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Required Rate of Return Formula
| Add a risk component to the
risk-free rate to determine Ke the total required rate of return. |
|
Ke = Rf + b (Km - Rf)
| Where: |
|
| Ke = Required rate of return |
|
| Rf = Risk-free rate |
|
| B = Beta coefficient |
|
| Km = Expected return for common stocks in the market |
|
| (Km-Rf) = Equity risk premium (ERP) |
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| The risk-free rate, in
practice is normally assumed to be the return on U.S. Treasury bills. Beta measures
individual company risk against market risk (usually the S & P 500 Stock Index).
Companies with betas greater than 1.00 have more risk than the market, companies with
betas less than 1.00 have less risk than the market, and companies with betas equal to
1.00 have the same risk as the market. It stands to reason then that high beta stocks (b
> 1.00) would have higher required returns than the market. |
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| The last term (Km - Rf),
the equity risk premium (ERP), is very difficult to observe because it represents the
extra return or premium the stock market must provide compared with the rate of return an
investor can earn on Treasury bills. Checking out the the historical relationship between
stocks and bills we see that large stocks have returned an average of 10.2 percent over
the period of 1926-1994, and Treasury bills have return an average of 3.7 percent over the
same time. This indicates a risk premium of 6.5 (that is 10.2 percent less 3.7 percent).
Since Km is not observable from the market, an analyst calculating Ke usually
uses (Km-Rf) as the one number which expresses the equity risk premium (ERP). |
|
| The time from 1926 to 1994 is
a very long period that included some extreme events such as the Depression of the 1930s,
World War II, the Vietnam War, and the inflation of the 1970s. Nevertheless, it is a good
starting point. For most of the post-World War II period, the normal equity risk premium
has been between 5.5 and 6.5 percent, depending on the risk perceived by investors. When
investors are more risk averse (pessimistic) the ERP tends to be higher, and when
investors are less risk averse (optimistic), the ERP is lower. |
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| The following example computes the
required rate of return for a sample company. The company's beta is 1.17, the Treasury
bill rate is 5 percent. If we assume that a normal equity risk premium (ERP) is 6 percent,
we should have a required return as follows: |
|
Ke = Rf
+ b(ERP) |
|
|
Ke = 5% = 1.17 (6%) |
|
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Ke = 5% + 7.02% |
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Ke = 12.02% |
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| Ke, the required rate
of return, can be used as a discount rate for future cash flows from an investment. This
methodology is valuable as you work through the dividend valuation models for common
stock. |
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