Corresponding author: Michael Corbey ( m.h.corbey@uvt.nl ) Academic editor: Chris D. Knoops
© 2019 Michael Corbey, Frans de Roon, Stef Hinfelaar.
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Citation:
Corbey M, de Roon F, Hinfelaar S (2019) Company life cycle models and business valuation. Maandblad Voor Accountancy en Bedrijfseconomie 93(9/10): 285-296. https://doi.org/10.5117/mab.93.37561
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Future free cash flow is a crucial element of most business valuation tools, such as the Discounted Cash Flow model, with the quality of the valuation depending heavily on its forecast accuracy. This paper explores the theory on business life cycle (and growth) models in an aim to improve that quality. Life cycle and growth models have been studied in the management and organization literature for decades, but the relevant aspects from a business valuation perspective remain unclear. Reviewing the existing literature, we argue that the five-stage Hanks model (Start-up, Growth, Maturity, Diversification, and Decline) is applicable for valuation purposes. We further argue that life cycle thinking provides useful insights for making grounded assumptions in predicting the future free cash flows and residual value of a company. This paper presents practical valuation approaches and insights for each of the five stages of the Hanks model.
Business Valuation, Life Cycle Models, Growth Models, Forecasting, Discounted Cash Flow, Free Cash Flow, Residual Value
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.
Assumptions and propositions of Stages of Growth and Dynamic State models (
Organic growth models | Dynamic state models | |
---|---|---|
Assumption | Organizations grow as if they were organisms | Each state represents management’s attempts to most efficiently/effectively match internal organizing capacity with the external market/customer demand |
Propositions | A specific number of progressive stages | Any number of states |
Sequence and order are predictable | Sequence and order may be predictable depending on context | |
Immanent program of development | Adaptive process of retaining the sustainability of a business model | |
Prefigured rules of development | Interdependent rules for development | |
‘Regulated’ by environment | Driven by market change and opportunity creation |
The majority of the models found in the literature are grounded in the organic growth model (
Another finding of
All these models are largely theoretical conceptual models, and in general, there is no “hard” empirical proof of the existence of the proposed phases (
“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.” (
These findings are summarized in Table
Characteristics of company life cycle stages (
Dimension | Start-up stage | Expansion stage | Maturity/consolidation stage | Diversification stage | Decline stage |
---|---|---|---|---|---|
Age | Young | Older | Any age | ||
Size | Small | Large | Larger | Declining | |
Growth rate | Inconsistent | Rapid positive | Slow growth | Slow growth, but acceleration possible | Declining |
Structural form | Undifferentiated, Simple | Departmentalized, Functional | Departmentalized, Functional | Divisional | Mostly functional |
Formalization | Very informal, Personal, Flexible, Few policies | Formal systems begin to emerge, but enforcement is lax | Formal, Bureaucratic, Planning & control, Systems are enforced | Formal, Bureaucratic | Excessively bureaucratic |
Centralization | Highly centralized in founder | Centralized, Limited delegation | Moderately centralized | Decentralized | Moderately centralized |
Business tasks | Identify niche, Obtain resources, Build prototype, Set up task structure | Volume production & distribution, Capacity expansion, Set up operating systems | Make business profitable, Expense control, Establish management systems | Diversification, Expansion of product market scope | Revitalization, Redefinition of mission and strategy |
Empirically,
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
The main difference between the model used by
Alignment between Hanks, Damodaran growth models.
