LOS c: Calculate and interpret the fixed rate on a plain vanilla interest rate swap and the market value of the swap during its life.

Q1. If the one year spot rate is 5%, the two-year spot rate is 5.5%, and the three year spot rate is 6%, the fixed rate on a 3-year annual pay swap is closest to:

A)   1.99%.

B)   4.50%.

C)   5.96%.

Q2. A U.S. firm (U.S.) and a foreign firm (F) engage in a plain-vanilla currency swap. The U.S. firm pays fixed in the FC and receives floating in dollars. The fixed rate at initiation and at the end of the swap was 5%. The variable rate at the end of year 1 was 4%, at the end of year 2 was 6%, and at the end of year 3 was 7%. At the beginning of the swap, $2 million was exchanged at an exchange rate of 2 foreign units per $1. At the end of the swap period the exchange rate was 1.75 foreign units per $1.

At the end of year 3, firm F will pay firm U.S.:

A)   280,000 foreign units.

B)   $140,000.

C)   $120,000.

Q3. A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. The value of the swap to the fixed-rate payer is closest to:

A)   $19,229.

B)   $15,633.

C)   $12,465.

The value of the swap to the fixed-rate payer is 10,113,580 – 10,097,947 = $15,633.

Q4. A U.S. firm (U.S.) and a foreign firm (F) engage in a plain-vanilla currency swap. The fixed rate at initiation and at the end of the swap was 5%. The variable rate at the end of year 1 was 4%, at the end of year 2 was 6%, and at the end of year 3 was 7%. At the beginning of the swap, $2 million was exchanged at an exchange rate of 2 foreign units per $1. At the end of the swap period the exchange rate was 1.75 foreign units per $1. At the end of year 1, firm:

A)   U.S. pays firm F 200,000 foreign units.

B)   F pays firm U.S. $200,000.

C)   U.S. pays firm F $200,000.

LOS c: Calculate and interpret the fixed rate on a plain vanilla interest rate swap and the market value of the swap during its life. fficeffice" />

Q1. If the one year spot rate is 5%, the two-year spot rate is 5.5%, and the three year spot rate is 6%, the fixed rate on a 3-year annual pay swap is closest to:

A)   1.99%.

B)   4.50%.

C)   5.96%.

Correct answer is C)

The fixed rate on the swap is: [1-(1/1.06³)]/[(1/1.05)+(1/1.055²)+(1/1.06³)]

=1-0.8396 / [0.9524 + 0.8985 + 0.8396]

=0.1604/2.6905 = 5.96%

Q2. A ffice:smarttags" />U.S. firm (U.S.) and a foreign firm (F) engage in a plain-vanilla currency swap. The U.S. firm pays fixed in the FC and receives floating in dollars. The fixed rate at initiation and at the end of the swap was 5%. The variable rate at the end of year 1 was 4%, at the end of year 2 was 6%, and at the end of year 3 was 7%. At the beginning of the swap, $2 million was exchanged at an exchange rate of 2 foreign units per $1. At the end of the swap period the exchange rate was 1.75 foreign units per $1.

At the end of year 3, firm F will pay firm U.S.:

A)   280,000 foreign units.

B)   $140,000.

C)   $120,000.

Correct answer is C)

A plain-vanilla currency swap pays floating on dollars and fixed on foreign. The floating rate cash flows on the settlement date are based on the previous period's ending floating interest rate 0.06 x $2,000,000 = $120,000.

Q3. A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. The value of the swap to the fixed-rate payer is closest to:

A)   $19,229.

B)   $15,633.

C)   $12,465.

Correct answer is B)

The fixed rate payments are 0.05 × (180/360) × 10,000,000 = 250,000. The present value of the remaining payments are 250,000/(1 + 0.05 × (90/360)) + 10,250,000/(1+ 0.054 × (270/360)) = $10,097,947.

The floating payment in 90 days is 0.048 × (180/360) = 240,000 and the present value is 240,000/(1 + 0.05/4) = $237,037. The second floating-rate payment combined with 1 at the end of the swap has a present value of 1 on the first payment date. The present value of 1 is 1/(1 + 0.05 × (90/360)) = 0.987654321 so the present value of the second floating rate payment combined with the principal amount is $9,876,543. The total value is 9,876,543 + 237,037 = $10,113,580.

The value of the swap to the fixed-rate payer is 10,113,580 – 10,097,947 = $15,633.

Q4. A U.S. firm (U.S.) and a foreign firm (F) engage in a plain-vanilla currency swap. The fixed rate at initiation and at the end of the swap was 5%. The variable rate at the end of year 1 was 4%, at the end of year 2 was 6%, and at the end of year 3 was 7%. At the beginning of the swap, $2 million was exchanged at an exchange rate of 2 foreign units per $1. At the end of the swap period the exchange rate was 1.75 foreign units per $1. At the end of year 1, firm:

A)   U.S. pays firm F 200,000 foreign units.

B)   F pays firm U.S. $200,000.

C)   U.S. pays firm F $200,000.

Correct answer is A)

A plain-vanilla currency swap pays floating on dollars and fixed on foreign. Fixed on foreign 0.05 × $2,000,000 × 2 foreign units per $1 = 200,000 foreign units paid by the U.S. firm.