Please show all work!

1. Dynamic Energy Systems is currently trading at $50 per share. The stock pays no dividends. A one-year European put option on Dynamic stock with a strike price of $41 is currently trading for $12.47. You currently hold 10 single share puts and borrowed $390.48. Assume the risk-free interest rate is 5% per year. Hint: Be extremely careful with cash flow signs.
   1. How you would hedge your position and what will be the cash flow when you hedge? 15 pts
   2. Demonstrate that the hedge works if the stock price is $70 at the end of the year. 15 pts