1. International vs. Domestic Measures of the Costs of Capital

When trying to estimate the value of firms in comparatively small capital markets such as Switzerland, the problem is obtaining the information necessary to estimate the various costs of capital. There are often few data about the firm one wants to value, and comparable firms are also unavailable. The temptation is therefore to use data from foreign capital markets. The question is how to do so without making too many mistakes. This section provides a few answers.

In perfect capital markets, the same asset should generate the same real return (inflation-adjusted return) all around the world. This parity relation implies that, for any given asset, the difference between the (nominal) return in the home currency (H) and the foreign currency (F) is related to the difference in the expected inflation rates (\( \pi \)) of the two countries. 

This general rule applies to any asset, including the risk-free asset (\( R_F \)) and the firm's assets (\( k_A \)). We can write for the risk-free asset (\( R_F \)):

 

\( \frac{1+R_{F,H}}{1+R_{F,F}} = \frac{1+\pi_H}{1+\pi_F} \)

  

And for the expected return on the firm's assets:

 

\( \frac{1+ k_{A,H}}{1+k_{A,F}} = \frac{1+\pi_H}{1+\pi_F} \)

 

Since both equations are identical on their right side, also their left side must be identical. We can therefore write:

 

\( \frac{1+R_{F,H}}{1+R_{F,F}} = \frac{1+k_{A,H}}{1+k_{A,F}} \)


If we rearrange this expression slightly, we find that a firm's cost of capital, expressed in home currency (\( k_{A,H} \)), is related as follows to the cost of capital of an identical firm in foreign currency (\( k_{A,F} \)):

 

\( k_{A,H} = (1+k_{A,F}) \times \frac{1+R_{F,H}}{1+R_{F,F}} - 1 \)

 

As we have pointed out, this parity relation applies to the cost of capital of any asset. Let's first illustrate this logic with a numerical example that involves the firm's overall cost of capital (\( k_A \)).

 

Example: Suppose a Swiss pharmaceutical company wants to estimate the overall cost of capital (\( k_{A,H} \)) for peptide producers because it is planning a domestic acquisition in that industry. Given that reliable Swiss data are unavailable, the firm has estimated the \( k_{A,F} \) of a sample of U.S. firms. Its estimate is 8 percent, expressed in USD. The long-term risk-free rate in Switzerland is 2 percent (\( R_{F,H} \)), compared with 3 percent in the U.S (\( R_{F,F} \)). What is the implied domestic overall cost of capital (\( k_{A,H} \))?

The solution is to apply the equation above. Based on that, one can write:

  

\( k_{A,H} = (1+k_{A,F}) \times \frac{1+R_{F,H}}{1+R_{F,F}} - 1 = 1.08 \times \frac{1.02}{1.03} \) = 6.95%.

  

Often, a useful approximation of the above relation is to write:

 

\( k_{A,H} \approx k_{A,F}+ (R_{F,H} - R_{F,F})= 0.08 + (0.02 - 0.03) \) = 7%.

 

In words: The firm's  cost of capital in home currency is approximately equal to the foreign currency cost of capital, adjusted for the interest rate differential between the two currencies.

  

The above parity relation can also be useful to estimate the cost of debt from foreign comparables. As we have pointed out before, credit spread data are often only available for foreign comparable firms. We cannot directly add these credit spreads in foreign currency to the domestic risk-free rate of return, as the interest enviromenent might be fundamentally different. Instead, what we should do is the following:

  1. Measure the risk-free rate in the same currency as the available credit spreads (\( R_{F,F} \)).
  2. Add the credit spreads to the foreign currency risk-free rate to obtain the cost of debt in foreign currency (\( k_{D,F} \))
  3. Use the above parity relation to estimate the cost of debt in the home currency (\( k_{D,H} \)).

Let's look at this with a simple example. Suppose we want to estimate the cost of debt of a German manufacturing company with a credit rating of BB. We have collected the following information:

  • Risk-free rate in Germany (\( R_{F,H} \)): 1.0%
  • Risk-free rate in the U.S. (\( R_{F,F} \)): 2.5%
  • Credit spread associated with a BB rating in the U.S.: 3.25%

If the manufacturing company were based in the U.S., its cost of debt would be:

 

\( k_{D,F}=R_{F,F}+CS_F \) = 0.025 + 0.0325 = 5.75%.

 

From the theoretical considerations above, we know that the domestic and foreign currency cost of debt must be related as follows:

 

\( k_{D,H} = (1+k_{D,F}) \times \frac{1+R_{F,H}}{1+R_{F,F}} - 1 \)

 

Consequently, the home currency cost of debt of the German manufacturing company is 4.2%:

 

\( k_{D,H} = (1+k_{D,F}) \times \frac{1+R_{F,H}}{1+R_{F,F}} - 1 = 1.0575 \times \frac{1.01}{1.025}-1 \) = 4.20%.