A Five-Year Currency Swap Involves Two AAA Borrowers and Has

Question

Examlex · Accepted Answer

The Answer is a. The new value of the swap is derived by considering the market value of two streams of cash flows:

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P_$: a bond in dollars with four years remaining, with annual cash flows of $10 million, and a principal repayment of $100 million;

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P_AUD: a bond in Australian dollars with four years remaining, with annual cash flows of AUD
14 million, and a principal repayment of AUD 200 million.
The swap to receive AUD and pay dollars is worth in AUD:
Swap= P_AUD (6%)- spot AUD/$ * P_$ (8%).
Swap =

\left( \frac { 14 } { 1.06 } + \frac { 14 } { 1.06 ^ { 2 } } + \frac { 14 } { 1.06 ^ { 3 } } + \frac { 214 } { 1.06 ^ { 4 } } \right) - 1.9 \left( \frac { 10 } { 1.08 } + \frac { 10 } { 1.08 ^ { 2 } } + \frac { 10 } { 1.08 ^ { 3 } } + \frac { 110 } { 1.08 ^ { 4 } } \right)

Swap = 206.93 - 1.9 (106.63) = AUD 4.34 million.
The U.S. dollar value of the swap is 4.34/1.9 = $ 2.28 million.
Of course, the seller of this swap who receives dollars for Australian dollars will realize a corresponding loss.
b. Without further information, we can assume that the value of a bond with a floating rate stays constant. Therefore, the swap value will change only because of a change in the AUD interest rate and a change in the exchange rate. This second swap is now worth:
Swap = 206.93 - 1.9 (100) =AUD 16.93 million.
Swap =$ 8.91 million.

A Five-Year Currency Swap Involves Two AAA Borrowers and Has

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