## In Practice Risk Cost of Equity and Private Firms

Implicit in the use of beta as a measure of risk is the assumption that the marginal investor in equity is a well diversified investor. While this is a defensible assumption when analyzing publicly traded firms, it becomes much more difficult to sustain for private firms. The owner of a private firm generally has the bulk of his or her wealth invested in the business. Consequently, he or she cares about the total risk in the business rather than just the market risk. Thus, for a business like Bookscape, the beta that we have estimated of 0.82 (leading to a cost of equity of 7.73%) will understate the risk perceived by the owner of Bookscape. There are two solutions to this problem:

1. Assume that the business is run with the near-term objective of sale to a large publicly traded firm. In such a case, it is reasonable to use the market beta and cost of equity that comes from it.

2. Add a premium to the cost of equity to reflect the higher risk created by the owner's inability to diversify. This may help explain the high returns that some venture capitalists demand on their equity investments in fledgling businesses.

Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively simple one, since the R squared of the regression measures the proportion of the risk that is market risk. Dividing the market beta by the square root of the R squared (which is the correlation coefficient) yields a total beta. In the Bookscape example, the regressions for the comparable firms against the market index have an average R squared of about 16%. The total beta for Bookscape can then be computed as follows:

Total Beta =

Market Beta 0.82

-^R squared

Using this total beta would yield a much higher and more realistic estimate of the cost of equity.

Cost of Equity = 4% + 2.06 (4.82%) = 13.93% Thus, private businesses will generally have much higher costs of equity than their publicly traded counterparts, with diversified investors. While many of them ultimately capitulate by selling to publicly traded competitors or going public, some firms choose to remain private and thrive. To do so, they have to diversify on their own (as many family run businesses in Asia and Latin America did) or accept the lower value as a price paid for maintaining total control.

## Lessons From The Intelligent Investor

If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.

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