Zinc Company's stock has a current price of $40 per share and a volatility of 30%. The stock pays no dividends. You are interested in valuing a one-year European put option on Zinc stock with a strike price of $45. Assume that the beta of Zinc stock is 0.9, and the risk-free interest rate is 4%. (a) What is the value of this put option? (b) What is the intrinsic value of the put option? What is the time value of the put option? Explain why this put option has a positive or negative time value. (4 marks) (c) Assume that the put price you get from part (a) is $6.8. You find that the corresponding European call option on Zinc stock with a strike price of $45 is currently selling for \$3. Describe what you could do to exploit this opportunity to make a profit. (6 marks) (d) What is the leverage ratio of the put option? What is the beta of the put option? Based on your answers, discuss why investors may want to include put options in their portfolios. (4 marks) (e) Describe the circumstance where it would be optimal to exercise an American put option prior to their expiration