Stages in the Hanks model | Stages in the Damodaran model |
Start-up | Start-up, Young growth |
Expansion | Growth |
Maturity/Consolidation | Mature |
Diversification | Mature |
Decline | Decline |
Economic links to life cycle and cash flow patterns (
Cash flow | Introduction stage | Growth stage | Mature stage | Shake-out stage | Decline stage |
---|---|---|---|---|---|
Operating | Firms enter market with knowledge deficit about potential revenues and costs | Profit margins are maximized during period of greatest investment | Efficiency maximized through increased knowledge of operations | Declining growth rates lead to declining prices. | Declining growth rates lead to declining prices |
Routines of established firms hinder competitive flexibility | |||||
(-) Cash Flows | (+) Cash Flows | (+) Cash Flows | (+/-) Cash Flows | (-) Cash Flows | |
Investing | Managerial optimism drives investment | Firms make early large investments to deter entry | Obsolescence increases relative to new investment as firms mature | Void in theory | Liquidation of assets to service debt |
Firms make early large investments to deter entry | |||||
(-) Cash Flows | (-) Cash Flows | (-) Cash Flows | (+/-) Cash Flows | (+) Cash Flows | |
Financing | Pecking order theory states firms access bank debt then equity | Pecking order theory states firms access bank debt then equity | Focus shifts from acquiring financing to servicing debt and distributing excess funds to shareholders, such that mature firms decrease debt | Void in theory | Focus on debt repayment and/or renegotiation of debt |
Growth firms increase debt | |||||
(+) Cash Flows | (+) Cash Flows | (-) Cash Flows | (+/-) Cash Flows | (+/-) Cash Flows |
The life cycle model used by
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.
Transition analysis based on
Starting Stage (t=0) | Transition to Stage at t+5 Years | ||||
Introduction | Growth | Mature | Shake-Out | Decline | |
Introduction | 24% | 28% | 29% | 8% | 11% |
Growth | 6% | 39% | 43% | 9% | 4% |
Mature | 5% | 29% | 56% | 8% | 2% |
Shake-Out | 9% | 28% | 44% | 13% | 6% |
Decline | 26% | 23% | 20% | 12% | 18% |
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.
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:
, (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 (
Summary of survival rates found in existing research in
Author(s) | Cumulative Survival Rate | Source of Data | |||||
1 Yr. | 2 Yrs. | 4 Yrs. | 5 Yrs. | 7 Yrs. | 10 Yrs. | ||
|
– | – | – | 43.4% | – | 26.3% | U.S. Census of Manufacturers; 219,754 manufacturing plants; 1963–1982 |
|
– | 77.4% | 63.1% | – | – | 35.4% | Small Business Database; 11,154 manufacturing firms; 1976–1986 |
|
93.6% | – | – | 66.1% | – | 48.7% | Thomas Register of Manufacturers; 3,431 firms; 1906–1991 |
Exponential model |
90.6% | 82.1% | 67.4% | 61.1% | – | 37.4% | Small Business Administration; 5.7 million firms in all sectors; 2003–2004 |
|
81.2% | 65.8% | 44.4% | 38.3% | 34.4% | – | Bureau of Labor Statistics Quarterly Census of Employment & Wages; 8.9 million firms in all sectors; 1998–2005 |
As Table
Exit rates for firms due to unfavorable mortality for selected size categories (
Morris’s literature review also analyzed variables that affect survival. A summary of his findings is given in Table
Summary of literature review by
Variable | Impact on Survival | References* | |
Economy | 1. Unemployment rate | – | 5 |
Industry | 2. Economy of scale | – | 4,5 |
3. Capital intensity | – | 4,5 | |
4. Growth | + | 1,5 | |
5. Profit margin | + | 4,5 | |
6. Innovation in industry | – | 4,5 | |
7. Industry life cycle stage | – | 1,2 | |
Firm | 8. Age | + | 1,2,7 |
9. Size | + | 1,2,3,4,5,6,7 | |
10. Liquidity | + | 3 | |
11. Reinvestment | + | 3 | |
12. Profitability | + | 3 | |
13. Financial leverage | – | 3 | |
14. Asset turnover | + | 3 | |
15. Earnings stability | + | 3 | |
16. Interest coverage | + | 3 | |
*References as cited in |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
, (2)
where qj is the probability of failure in period j, conditional on having survived through period j-1;
Pj is the unconditional probability of surviving through j periods; Lj 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.
. (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
In a similar way,
. (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.
