Currency Swap

At the inception of the contract (0 day):

USD/MXN

Time			USD/MXN
0 day			$0.0893

Current term structure

Time		USD	MXN
360 days		4.0%	5.0%
720 days		4.5%	5.2%

Maturity = 2-year (fixed for fixed)
Payment = annual
Exchange of notional principal: at the beginning and end of the swap term
Notional principal: $100 million

[1] Annual fixed payments in MXN
To calculate the fixed payment in MXN, first use the Mexican term structure to derive the present value factors:

Z_{360(0 day),MXN} = 1/(1+5.0%*360/360) = 0.9524
Z_{720(0 day),MXN} = 1/(1+5.2%*720/360) = 0.9058

The annual fixed payment per peso of notional principal would then be:
SF(0,2,360) = (1-0.9058)/(0.9524+0.9058) = 0.0507

The annual fixed payment would be:
0.0507*$100 million*(1MXN/$0.0893) = 56.8 million MXN

---

Six months have passed (180 days):

USD/MXN

Time			USD/MXN
180 day passed (current)			$0.0850

Current term structure

Time		USD	MXN
180 days		4.2%	5.0%
540 days		4.8%	5.2%

[2] Present value of the dollar fixed payments for the two-year currency swap six months after the initial analysis

Z_{360(0 day),USD} = 1/(1+4.0%*360/360) = 0.9615

Z_{720(0 day),USD} = 1/(1+4.5%*720/360) = 0.9174

Fixed rate (USD, 0 day) = (1-0.9174)/(0.9615+0.9174) = 0.044

Z_{180(180day), USD} = 1/(1+4.2%*180/360) = 0.9794
Z_{540(180 day), USD} = 1/(1+4.8%*540/360) = 0.9328


0.044 * 100 * (0.9794+0.9328) + 100 * 0.9328 = $101.69 million




[3] Value of the 2-year currency swap from the perspective of the counterparty paying dollars six months after the initial analysis
Fixed rate (USD, 0 day) = 0.044
Fixed rate (MXN, 0 day) = 0.0507

Z_{180(180 day),MXN} = 1/(1+5.0%*180/360) = 0.9756

Z_{540(180 day),MXN} = 1/(1+5.2%*540/360) = 0.9276

The present value of the fixed payments plus the principal is:

0.0507*(0.9756+0.9276)+1*0.9276 = 1.0241 (per MXN)

Apply this to notional principal and convert at current exchange rate:

1.0241 (per MXN) * ($100 million/$0.0893)*$0.085

= 1.0241 * (100/0.0893)*0.085 = $97.48 million

The value of the swap is the difference between this value and the pay dollar fixed present value derived in the previous question:

$97.48 million - $101.69 million = 97.48 - 101.69 = -$4.21 million