The stock price of a company is currently $100 per share. The company's risk manager believes that the stock price will either increase to $120 per share or decrease to $80 per share with equal probability over the next year. The risk-free interest rate is 5%. The risk manager is considering using a put option to hedge against a potential decrease in the stock price. The put option has a strike price of $90 and a premium of $10 per share. If the risk manager purchases 100 put options, what is the expected profit or loss on the position in one year, assuming the stock price does decrease to $80 per share? Show all calculations and assumptions made.

(1) What is the payoff of the put option if the stock price is $80?
(2) What is the expected payoff of the put option if the stock price is $80 or $120, with equal probability?
(3) What is the cost of the put option for 100 shares?
(4) What is the breakeven stock price, below which the risk manager will be better off using the put option to hedge the position?
(5) What is the expected profit or loss on the position in one year, assuming the stock price does decrease to $80 per share, if the risk manager purchases 100 put options?