Discounted Cash Flow is a common valuation method that relies on difficult-to-make estimations of future Free Cash Flow (FCF) and Residual Value (RV). We argue that practitioners may benefit from including business life cycle modeling in assessing the expected FCF and RV to improve the quality of their valuations.

Cash that is not retained or reinvested in a company is known as free cash flow (FCF). Business valuation models such as Discounted Cash Flow (DCF) are based upon a company’s expected future FCFs, but forecasting these can be difficult in practice for several reasons. First and foremost, one has to determine the forecast horizon, which is often set (rather arbitrarily) to between three and ten years. Second, the FCFs during that horizon must be forecasted. And third, one has to estimate the residual value (RV) of the business at the end of the forecast horizon. The most prevalent problem is that the uncertainty of the cash flow projections increases for each year in the forecast.

One key issue is that the characteristics of a company can change over time, and this impacts FCFs. The dynamics of company characteristics have been studied extensively in the management and organization literature, typically in the area of growth and life cycle models. This paper explores the relationship between the theory on growth and life cycle models and that on FCF. The general idea is that practitioners may benefit from using these models in assessing future FCFs, including in estimating the RV of a firm.

The remainder of this paper is organized as follows. The literature on growth and life cycle models is explored in Section 2. This leads to the presentation of a model that seems most suited to the business valuation setting. Subsequently, in Section 3, the link between this life cycle model and future FCF is established. The impact of stage transitions on FCF is discussed in Section 4, and RV issues are introduced in Section 5. Relationships between particular lifetime stages and FCF and RV are subsequently dealt with in Sections 6 and 7. The paper ends with conclusions in Section 8.

Levie and Lichtenstein (2010) argue in their literature review on growth and life cycle models that a distinction can be made between models based on “sequential” (organic) versus “dynamic” states. The first approach assumes logical successive phases, while the second centers on events that bring a company to a certain ‘state’. Table 1 contrasts the two approaches. It shows that organic growth models are characterized by a more predictable and predefined growth path as opposed to dynamic state models.

The majority of the models found in the literature are grounded in the organic growth model (Levie and Lichtenstein 2010). We will therefore take that as a starting point. In addition to the fact that this model is dominant in the literature, we argue that it relates to relevant and measurable business valuation aspects. Furthermore, Levie and Lichtenstein (2010) analyzed the attributes used in the models for identifying stages of growth. The most-used attributes (in the 104 models studied) were: the extent of formal systems (e.g., planning and control); the growth rate (sales, employees, etc.); the organizational structure; the characteristics of management; the formality of communication systems; the primary focus of the organization; and complexity, age, and size. These attributes were found in 35–50% of the models. Levie and Lichtenstein (2010) coded all the attributes as elements of corresponding categories. Their results are shown in Figure 1, where the categories Outcomes (age, size, and growth) and Management Characteristics (owner involvement, nature of top management, managerial style, etc.) are present in over 65% of the models.

Another finding of Levie and Lichtenstein (2010) is the repartition of the number of stages described in the different models: there is no consensus about the number of distinct stages (see Figure 2). In general, the key difference between models of four (or fewer) and five (or more) stages is that the latter include a decline phase.

All these models are largely theoretical conceptual models, and in general, there is no “hard” empirical proof of the existence of the proposed phases (Levie and Lichtenstein 2010; McMahon 1998; Solli-Sæther and Gottschalk 2010). While some studies do take an empirical approach, including Hanks (1990), Hanks and McCarrey (1993), Hanks et al. (1994), Kazanjian (1988), Kazanjian and Drazin (1989, 1990), and Miller and Friesen (1984), all of them conclude that validation is problematic.

Hanks et al. (1994) compared ten well-known life cycle models and concluded that seven dimensions were particularly relevant when it comes to identifying the five different stages:

“While there is considerable variability between models, all included some dimensions related to organization context and organization structure. Common contextual dimensions included organization age, size, growth rate, and focal tasks or challenges faced by the firm. Common structural dimensions included structural form, formalization, centralization, and vertical differentiation, the number of organization levels. Within models, stages are distinguished one from another by differences in the pattern and magnitude of these dimensions.” (Hanks et al. 1994)

These findings are summarized in Table 2.

