares for sale. One of these firms is a HOT IPO in the following sense. HOT IPOs have a 70% chance of being worth $35 per share, and 30% chance of being worth $10 per share at the end of the first day of trading. The other firm is a COLD IPO in the following sense. COLD IPOs have a 50% chance of being worth $30 per share and 50% chance of being worth $8 per share at the end of the first day of trading. Informed investors know which of the two firms going public is a HOT IPO. Uninformed investors are unsure. Informed investors bid for 10,000 shares on the HOT IPO and do not bid on any shares in the COLD IPO. Uninformed investors bid for 10,000 shares on each of the HOT and COLD IPOs, Shares for the HOT IPO are therefore over-subscribed. Assume that oversubscribed IPOs are filled on a pro-rata basis. Assume that for each informed investor, there are four uninformed investors. a) Ignoring discounting, what is the expected value of an IPO of unknown type? (2 point) b) If the offer price is the expected value of an IPO of unknown type as in part a), what are the expected profits for uninformed investors from purchasing shares in IPOs? What are the expected profits for informed investors from purchasing shares in IPOs? (4 points) c) At what price could the firm offer their shares that would ensure that uninformed investors break even on their investment? (2 points) d) What are "Winner's Curse" and IPO underpricing respectively? Explain why (or why not) your answers to parts a)-c) imply IPO underpricing. (4 points) e) Suppose one of these firms goes public offering 10,000 shares with an offer price of $20 per share. Its IPO includes an overallotment option of 15%. What is the total expected payoff from the overallotment option if with 50% probability the opening price is $35 per share and with 50% probability the opening price is $15 per share? (2 points)