Question

A currency swap has a remaining life of 5 months. It involves exchanging interest at 10% on £20 million for interest at 6% on $30 million once a year. If the swap were negotiated today the interest rates exchanged would be 5% in dollars and 8% in sterling. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound sterling) is 1.8500. What is the value of the swap to the party paying sterling? What is the value of the swap to the party paying dollars?

Answer 1

1). Value of the swap to the party paying sterling i.e. receiving $:

This is calculated as given below:

Amount of $ to be received - Amount of sterling to be paid.

= ($30 million * 6%)- (£20 million * 10%)

=($1.8 million) - (£ 2 million)

Using exchange rate given in the question,$/£ = 1.85

=($1.8 million) - ($3.7 million)

=$-1.9 millions

The present value of the swap using the dollar interest rate of 5% given in the question,

Value of the SWAP = $-1.9millions/(1.05)^5/12

^₌ -$1.8618 millions.

2). Value of the swap to the party paying dollars i.e. receiving £ :

This is calculated as given below:

Amount of £ to be received - Amount of $ to be paid.

=(£ 20 million *10%) - ($30 million * 6%)

=(£ 2 million) - ($ 1.8 million)

Using exchange rate given in the question,$/£ = 1.85

=(£ 2 million) - (£ 0.9729 million)

=£1.0271 million

The present value of the SWAP using the pound interest rate of 8% given in the question:

Value of the SWAP=£1.0271 million/(1.08)^5/12

=£ 0.9947 millions