Accessing your inbox, you find an unsolicited e-mail from Shadyside Stock Brokers offering to sell you "bargain shares". For example, one bargain share of Amalgamated Consolidated Enterprises is offered for $41.50 even though ACE is now trading at $42. Reading more closely you learn that if you buy and pay for a bargain share today, the stock itself will not be delivered until Jan. 2 (.25 - one quarter - year from today) and even then, if ACE is trading above $45 per share on Jan. 2, you will not receive the stock, but rather a payment of $45. Thus the payoff for a bargain share is: State of market ST 45 bargain share pays ST 45 a) (5 points) Diagram the payoff function for a bargain share, that is the value you will receive for a bargain share on Jan. 2 as a function of value of ACE stock on that date. Indicate on the diagram the value of the maximum and minimum possible payoff as well as the location of any "kinks" in the payoff function. b) (4 points) Doing further research you learn that ACE pays no dividend, the continuously compounded risk-free rate is 6.99% and that European call options on ACE stock (expiring Jan. 2 with a $45 strike price) now trade at $0.93 while puts with the same strike and expiration trade at $3.15. What instruments would you use if you wished to construct a portfolio that replicates the payoffs of a bargain share? Please specify i) the type of instrument ii) including relevant parameters such as strike price, face value, etc., and iii) type of position (long or short). c) (7 points) Based on your answer to (b), what is the fair-market (no arbitrage) price of a bargain share and would you be willing to buy one from Shadyside for $41.50