Currency Swap

USD/MXN

Time			USD/MXN
Inception of the contract			$0.0893
180 days later			$0.0850

Term structure of interest rates: Inception of the contract

Time Period		U.S. Interest Rates	Mexican Interest Rates
360 days		4.0%	5.0%
720 days		4.5%	5.2%

Term structure of interest rates: 180 days later

Time Period		U.S. Interest Rates	Mexican Interest Rates
180 days		4.2%	5.0%
540 days		4.8%	5.2%

Currency swap

Item
Interest rates			USD fixed - MXN fixed
Maturity			2 years (720 days)
Notional principal			$100 million
Payment			annual

Fixed Rate

Time Period		USD payer	MXN payer
Inception		4.40% (*2)	5.07% (*1)
180 days later

(*1)
(1-1/(1+5.2%*720/360))/(1/(1+5.0%*360/360)+1/(1+5.2%*720/360))
= (1-1/(1+5.2%*2))/(1/(1+5.0%)+1/(1+5.2%*2))
= (1-1/1.104)/(1/1.05+1/1.104)
= 0.05069... = 5.07%

(*2)
f_USD,0 = (1-(1/(1+4.5%*720/360)))/((1/(1+4.0%*360/360)+(1/(1+4.5%*720/360)))
= (1-1/(1+9.0%))/(1/(1+4.0%)+1/(1+9.0%))
= 0.04394.. = 4.4%

Cash flows

Time Period		USD payer	MXN payer
Inception
In the middle			56.8 million (MXN) (**1)
Maturity

(**1) 100 million (USD) *5.07% / $0.0893(USD/MXN) = 56.8 million (MXN)

Present Value

Time Period		USD payment	MXN payment	Value to USD payer
Inception
180 days later		101.69 million (***1)	97.48 million USD (***2)	97.48 - 101.69 = -4.21 million USD

(***1)
4.4%*100/(1+4.2%*180/360)+(4.4%*100+100)/(1+4.8%*540/360)
=4.4/(1+2.1%)+104.4/(1+7.2%)
= 101.6975... = $ 101.69 million

(***2)
Z_{MXN,360D,t=180D} = 1/(1+5%*(180/360)) = 1/1.025
Z_{MXN,720D,t=180D} = 1/(1+5.2%*(540/360)) = 1/1.078

The present value of the fixed payments plus the principal is:
5.07% * 1 * (1/1.025+1/1.078) + 1*1/1.078 = 1.02413...  = 1.0241 (per 1 MXN)

Apply this to notional principal and convert at current exchange rate:
1.0241 (per 1 MXN) * 100 million (USD) / 0.0893 (USD/MXN) * 0.0850 (USD/MXN)
= 1.0241 * 100 / 0.0893 * 0.0850
= 97.4787234...= 97.48 million USD