In: Finance
A financial institution has entered into a 10-year currency swap with company Y. Under the terms of the swap, the financial institution receives interest at 3% per annum in Swiss francs and pays interest at 8% per annum in U.S. dollars. Interest payments are exchanged once a year. The principal amounts are 7 million dollars and 10 million francs. Suppose that company Y declares bankruptcy at the end of year 6, when the exchange rate is $0.80 per franc. What is the cost to the financial institution? Assume that, at the end of year 6, the interest rate is 3% per annum in Swiss francs and 8% per annum in U.S. dollars for all maturities. All interest rates are quoted with annual compounding.
When interest rates are compounded annually
F = S ( 1+r / 1+rf )
where F is the T-year forward rate, S is the spot rate,
r is the domestic risk-free rate, and rf is the foreign risk-free
rate. As r = 0.08 and rf = 0.03 , the spot and forward exchange
rates at the end of year 6 are
Spot: 0.8000
1 year forward ( 7th Year ) 0.8388
2 year forward:( 8th Year ) 0.8796
3 year forward: ( 9th Year ) 0.9223
4 year forward: ( 10th Year ) 0.9670
The value of the swap at the time of the default can be calculated on the assumption that forward rates are realized.
The cash flows lost as a result of the default are therefore as follows:
Year |
Dollar Paid |
CHF Received |
Forward Rate |
Dollar Equiv of CHF Received |
Cash Flow Lost |
6 |
560,000 |
300,000 |
0.8000 |
240,000 |
-320,000 |
7 |
560,000 |
300,000 |
0.8388 |
251,600 |
-308,400 |
8 |
560,000 |
300,000 |
0.8796 |
263,900 |
-296,100 |
9 |
560,000 |
300,000 |
0.9223 |
276,700 |
-283,300 |
10 |
7,560,000 |
10,300,000 |
0.9670 |
9,960,100 |
2,400,100 |
Discounting the numbers in the final column to the end of year 6 at 8% per annum, the cost of the default is $629,480. as under
Year Cash flow Present Value Factor Present Value of Cash Flow
6 ( 320,000 ) 0.93 (296,296)
7 ( 308,400 ) 0.86 (264,403)
8 ( 296,100 ) 0.79 (235,054)
9 ( 283,300 ) 0.74 (208,234)
10 2,400,100 0.68 1,633,468
Sum = $ 629, 480
Note that, if this were the only contract entered into by
company Y, it would make no sense for the company to default just
before the exchange of payments at the end of year 6 as the
exchange has a positive value to company Y. In practice, company Y
is likely to be defaulting and declaring bankruptcy for reasons
unrelated to this particular transaction.