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

## Abstract

**:**

## 1. Introduction

## 2. The Concept of the Simulation-Based Company Valuation

- consideration of the corporate risks,
- and application of a Monte Carlo simulation for risk aggregation.

- Only simulation-based planning can derive the comprehensible, unbiased, expected values of cash flows.
- A plausibility check of the planning and planning logic is carried out through risk identification, risk quantification, and risk aggregation.
- With a simulation-based valuation, the effects of insolvency risk on the company value can be easily incorporated into the valuation model.
- A simulation-based business valuation enables the derivation of a risk-adequate cost of capital directly from the risk analysis of the simulation results.
- The simulation-based valuation is also a suitable basis for the preparation of entrepreneurial decisions.
- A simulation-based valuation is the only valuation method that meets the legal requirements and auditing standards for risk management.

- the certainty equivalent method or
- the risk premium method.

## 3. Valuation with the Certainty Equivalent Method

## 4. Valuation with the Risk Premium Method

## 5. A Comparison between the Certainty Equivalent Method and the Risk Premium Method

## 6. Calculation of Simulation-Based Cost of Capital for the Risk Premium Method

## 7. Calculating the Simulation-Based Enterprise Value

#### 7.1. Valuation Equations for the Risk Premium Method

#### 7.1.1. Calculation of the Terminal Value in the Continuation Phase

#### 7.1.2. Calculating the Enterprise Value in the Detailed Planning Phase

#### 7.2. Valuation Equations for the Certainty Equivalent Method

#### 7.2.1. Calculating the Terminal Value in the Continuation Phase

_{0}with the factor a and is then multiplied by a rate q in each case up to period n, has the following equation.

- Rate 1: the risk rate RR, which reduces the factor a in each period, acts like a negative growth rate, and leads to a decreasing geometric sequence.
- Rate 2: the insolvency probability p, which reduces the factor a in each period, acts similarly to a negative growth rate, and leads to a decreasing geometric sequence.
- Rate 3: the growth rate g, which increases the factor a in each period and leads to an increasing geometric sequence.

#### 7.2.2. Calculating the Value of the Company in the Detailed Planning Phase

## 8. Application of the Valuation Formulas

- Creation of the distribution functions of the risk parameters for the Monte Carlo simulation.
- Integration of the risk parameters into the planning of the income statement and the balance sheet.
- Calculation of the probability of insolvency.
- Calculation of cash flows to equity as a target values of the Monte Carlo simulation.
- Risk analysis of the cash flows to equity.
- Pricing of the risk.
- Derivation of the cost of equity for the risk premium method.
- Calculation of the risk-adjusted cash flow to equity for the certainty equivalent method.
- Calculation of the company value with the risk premium method.
- Calculation of the company value with the certainty equivalent method.

