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According to the International Assessment Standards, in order to obtain a certain type of value, the three approaches of the unanimously acknowledged and applied value may be used, that are substantiated on the economic principles of substitution, variable proportions or benefits anticipation: the cost, market and income approach. In the article hereby we present aspects concerning the income approach, which consists of setting the value of the enterprise from the perspective of taking into consideration its capacity to generate profits/earnings for its future functioning. Financially, no investment has sense than by the cash flows likely to be achieved as a result of it. Thus, it is deemed that the amount of any invested capital must be estimated in terms of the earnings brought in the future.

Abstract The objective of our paper is to analyze, how valuation practice deals with inflation especially for the terminal value, and how company value is influenced by assumptions set by practitioners. For that reason, we examine how vulnerable companies could be regarding struggles to pass on inflationary effects to their customers. We analyze the inflation rates assumed for the steady-state (terminal value) by comparing them to different estimators for the inflation rate expected at the valuation date (Survey of Professional Forecasters, inflation rates derived by comparing real and nominal rate of returns, inflation swaps). We quantify the implications of using different inflation rates for future cash flow development, terminal value and the company value at the valuation date, and compare nominal reported values with company values in a (hypothetical) world without inflation. Our sample consists of 263 valuation reports written by German auditors with valuation dates between 2000 to 2021. Most of the reports aim at determining the price per share to compensate minority shareholders during a squeeze-out. Our results question inter alia the preference for a constant company specific inflation rate of around 1% on average, and we quantify a number of value effects.

In this paper, the surplus process (before taxes are deducted) for an insurance company evolves as a spectrally negative Lévy process with the usual exclusion of negative subordinator or deterministic drift. Tax payments are collected according to the very general loss-carry-forward tax system introduced in [20]. We consider an optimal tax problem taking into account both the expected discounted tax payments and the time value of ruin. The optimal tax value function and the optimal tax strategy are derived, some numerical examples are also provided. [ABSTRACT FROM AUTHOR]

The objective of our paper is to analyze, how valuation practice deals with inflation especially for the terminal value, and how company value is influenced by assumptions set by practitioners. For that reason, we examine how vulnerable companies could be regarding struggles to pass on inflationary effects to their customers. We analyze the inflation rates assumed for the steady-state (terminal value) by comparing them to different estimators for the inflation rate expected at the valuation date (Survey of Professional Forecasters, inflation rates derived by comparing real and nominal rate of returns, inflation swaps). We quantify the implications of using different inflation rates for future cash flow development, terminal value and the company value at the valuation date, and compare nominal reported values with company values in a (hypothetical) world without inflation. Our sample consists of 263 valuation reports written by German auditors with valuation dates between 2000 to 2021. Most of the reports aim at determining the price per share to compensate minority shareholders during a squeeze-out. Our results question inter alia the preference for a constant company specific inflation rate of around 1% on average, and we quantify a number of value effects. [ABSTRACT FROM AUTHOR]

Suppose that insurer can control dividend, refinancing and reinsurance strategies dynamically. Different from the past, there are multiple reinsurers rather than sole reinsurer in the market. The insurer aim at finding the optimal strategies for maximizing the company's value. It illustrates that refinancing can be considered iff the company has strong profitability; It should reduce reinsurance purchase when the surplus increases. The amount of risk ceded to the reinsurer depends on its risk attitude. The optimal dividend policy is of barrier type when the dividend rate is unbounded and is of threshold type when the dividend rate is bounded. • Study the optimal dividend, reinsurance and refinancing control problem. • Assume that there are multiple reinsurers with different risk attitudes. • Take into account the transaction costs and the terminal value at bankruptcy. • Demonstrate how solutions can be found and provide the explicit solutions. [ABSTRACT FROM AUTHOR]

We extend risk-value models for valuing streams of risky cash flows by establishing the well-known concept of terminal value in this context. For a constant growth assumption we are able to derive upper and lower bounds for the terminal value in the case of a translation-invariant and in the case of a position-invariant risk measure. For both cases we also obtain an exact formula under a special growth assumption for the future cash flows. Furthermore, we provide results on the applicability of the general findings for the case that the log-return of the risky investment follows a Brownian motion. [ABSTRACT FROM AUTHOR]

In the setting adopted by Edmond and Thibault [Relaxation of an optimal control problem involving a perturbed sweeping process, Math. Program. 104 (2005), 347-373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for the perturbed sweeping processes with the constraint sets being prox-regular sublevel sets. The results are applied to the behavior of some concrete mechanical sweeping processes, which appear for the first time in this paper. [ABSTRACT FROM AUTHOR]

