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# Apply a Complexity Discount

You could do a conventional valuation of a firm, using unadjusted cashflows, growth rates and discount rates, and then apply a discount to this value to reflect the complexity of its financial statements. But how would you quantify this complexity discount? There are several options:

1. One is to develop a rule of thumb, similar to those used by analysts who value private companies to estimate the effect of illiquidity. The problem with these rules of thumb is that they are not only arbitrary but that the same discount is applied to all complex firms.

2. A slightly more sophisticated option is to use a complexity scoring system, similar the one described in appendix 1 to measure the complexity of a firm’s financial statements and to relate the complexity score to the size of the discount.

3. You could compare the valuations of complex firms to the valuation of simple firms in the same business, and estimate the discount being applied by markets for complexity. Since it is difficult to find otherwise similar firms, you can estimate this discount by looking at a large sample of traded firms and relating a standard multiple of value (say price to book ratios) to financial fundamentals (such as risk, growth and cashflows) and some measure of complexity (such as the complexity score). We did this on a limited basis for the hundred largest market capitalization firms and related price earnings ratios to expected growth rates, betas, payout ratios and number of pages in the 10K for each of these firms (as a measure of complexity). The regression is summarized below: PBV = 0.65 + 15.31 ROE – 0.55 Beta + 3.04 Expected growth rate – 0.003 # Pages in 10K Thus, a firm with a 15% return on equity, a beta of 1.15, and expected growth rate of 10% and 350 pages in the 10K would have a price to book ratio of PBV = 0.65 + 15.31 (.15) – 0.55 (1.20) + 3.04 (.10) - .003 (350) = 1.54

4. If a firm is in multiple businesses, and some businesses are simple and others are complex, you could value the company in pieces attaching no discount to the simple pieces and a much greater discount to the more complex parts of the firm. This may be the best strategy for a firm like General Electric, where information on some parts of the firm is easy to access while other parts of the firm are more complicated and difficult to value.

Relative Valuation

Most analysts value companies using multiples and comparable firms. How can this approach be modified to consider firms that are complex? While it is more difficult to assess the effect of complexity on relative value, you should consider the following options:

a. If a firm is in multiple businesses, you could value each business using a separate relative valuation and different comparable firms, rather than trying to attach one multiple to the entire company. If the firm reports revenues or earnings from unspecified businesses (where information is not provided or is withheld), your estimate of relative value for these businesses should be conservative. For instance, you could treat these earnings as both risky and low growth and apply a low multiple to estimate value.

b. As in the case of discounted cashflow valuation, you could do a conventional relative valuation (with no adjustment for complexity) and then discount the relative value for the complexity of the firm. The adjustment process would mirror that used for the discounted cashflow value. As firms become more complex, relative valuation becomes much more difficult across the board since you need pure play firms with market prices to estimate the appropriate multiples.

Prof. Aswath Damodaran