Question 21. FRA Pricing, Valuation, Payoff, and Hedging (20 marks)

Today is June 1. Sustainable Corporation has an obligation of $25 million coming due on August 1. The company is planning to borrow this amount on August 1 to fulfill its obligation, and plans to pay back the loan on December 1. The company's borrowing rate is LIBOR + 125 basis points. The company's bank presents it with the following LIBOR term structure:

# days

LIBOR

30

0.90%

60

1.00%

90

1.05%

120

1.10%

150

1.15%

180

1.18%

210

1.20%

240

1.21%

For the calculation of interest, the bank assumes 30 days in a month, and 360 days in a year.

Ms. Devro, the VP Finance of Sustainable, is worried that LIBOR will increase between June and August, thus increasing the company's borrowing cost. She advises that the company enters into a forward rate agreement (FRA) with its bank to hedge its interest rate risk. She has asked you, the treasurer of the company, to present her with answers to the following questions:

a.Should Sustainable take a long or short position in the FRA? (1 mark)

b.What is the fixed rate on the FRA, based on the LIBOR term structure provided by the bank? (4 marks)

c.July 1 is the end of the company's third quarter of operations, and the company must estimate the fair value of all its contracts, including derivatives, for its quarterly financial statements. What is the value of this FRA if the LIBOR term structure turns out to be the following on July 1? (5 marks)

# days

LIBOR

30

0.90% + 0.50%

60

1.00% + 0.50%

90

1.05% + 0.50%

120

1.10% + 0.55%

150

1.15% + 0.55%

180

1.18% + 0.55%

210

1.20% + 0.60%

240

1.21% + 0.60%

d.What will be the payoff on the FRA on August 1 if the company's business analysts expect the LIBOR term structure to turn out to be the following when the FRA expires? (3 marks)

# days

LIBOR

30

0.90% + 0.50%

60

1.00% + 0.50%

90

1.05% + 0.50%

120

1.10% + 0.55%

150

1.15% + 0.55%

180

1.18% + 0.55%

210

1.20% + 0.60%

240

1.21% + 0.60%

e.Given the LIBOR term structure given for August 1 in Question 3, what are the effective annual rates with and without the FRA hedge? For compounding interest calculations, the company uses 365 days per year. (6 marks)

f.Should Sustainable hedge its interest rate risk with this FRA? (1 mark)