Question

Suppose that the term structure of interest rates is flat in the US and UK. The USD interest rate is 2.5% per annum and the GBP rate is 2.9% p.a. Under the terms of a swap agreement, a financial institution pays 3% p.a. in GBP and receives 2.6% p.a. in USD. The principals in the two currencies are GBP20 million and USD32 million. Payments are exchanged every year, with one exchange having just taken place. The swap will last 3 more years NOTE: 1 USD = 0.8 GBP

i) Show the payments to be made in a table and then calculate the value of the swap to the financial institution. Assume all interest rates are compounded continuously.

Answer 1

Given the above information we can calculate the desired result as follows

The US interest rate is 2.5% and the GBP rate is 2.9%

Interest rate for financial Institution is 2.6% received in US and 3% paid in GBP

Principal amount in USD is 32 Million and that of GBP is 20 Million

Also we know that 1 swap has already taken place and 3 swaps are pending.

The swap involves exchanging the interest rates which are as below, so the payment that is to be made is

GBP interest = Principal Amount * Interest rate paid by financial institution

= 20,000,000 * 3% = GBP 0.60 million

This will be same for all the upcoming years also.

Also the value of USD interest that is receivable is

USD interest = Principal Amount * Interest rate received by financial Institution

= 32,000,000 * 2.6% = $ 0.832 million

Value in terms of USD rate can be calculated using the below formula

= (USD interest * Exp. value at rate of 2.5% for 1 year) + (Principal + Interest)* Exp value at rate of 2.5% for 3 years

=

= 0.832 * 0.9753 + (32.832) * 0.9277

= 0.811 + 30.46 = $ 31.27 Million = $ 31,270,000

So, this is the future value of the swaps receivable in USD

Now the Value in terms of GBP rate can be calculated as folows

=

= 0.60 * 0.9714 + ( 20.60) * 0.9167

= 0.583 + 18.88 = GBP 19.47 Million = GBP 19,470,000

So, this is the future value of the swaps Payable in GBP

Value of SWAP to the financial institution is

= (value of GBP Swap * Exchange rate) - value of USD swap

= ( 19,470,000 * 1.25 ) - 31,270,000

= 24,337,500 - 31,270,000

= $ -6,932,500

So the final value of swap comes out to be $ -6,932,500, which will be a loss for the financial institution

Note that Currency from GBP to USD = 1/0.80 = $ 1.25

Means 1GBP can be exchanged for $ 1.25.