Question

German company and the swap dealer pays and receives under the swap contract that satisfies the following:

 The same swap dealer is involved in this currency swap with the US company and the German company.

 The US company’s net borrowing cost is 5.2% p.a. on $ and the German company’s net borrowing cost is 6.1% p.a. on €.

 The swap dealer pays and receives $ at 5.2% p.a.

(b) Suppose the US company has entered into a 5-year currency swap with the swap dealer regarding the swap mentioned above. The principal amounts are $15 million and €10 million. Suppose that the US company declares bankruptcy at the end of year 3 just before the exchange of payment, when the exchange rate is $1.6/€. What is the cost to the swap dealer in US dollars? Assume that, at the end of year 3, the risk free interest rate is 4% per annum in US dollars and 3% per annum in euros for all maturities. All interest rates are quoted with annual compounding. Assume that the theoretical forward exchange rates can be realized. Also assume there are 360 days in a year.

Hint: In the event of default at the end of year 3, the swap dealer will not receive cashflows from the US company nor pay cashflows to the US company. The cost of default to the dealer is the value of the swap to the swap dealer if the US company had not defaulted at Year 3.

Plz answer 2 sunb-question as a whole. thanks so much. will thumbsup if you did.

Answer 1

The swap dealer pays € at 6.1% p.a. and receives $ at 5.2% p.a.

Annual Payment by dealer = 6.1% x Euro notional principal amount = 6.1% x €10 million =  € 610,000

Annual receipt by dealer = 5.2% x Dollar notional principal amount = 5.2% x $ 15 million = $  780,000

Spot rate for year 3 payments swap, S = $1.6/€

Expected spot rate for year 4 payments swap = one year forward rate one year from now = S x (1 + r_$) / (1 + r_€) = 1.6 x (1 + 4%) / (1 + 3%) = $1.6155/€

Expected spot rate for year 4 payments swap = one year forward rate two years from now = S x (1 + r_$)² / (1 + r_€)² = 1.6 x (1 + 4%)² / (1 + 3%)² = $1.6312/€

Please see the table below. First column shows the three forward years for which swap are pending as of now. The swap was entered for a period of five years. Three payments are pending. We translate this into period in the next column. We are at a time period, just before swap of payment at the end of year 3. So this becomes period 0. Year 4 is one year away from now. Hence it becomes period 1 and so on. In year 3 & 4 only interest swaps are due. However in final year i.e. year 5, interest as well notional principal both are due. Exchange rates in the next column are the spot and expected spot rates we have calculated above.

Please refer to the second row to understand the mathematics. In the last column, we have discounted the periodic cash flows at $ cost of borrowing i.e 5.2%. The last row highlighted in yellow is your answer. Figures in parenthesis mean negative values.

End of year	Period	Nature	Payment by dealer (€)	Exchange rate ($ / €)	Equivalent $ amount ($)	Receipt by dealer ($)	Cash flow loss to dealer ($)	Discount factor @ $ interest rate of 5.2%	PV of cash flows lost ($)
t	n = t - 3		A	B	C = A x B	D	E = D - C	PV = (1 + 5.2%)^(-n)	E x PV
3	0	Interest	610,000	1.6000	976,000	780,000	(196,000)	1.0000	(196,000)
4	1	Interest	610,000	1.6155	985,476	780,000	(205,476)	0.9506	(195,319)
5	2	Interest + Notional Principal	10,610,000	1.6312	17,307,231	15,780,000	(1,527,231)	0.9036	(1,379,982)
		Total							(1,771,301)

Hence, the cost to dealer in $ = - $ 1,771,301

(Please try your answer with / without the minus sign if you have to input your answer in answer box)