There was a time in the not so distant past, where analysts could do their analysis in their local currencies and care little or not at all about foreign currencies, how they moved and why. This was particularly true for US analysts in the last half of the last century, where the US dollar was the unchallenged global currency and the US economy bestrode the world. Those days are behind us and it is almost impossible to do valuations or corporate financial analysis without understanding how to deal with currencies correctly. Since the perils of misplaying currencies can be catastrophic, I decided to spend this post getting up to speed on the basics of how currency choices play out in valuation and where the numbers stand at the start of 2017.

### A Currency Primer in Valuation

In intrinsic valuation, the value of an asset is the expected cash flows on that asset, discounted back at a risk adjusted discount rate.

Note that there is no currency specification in the DCF equation and that analysts are given a choice of currencies. So, what currency should you use in valuing a company? While some analysts view this choice rigidly as being determined by the country in which the company operates in or the currency that it reports its financial statements in, there are two basic propositions that govern this choice.

- The first is that currency is a measurement mechanism and that you should be able to value any company in any currency, since all it will require is
__restating cash flows, growth rates and discount rates in that currency__. - The second is that in a robust DCF valuation,
__your value should be currency invariant__. Put differently, the value of Petrobras should be unchanged, whether you value the company in nominal Brazilian Reais ($R), US dollars or Euros.

The second proposition may strike some as impractical, since risk free rates vary across currencies and some currencies, like the $R, have higher risk free rates than others, like the US dollar. But the key to understanding currency invariance is recognizing that currency choices affect both your cash flows and your discount rate and if you are being consistent about your currency estimates, those effects should cancel out.

Intuitively, picking a high inflation currency will lead to higher discount rates but also to higher cash flows and growth rates. In fact, if the currency effect is a pure inflation effect, you can see very quickly that you could make your valuation currency-free by doing your entire analysis in real terms, where you cash flows reflect only real growth (without the boost offered by inflation) and your discount rate is built on top of a real risk free rate. Your value should be again equivalent to the value you would have obtained by using the currency of your choice in your valuation.

To make these estimation choices real, consider valuing a company that derives half its cash flows in the United States (in US dollars) and half in Brazil (in nominal $R). You can value the company in US dollars, and to do so, you would have to estimate its cost of capital in US $ and convert the portion of its cash flows that are in $R to US$ in future years; that would require forecasting exchange rates. Alternatively, you can value the company in $R, converting the portion of cash flows in US$ to $R and then estimating a cost of capital in $R. This may sound simple, even trivial, but a whole host of estimation challenges lie in wait.

### Expected Exchange Rates

If you want to make your valuations currency invariant, and inflation is what sets currencies apart, the way to estimate expected future exchange rates is to assume purchasing power parity, where exchange rates move to capture differential inflation. Specifically, you can get from the current exchange rate of local currency (LC) for the foreign currency (FC) to an expected exchange rate in a future year (t) using the expected inflation rates in the two currencies:

Simply put, if the inflation in the local currency is 5% higher than the inflation in the US$, you are assuming that the local currency will depreciate about 5% a year. I know that exchange rate movements deviate from purchasing power parity significantly over short and perhaps even extended periods and that expected inflation can be difficult to estimate in many currencies, but there is a simple reason why you should stick with this simplistic way of forecasting exchange rates, at least when it comes to valuation. First, it is far easier (and less expensive) that creating a full-fledged exchange rate forecasting model or paying a forecaster, especially because you have to forecast exchange rate changes over very long time periods. Second, it forces you to be explicit about your inflation expectations and by extension, at least be aware of inconsistencies, where you assume one measure of inflation for exchange rates (and cash flows) and another for discount rates. (You can use forward exchange rates for the near years, as long as you are willing to then use interest rate differentials as proxies for inflation differentials.)

But what if you have strong views on the future direction of exchange rates that deviate from inflation expectations? I would argue that you should not bring them into your company valuations for a simple reason. If you incorporate your idiosyncratic exchange rate forecasts into cash flows and value, your final valuation of a company will be a joint consequence of your views on the company and of your views on exchange rates, with no easy way to separate the two. Thus, if you expect the Indian rupee to appreciate over the next five years, rather than depreciate (given your expectations of inflation in the rupee), you will find most Indian companies that you value to be cheap. If that conclusion is being driven by your exchange rate views, why invest in Indian companies when there are far easier and more profitable ways of playing the exchange rate game?

### Currency Costs of Capital

Let’s start with the challenge of estimating costs of capital in different currencies. There are two general approaches that you can use to get there. One is to compute the cost of capital in a currency from the ground up, starting with a risk free rate and then estimating and adding on risk premiums to arrives at costs of equity, debt and capital. The other is to compute the cost of capital in a base currency (say the US dollars) and then converting that cost of capital to the local currency.

*Currency Risk Free Rates*

Every economics student, at some point early in his or her education, has seen the Fisher equation, where the nominal interest rate is broken down into an expected inflation component and an expected real interest rate:

Nominal Interest Rate = Expected Inflation + Expected Real Interest Rate

Note that this is neither a theory nor a hypothesis, but a truism, if you add no constraints on either the expected inflation and real interest rate. It is also a powerful starting point for