$[8$pts$]$ Mr$.$ Devine is a fixed$-$income portfolio manager. He forecast a cash outflow of $$10$ million in June and plans to sell his baseline bond portfolio. The fund currently is worth $$10$ million, has an $"$A$"$ quality rating, duration of $7$ years, weighted average maturity of $15$ years, annual coupon rate of $10\mathrm{.}25\%,$ and YTM of $10\mathrm{.}25\%($note: the fund is selling at its par value$).$ Suppose Mr$.$ Devine is afraid that long$-$term interest rates could increase and decides to hedge his June sale by taking a position in June T$-$bond futures contracts when the June T$-$bond contract is trading at $80-16,$ and the T$-$bond most likely to be delivered on the contract has a YTM of $9\mathrm{.}5\%,$ maturity of $15$ years, and a duration of $9$ years. $(1)[4$pts$]$ Using the price$-$sensitivity model, show how Mr$.$ Devine could hedge his June bond portfolio sale against interest rate risk. $(2)[4$pts$]$ Suppose long$-$term interest rates increase over the period such that at the June expiration, Mr$.$ Devine's baseline portfolio $($A$-$rated, $10\mathrm{.}25\%$ coupon rate, $15-$year maturity, and $7-$year duration$)$ is trading at $96$ of par, and the price on the expiring June T$-$bond contract $($fr$)$ is $76.$ Determine Mr$.$ Devine's revenue from selling his baseline bond portfolio, his profit on the futures contracts, and his total revenue.