Empirically, Hanks et al. (1994) identified six stages: four Development (or Growth) stages and two Disengagement stages. Remarkably, they also found two atypical phases (“life style” and “capped growth”) that could also be described as disengagement phases. These relate to companies that deliberately remain in a certain phase without wanting to develop further; they generate sufficient stable income, have sufficient scale and market penetration, and are reasonably profitable. It is important to consider these disengagement phases when valuing a company. The life style company is small, has existed for a long time (> 10 years), and has an average of seven employees. It is centrally managed, informal, and simply structured, has international specialization, and is often dependent on the founder. The capped growth company is larger and has also existed for more than 10 years, has about 25 employees with specialized positions, is functionally organized, and is clearly more structured and professionalized. The taxonomical findings of Hanks et al. (1994) in relationship to the existence of stages are consistent with McMahon (1998) and confirmed by the empirical findings of Lester et al. (2003). However, the latter are more specific in defining a Decline stage, with an “identifiable set of organizational activities and structures”.

As stated before, life cycle models are prevalent in the management and organization literature but much less so in the valuation literature. Nevertheless, authors such as Damodaran (2010), Dickinson (2011), and Duff and Phelps (2013) have considered them in the context of business valuation. Their findings are referenced below, while the life cycle model of Hanks et al. (1994) serves as the benchmark for the remainder of the paper.

Damodaran (2010) uses a five-stage model in discussing valuation issues. These elements that need to be taken into account in business valuation will change over the lifetime of a company. This is visualized in Figure 3, where the valuation elements are placed on the vertical axis and the life cycle stages on the horizontal axis.

The main difference between the model used by Damodaran (2010) and the Hanks et al. (1994) model is the Diversification phase, which Hanks refers to as the phase in which a company can grow again after a Maturity / Consolidation phase. Damodaran (2010) does not include this phase in his model, but he does elaborate on the issue in his description of the Mature phase, applying Real Options Theory for when a company starts diversifying. The two approaches are contrasted in Table 3.

Dickinson (2011) introduces an approach by which she explicitly connects cash flow patterns to the life cycle model, thereby allowing her to classify the phase a company is in based on its operating, investment, and financing cash flows. In her view, “cash flows capture differences in a firm’s profitability, growth, and risk, and the combination of the three types of cash flows are mapped into life cycle theory to derive the life cycle classification”. Table 4 shows Dickinson’s mapping of the different effect of each stage on the three types of cash flow. In the Introduction phase, for example, there will be a negative cash flow (minus sign: -) due to the operating costs and necessary investments and a cash inflow (plus sign: +) from financing.

The life cycle model used by Dickinson (2011) is similar to the Hanks model, with Dickinson introducing the Shake-out phase, which could be seen as the inverse of Hanks’s Diversification phase. Dickinson (2011) asserts that cash flow patterns are a better predictor of (proxy for) the growth phase than the age or size of a company. This supports previous research by Anthony and Ramesh (1992) and Black (1998).

The concept of company life cycles implies, as discussed, a transition through stages. There is a common understanding in the literature regarding the non-linearity of these transitions (see also Section 2). In other words, companies can regress in stages or skip one or more of them. This transitioning needs to be integrated into estimations of a company’s FCF development. Starting with the initial/starting stage, a quantitative estimation needs to be made of the residence time in that stage; then, the next stage and residence time there needs to be predicted and the one after that and so on. In other words, what does the probable life cycle chain look like?

Little is found in the literature that specifically addresses this chain. Hanks et al. (1994) mention the age of a firm in their taxonomy study but provide no real data on residence times or the possible sequences of stages. Dickinson (2011) presents more explicit transition estimates. Using data over a five-year period, she provides indications of residence time and the probability of transitioning to another stage. These findings are summarized in Table 5.

In this table, a company is initially in one of the stages in the first column. We then see, for each row, the fraction of companies in that category that have transitioned to another stage after five years. For example, of the companies in the Introduction stage at the starting date of observation, 24% are still in that stage after five years; 28% have moved on to the Growth stage; 29% are Mature; and so forth. On the diagonal, the orange fields equal the “non-transitions”: cases where a company is still in the same stage after five years.

