2. Logic of the Module

What we are looking for is a relatively simple framework to estimate the discount rate. Let k denote that discount rate. As we will see, there is generally a trade-off between risk and return: If we want to earn a higher return, we generally have to accept more risk.

Readers who have already gained some experience with financial investments are well-aware of this fact. Allegedly, already Rockefeller has state that "you cannot get rich by saving." If you want to get rich, you have to move out of savings accounts and into riskier investments such as equities. For the additional risks of these assets, investors who hold them require a compensation in the form of a higher expected rate of return. 

Consequently, we are looking for an expression that looks as follows:

  

k = Risk-free Rate + Compensation for risk

  

In words:

  • The risk-free rate of return denotes the minimum rate of return that investors expect to earn.
  • For additional risks of an investment, investors require a compensation. That's the so-called Risk Premium.

 

The tricky part will be to estimate the compensation for risk. To tackle this challenge, it makes sense to break this risk compensation into two parts:

 

Compensation for risk = Amount of risk × Price of risk.

 

Consequently, we can write the expression for the discount rate k as:

 

k = Risk-free Rate + Amount of Risk × Price of Risk.

  

Example 1

Let's assume that the risk-free rate of return is 2% and that a "normal" project with one "unit" of risk earns a risk premium of 5%. Our task is to value a project that is twice as risky as the "normal" project. Consequently, it has 2 "units" of risk.

Based on this information, the discount rate for the project is 12%:

 

k = Risk-free Rate + Amount of Risk × Price of Risk = 0.02 + 2 × 0.05 = 0.12 = 12%.

 

 These introductory remarks have laid out the relevant dimensions that we need to know in order to estimate discount rates. Namely:

  • Return of a risk free asset
  • Riskiness of a project
  • Price of risk.

 

The module presents the necessary theoretical and practical framework to estimate discount rates. 

  • We start by looking at the basic trade-off between risk and return using real world data. This allows us to get to know a first risk measure, the standard deviation of the asset return. 
      
  • Second, we show how we can reduce the risk of our investments via portfolio diversification. We illustrate the basics of diversification with simple portfolios that only contain two assets (stocks and bonds).
     
  • Once we have established the basics of diversification, we move to portfolios with multiple assets. This allows us to cover the basic principles of "modern portfolio theory:"
    • The limits to diversification with risky assets (the so-called Efficient frontier)
    • The optimal portfolio choice when we can invest in risky and risk-free assets (the so called Capital Market Line).
  • Once we know the basics of portfolio theory, we can develop its implications for the estimation of discount rates. To this end, we introduce the Capital Asset Pricing Model (CAPM), which allows us to formalize the relation between the average expected return and the systematic risk of an asset.
     
  • We discuss how to estimate the CAPM in practice and what additional steps we usually have to take to identify the appropriate discount rate to value firms or projects, the so-called Weighted Average Cost of Capital (WACC).
     
  • The module ends with a comprehensive example that shows us how to estimate the WACC of a company for which we have no direct information about its systematic risk.