FRA (Forward Rate Agreement)

• A project has eight months until project completion.
• Funding for the project will run out in approximately six months. Need to cover the funding gap.
• Funding = $1,275,000

To mitigate the interest rate uncertainty, you have decided to enter into a FRA based on LIBOR.

LIBOR rates on July 1 (current)

Day			All-current
90			4.28%
180			4.52%
240			5.11%
360			5.92%

LIBOR rates on October 1

Day			All-current
90			5.12%
150			5.96%
210			6.03%
300			6.41%

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[Question 1]

What is the price of the FRA on the date of the contract inception?

(1+R₂₄₀*240/360) = (1+R₁₈₀*180/360)(1+FRA_6x8*60/360)
FRA_6x8 = ((1+R₂₄₀*240/360)/(1+R₁₈₀*180/360) - 1)*(360/60)
= ((1+5.11%*240/360)/(1+4.52%*180/360) - 1 )*(360/60)
= 0.067279

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[Question 2]

What is the value of the forward rate agreement three months after the inception of the contract (from fixed-payer's perspective)? For this question only, assume that the interest rate at inception was 6.0%.

(1+R₁₅₀*150/360) = (1+R₉₀*90/360)(1+FRA_3x5*60/360)

(1)

FRA_3x5 = ((1+R₁₅₀*150/360)/(1+R₉₀*90/360) - 1)*(360/60)

= ((1+5.96%*150/360)/(1+5.12%*90/360) - 1)*(360/60)

= 0.071288 = 7.13%

or

(2)

FRA_3x5 = ((1+R₁₅₀*150/360)/(1+R₉₀*90/360) - 1)*(360/60)

= ((1+5.96%*150/360)/(1+5.12%*90/360) - 1)*(360/60)

= (1.0248/1.0128 - 1)*(360/60)

= 0.0118*(360/60)

= 0.0708 = 7.08%

(1)

(7.13%-6.0%)*(60/360)*$1,275,000/(1+5.96%*150/360)
= 2343.064

(2)

(7.08%-6.0%)*(60/360)*$1,275,000/(1+5.96%*150/360)

= 2239.389