Reading: Estimating the Cost of Capital

The first element of the CAPM-equation is the risk-free rate of return, \(R_F\).

What we are looking for are yields-to-maturity on zero-coupon (pure discount) government bonds. The assumption, of course, is that the probability of default on those bonds is zero. Consequently, there is no uncertainty about the average return the investor will earn when buying the bonds and holding them until maturity.

Current yields-to-maturity on riskless zero bonds (yields on riskless pure discount papers) are also known as current spot rates or current spot yields. You can think of the spot rates as the rates the market uses to compute the current value of future riskless cash flows. For each maturity, there is generally a different spot rate.  Hence, the risk-free rate depends on the maturity we are considering. The so-called term structure of interest rates plots the currency's yields by maturity.

Obtaining government bond yields

Government bond yields are fairly easy to obtain. Various online sources publish them in real time. For example Bloomberg, Marketwatch, Retuers, etc. A useful source is the website investing.com, which contains a comprehensive list of government bond yields by country and maturity. The following graph uses data from that website to illustrate the term structure of interest rates for Switzerland, Germany, the U.K., the U.S., and China with maturities up to 30 years:

Takeaways and practical recommendations

There are a few important takeaways from this graph:

• First, there is no such thing as the risk-free rate of return. For each country, yields differ by maturity. Bonds with short maturities generally have a lower yield than bonds with a long maturity. Consequently, the yield curve is typically upwards-sloping.
   
• This has implications for the estimation of discount rates:
   
  • In principle, we should use a different discount rate for different cash flow maturities to respect the term structure of interest rates.
     
  • In reality, the term structure of interest rates is often not very steep (similar yields on the short and the long end). Therefore, it is often acceptable to use an average discount rate that is the same for all cash flow maturities.
     
  • In firm valuation, the general practice is to approximate the risk-free rate with the yield to maturity of a 10-year government bond. As it turns out, equity often has a "duration" that is similar to a 10-year bond (it's cash flows approximately arrive at the same time as those of the bond).
     
  • In the context of project valuation, we should look at the duration of the project. The discount rate for a short-term project should rely on a short-term interest rate whereas for a long-term project, it makes sense to use a bond with longer maturity.

• Second, government bond yields also differ across currencies. As the graph above shows, the 10-year government bond yield was 3% in China and -0.3% in Switzerland in February 2019. There are two main reasons for such differences in yields:
    
  • First, countries and currencies differ in risk. Switzerland, for example, is often considered a safe haven for investors, with high social, political, legal, fiscal, and economic stability as well as a strong currency. Other countries might be considered less safe by investors.  A case in point could be Turkey, which is struggling with significant economic problems and therefore poses additional risks for investors. This is also reflected in the Turkey's government 10-year government bond yield, which was larger than 14% in February 2019.
     
  • Second, even if countries have similar solvencies and credit qualities, they might be exposed to different inflation environments. In fact, assuming identical risk, the difference in yields should be the result of differential inflation expectations for the respective currencies. This issue is discussed in more detail in the module "Cost of Capital and Valuation."

• Again, this has important practical implications for the estimation of the risk-free rate:
   
  
  • First, we should make sure to use bonds of governments that are, in fact, as close to risk-free as possible. Relating to the above example, the Turkish bond yield of >14% might be an inadequate starting point for the computation of discount rates, as this yield presumably contains a significant premium for the country's economic risks. Ideally, the country's credit rating should be AAA.
     
  • If we are valuing projects in a country with higher risk, it might make sense to express the whole project valuation in a more stable currency. In the context of the example of Turkey discussed above, one could value the project in question in EUR (using EUR-denominated cash flows and starting out with a euro-zone bond yield). Once we have the EUR-denominated project value, we could then adjust the resulting valuation for the specific political and economic risks that the project is exposed to. 
     
  • More generally speaking, whenever we estimate the cost of capital, we therefore have to make sure that we treat currencies consistently: For example, if the cash flows are denominated in U.S. dollar, we also have to estimate the discount rate based on U.S. dollar denominated assets!