5. Putting Everything Together

Now we are ready to bring the various pieces together and estimate the cost of capital.

 

Since we have just analyzed the systematic risk of one specific company, Amazon, let us now stick to that company and use the results from the other sections to estimate Amazon's cost of capital. We have the following ingredients:

 

Variable Description Value
\(R_F\) Risk-free rate in the U.S.
(Yield of 10y Treasury bond)		 2.68%
\(MRP\) Market risk premium for the U.S.
(Median from Fernandez survey)		 5.00%
\(\beta_{Amazon}\) Beta coefficient of Amazon
(own regression estimate)		 1.17

   

According to the CAPM, Amazon's risk adjusted cost of capital, therefore, is 8.53%:

   

\(k_{Amazon} = R_F + \beta_{Amazon} \times MRP = 0.0268 + 1.17 \times 0.05 = 0.0853 = 8.53\% \)

   

In words: For the risk associated with the Amazon stock, our estimates imply that investors expect to earn a rate of return of roughly 8.53%. This return corresponds to the risk-free rate of 2.68% plus a risk premium of 5.85% to compensate investors for the systematic risk of the Amazon stock.

 

This is, in a nutshell, the basic logic behind discount rates.

 

Implementation issues

There are a few important implementation issues that we need to address briefly:

(1) Intervals, not point estimates

The discussion of the various ingredients of the cost of capital has shown that estimating these parameters is often not an exact science.

 

Put differently, we are not dealing with point estimates based which we can say that the market risk premium is exactly 5% and the beta of the stock is exactly 1.17. It could also be that the market risk premium is 5.3% (the average as opposed to the median survey value) and the beta of the stock is 1.71, as suggested by the internet platform Yahoo Finance at the time of this writing. Alternatively, it could also be that the market risk premium and the beta (and the risk-free rate) are smaller than the values that we have assumed.

  

Consequently, we should never treat valuation parameters as point estimates. We should treat them as variables that have a certain distribution around the values that we have estimated. For example, in the case of Amazon, the conclusion could be that with high confidence the firm's appropriate discount rate is somewhere between 7.5% and 9.5%.

 

By treating the key value drivers as intervals rather than point estimates, it follows that any serious valuation exercise will provide an interval estimate of project of firm value rather than a point estimate!

 

(2) The appropriate discount rate for what exactly?

The second implementation question is for what kind of projects exactly it would now be appropriate to use an average discount rate of 8.5% (to stick to the example of Amazon). The answer to that question is, unfortunately, a bit longer, so we discuss it in the following section.