Question

You enter into a 3-year fixed-for-fixed currency swap, such that the cash-flow stream you are paying is in U.S. dollars and the cash-flow stream you are receiving is in euros. The swap contract is based on a notional principal of $1 million. The contract is an at-market swap, the swap rates are 4.13% for dollars and 2.96% for euros, and the spot exchange rate is €1 = $1.23 $/ at origination? a. What will be your cash flows in each of the next three years? (Assume the notional principal is exchanged in four years as well as annual payments) b. Immediately after the second annual payment-exchange, you want to terminate the contract. At that time, 1-year interest rates are 4.96% for dollars and 5.18% for euros, and the exchange rate is €1= $1.29. What should you receive (or pay) upon termination? (That is, how much is the contract now worth?)

Answer 1

Part(a)

Notional principal in Euro = $ 1 mn converted at exchange rate (of 1 Euro = $ 1.23) = 1 / 1.23 = Euro 0.8130 mn

In each of the next three years,

• you will pay interest in US dollars term. So, cash outflow from you each year = I_US$ x P_US$ = 4.13% x $ 1 mn = $ 0.0413 mn
• You will receive interest in Euros. So, cash inflow for you each year = I_Euro x P_Euro = 2.96% x Euro 0.8130 mn = Euro 0.0241 mn

Part(b)

Please see the table below. We have to find the NPV of the balance inflows and outflows at the end of year 2.

The final answer is highlighted in yellow colored cell. Please see the last column "How it has been calculated?". That will help you understand the mathematics in each step.

Initially		Year 3	Year 4	Calculated as
Now		Year 1	Year 2	Two years have passed by
Pay interest	$ mn	0.0413	0.0413	Interest you pay as calculated in part (a) - A
[+] Pay principal	$ mn		1	Notional Principal is also swapped - B
Total Cash flows	$ mn	0.0413	1.0413	C = A + B
Interest rate now		4.96%	4.96%	D
PV factor		0.9527	0.9077	(1+D)-1 and (1+D)-2
PV of outflows	$ mn	0.0393	0.9452	E = D x PV factor
Total PV of outflows	$ mn	0.9846		F = Sum of E
Receive interest	Euro mn	0.0241	0.0241	Interest you receive as calculated in part (a) - G
Receive Principal	Euro mn		0.8130	Notional Principal is also swapped - H
Total Cash flows	Euro mn	0.0241	0.8371	I = G + H
Interest rate now		5.18%	5.18%	J
PV factor		0.9508	0.9039	(1+J)-1 and (1+J)-2
PV of inflows	Euro mn	0.0229	0.7567	K = I x PV factor
Total PV of inflows	Euro mn	0.7795		L = Sum of K
Exchange rate	Euro 1 = __$	1.29		M
Total PV of inflows	$ mn	1.0056		N = L x M
Receive	$ mn	0.0210		N - F

Hence, you should receive $ 0.0210 mn upon termination.