Finance. Answer in Excel or Handwritten. You think that the stock of Grands, Inc is likely to rise in the next six months, but there is also a chance it will fall significantly. The stock is currently trading for $40 per share. You are considering making an investment in a portfolio of Grands stock and options consisting of: 300 shares of the stock, three at-the-money call option contracts with six month maturity, and three put option contracts with a strike price of $30 and a six month maturity (note that each call or put option contract represents options on 100 shares). The call option contract will increase your payoff if the price goes up, while the put option contract will protect the value of your stock investment if the price falls by more than $10. The current risk-free rate is 2% and the company does not pay dividends.

a. What will be the overall value of your portfolio at expiration at the following possible stock prices: $10, $30, $50, and $70?

b. An at-the-money put option on Grands, Inc. stock with three months to expiration currently sells for $3.50 (on a per share basis). Given this, what is the estimated total cost of the call option contracts you plan to buy, according to Put-Call Parity?

c. If the stocks volatility (i.e., the standard deviation of its return) is expected to be 33%, what is the estimated total cost of the put option contracts you plan to buy, according to the Black-Scholes model?

d. How much would the stock price have to fall from its current price for the put option contracts to be worthwhile (i.e., for their payoff to exceed their cost)?