## 9. Results

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Brennan, Michael J., and Ashley W. Wang. 2010. The mispricing return premium. Review of Financial Studies 23: 3437–68. [Google Scholar] [CrossRef]
- Dempsey, Mike. 2013. The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance? Abacus 49: 7–23. [Google Scholar] [CrossRef]
- Dorfleitner, Gregor. 2020. On the use of the terminal-value approach in risk-value models. Annals of Operations Research, 1–21. Available online: https://epub.uni-regensburg.de/43131/1/Dorfleitner2020_Article_OnTheUseOfTheTerminal-valueApp.pdf (accessed on 22 February 2022). [CrossRef]
- Dorfleitner, Gregor, and Werner Gleißner. 2018. Valuing streams of risky cashflows with risk-value models. Journal of Risk 20: 1–27. [Google Scholar] [CrossRef]
- Ernst, Dietmar, and Joachim Häcker. 2017. Financial Modeling: An Introduction Guided to Excel and VBA Applications in Finance. London: Palgrave Macmillan. [Google Scholar]
- Ernst, Dietmar, and Joachim Häcker. 2021. Risikomanagement im Unternehmen. Bandar Seri Begawan: UTB. [Google Scholar]
- Ernst, Dietmar, and Uwe Wehrspohn. 2022. When Do I Take which Distribution? Berlin: Springer. [Google Scholar]
- Fama, Eugene F., and Kenneth R. French. 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33: 3–56. [Google Scholar] [CrossRef]
- Fama, Eugene F., and Kenneth R. French. 2008. Dissecting Anomalies. Journal of Finance 63: 1653–78. [Google Scholar] [CrossRef]
- Fama, Eugene F., and Kenneth R. French. 2012. Size, Value, and Momentum in international Stock Returns. Journal of Financial Economics 105: 457–72. [Google Scholar] [CrossRef]
- Fama, Eugene F., and Kenneth R. French. 2015. A five-factor asset pricing model. Journal of Financial Economics 116: 1–22. [Google Scholar] [CrossRef][Green Version]
- Fishburn, Peter C. 1977. Mean-risk analysis with risk associated with below target returns. American Economic Review 67: 116–28. [Google Scholar]
- Gleißner, Werner. 2019. Cost of capital and probability of default in value-based risk management. Management Research Review 42: 1243–58. [Google Scholar] [CrossRef]
- Gleißner, Werner. 2020. Risikoanalyse und moderne Unternehmensbewertungsverfahren als Alternative zum CAPM. Controlling 32: 35–37. [Google Scholar] [CrossRef]
- Gleißner, Werner. 2021. Unternehmensbewertung: Methode und Nutzen. BewertungsPraktiker 3: 84–87. [Google Scholar]
- Gleißner, Werner, and Dietmar Ernst. 2019. Company valuation as result of risk analysis: Replication approach as an alternative to the CAPM. Business Valuation OIV Journal 1: 3–18. [Google Scholar] [CrossRef]
- Gordon, Myron. 1962. The Investment, Financing, and Valuation of the Corporation. Publisher Homewood, IL: Irwin. [Google Scholar]
- Haugen, Robert A. 2002. The Inefficient Stock Market: What Pays Off and Why. Hoboken: Prentice Hall. [Google Scholar]
- Hazen, Gordon. 2009. An extension of the internal rate of return to stochastic cashflows. Management Science 55: 1030–34. [Google Scholar] [CrossRef][Green Version]
- Novy-Marx, Robert. 2013. The other side of value: The gross profitability premium. Journal of Financial Economics 108: 1–28. [Google Scholar] [CrossRef][Green Version]
- Robichek, Alexander A., and Stewart C. Myers. 1966. Conceptual problems in the use of risk-adjusted discount rates. The Journal of Finance 21: 727–30. [Google Scholar]
- Rubinstein, Mark E. 1973. The Fundamental Theorem of Parameter Preference security valuation. Journal of Financial and Quantitative Analysis 8: 61–69. [Google Scholar] [CrossRef]
- Shiller, Robert J. 1981. The use of volatility measures in assessing market efficiency. Journal of Finance 36: 291–304. [Google Scholar] [CrossRef][Green Version]
- Shleifer, Andrei. 2000. Inefficient Markets: An Introduction to Behavioral Finance. OUP Catalogue. Oxford: Oxford University Press. [Google Scholar]
- Smith, James E. 1998. Evaluating income streams:a decision analysis approach. Management Science 44: 1690–708. [Google Scholar] [CrossRef][Green Version]
- Tversky, Amos, and Daniel Kahneman. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47: 280–84. [Google Scholar] [CrossRef][Green Version]
- Zhang, Chu. 2009. On the explanatory power of firm-specific variables in cross-sections of expected returns. Journal of Empirical Finance 16: 306–17. [Google Scholar] [CrossRef]

**Figure 1.**Distribution functions for modelling total sales, COGS, and general administrative expenses.

**Figure 10.**Calculation of the risk-adjusted cash flow to equity for the certainty equivalent method.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ernst, D. Simulation-Based Business Valuation: Methodical Implementation in the Valuation Practice. *J. Risk Financial Manag.* **2022**, *15*, 200.
https://doi.org/10.3390/jrfm15050200

**AMA Style**

Ernst D. Simulation-Based Business Valuation: Methodical Implementation in the Valuation Practice. *Journal of Risk and Financial Management*. 2022; 15(5):200.
https://doi.org/10.3390/jrfm15050200

**Chicago/Turabian Style**

Ernst, Dietmar. 2022. "Simulation-Based Business Valuation: Methodical Implementation in the Valuation Practice" *Journal of Risk and Financial Management* 15, no. 5: 200.
https://doi.org/10.3390/jrfm15050200