On the use of the terminal-value approach in risk-value models

Abstract

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 translationinvariant 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.

A decision model to value football player investments under uncertainty

“…For the valuation, we need to quantify the market return λtσ. We assume that the return of the market index follows a log-normal distribution, which can be modeled via Brownian motion (Dorfleitner and Gleißner, 2018; Dorfleitner, 2022) [9]. We can describe λtσ asλtσ expresses the additional return of an investment in the risky alternative investment (market index) compared to a risk-free investment (with interest r f ) per unit of risk.…”

“…However, earning risks and insolvency risks are considered in the valuation. To this end, the risk factors are analyzed on a quantitative basis using Monte Carlo simulation (for see Dorfleitner and Gleißner, 2018; Dorfleitner, 2022). To date, the main field of application has been company valuation (e.g.…”

“…Markowitz, 1952;Sharpe, 1964;Modigliani and Modigliani, 1997), which expresses the amount of risk via the extent of possible fluctuations around the expected value. The standard deviation is a coherent risk measure according to Artzner et al (1999; see also Rockafellar et al, 2002), and it meets the characteristics of homogeneity and position invariance, which makes it a suitable basis for a risk-adequate assessment using the method of imperfect replication (see Dorfleitner and Gleißner, 2018;Dorfleitner, 2022). Furthermore, we use this risk measure in the case study because it corresponds to the usual understanding of risk in a company and to investment valuation due to the m,σ-principle on which the CAPM is based.…”

Paradigm Shift in Finance: The Transformation of the Theory from Perfect to Imperfect Capital Markets Using the Example of Company Valuation

“…The risk content of the cash that flows from the simulation can be expressed by a risk measure, such as the standard deviation or the value at risk of the cash flows. The risk measure can be directly converted into a matching risk-adjusted discount rate (or a certainty equivalent; for the basics of valuation with risk-value models and the procedure of "imperfect replications", see Dorfleitner and Gleißner 2018;Dorfleitner 2020). In contrast to the traditional "capital market-oriented" valuation, the cost of capital in a simulation-based valuation can be derived directly from the earning risk.…”

Simulation-Based Business Valuation: Methodical Implementation in the Valuation Practice

“…The insolvency scenarios, possibly as a result of the risks, and thus the insolvency risk, can also be easily reflected in the valuation calculation. Dorfleitner andGleißner (2018), andDorfleitner (2020), have presented the formal framework of the simulation-based valuation. It has not yet been shown how the connection to the DCF models used in the valuation practice can be established.…”