The table allows for the following interpretations:

81% of Introduction stage firms are likely to either stay in that stage or move to the Growth/Mature stage.

43% of Growth firms move to the Mature stage. The Mature stage firms are the most stable and if they move, they mainly transition back to the Growth stage.

A small proportion of Shake-out (13%) and Decline (18%) firms remain in their initial stage, but there is strong movement to the Mature, Growth, and even Introduction stages. This could possibly be explained by an urge to change their business model.

Dickinson’s (2011) findings have some limitations: first, the scope of a period of only five years is limited; and second, the history of the firms before t = 0 is not considered. Her results do provide an empirical basis for the conceptual thinking of Phelps et al. (2007) and Levie and Lichtenstein (2010), which rejects the stages framework and introduces dynamic states. Despite the absence of research on life cycle transitions, the fact that they are clearly neither linear nor sequential emphasizes that practitioners should not take the logic of sequential organic growth in stages for granted.

In the actual practice of business valuation, it is common to assume an infinite lifetime for the company in the cash flow estimation beyond the forecast horizon. Consequently, the RV will be treated as a perpetuity (going-concern) depending on the future cash flows (CFs), the growth rate (g), and the cost of capital (k), resulting in the equation:

RV=CFt=n*(1+g)/(k-g), (1)

where n is the last year in the (explicit) forecast period. The relevance of estimating the RV relates to its importance as part of the total value of a company. In reality, companies have a limited life expectancy: less than 50 percent of new firms have a lifetime beyond 10 years (Morris 2009). This is supported by the findings of Dickinson (2011) and Damodaran (2010). The consequences of limited life expectancy should be considered in a company’s FCF and will be explored in this section.

Morris (2009) and Damodaran (2010) studied these topics based on their own research combined with a review of other studies. Morris studied the mortality of firms and the impact of mortality and survivorship on value and concluded that the effect was material. He used scenario analysis to show that the magnitude of the value effect from mortality could range from 40% to over 200%. Based on previous literature and surveys, he was able to provide an overview of expected life expectancy and the probability of dying or surviving. Damodaran (2010) included the results of studies he cited by Knaup (2005) and Knaup and Piazza (2007) on the longevity of over eight million U.S. companies from 1998 to 2005. Table 6 provides a summary of Morris’s and Damodaran’s findings and the other research they cited.

As Table 6 shows, the majority of companies exit business life within the first ten years of existence, with only a minority (26.3% – 48.7%) surviving beyond that. Morris (2009) further cites an examination of business mortality rates, defined as exit rates due to unfavorable mortality, by Queen and Roll (1987). Their results are illustrated in Figure 4. Based on the work of both Queen and Roll (1987) and Morris (2009), we can conclude that there is a strong inverse relationship between firm size and mortality.

Morris’s literature review also analyzed variables that affect survival. A summary of his findings is given in Table 7. These variables are related to dimensions of the life cycle model.

Morris (2009) emphasizes the need for incorporating the probabilities of survivorship/failure in estimating FCFs, as do Dickinson (2011) and Damodaran (2010). He integrates the concept of mortality into the estimate of the present value of a company, defining this as the present value of expected liquidation payments (L) plus the present value of expected future CF plus the present value of the expected terminal value (V_N). Thus, the formula for calculating the present value V₀ is:

V0=∑j=1NPj*qj*Lj*ρj+∑j=1NPj*CFj*ρj+PN*VN*ρN, (2)

where q_j is the probability of failure in period j, conditional on having survived through period j-1;

P_j is the unconditional probability of surviving through j periods; L_j is the payoff to security holders if the firms defaults in period j; p ^j equals [1/(1+k)]^j; CF is the expected cash flow in period j to the security holders from the firm’s normal operations when it does not fail; and N is the expected residual time.

