Question

A bank needs to borrow $10 million in three months for a nine-month period. It buys a“three against twelve” FRA for $10 million at a rate of 8% to hedge its exposure. In three months the FRA settles at 7.5%. There are 273 days in the FRA period. What is the bank’snet borrowing cost for the 273 days (at an annualized rate)?

Answer 1

FRA payment = ((( R- FRA)* P* t)/ 273)*(1/(1+R*(t/273)))

Where P is the amount of the contract, R is the floating rate, FRA is the fixed rate and t is the time period of contract.

First lets understand how to calculate Forward rate agreement:

1. Calculate the difference between the forward rate and the floating rate or reference rate.
2. Multiply the difference by the amount of the contract and by the number of days in the contract. Divide the result by 273 (days).
3. Divide the number of days in the contract by 273 and multiply the result by 1 + the floating rate. Multiply the result from the right side of the formula by the left side of the formula.

Net borrowing cost= ((( 8%- 7.5%)* 10000000*90)/ 273)*(1/(1+ 8%*(90/273)))

= 1648351.65* 0.9743= 1605989.01