Question

You are going to be paid 500,000 CHF (Swiss francs) in one year, but you would prefer dollars. If you wish to hedge your exchange rate risk on this transaction using a forward market hedge, how many Swiss francs should you borrow (or lend) today to set up your hedge? The exchange rate from one year ago is $1.035 per CHF, the current exchange rate is $0.992 per CHF, and your dollar cost of debt is 5.6%. Represent borrowing as positive numbers, lending as negative numbers

Answer 1

Solution:

A year from now, we expect to receive 500,000 CHF. We will convert the CHF into $ at the prevailing spot rate and use it to repay a loan with interest we will take in the present.

So we need to estimate the spot rate a year from now but we only have the current spot rate and a rate from one year ago.

One year ago rate: $1.035 per CHF and Spot rate: $0.992 per CHF

Assuming this trend to continue a year from now i.e. the CHF depreciates by:

$0.992 x (1.035 - 0.992) / 1.035

= $0.992 x 0.041546

= $ 0.041

So the estimated spot rate would be $0.992 - $ 0.041 = $ 0.951 per CHF

We would thus convert the 0.50 million CHF @ 0.951 to receive $ (500,000 x 0.951) = $ 475,500

This would be used to repay the loan we take at present with interest @5.6%

So the present value / principal of the loan is $475,500 / (1 + 0.056) = $ 450,284

Hence, we have to take a dollar loan of $450,284 to set up the hedge.