In the Start-up and Young Growth stages, there is a lack of historical data and the accounting setup is often poor and non-structured. This makes it difficult to extract the operating costs versus the expenditures for the existing assets. The future CFs have to be generated by new assets, with estimation starting from almost zero due to the lack of historical data. Moreover, the Start-up stage is often split into sub-stages because of the major financial and marketing transitions involved. The first Start-up sub-stage starts with an idea or concept product, without sales and with only cash outs. The next sub-stage starts with the initial sales, though still with negative earnings while acquiring knowledge about the product and the market. The final sub-stage is when sales start to increase and positive earnings are generated (see Figure
Several authors, such as
Sub-stages within the Start-up stage in
Stage of development | Need for funding | Duration of the investment (in years) |
---|---|---|
Seed and Start-up | To finance support of the entrepreneur’s exploration of an idea up to the funding of the organization of a firm that is prepared to commence operations. | More than 10 |
First stage | To fund the operations of an ongoing business that is typically not yet profitable. Funds are used to establish initial marketing efforts and to hire the necessary personnel to support the anticipated growth in sales. | 5–10 |
Second stage | At this stage, the company has a proven product or service and funding is needed to support working capital and fixed assets for growing sales. | 4–7 |
Bridge | Funding is used to carry the company until its initial public offering (IPO). | 1–3 |
In the start-up world, measures from marketing inputs/outputs are commonly used to build a business case (
This bottom-up (marketing) approach is also used for firms in the Growth stage, where a considerable portion of future value will be generated by investments in new assets. Due to the uncertainty of the future CFs, other valuation models are used in these stages, such as relative valuation and real options.
In addition to what has been described above,
(5)
The discount rate (k) for calculating the value of the status quo and the value of the key person lost are the same. Only the FCF estimation differs in the two situations.
In the literature reviewed here, studies on valuing Start-up, Early Growth, Young Growth, and High Growth companies in the high-tech environment predominate. This can be explained by its characteristics: the turbulence of the internet bubble, fascination with innovative firms, drive to find the next Google or Apple, lack of other available data, and potentially high returns.
In the Growth stage, the main source of growing CFs is from investments in new assets, although existing assets do continue to generate CFs. When a company is aiming to invest or has already invested, its allocation of costs is often poor. This results in understating both the earnings and the value of existing assets. A feature of the Growth firm is that, over time, margins and returns change significantly. The need to address such issues as whether the upscaling and growth shown are sustainable in future years or competitors will enter the market make it more difficult to forecast future CF (
Estimating the growth rate at this stage is the main problem: there is uncertainty about the tenability of the historical growth rate and the prediction of the future growth rate (
Another issue up for debate concerns the justification for applying the current margin or target margin and the period of change for reaching the target margin. One possible approach is to analyze the industry and make a judgment call (
Companies in the Mature stage mainly obtain their CF from existing assets. Valuing these assets becomes more critical than it was at earlier stages and includes considering the following issues, as outlined in
Accordingly,
At the Decline stage, two particular aspects complicate the estimation of FCFs from existing assets and their discounting in the DCF model (
A framework for dealing with decline and distress (Damodaran, 2010).
No or low distress (little debt, investment grade rating) | High distress (high debt commitments, low ratings) | |
Irreversible (sector in trouble) | Value the firm with existing management and expected decline (going-concern value). | Start with the expected value (irreversible, no distress). |
Value the firm assuming orderly liquidation of all its assets. | Estimate the probability of distress and proceeds from forced liquidation of the firm. | |
Expected value = maximum (going-concern value, orderly liquidation value) | Recompute the expected value, adjusting for distress. | |
Reversible (firm outlier in healthy sector) | Value the firm with existing management and expected decline. | Start with the expected value (reversible, no distress). |
Value the firm with better management and recovery. | Estimate the probability of distress sale of the firm. | |
Expected value = status quo | Recompute the expected value, adjusting for distress. | |
Value * probability of no management change + optimum | If equity investors run the firm, value the option to liquidate. | |
value * probability of management change |
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:
(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.
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.
. (7)
The reinvestment rate is defined as Stable Growth Rate / Return on Capital in the stable phase.
