Question
In: Finance
A French firm enters into a two-year interest rate swap in euros on April 1, 2005....
A French firm enters into a two-year interest rate swap in euros on April 1, 2005. The swap is based on a principal of €80 million, and the firm will receive 7% fixed and pay six-month Euribor. Swap payments are semiannual. The 7% fixed rate is quoted as an annual rate using the European method, so the implied semiannual coupon is 3.44% [since (1.0344)2 = 1.07]. Two years later, the swap is finally settled, and the following Euribor rates have been observed: Apr. 1, 2005 Oct. 1, 2005 Apr. 1, 2006 Oct. 1, 2006 Apr. 1, 2007 5.5% 6.5% 7.5% 8% 6.5%
(a) What have the swap payments or receipts for the firm been on each swap payment date?
(b)The same French firm also entered another two-year interest rate swap in euros on April 1, 2005. The swap is based on a principal of €80 million, and the firm contracted to receive 7% fixed and pay six-month Euribor. On this swap, the payments are annual. Hence, the two successive six-month Euribor are compounded. Assuming that the Euribor rates given in the previous problem (5a) have been observed, what have the two annual swap payments been?
Solutions
Expert Solution
NOTE : It is standard that rates of Euribor provided are before the actual period. For example for rate between 1 april 2005 to 1 oct 2005 will be provided of 1 april 2005. However, since the question is silence, I have solved the question in both ways.
Rates as per standards
| Euribor Rate | Quoted Rate/2 |
| 1-Oct-05 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 2.75% |
| Difference | 0.69% |
| Amount received | 0.552 |
| 1-Apr-06 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 3.25% |
| Difference | 0.19% |
| Amount Received | 0.152 |
| 1-Oct-06 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 3.75% |
| Difference | -0.31% |
| Amount Receieved | -0.248 |
| 1-Apr-07 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 4.00% |
| Difference | -0.56% |
| Amount Receieved | -0.448 |
Now, find the rates as per the question.
| Euribor Rate | Quoted Rate/2 |
| 1-Apr-05 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 2.75% |
| Difference | 0.69% |
| Amount received | 0.552 |
| 1-Oct-05 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 3.25% |
| Difference | 0.19% |
| Amount Received | 0.152 |
| 1-Apr-06 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 3.75% |
| Difference | -0.31% |
| Amount Receieved | -0.248 |
| 1-Oct-06 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 4.00% |
| Difference | -0.56% |
| Amount Receieved | -0.448 |
| 1-Apr-07 | |
| Fixed Rate | 3.44% |
| Euribor Rate | 3.25% |
| Difference | 0.19% |
| Amount Receieved | 0.152 |
b.
I have done this assuming rates are given before as it illogical to take rate of april 1 2007 to caculate previous periods interest.
| Euribor Rate | (Quoted Rate starting year+Quoted rate between period)/2 |
| 1-Apr-06 | |
| Fixed Rate | 7.00% |
| Euribor Rate((5.5%+6.5%)/2) | 6.00% |
| Difference | 1.00% |
| Amount received | 0.8 |
| 1-Apr-07 | |
| Fixed Rate | 7.00% |
| Euribor Rate | 8.00% |
| Difference | -1.00% |
| Amount Received | -0.8 |
If you have any doubt ask me in the comment section.
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