The art (or is it science?) of company valuation

When it comes to valuing companies, some people seem to suffer from what could be called 'reverse number blindness': if there's a lot of numbers and formulas involved, it must be good. However, as Aswath Damodaran points out, 'the test of a valuation is not in the inputs or in the modeling, but in the story underlying the numbers and how well that story holds up to scrutiny'. If the numbers you put in your valuation model do not reflect reasonable expectations about future cash flows and risk, your valuation is worthless however sophisticated your model is. Which raises the question: what are reasonable expectations? As a wise man once said: 'it's tough to make predictions, especially about the future'. When valuing a company, it is important to understand that valuations are only informed guesses, typically based on limited and (very) noisy information.

The Financial Times recently discussed an interesting illustration of this problem. In 2011, a company called Rural-Metro was acquired by private equity firm Warburg Pincus. Afterwards, shareholders sued Rural-Metro's directors for breaching their fiduciary duties, and Rural Metro's bankers - including Royal Bank of Canada - for aiding the directors in selling the company too cheaply, supposedly to get new lucrative financing assignments. While the other parties settled before a trial, Royal Bank of Canada contested the charges in a court in Delaware.

This led to a discussion about the valuation of Rural-Metro. In any discounted cash flow valuation (DCF), expected future cash flows are discounted at the cost of capital. According to the Capital Asset Pricing Model (CAPM) (basic version), the cost of equity = the risk free rate + beta x equity risk premium. In this model, beta measures the 'systematic risk', i.e. the extent to which the equity returns co-vary with the overall market return. There are two big problems with this approach. To begin with, it isn't even clear whether CAPM is a good approach to measure the cost of equity. Basically, people use it because (a) it is very simple to apply, and (b) there do not seem to be any significantly better approaches when it comes to valuation in the real world.

A second problem is that beta can be measured in different ways, and different approaches can lead to very different valuations. In the case of Rural-Metro, both parties made different assumptions with respect to beta. While they both used regression analysis and historical returns to estimate beta, the plaintiffs based their analysis on the weekly returns over a two year period, and the Royal Bank of Scotland advocated the use of monthly returns over a five year period. Both approaches are considered valid ways to estimate beta, but in this case the results were markedly different. The weekly data yielded a beta of 1.2, while the monthly data generated a higher beta of 1.454. It will probably not surprise you that the approach chosen be the parties confirmed their respective view points. The plaintiffs argued that the price at which Rural-Metro was sold was too low, which was disputed by the bank. A higher beta implies a higher cost of capital, and hence a lower DCF-valuation. The higher the DCF-value of Rural-Metro, the greater the damages to which the plaintiffs were entitled. The beta of 1.2, advocated by the plaintiffs, yielded a value of $21.42 per share, while the beta of 1.454, defended by the Royal Bank of Canada, yielded a 21% lower value of only $16.91 per share, decreasing total DCF value by no less than $100 million.

Which of these two approaches is the best? Personally, I would use neither: beta coefficients of individual stocks are often very unstable over time. You may try it yourself: calculate the beta of any stock over different periods of time, and you often end up with very different beta estimates. An extreme example is the beta of bank stocks, which for some banks exploded during the recent financial crisis. (*) A more reliable way to estimate beta is to use the mean or median 'unlevered beta' (i.e. adjusted for differences in leverage) of the industry in which the firm is operating. This is a much more stable measure, and it has been found that the betas of individual stocks tends to evolve towards industry averages.

However, the broader problem here is the reliability of DCF valuations. Any valuation will depend on the underlying assumptions, and a minor change in assumptions can lead to very different valuations. Does this mean that DCF valuations are worthless? According to Marc Andreessen, DCF valuations only serve to justify existing market valuations. I think mr. Andreessen is a bit too cynical here. (**) The big advantage of DCF valuation is that it allows to assess the assumptions on which a company valueis based. Are the underlying assumptions about the cost of capital and growth prospects in any way realistic? Let's say you would consider to buy Apple stocks: what does the current market valuation of Apple imply with respect to growth rates? DCF will help you understand this and will you help to decide whether to buy or sell Apple.

(*) Yes, I am aware that the 2007-2008 crisis was an unexpected, exceptional event, but unexpected exceptional events are basically happening all the time: any approach which does not take into account the possibility of such events is problematic in my view.

(**) Although I do like Andreessens' statement that the 'Efficient Market Hypothesis is correct if for "all information" you substitute "all information, theories, noise, and bullsh*t"'. It's a strange beast, this so-called Efficient Market.