Aurora Borealis
1 February 2013 CFA Institute Journal Review

Economic Profitability and the Valuation of the Firm (Digest Summary)

  1. Stuart Fujiyama, CFA

Practitioners continue to use standard discounted cash flow (DCF) models because of their ease of use in valuing a firm. The author presents and assesses the performance of an enhanced DCF model that explicitly incorporates both return on invested capital growth and free cash flow growth.

What’s Inside?

Gordon (Review of Economics and Statistics 1959) developed a firm valuation model that incorporates the assumption of a steady-state period for free cash flow growth into a formula that is relatively straightforward to calculate. Fuller and Hsia (Financial Analysts Journal 1984) attempted to improve on this model with the H-model, which allows practitioners to specify a pre-steady-state transition period and corresponding transition growth rate. The author proposes a model that offers potential improvements in accuracy and reductions in variability by using the forecast of one additional model input—free cash flow at the beginning of the steady state.


How Is This Research Useful to Practitioners?

The author explains how, unlike the H-model, his model allows an analyst to ensure that return on invested capital (ROIC) approaches sustainable levels during the pre-steady-state transition period. Unlike the Gordon model and the H-model, it accommodates the fairly common scenario of negative initial cash flow. The proposed model also ties transition-period growth rates to capital instead of free cash flows, and the author presents historical compound annual growth rate (CAGR) data that indicate this feature may lead to more-accurate valuations.

With the help of what he calls “reality ratios,” which are ratios of estimated to actual market equity values, the author demonstrates empirically that the proposed model approximates stock market values more accurately and with less variability than the Gordon model or the H-model. Overall, the proposed model yields mean and median reality ratios that indicate a higher degree of accuracy (ratios closer to 1) in three tests: in sample, out of sample, and split sample. The Gordon model and the H-model yield mean reality ratios that differ significantly from the ratios yielded by the proposed model and indicate a lower degree of accuracy (ratios further from 1) across the three tests. In addition, they yield median reality ratios that indicate a lower degree of accuracy within the in-sample and split-sample tests.

The proposed model yields the smallest standard deviation and interquartile range in every tested case (24 in sample, 48 split sample, and 6 out of sample). For the split-sample test, the changes in both mean and median between two time periods are smallest for the proposed model. The author notes that these indications of reduced variability and improved consistency may be of particular interest to practitioners.

How Did the Author Conduct This Research?

The author calculates monthly model estimates of the December 1996–March 2011 equity values of firms in the S&P 500 Index, primarily using FactSet data. He lags income statement and balance sheet items by 45 days from the reported quarter-end date to prevent look-ahead bias. To ensure that estimates for all three of the models can be calculated for every observation, he removes observations for which the trailing 12-month free cash flow is negative, resulting in the exclusion of 30% of the observations from the sample.

To estimate equity values using the H-model and the proposed model, the author uses a 10-year transition period and transitional growth rate mean and median calculated using 10-year Compustat CAGR data from September 1987 to July 1999.

The author first runs in-sample tests with the models by calculating their reality ratios for two types of transitional growth rates (mean versus median). He evaluates four levels of steady-state growth (2.5%, 3.0%, 3.5%, and 4.0%) and three levels of constant premium (0.0%, 0.5%, and 1.0%) to be added to a firm’s weighted average cost of capital to find the firm’s steady-state ROIC. He then splits the sample into two subperiods—December 1996 to May 2005 and June 2005 to March 2011—and runs the same test cases. Finally, he runs out-of-sample tests with the models by splitting the sample into two subperiods, as in the split-sample test, and using Period 1 solely to derive steady-state growth rates to be used as inputs for Period 2.

Abstractor’s Viewpoint

The author presents a compelling case for his model while keeping the concerns of the valuation practitioner foremost in mind. But a DCF model’s ease of use needs to be weighed against its inherent sensitivity to a set of inputs whose specification is often subject to considerable judgment. Other researchers have surveyed academics’ and practitioners’ accounts of how they select their valuation inputs. See, for example, “US Market Risk Premium Used in 2011 by Professors, Analysts, and Companies: A Survey with 5.731 Answers” by Fernandez, Aguirreamalloa, and Avendaño (

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