Alcibiades Thoroughbred Inc. is a small horse syndicate that owns a three-year-old racehorse named Butterfly Spread. Based on Butterfly Spread's racing record and potential breeding value, the estimated value of the horse and therefore Alcibiades Thoroughbred Inc. is \$1,000,000. Alcibiades has 10 shareholders, each with 100 shares (total shares \(=n=1,000\) ) and no debt. In addition, Alcibiades also has a warrant that it sold to Mr. Lucky giving him the right to buy 100 shares of Alcibiades for \(\$ 1,300\) per share.

a. What would be the intrinsic value of Mr. Lucky's Alcibiades warrant if Butterfly Spread won the Bluegrass Stakes, a major stakes race, causing the value of the horse and ABC Inc. to increase to a value of \(\$ 2,000,000\) ?

b. Instead of an Alcibiades warrant, suppose one of the Alcibiades equity holders sold a call option to Mr. Lucky giving him the right to buy 100 shares of Alcibiades stock at \(\$ 1,300\) per share. What would be the IV of the call if Butterfly Spread won the Bluegrass Stakes?

c. Explain intuitively the difference between the call's IV and the warrant's IV.

d. Show the algebraic relationship between the values of a warrant and a call.