Consider a stock that has a price of $50. A put and call on this stock have an exercise of $50 and expire in one year. The call costs $5 and the put costs $4. A risk free bond will pay $50 in one year and has a current price of $45. Can you take advantage of this situation, and how would you do it?

Put Call Parity:

So-Co+Po= Xe^-rt

Therefore, $50- 5+4= $49 should be equal to the present value of a bond that matures at a value of $50. I can buy such a bond for $45. There is an arbitrage profit of $4/ share. I can take advantage of it by selling short the stock, buying the call, and writing the put. I then would take $45 of the $49 and buy a risk-free bond that matures at $50.

My question is, how can you determine that there is arbitrage? You buy a stock at $50, buy a call at $5, and sell a put at $4, which results in a value of $49. How can you take $45 of the $49 and buy a risk free bond with that money? How does the Put call parity make this possible?