Consider a risky portfolio. The end$-$of$-$year cash flow derived from the portfolio will be either USD $80000$ with a probability of $35\%,$ USD $115000$ with a probability of $35\%,$ or USD $130000$ otherwise. The alternative risk$-$free investment in T$-$bills pays $4.\%$ per year.

a$)$ If you require a risk premium of $9.\%,$ how much will you be willing to pay for the portfolio?

b$)$ What is the Sharpe ratio of the portfolio if you can purchase it at the price calculated above?