As discussed in section 6.1, the estimation of the FCF at this stage must address uncertainties, and therefore also assumptions based on those uncertainties. The estimation of RV adds further uncertainty caused by looking into the future beyond the horizon of the FCF forecast. For this stage, too, the risk of failure is important, and it is therefore preferable to apply a failure probability in estimating the FCF.
The specificity of this stage regarding RV is reflected in the question of when and how to incorporate the trans ition from a fast-growing company to a mature company with a lower growth rate (
RV accounts for a large share of the overall value of a Mature firm, and its estimation might seem easier than in the Growth stage, because the growth rate tends to converge to the economic growth rate. The economic growth rate is the percentage change in the value of all of the goods and services produced in a nation during a specific period of time, as compared to an earlier period. Some factors could distort the estimation, however. The first concern is the profile of the company. Although the growth rate is stable and lower than the economic growth and risk-free rate, a company in the Mature stage can have a high risk (e.g., beta > 2) and needs a reinvestment level close to its total income, making the estimation of RV more complicated. Moreover, as noted in section 6.3, inefficiencies related to the running of companies in the Mature stage could also affect their RV and thus the risk of undervaluation (
At the Decline stage (with/without distress), the estimation of RV requires specific approaches similar to those already shared for FCF estimation in section 6.4. Here, there is a possibility that the firm may not make it to stable growth. Many distressed firms default and go out of business or liquidate. For those that achieve a steady state, the growth rate may be far below the economic growth rate and even negative. The firm continues to exist, but it becomes progressively smaller as its market share shrinks (
, (8)
where pdistress is the cumulative probability of distress over the valuation period.
Despite the fact that the magnitude of the growth rate for deriving the RV is often limited, the impact of the total RV is important. The life cycle approach supports the choice for the most suitable assumptions for the RV estimation. The use of the shortcut of RV calculation as perpetuity should be skipped when integrating the probability of failure into the FCF estimation.
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
Summary of practical insights and approaches.
Stage in Life Cycle | Estimation of: | |
FCF | RV | |
Start-up and Young Growth | Combine different sources/approaches for estimating the FCF. The projections of the management are too restrictive. There is a knowledge deficit, and there are often large investments. | Include the probability of failure. |
Growth rates are often inconsistent. | ||
Look for proven (non-financial) metrics as predictors of FCF. | ||
Take into account the dependency on key persons. | ||
Growth | Separate FCF prediction from existing assets and new assests. | In beginning, include the probability of failure. |
Use comparables and literature studies for estimating the growth rate. Growth is rapid and positive. | Use stable (lower) growth rate, e.g., growth rate based on reinvestment rate explained in Section 7. | |
Good assessment of the needed reinvestment level/rate possible. | ||
Mature | In-depth analyses of the accounted results to produce explicit real operational versus bookkeeping results. | Growth rate often below risk-free rate and/or economic growth. |
Split FCF between historical operations and acquisitions. | Special attention: agency effects (inefficiencies) could increase growth rate. | |
Growth rate is declining. | ||
If growth depends on acquisitions, dive into historical success rate of doing this. Natural growth is slow. Dive into the way the company is managed for agency effects (inefficiencies). | ||
Decline | In-depth analyses of the accounted results to produce explicit real operational versus bookkeeping results. | No use of RV calculation as perpetuity. |
Assessment of the level of (potential) distress and inclusion of this in the FCF prediction. | Include distress or failure probability. | |
Split FCF between historical operations and acquisitions. | ||
Growth rate is declining. |
Transitions from one stage/state to another and residence times in particular stages have not been extensively studied in the literature;
Drs. Ing. Stef Hinfelaar MiF MBV is an alumnus of the Executive Master in Finance and the Executive Master of Business Valuation programs, TIAS School for Business and Society, Tilburg University.
Prof. dr. ir. Michael Corbey is Full Professor of Management Accounting and Control and Academic Director of the Executive Master of Finance and Control / Register Controller programs, TIAS School for Business and Society, Tilburg University.
Prof. dr. Frans de Roon is Full Professor of Finance and Academic Director of the Executive Master in Finance and the Executive Master of Business Valuation programs at TIAS School for Business and Society, Tilburg University.