# 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

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**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.

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**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