Consider a currency swap between a financial institution and a company. Under th
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Question
Consider a currency swap between a financial institution and a company. Under the terms of the swap, the financial institution receives interest at 3% per annum in EUR and pays interest at 7% per annum in USD. The principal amounts are 7 million USD and 6 million EUR. Interest payments are exchanged once a year. The swap has 4 remaining exchanges. The current exchange rate between EUR and USD is 1.10 (USD per EUR). The continuous compounded risk-free interest rate is 3.5% per annum in EUR and 7.5% per annum in USD for all maturities. Note: You can present all calculations in million dollars for simplicity. A. Find the value of the swap (in USD) using the forward exchange rates (Method 1). B. Find the value of the swap (in USD) using the bond valuation (Method 2). Verify that your answer is identical to the answer in (A).
Explanation / Answer
A. VALUE OF BOND USING FORWARD RATES
Under the Forward rate valuation method, we first calculate the forward rates for each of the due dates. Then the periodical payment and receipt amount are calculated in the domestic currency (here the USD) based on the forward exchaneg rates. Then the PV of these amounts is calculated based using Domestic risk free rate as the discount rate.
1. Calculate the forward rates.
Forward Raten = Spot Rate x (1+ Risk free rate of dosmestic currency)n / (1+ Risk free rate of foreign currency)n, where:
n = time period in years (here 1 to 4 years)
domestic currency = USD and
Foreign currency = EUR
FR(n=1) = 1.10 x (1+0.075)1 / (1+0.035)1 = 1.14 USD/ EUR
similarly FR(n=2) = 1.19 USD/ EUR,
FR(n=3) = 1.23 USD/ EUR, and
FR(n=4) = 1.28 USD/ EUR
2. Calculate the value of payment and receipt leg based on forward rates calulated above:
In the above table, following formulas are used:
Payment Amount in USD = 7% of USD 7 mn = USD 490,000
Receipt amount in EUR = 3% of EUR 6 mn = EUR 180,000
Receipt amount in USD = EUR amount (t=n) * FR(t=n)
PVF is calculated based on USD risk free rate as all the payments and receipts (after conversion) are in USD amount. PVF(t=n) = 1/ (1+Rf)n
3. Calculate Value of Swap:
Value of swap = Value of receipt leg - value of payment leg
= 726980-1641170 = - USD 914,190
B. VALUE OF SWAP USING BOND VALUATION:
Under bond valuation method, the PV of each leg is calculated based on the respective cash flow currency. The present value of foreign currency leg is then coverted into domestic currency using the Spot exchange Rate.
1. Calculate the present value of payment and receipt in the respective currency:
Here, the discount rates used are: USD risk free rate for the payment leg and EUR risk free rate for receipt leg as all payments and receipts are in USD and EUR respectively.
2. Calculate the value of Swap:
Value of Swap = (PV of Receipt leg in EUR * Current Exchange Rate) - (PV of payment leg)
= (661,154*1.10) - 1,641,170 = - USD 913,900
The answer as per method 2 (USD 913,900) is identical to the answer as per method 1 (- USD 914,190), with a difference of only $290.
Payment = 7% pa on USD 7 million Receipt = 3% pa on EUR 6 mn Year Amount (in USD) PVF @ 7.5% PV Year Amount (in EUR) Amount (in EUR)* PVF @ 7.5% PV 1 490,000 0.9302 455,814 1 180,000 205,200 0.9302 190,884 2 490,000 0.8653 424,013 2 180,000 214,200 0.8653 185,354 3 490,000 0.8050 394,431 3 180,000 221,400 0.8050 178,218 4 490,000 0.7488 366,912 4 180,000 230,400 0.7488 172,524 Total 1,641,170 *converted using above calculated forward rates 726,980Related Questions
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