In my last three posts, I have looked at country risk, starting with measures of that risk and then moving on to valuing and pricing that risk. You may find it strange that I have not mentioned currency risk in any of these posts on country risk, but in this one, I hope to finish this series by looking first at how currency choices affect value and then at the dynamics of currency risk.

**Currency Consistency**

A fundamental tenet in valuation is that y__ou have to match the currency in which you estimate your cash flows with the currency that you estimate the discount rate that you use to discount those cash flows__. Stripped down to basics, the only reason that the currency in which you choose to do your analysis matters is that different currencies have different expected inflation rates embedded in them. Those differences in expected inflation affect both our estimates of expected cash flows and discount rates. When working with a high inflation currency, we should therefore expect to see higher discount rates and higher cash flows and with a lower inflation currency, both discount rates and cash flows will be lower. In fact, we could choose to remove inflation entirely out of the process by using real cash flows and a real discount rate.

*Currencies and Discount Rates*

There are two ways in which you can incorporate the expected inflation in a currency into the discount rate that you estimate in that currency. The first is through the risk free rate that you use for the currency, since higher expected inflation should result in a higher risk free rate. The second is by converting the discount rate that you estimate in a base currency into a discount rate in an alternate currency, using the differential inflation between the currencies.

[drizzle]* a. Risk free rate*

A risk free rate is more than just a number that you look up to estimate discount rates. In a functioning market, investors should set the risk free rate in a currency high enough to cover not only expected inflation in that currency but also to earn a sufficient real interest rate to compensate for deferring consumption.

Risk free rate in a currency = Expected inflation in that currency + Real interest rate

The risk free rate should therefore be higher in a high-inflation currency than using that higher rate should bring inflation into your discount rate.

But how do we get risk free rates in different currencies? While most textbooks would suggest using the rate on a government bond, denominated in the currency in question, that presumes that governments are default free and that the government bond rate is a market-determined rate. However, governments are not always default free (even with local currency borrowings) and the rate may not be market-set. In July 2015, I started with the government bond rates in 42 currencies and cleansed them of default risk by subtracting out the sovereign default spreads (based on local currency sovereign ratings) from them to arrive at risk free rates in these currencies, which you can find in the table below:

Note that the default spread is set to zero for all Aaa rated governments, and the government bond rate becomes the risk free rate in the currency. Thus, the risk free rates in US dollars is 2.47% and in Swiss Francs is 0.16%. To compute the risk free rate in $R (Brazilian Reais), I subtract out my estimate of the default spread for Brazil (1.90%, based on its Baa2 rating) from the government bond rate of 12.58% to arrive at a risk free rate of 10.68%. To estimate a cost of equity in nominal $R for an average risk company with all of its operations in Brazil, you would use the 10.68% risk free rate in $R and the equity risk premium of 8.82% that I reported in my last post to arrive at a cost of equity of 19.50% in $R. That number would be higher for above-average risk companies, with a beta operating as your scaling mechanism.

*b. Differential inflation*

There are two problems with the risk free rate approach. The first is that it not only requires that you be able to find a government bond rate in the currency that you are working with, but also that the rate be a market-determined number. It remains true that in much of the world, government bond rates are either artificially set by governments or actively manipulated to yield unrealistic values. The second is that you are adding equity risk premiums that are computed in dollar-based markets (since the default spreads that they are built upon are from dollar-based bond or CDS markets) to risk free rates in other currencies. You could legitimately argue that the equity risk premium that you add on to a $R risk free rate of 10.68% should be higher than the 8.82% that you added to a US $ riskfree rate of 2.25% in July 2015.

If the differences between currencies lies in the fact that there are different expectations of inflation embedded in them, you should be able to use that differential inflation to adjust discount rates in one currency to another. Thus, if the cost of capital is computed in US dollars and you intend to convert it into a nominal $R cost of capital, you could do so with the following equation:

To illustrate, if you assume that the expected inflation rate in $R is 9.5% and in US $ is 1.5%, you could compute the cost of equity in US$ and then adjust for the differential inflation to arrive at a cost of equity in $R:

*Cost of equity for average risk Brazilian company in US $ = 2.25% + 8.66% = 10.91%*

The cost of equity of 19.65% that we derive from this approach is higher than the 19.50% that we obtained from the risk free rate approach and is perhaps a better measure of cost of equity in $R.

This approach rests on being able to estimate expected inflation in different currencies, a task that is easier in some than others. For instance, getting an expected inflation rate in US dollars is simple, since you can use the difference between the 10-year T.Bond rate and the TIPs (inflation-indexed) 10-year bond rate as a proxy. In other currencies, it can be more difficult, and you often only have past inflation rates to go with, numbers that are prone to government meddling and imperfect measurement mechanisms. Notwithstanding these problems, I report inflation rates in different countries, using the average inflation rate from 2010-2014 for each country.

I also report the inflation rate in 2014 and the IMF expectations for inflation (though I remain dubious about their quality) for each country.

*Currencies and Cash Flows*

Following the currency consistency principle is often easier with discount rates, where your inflation assumptions are generally either explicit or easily monitored, than it is with cash flows, where these same assumptions are implicit or borrowed from