### Required And Expected Returns: Very Different Concepts

University of Navarra – IESE Business School

University of Navarra

April 7, 2015

**Abstract: **

The expected return is different than the required return. We explain it for an investment project, for the valuation of a share of Coca-Cola and for the market risk premium.

However, there are many valuations that assume that the expected return is equal to the required return. Similarly, Expected Equity Premium (EEP) and Required Equity Premium (REP) are two very different concepts, although many books and financial literature do not distinguishing them. Both, the REP and the EEP differ for different investors.

The topic of this short paper (4 pages) is “thinking about valuation”: it is important to understand what we are doing.

### Required And Expected Returns: Very Different Concepts – Introduction

**1. An investment project**

Table 1 contains investment project A. The equity investment required today (year 0) is $100 million. The expected cash flows for the next 3 years are $30, $40 and $50 million.

The internal rate of return (IRR) of these expected cash flows is 8.9%. Obviously, 8.9% is the expected return of project A.

The company requires a 10% return for project A (and for all projects with risks similar to those of project A). The Net present value (NPV) of the expected cash flows of project A using the 10% (the required return) is – $2.1 million. The NPV is negative because the required return is higher than the expected return.

It is obvious that the expected return is different than the required return. And it is also obvious that different persons may have different expected returns (different expected cash flows) and different required returns for investment project A.

**2. Shares of Coca-Cola**

Table 2 contains the valuation of a share of Coca-Cola’s common stock according to a financial analyst. The expected Equity Cash Flows of the analyst are in line 1. The required return to equity of the analyst is 7.76%. Lines 2 and 3 show how the analyst values each share of Coca-Cola at $51.56.

The current price of the share is $40.08. The internal rate of return (IRR) of the current price ($40.08) and the expected cash flows of line 1 is 9.88%. Obviously, 9.88% is the expected return of “buying a share of Coca-Cola” according to the analyst.

The analyst gets a value ($51.56 / share), higher than the current market price ($40.08 / share) because his required return (7.76%) is smaller than his expected return (9.88%)

It is obvious that the expected return (9.88%) is different than the required return (7.76%). And it is also obvious that different persons may have different expected returns (different expected cash flows) and different required returns for the shares of Coca-Cola.

**3. Market risk premium (MRP)**

The equity premium (also called market risk premium, equity risk premium, market premium and risk premium) is an important, but elusive, parameter in finance. Some confusion arises from the fact that the term equity premium is used to designate different concepts1.

Two of these are:

1. Expected Equity Premium (EEP): expected differential return of the stock market over treasuries.

2. Required Equity Premium (REP): incremental return of the market portfolio over the risk-free rate required by an investor in order to hold the market portfolio2. Many people use it for calculating the required return to equity (Ke).

The two concepts are different. The REP and the EEP are different for each investor and are not observable magnitudes.

The Expected Equity Premium (EEP) is the answer to a question we would all like to answer accurately in the short term, namely: what incremental return do I expect from the market portfolio over the risk-free rate over the next years? Numerous papers and books assert that there must be an EEP common to all investors (to the representative investor). Without “homogeneous expectations” there is not one EEP (but several), and there is not one REP (but several).

The CAPM is a useless attempt3 to calculate the EEP. However, many books, analysts… use it to calculate the REP. However, some authors assume that 1) EEP = REP [for example, Brealey and Myers (1996); Copeland et al (1995); Ross et al (2005); Stowe et al (2002); Pratt (2002); Bodie et al (2003); Damodaran (2006); Goyal and Welch (2007); Ibbotson Ass. (2006)]; and that 2) There is a unique EEP [for example, Damodaran (2001a); Arzac (2005); Jagannathan et al (2000); Harris and Marston (2001); Claus and Thomas (2001); Fama and French (2002); Goedhart et al (2002); Harris et al (2003)].

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