In mid-December, a bank Treasurer projects that loan demand will require a $10 m

Question

In mid-December, a bank Treasurer projects that loan demand will require a $10 million borrowing on March 15. The contractual loan rate is 125 basis points over LIBOR. As of December 15, the 3-month LIBOR rate was 8.375 percent and the March Eurodollar futures rate was 11.85 percent (price 88.15). The Treasurer is concerned that interest rates may rise between December and March. The projection for the future is that on March 15, the 3-month LIBOR rate would be 11.125 percent, and the Eurodollar futures rate would be 14.75 percent (price 85.25).

a. State what kind of hedge would he take and why.

b. Compute the firm’s actual interest cost in dollars.

c. Compute gain or loss in the futures market after describing the transactions.

d. Calculate effective annualized interest cost.

Explanation / Answer

a)He would short Eurodollar futures(10 contracts) so as to hedge against Libor/interest rate.Becasue he is exposed to Interest rate(Libor) movements in future he should hedge against it by eliminating uncertainty in rates at which he can take loan by short Eurodollar futures.Because he is exposed to rising libor rates he can gain from short Eurodollar futures if this happens thereby eliminating libor rate rise risk at which he would pay interest on loan.

b)

firm’s actual interest cost in dollars=(Libor+.125%)* $10 million*(3/12)

firm’s actual interest cost in dollars=(11.125%+.125%)* $10 million*(3/12)=.1125*$10 million*(3/12)=$ 281250

c) gain in Eurodollar futures=$25*10*(88.15-85.25)*100=$ 72500

Loss on Libor rate rise on Loan in form of increased interest cost=$10 million *(3/12)*(.11125-.08375)=$ 68750

Net gain if short Eurodollar futures=72500-68750=$3750

d)He needs to borrow only $10000000-72500=9927500, Now he borrows only 9927500 at 11.25% due to gain in Eurodollar futures of $ 72500 after 3 months,interest cost =[(1+.1125*(3/12))*9927500 /10000000]-1=2.067%

Thus effective annualized interest cost=(1.02067)4-1=0.0853 or 8.53%

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