In this paper we consider two cases of optimal implementation delay of taxation with trade-off under spectrally negative Lévy insurance risk processes. In the first case, we assume that the insurance company starts to pay tax only when its surplus level reaches a certain level, and at the termination time of the business there is a terminal value incurred to the company. A method is developed to determine the optimal starting-tax surplus level at which the total expected discounted value of all tax payments up to the termination time plus the discounted terminal value is maximized. In the second case, the company still pays tax subject to a starting-tax surplus level, but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the total discounted capital injection costs is maximized to determine the optimal starting-tax surplus level. Numerical examples are given at the end to illustrate the existence of positive optimal starting-tax surplus levels for both cases considered in this paper. [ABSTRACT FROM AUTHOR]

Corporate valuation often relies on the assumption of a constant and homogenous growth rate. However, large firms frequently (re)balance their activities by diverting cash flows from some business units to fund investments in other units. We develop a value driver model of terminal value for a firm with two units. The model relaxes common assumptions and allows for cross-unit differences in the return on invested capital. We consider intra-unit and cross-unit investments and show their implications for firm value and the long-term development of key accounting variables. Our results help characterize business unit strategies that can be reconciled with popular firm strategies such as the constant payout and constant growth strategies. We find that popular valuation methods that assume both constant payout ratios and constant growth rates (e.g., Gordon and Shapiro, Manage Sci 3:102–110, 1956) constitute a restrictive special case of our model and should only be applied to firms with homogenous business units. We use a simulation analysis to compare our results with alternative valuation models and to illustrate the economic relevance of our findings. The simulation shows that an accurate depiction of business unit strategy is particularly useful if firms plan large-scale cross-unit investments into business units with high returns and if the cost of capital is low. [ABSTRACT FROM AUTHOR]

Novel suggestions and insights on corporate valuation are provided adopting a still unconventional approach: fuzzy logic. It recalls the (Sophist) concepts of imprecision, vagueness, and ambiguity, overcoming the common (Aristotelian/Boolean) logic founded on dichotomy. Fuzziness has been applied to economics and appears, for most part in cognitive contexts characterized by uncertainty and complexity, growingly adequate to business and information sciences. In this paper, our goal is to revisit and expose the future horizon value attributable to a business after n years (in the medium and long term, beyond the normal five-to-ten-year forecast period) through a fuzzy multivalent number, rather than a limiting crisp (single-valued) one. Since the “continuing” or “terminal” value is a big slice of the overall corporate value, such “picture” results in an amusing and suggestive (impressionistic) visualization, as financial numbers are looked through deconstructing and zooming lens. Abductively, absolute conclusions on business values are precluded, but several levels of feasibility or adequacy are possible, showing a blurry multiplicity of gathered numbers. The fuzzy approach enlarges the extent of the sensitivity analysis made by the expert (appraiser) and enables the decision makers (administration) having for processes or predictions more information with characteristics of completeness, transparency, and credibility. Finally, the approach sheds light on different value possibilities rather than sharply estimating and releasing only one single (most likely) value. [ABSTRACT FROM AUTHOR]

In any context where a discounted cash flow valuation is required, there is the issue of estimating the continuing value. The most common way to do that is to assume that by the terminal horizon the company is in a steady state and is growing at a constant rate. The issue is how to handle inflation. The problem is that it is often done wrong and the impact is typically material. Because there remains significant confusion, in this paper we simplify the analysis by isolating the two key issues and providing example calculations. We show that even at the current 2% level proper treatment of inflation has a sizeable impact on valuation. If inflation were to accelerate as a result of current monetary and fiscal policies, the significance of this issue will increase. [ABSTRACT FROM AUTHOR]

When a firm is at the edge of bankruptcy, it would endeavour to attract bailouts from governments or financial institutions to cast off bad situation. If this effort fails, then the firm would face to sell off their properties to pay their debts to loaners or shareholders. In this paper, from these two cases of bankruptcy, two optimal dividend policies are considered and analysed, respectively. In the case of unrestricted dividend payment rate, a terminal bankruptcy model with non-zero terminal value is put forward. An analytic solution for the optimal objective function, which maximizes the expected value of total discounted dividends before bankruptcy and the residual value at bankruptcy, is provided and verified. As a significant application, a non-terminal bankruptcy problem with bailouts is considered, an explicit solution and the corresponding control policies are also obtained. In the end, some numerical examples are listed and the influence of the recovery rate on the optimal strategies is also discussed. [ABSTRACT FROM AUTHOR]

