Timothy, as an option trader, is constantly looking for opportunities to make an arbitrage transaction. Assume Timothy observed the following prices for options on CMC stock: $$4\mathrm{.}15$ for a call with an exercise price of $$50$ and $$4\mathrm{.}50$ for a put with an exercise price of $$50.$ Both options expire in exactly six months and the current bank bill swap reference rate is $6$ percent. Contract multiplier $=100$ for put options, call options and stocks; face value for treasury bills is $$10,000$

a$)$ Given the current market prices for the two options, calculate the no$-$arbitrage price of a share of CMC stock.

b$)$ If the actual market price of CMC stock is $$50,$ demonstrate the arbitrage transaction you could create to take advantage of the discrepancy. Be specific as to the positions you would need to take in each security and the dollar amount of your profit.