Can anyone explain to me how the answer to this question was calculated (or why it is calculated this way)? I cannot seem to see the logic behind it.
90 days ago the exchange rate for the Canadian dollar (C$) was $0.83 and the term structure was:
180 days
360 days
LIBOR
5.6%
6%
CDN
4.8%
5.4%.
A swap was initiated with payments of 5.3% fixed in C$ and floating rate payments in USD on a notional principal of USD 1 million with semiannual payments.
90 days have passed, the exchange rate for C$ is $0.84 and the yield curve is:
90 days
270 days
LIBOR
5.2%
5.6%
CDN
4.8%
5.4%
What is the value of the swap to the floating-rate payer?
A) $10,126. B) −$2,708. C) $3,472.
Your answer: C was incorrect. The correct answer was A) $10,126.
The present value of the USD floating-rate payment is:
(1.028 / 1.013) = 1.014808 1.014808 × 1,000,000 = $1,014,808
The present value of the fixed C$ payments per 1 CDN is:
(0.0265 / 1.012) + (1.0265 / 1.0405) = 1.012731 and for the whole swap amount, in USD is 1.012731 × 0.84 × (1,000,000 / 0.83) = $1,024,932
−1,014,808 + 1,024,932 = $10,126