Valuation in another currency: Exchange rate forecast x Country Risk

This is a topic about cross border valuation. If you are making a valuation of a company in a country, but want to discount the cash flows using a WACC in your own currency, you need to convert the forecasted cash flows to your own currency, and for that you need to forecast the evolution of the exchange rate. Why does it make sense to discount the cash flows using a WACC in your own currency? It makes sense when you have a more developed capital market and can best assume it is an efficient market. This premise is very important to me, so even if I'm not making a cross border valuation, but I'm in an emergent country, I prefer to convert all the cash flows forecast to US Dollars.

So... the point is: How to best forecast the evolution of exchange rates? Well... many authors suggest us to consider the purchansing power parity theory and that the real intrest rate i the same around the world. With this assumptions, the exchange rate varies according to the differential of inflation between countries. In this case we should add the country risk to the CAPM cost of equity.

But I argue something: If we assume that currency forward contracts are the best market estimation for the exchange rate in the future, we should consider the differential of nominal rates between countries, and not only the inflation. Remember thar F = S x (1+r1) / (1+r2), where r1 and r2 are nominal rates. We know that consistently the real interest rates paid by emerging countries is higher than by developed countries, so this premises doesn't fit. We can say that this extra yield paid is the country risk and it is being considered on the CAPM cost of equity. However I'll show later that going to some real data usign this methodology we are creating some anomalies. If we have a good cash flow forecast in local currency, if we hedge our cashflows to our currency with forward contracts, we are assuming that the evolution of exchange rates is based on differential of nominal rates. In this case we shouldn't use the country risk factor on the CAPM cost of equity as we will see next.

Consider the following data taken from the market on 01/12/2009 (approximate figures):

1o year yields:

Brazilian Real:
Nominal rate 13.5%
Expected Inflation 5%
Risk Free rate 8.1% (from the other 2 numbers)

US Dollar:
Nominal Rate 3.2%
Expected Infation 2%
Risk Free rate 1.18% (from the other 2 numbers)

Present excange rate: 1.7 BRL/USD

Brazilian Global Bond 4.2%
Country Risk 0.97% (taken from the difference between US Treasury and US Dollar denominated Brazilian Global Bond)

If we consider that the evolution of the exchange rate is based on differential of inflation, in 10 years it would be 2.27 BRL/USD. If we have one dollar to invest in Brazil, we convert today to 1.7 BRL, invest yielding 13.5% and in the end of 10 years I get back my dollar converting using the 2.27 exchange rate. It yelds a return of 10.26%, much higher than the yield paid by the US Treasuries plus the Country Risk. We created arbitrage opportunities.

However, if we consider the forward contracts premise, we would convert back my dollars using an exchange rat of 4.4 BRL/USD, after hedging my cash flows. This yields 3.2%, exactly the yield paid by the US Treasuries. In this case we don't have to add the Country Risk premium to the CAPM cost of equiy, as it was already incorporated in the differential of real interest rates considered before.

So, my advice is... Exchange rates based on currency forward contracts and no countyr risk premium.