On the London Metals Exchange, the price for copper to be delivered in one year is $$6,220$ a ton. $($Note: Payment is made when the

copper is delivered.$)$ The risk$-$free interest rate is $2\mathrm{.}00\%$ and the expected market return is $10\%.$

a$.$ Suppose that you expect to produce and sell $12,100$ tons of copper next year. What is the PV of this output? Assume that the sale

occurs at the end of the year.

Note: Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.

b$-1.$ If copper has a beta of $1\mathrm{.}38,$ what is the expected price of copper at the end of the year?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$-2.$ Assume copper has a beta of $1\mathrm{.}38.$ What is the certainty$-$equivalent end$-$of$-$year price?