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The Flawed Perpetual Growth Assumption and Its Impact on Terminal Value

  • Sutter Securities Financial Services, San Francisco


In the customary determination of terminal value in a discounted cash flow analysis, it is assumed that a mature company will grow at a constant rate in perpetuity. This article explains why the perpetual growth concept is flawed and needs to be reexamined. It also discusses proposals to recognize the risks of corporate decline and corporate mortality and to make appropriate adjustments.
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We extend the analytical framework of traditional DCF models to allow for the possibility of a time-varying cessation risk for cash flows. We first set out a parsimonious functional form for timedependent survival probability of cash flows and then derive a closed-form solution for cessation risk-adjusted discount rates within a DCF model. Application of the model to a new data set, created for this paper, demonstrates that U.S. start-up firms face considerable risk of cessation, particularly during the first five years of their existence. This finding suggests that the time-varying discount rates that are appropriate to value them are considerably higher than those used in traditional DCF models.
Firms typically do not make it to old age. We want to know whether the deterioration in performance they experience eventually drives older firms into financial failure. We find that not to be the case. Conditionally and unconditionally, the failure hazard declines as firms grow older. The competing hazard of takeover initially declines as well, yet it increases with age eventually. On average, and consistent with Schumpeter’s gale of creative destruction, older firms are therefore more likely to be absorbed and recycled in other organizations. However, there is little evidence of survival of the fittest at old age, since poor performance and inefficient cost structures actually reduce the takeover hazard of old firms. New assets and plenty of cash have the same effect. It looks as if old clunkers have trouble finding merger partners. We also provide novel evidence about how industry characteristics affect both hazards of financial failure and takeover.
This paper incorporates an annual probability of corporate failure into a standard equity valuation model, as an alternative or complementary correction for risk that improves in several ways over conventional risk premia or ad hoc adjustments to assumed growth rates. Though the correction is nonlinear, it can be reduced to an equivalent function that enters the valuation equation in the traditional additive way. Empirical benchmarking suggests that, even without assuming risk averse investors, this approach comes closer to predicting observed equity premia than the traditional approach. Extensions of the model provide valuation under two growth regimes with stochastic transition time. The author is grateful for suggestions from Anil Kashyap and Fred Sterbenz.
Previous analysis of equity duration and convexity has either ignored the risk that firms can fail or stop growing, or else has incorporated the risk of failure in an ad hoc way. This paper derives equity duration and convexity rigorously corrected for the risk of failure or stagnation. We show that the correction is large enough to be important in standard applications. Further, equity duration is unaffected by any liquidation payout at the time of failure.
Neither the literature of finance nor the literature of valuation practitioners has taken account of the relatively short life expectancy of firms. Fewer than fifty percent of new firms live longer than ten years; yet, it is common practice to estimate firm value with a very long term horizon model such as the constant growth model. The purpose of this paper is to increase awareness of the life expectancy of firms and show how to take account of the likelihood of firm death in valuation. Data on firm death rates and life expectancy that is available in the field of industrial organization is reviewed and summarized so that valuation practitioners can take it into account in their valuations.
Creative Destruction Whips through Corporate America
  • Richard N Foster
Richard N. Foster, "Creative Destruction Whips through Corporate America," Innosight Executive Briefing, Winter 2012, available at
Firm Mortality and Business Valuation
  • James R Morris
James R. Morris, "Firm Mortality and Business Valuation," Valuation Strategies (September/October 2009), p. 10. The data cover the years 1990-2004.
  • Claudio F Loderer
  • Klaus Neusser
  • Urs Waelchli
Claudio F. Loderer, Klaus Neusser, and Urs Waelchli, " Firm Age and Survival, " SSRN (2011), available at
The Mortality of Companies However, their definition of lifespan included mergers and acquisitions
  • I G Madeleine
  • Marcus J Daepp
  • Geoffrey B Hamilton
  • Luís M A West
  • Bettencourt
Madeleine I.G. Daepp, Marcus J. Hamilton, Geoffrey B. West, and Luís M. A. Bettencourt, " The Mortality of Companies, " Journal of The Royal Society Interface (2015), available at However, their definition of lifespan included mergers and acquisitions, which were the terminal events for about half of the companies.
Life and Death of Businesses
  • Morris
Morris, "Life and Death of Businesses," p. 4.