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Homework answers / question archive / A currency swap has a remaining life of 27 months

A currency swap has a remaining life of 27 months

Finance

A currency swap has a remaining life of 27 months. It involves exchanging interest at 9% on £20 million for interest at 5% on $32 million twice a year. The term structure of interest rates in both the United Kingdom and the United States is currently flat, and if the swap were negotiated today the interest rates exchanged would be 2% in dollars and 4% in sterling. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound sterling) is $1.2500/£. What is the value of the swap in dollars to the party paying sterling?

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Answer:

 

Swap involves exchanging of sterling interest for dollar interest  
Sterling Interest = £20 million x 9% £1.8
Dollar interest = $32 million x 5% $1.6
Principal amount will be swapped at end of life  
Value of sterling bond underlying the Swap = £1.8/(1+4%)^2/24 + (£20 + £1.8)/(1+4%)^(27/24) $33.84
   
Value of Dollar bond underlying the Swap = $1.6/(1.02)^(2/24)+$32 +$1.6/(1.04)^(27/24) $34.46
Value of swap in Dollars to the party paying sterling = $34.46 - ($33.84 x $1.25) -$7.84

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