Morris (2009) simplifies this formula for situations in which a firm faces a probability of failure of q for each period, with the CF growing at a mean rate g from CF₁ in period 1, resulting in the constant growth value:

V0=CF1*[1k-g+q+g*q]. (3)

This formula is like the standard perpetual growth model, but with the addition of the constant hazard of failure, q + g * q, to the usual denominator, k – g. The derivation of this equation is given in Morris (2009). As was shown in Table 6 and Figure 4, the q is different at various stages of the life cycle; estimates for it are given in Morris (2009). Adjustment with q + g × q decreases value. An example of the effect of the mortality rate is given in Figure 5.

In a similar way, Damodaran (2010) adds the probability of failure (p_failure), as well as the distress sales value (liquidation value). He proposes the following formula:

Vadapted=Valuecoing conern*(1-pfailure)+Distress Sale Value*pfailure. (4)

For practitioners, the estimation of this probability can be obtained from industry overviews, by analyzing comparable firms that survived or failed, or by using simulations. This approach of integrating the probability of mortality into future CFs requires that a choice be made in terms of either applying the approach of estimating the FCF for every year or using the shortcut of the perpetuity formula with constant growth for estimating the RV.

Having discussed the estimation of FCF per life cycle stage, we will now discuss a way to estimate RV while accommodating the characteristics/dimensions belonging to particular stages. In practice, the RV is treated as a perpetuity (going-concern) depending on the future CFs, the growth rate (g), and the cost of capital (k), resulting in the equation:

RV=CFt=n*1+gk-g (6)

In this section, we focus on the growth rate of the CF linked with the life cycle stage.

Beyond survivorship, the expected growth rate of CFs influences RV, while the life cycle stage defines the target growth rate. Damodaran (2010) mentions a number of issues to take into consideration. First, the growth rate has to be capped, and the effect of the growth rate on the RV is significant when using a rate approaching the discount rate (k). Moreover, a firm cannot grow infinitely at the same (high) rate over time, whereby he argues that in the long term, the growth rate cannot exceed the economic growth rate. Damodaran (2010) suggests as a rule of thumb that the stable growth rate should not exceed the risk-free rate used in the valuation.

Stable growth firms tend to reinvest less than high growth companies. The growth rate estimation has to balance between the implied lower growth rate and the reinvestment rate for maintaining a sustainable growth rate in the terminal phase. Damodaran (2010, p. 48) concludes that “the key assumption in terminal value computation is not what growth rate you use in the valuation, but what excess returns accompany that growth rate”. As a result, he proposes using the reinvestment rate in the RV (going-concern) calculation as follows:

RV=EBITn+1*(1-t)*(1-Reinvestment Rate)/(COCn-Stable Growth Rate). (7)

The reinvestment rate is defined as Stable Growth Rate / Return on Capital in the stable phase.

Damodaran’s (2010) approach of introducing reinvestment in the RV can be traced back to the conceptual work of O’Brien (2003). In his model of valuation, which was based on Miller-Modigliani, O’ Brien introduced a decay factor or rate (d), defined as the fade rate at which the return on equity for new investments is expected to converge towards the firm’s cost of equity (f) minus the expected growth rate of incremental investments (g).

In this article, we have shown that integrating the concept of a company life cycle into the daily practice of business valuators improves the quality of the value estimation. Including life cycle models in the process of determining the value of a company provides insights for making more grounded assumptions. Life cycle thinking helps practitioners assess the risks and structurally improves prediction of future CFs. It is critical to take aspects such as mortality, expected growth rates, distress risk, and future investments explicitly into account in the valuation process. We analyzed the implications for the estimation of FCF and the RV for each stage of the life cycle and translated them into practical insights and approaches for valuation practitioners. These findings are summarized in Table 10 below.

Transitions from one stage/state to another and residence times in particular stages have not been extensively studied in the literature; Dickinson’s (2011) was the only work found in this area. Yet, aspects such as estimated stage residence time and probability of passing to the next stage or state are relevant to life cycle thinking and the valuation process. In the models presented, we have broadly discussed specific elements of this thinking in terms of stage transitions within the life cycle. Further empirical research is needed to provide more insight into such time aspects (stage residence time) and would also enrich the theoretical insights into the sequence or of business lifetime stages.