How does the exchange rate impact the liability of companies that have borrowed in foreign currencies like the US Dollar?

It is always best to understand currency risk with a real example. Assume that Trent Ltd had borrowed a 1 year loan of $5 million through Foreign Currency Bonds at 5% interest. You can also assume that when this loan was taken on Jan 01^st the INR was at 63.30/$ and when the loan is repaid after 1 year, the INR is at 69.20/$. Check the table below:

Now when you look at the table above you realize the cost that the currency imposes on the borrower. This risk is always there because the rupee has been consistently weakening against the dollar over the last many years. Normally, when companies borrow in dollars, they hedge with a forward cover or in the USDINR futures market or even in the options market subject to liquidity being available. Had the company not taken the forex cover, then the actual rupee interest cost would have been 14.32% instead of 5% after considering the currency effect. In other words the currency risk has added 9.32% to your cost of borrowing.

To cut a long story short, the currency value has a deep impact on markets. Economists argue that weak rupee encourages exports and solves a lot of problems. Btu that argument has hardly worked for India. India has always been a net importer and also a net borrower in foreign currency and hence weak rupee has always worked against the Indian corporates.