Please answer this question about FRA contracts!

It is March. A firm signs an agreement to invest in a wealth management product. With a purchase price of 20 million in 3 months. The product is a 6 month floating rate money market instrument. The interest rate of the product is determined by the 6 month LIBOR rate when the agreement starts. Upon expiration mid-December, the product make a lump sum payment to its buyer, which includes both the principal amount (I.e. 20 million) and the interest income. There is NO interim cash flows from the product before the expiry date. Right after signing the purchase agreement, the firm starts to worry about future interest rates. Note the firms operational expenses are fixed over time. An increase or decrease in market interest rate will NOT lead to an increase or decrease in its expenses. However the treasurer of the firm is concerned about the unexpected interest rate movement that might decrease the firms revenue (i.e., lower interest income) and proposes to the CEO to hedge the interest rate risk by using FRA contracts. Suppose the following FRAs are available in the marked in mid-March. The principal amount is $20 million for all the FRAs. All FRAs are the standard US FRAs.

FRA Contract	Rate(p.a)
1x6	4.8%
2x6	5.0%
3x6	5.2%
1x9	5.0%
2x9	5.2%
3x9	5.4%

*The rates are simple rates

Question part 1: Which FRA contract is MOST appropriate for hedging against the interest rate risk for the firm and why? Also explain whether to short or long the FRA contract.

Question part 2: Then, suppose the firm fully hedges the interest rate risk using the most appropriate FRA contract. Use calculations to explain whether the firm make a profit or loss on the FRA contract if the 6 month LIBOR rate is 4% per annum in mid-June. (ignore the day count convention, and assume that one-, two-, month corresponds to 1/12, 2/12..of a year) when using LIBOR rates and FRA rate in calculating the settlement amount.

Question part 3: Suppose the CEO rejects the proposal to use FRAs to hedge, and said "hedging is costly and unnecessary for us, and it's not needed even if market interest rates drops sharply after March 1st." Explain whether his judgement is justified or not in a short paragraph.