When you use conventional risk and
return models (such as the CAPM, APM and multi-factor models)
to estimate costs of equity for a private firm, you will tend
to under estimate the risk in the firm. This is because these
models look at only the portion of the risk that is not diversifiable
and assume that the remaining risk will be diversified away.
To the extent that private business owners or the investors in
closely held firms are not diversified, they will be cognizant
of all risk (and not just the market risk). In fact, if you know
how much of the risk in the firm is market risk, you can compute
a modified beta for the CAPM:
Total Beta = Market Beta/ Correlation
between stock and the market
For a private business, both the
market beta and the correlation will have to come from looking
at publicly traded firms in the same business. For example, assume
that you have to estimate the cost of equity for a private software
firm. If the average market beta of software firms is 1.20 and
only 25% of the risk in software firms is from the market (correlation
with the market), the total beta for the software firm will be:
Total beta = 1.20/ .25 = 4.80
This total beta can be used to come
up with a much higher cost of equity for a private business.
As the owner of the private firm diversifies (either by taking
his firm into other business or by withdrawing some of his or
her wealth out of the business and investing in an index fund
or a pension fund), the total beta will decrease.
|