This study focuses on answering whether EV/EBITDA multiple of public companies in the food industry can be useful to obtain the Terminal Value (TV) in the valuation of unlisted small and medium-sized food companies. A case study into Spanish unlisted agribusinesses is designed for several samples and accounting years from 2010 to 2013. By means of a discounted cash flow (DCF) model combined with bootstrap techniques, the TV/EBITDA empirical distribution of the unlisted multiples is obtained for two different scenarios of free cash flow (FCF) growth, and then compared with the EV/EBITDA of the listed companies in the same industry. The results show that the stock market EV/EBITDA multiple may be used to determine the TV in the valuation process of unlisted small and medium-sized food companies that consistently obtain positive cash flows. [ABSTRACT FROM AUTHOR]

This paper assumes that an insurer can control the dividend, refinancing and reinsurance strategies dynamically. Particularly, the reinsurance is provided by two reinsurers and the variance premium principle is applied in pricing insurance contracts. Using the optimal control method, we identify the optimal strategies for maximizing the insurance company's value. Meanwhile, the effects of transaction costs and terminal value at bankruptcy are investigated. The results turn out that the insurer should consider refinancing when and only when the transaction costs and terminal value are relatively low. Also, it should buy less reinsurance when the surplus increases, while the proportion of risk allocation between two reinsurers remains constant. When the dividend rate is unbounded, dividends should be paid according to the barrier strategy. When the dividend rate is restricted, dividends should be distributed according to the threshold strategy. Some examples are provided to illustrate the implementation of our results. [ABSTRACT FROM AUTHOR]

The paper presents an empirical verification of the main assumptions underlying the calculation of terminal value in DCF valuation models. The test results suggest that the volatility of free cash flows and the dynamism of the operating environment do not allow us to make a reliable long-term forecast of value creation potential of the public companies in Poland. Regardless of their organic growth phase, the overwhelming majority of the sampled firms are evidenced to exhibit extreme year-on-year fluctuations of sales, investments and cash flows over the short- and medium-term observation windows. The variability of operating results and the probabilistic nature of company- -level fundamentals may preclude the possibility of constructing a reliable cash flow forecast for the purposes of a DCF valuation. This methodological issue appears to pose a particular challenge during the calculation of terminal value, which is heavily dependent on highly subjective and uncertain steady-state fundamentals. Therefore, the predictive power of the deterministic DCF models may be reduced to a snapshot of the current market sentiment regarding a particular stock. The paper postulates that a further discussion on the tenets of terminal value calculation may be necessary in order to overcome the existing flaws and increase the accuracy of valuation models. We contribute to this discussion by outlining the principal methodological and theoretical issues which challenge the practicing valuators at the stage of terminal value calculation. Our conclusions may help to shed light on the problems of market short-termism, and high inconstancy of investment recommendations. [ABSTRACT FROM AUTHOR]

The aim of the present article is to reveal the peculiarities of assessing the impact of innovations on the cost of the company capital. According to scientific and methodological approaches presented in this article, the innovation process is represented by the complex events that can be decomposed into factors as a result of the analysis of the principal characteristics and forms of innovation. This approach allows using the available statistical tools to identify the most important factors affecting the growth of the company value. The company valuation is carried out on the basis of assessment of the impact of factors on the innovation process as a result of which the company value may increase. On one hand, this allows to provide a set of key financial indicators characterizing the results of the innovation process and, on the other hand, correctly assess the future economic benefits of the company as a result of innovations. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to establish whether a terminal value is a substantial amount of the final figure in a hotel’s valuation. Malta’s scenario has been delved into. This due to the fact that owing to Malta’s high population density and its restrictive land area, land values attract a high premium as compared with larger developed countries. Other matters such as earnings’ multipliers derived from a cap rate (initial yield), CAPEX has also been delved into. Design/methodology/approach – The methodologies adopted in hotel valuation practice has been delved into. An extensive literature review is undertaken to analyse the earnings multiplier adopted by various authors over the past 30-year period. The hotel cap rate (initial yield) has been compared with similar yields adopted in the institutional and property markets and then compares to market-based data. A discussion is undertaken on the validity of adopting discounted cash flow, as against the short cut market appraisal approach. Capitalization rates, cap rates have also been referred to as obtained from the academic and practitioners field and compared. Depreciation and the anticipated annual accommodation charges have been analysed. A database of hotel rooms value over the past 20-year period has been referred. Findings – A table outlines the earnings’ multipliers in perpetuity or for the limited expected design life for various cap rates. This data will act as a guide in guiding practitioners to establish an earnings’ multiplier to be applied in their valuation methodology. An example in the Appendix clarifies the manner in which this data table is to be utilized. The finding of this example notes that for this hotel in Malta, as constructed on private land, the terminal value for this development hovers around the 30 per cent of the market value. Research limitations/implications – This analysis is based on five valuations as undertaken on five hotels in Malta with classification grades varying from III to V. This notes that the terminal value varies within a range of 9-45 per cent of the total value. This analysis has to be undertaken for other countries for a global range of land terminal values percentages to be established. Practical implications – Establishing the terminal value of a hotel business, will offer greater security for secured lending facilities required. It will further act as an important tool to establish the feasibility of a hotel development. Originality/value – Updated insight is given to existing hotel valuation methodologies by delving into the workings of the earnings’ multiplier and establishes that in today’s market the terminal value of the hotel basis has to be accounted for. The above findings are based on a link between theory and practice. [ABSTRACT FROM AUTHOR]

