A Firm swaps 5 on 30 million for 75 on 20 million sterling T

A Firm swaps 5% on $30 million for 7.5% on 20 million sterling. There are now 6 months remaining in the swap and the next coupon payment is in 6 months, the term structures of interest rates are flat in both countries, with dollar rates currently at 4.25% and Sterling rates currently at 7.75%. The current $/sterling exchange rate is $1.65. How do you calculate the value of this swap please?

Solution

Greetings,

Value of the swap = One leg - second leg

We assume investor is long on dollar and short on pound sterling. So value of swap to him is - dollar leg - pound leg

Value of dollar leg

Payment to be received after 6 months = FV + Coupon = 30 + 30*0.05*6/12 = 31.5m. PV of Dollar receipts today @ 4.25% is

31.5m / (1+0.0425*6/12) = 30.84m

Value of the pound leg

Payment to be made after six months = FV + Coupon = 20 + 20*0.075*6/12 = 20.75m. PV of this payment @ 7.75% is

20.75m/(1+0.0775*6/12) = 19.98m. This is in pound terms. Let us convert it in dollar terms using exchange rates.

Value in dollar terms = 19.98*1.65 =32.96m

So value of the swap = 30.84-32.96= -2.12m in dollar terms