Currency Swap Valuation

Suppose that a global agriculture company needs to borrow BRL 100,000,000 (USD 32,000,000) for five years for its new manufacturing facility in Brazil, so it decides to enter into a fixed-for-fixed currency swap. Now, after two years, the company needs to evaluate the swap and find its current value. Given the currencies involved, what risks do you think it needs to assess?

You got it! In fact, it's both risks because interest rates and exchange rates impact the currency and notional value that's paid at the end of the currency swap.

Recall that a fixed-for-fixed swap can be evaluated by using two fixed-rate bonds, one in each currency (BRL and USD). Finding the value of its fixed-for-fixed interest rate swap after two years is simply taking the difference between the two bonds. But there's one issue with the bonds. What is it?

No, actually. The bonds are supposed to have different interest rates to make the cash flows equal throughout the swap period.

No. The notional values will be different to equalize the cash flows over the swap period.

You got it! The bonds are in different currencies, so simply taking the difference in price won't work. So the company will need to convert the USD bond to a BRL bond through a spot foreign exchange rate transaction. So the first step is to find the value of each bond, then, after converting the BRL bond, it will take both values times each notional amount at the initiation (for BRL it's 100,000,000, for USD it's 32,000,000) before finding the difference.

To sum it up: [[summary]]

$$\displaystyle V_{CS} = NA_{BRL} \left( r_{FIX,BRL} \sum^{n}_{i=1} PV_i(1) + PV_n(1) \right) - S_t NA_{USD} \left( r_{FIX,USD} \sum^{n}_{i=1} PV_i(1) + PV_n(1) \right)$$ The fixed rate BRL swap is $$\displaystyle r_{FIX,BRL}$$, and the summations represent present values of each spot interest rate. The present value of the last spot interest rate captures the notional amount at the close of the transaction. Note that the notional amount is indicated by _NA_ at the beginning of each bond value, so it doesn't need to be included within the equation. For the USD bond, the notations are the same, just in USD.

Interest rates

Exchange rates

They are in different currencies

They have different interest rates

They have different notional values

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