It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution continuously depends on the given function, the initial value, and the order of the derivative. Here, we extend this well-posedness concept to the extent that we also allow the location of the starting point of the differential operator to be changed, and we prove that the solution depends on this parameter in a continuous way too if the usual assumptions are satisfied. Similarly, the solution to the corresponding terminal value problems depends on the location of the starting point and of the terminal point in a continuous way too. [ABSTRACT FROM AUTHOR]

The merits of accruals in forecasting cash flows or mitigating the volatility of financials shortly after the valuation date are indisputable. However, the usefulness of accounting in equity valuation is very limited if we step beyond a certain forecasting horizon. In this paper, this limitation is emphasized by shedding new light on the accounting-based value driver model ( VDM), a widely used constant-growth terminal value tool that uses accounting variables as input. The paper shows that, if the lifetime of a firm's assets is, on average, longer than one period, the VDM works accurately only in an idealized academic environment with an even historical corporate investment activity, a single depreciation method for all assets, and no historical inflation volatility. Artificially adjusting real-world figures to this steady state is possible in principle, but bloats the valuation model and requires exactly the same information that is used in our cash flow-driven benchmark model (where no adjustment phase is necessary). Beyond these theoretical shortcomings, the VDM is also prone to being misused in valuation practice due to its reliance on book (rather than economic) rates of return, and to its shortcomings in dealing adequately with the assets with an ex ante indefinite lifetime. [ABSTRACT FROM AUTHOR]

We formulate a generalized constant growth valuation model incorporating inflation and capital maintenance. We find that in general there are two sources of growth: growth due to capital maintenance and growth due to net new investments. The generalized version of the constant growth model allows the reconciliation of the existing literature, particularly the works of Gordon and Shapiro (1956), Lally (1988), and Bradley and Jarrell (2008), which all employ particular definitions of capital maintenance. Evaluating the practical relevance of either model we find that each model is best suited for a very particular company set-up, which does not necessarily correspond to the commonly observed business models. The generalized version of the constant growth valuation model, however, presents a flexible approach that is capable of capturing various conceptions of capital maintenance. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then the objective is set to make a dynamic choice of reinsurance policy and dividend distribution policy, which maximizes the sum of the expected discounted dividends up to ruin time and the expected discounted terminal value. There are two novelties in this paper. Firstly, we formulate the optimal control problem in terms of general reinsurance control policies. Each of the proportional reinsurance, the excess-of-loss reinsurance and combination of the two can be treated as a special case. It is shown that, under an expected premium principle, the dynamic excess-of-loss reinsurance is of optimal type within the general reinsurance contracts. Secondly, considering the excess-of-loss reinsurance policy and terminal value, we obtain the explicit expressions for the value function and optimal control policies by solving the HJB equation method. At the end of this paper numerical calculations are done to illustrate the influence of the terminal value on the value function and optimal policies as well. [Copyright &y& Elsevier]

The article focuses on the debate on dividend policy in the academic and practitioner communities. American economist Fischer Black found the idea of firms paying dividends puzzling. Although past research has studied how dividends affect the value of a stock and to the stream of cash dividends. Black said that the duration of the stock changes when dividends are paid.

This paper analyses the issue of the timing of expenditures in replacing fixed assets within the context of valuing firms using the free cash flow approach. Standard practice amongst both practitioners and academics is to assume a smooth pattern in these expenditures past some future point, and such a pattern is improbable. This paper develops a model that rests upon much less restrictive assumptions, shows that the model is readily amenable to implementation, and that the difference in valuation results could be quite substantial. [ABSTRACT FROM AUTHOR]