## Introduction

In business consulting, company valuations are getting harder. 90’s stability is over and now we hear about shark tanks or machine learning estimation techniques. However, guidelines and practitioners are becoming ever more prepared in calculating business value, even in particular cases such as real estate or family law and divorce valuation. In this context, a contingency approach can provide a reliable and actual analysis.

## Table of Contents

- Introduction
- Business valuation: definition and state of the art today
- How company valuation is done?
- The contingency approach
- Bibliography

## Business valuation: definition and state of the art today

Business valuation can be defined as the complex process of analysis designed to

abstractfrom a business its, with reasonable confidence.actualvalue

Analytically:

**Complex process**, because the analysis assesses the company, that is inherently complex;**Abstract (and extract)**, because the appraiser has to bring the valuation in another dimension, with a point of view as omniscient as possible;**Actual value**, because the goal is to estimate how much the business is actually worth;**Reasonable confidence**, because unequivocal assessments are out of question. The company is also an entropic system, so not entirely measurable.

Not so long ago, valuation experts were alerting us about the progressively models’ **inconsistency** due to the hyper-competition, uncertainty and turbulent times. There is a massive literature about valuation and at the same time, we have practically learned how to manage and adjust techniques according to the specific valuation project.

Nevertheless, it is not enough. It is opening up a post-pandemic wave, but we are already able to state that models are needed to be revised: it is crucial to change the role of risk, from input variable to the **main driver** to be considered when approaching the estimation of corporate value (Massari, Gianfrate, Zanetti, 2016). It is not a chance that Basil IV has been showing concern for **risk** recently.

### Value: a clarification

The company value is determined by a set of tangible and intangible factors **technically estimated** by the practitioner. Indeed, it is useful to mention the difference between value and price: the first is what you *[the assessor –Ed.]* think it is worth; while the price is decided by the market. The **degree of subjectivity** is different.

Having said that, we can decline value into two dimensions:

Valuation Categories | Book Value | Market Value |
---|---|---|

Equity Value | Shareholders’ equity | Market Capitalization |

Enterprise Value | Shareholders’ equity + Any potential debts and obligations – Cash and Cash-equivalents | Market Capitalization + Any potential debts and obligations – Cash and Cash-equivalents |

It is now clear that, beyond interpretation, value differs according to the object-category. The balance sheet returns the book value and the capitalization – that is based on stock price – returns the market value. In this way, in order to obtain the **enterprise value**, we have to add back any potential debts and obligations less cash and cash-equivalents.

### Start-up and SMEs: valuing companies lacking in historical data

Each evaluation should depend on the range that is being gone through by the company in its **lifecycle**. This is the rule of thumb. In addition to lacking in historical data, startups and SMEs are often dependent on private equity, systematically at a loss and in a high-risk phase or in any case many do not survive (Damodaran, 2010). Something similar can be told regarding **family law** and **divorce**.

In light of this, we have to deal with these variables in order to avoid assessment’s inconsistencies. Thus, applying Discounted Cash Flow (DCF) and Capital Asset Pricing Model (CAPM), some adjustments need to be done. For instance, Marcello & Pozzoli (2019) suggest:

- Adjustments about public insights from data sources related to big companies;
- Adjustments about risk (higher in SMEs than MNEs);
- Adjustments about the lack of reliable peer groups for β;
- and so on.

A further well-known limit of CAPM is that its does not entirely explain the risk/reward relationship, especially in case of SMEs (Guatri e Bini, 2007). Indeed, smaller companies have shown **higher rewards** on equal Beta, sign that investors and analysts apply an higher cost of capital to there companies: it is the so called *small size effect*. These are the challenges that **venture capitalists** have faced for decades when providing “angel financing” to small companies (Damodaran, 2010).

## How company valuation is done?

The 5 basic phases in the business valuation process are:

### 1) Assignment to the valuation expert according to the **valuation purpose**

Standards and premises of value change the perspective (e.g. going concern or liquidation?);

### 2) Data gathering and cleaning

Developing a solid, demonstrable and suitable **information base** for the fundamental analysis is crucial. According to Guatri e Bini (2009), the information base is divided into:

– Information base for absolute valuations (strategic and historical analysis, rates, assets, etc.);

– Information base for acquisitions (dormant opportunities, synergies, etc.);

– Information base for relative valuations (comparable companies and transactions).

### 3) Fundamental analysis in practice

It is the core step because the assessor is making assumptions, accounting data is being normalized and aligned to IAS/IFRS, the intangibles are being integrated and the cost of capital as well as future projections are being estimated;

### 4) Application of absolute and relative criteria

Once data is speaking, it is crucial to design a model kit coherent to previous steps, thus the business assessor will choose models (asset based valuation, DCF, etc.) and formulas (P/E, EV/EBIT, etc.), in line with the aim;

### 5) The integrated valuation report

Here, the entire process has to be made **accessible** to the end-user (the company itself, the bank, the market, etc.). Authorities such as CBV in Canada, IdW in Germany, OIV in Italy and so on have made a great contribution about the content of the report in order to be as much solid as possible.

### Valuation methods

As can be imagined, there is not a single method better than others, nor one most accurate. Hereafter, we will distinguish:

*Going concern*premise:- Equity methods (well known in real estate valuation): for instance the asset-based valuation;
- Income methods (big in the ’60/70s): average expected income;
- Mixed methods;
- Financial methods (progressively preferred after the inflation stabilization): DCF, Monte Carlo, etc.;
- Multiplies and Comparables: P/E ratio, EV/EBITDA, FCF, etc.

*Liquidation*premise:- Summation of single assets/liabilities (recoverable value vs market value approach).

### Discounted Cash Flow (DCF) analysis

We are going to analyze here the conventional DCF method because of it is simplicity and rationality. More importantly, it factors in the time value of money by discounting consecutive cash flows, it is roughly insensitive to different accounting conventions, and it includes a basic risk structure, captured by the **risk-adjusted discount rate** (Massari, Gianfrate and Zanetti, 2016).

The basic Discounted Cash Flow (DCF) formula is:

As can be seen, the strength of this model is provided by:

**Present Value (PV)**, because it considers the discount factors: time and rate, as the vehicle for all uncertainty (Damodaran, 2010). It is calculated as*UFCF * (1 + r)*^{Period};**Discount rate (r)**, because it is based on investors’ expectation to be returned. For the sake of simplicity, we can use the Weighted Average Cost of Capital (WACC), that is calculated as:*Debt/(Debt + Equity) * Cost of debt * (1 – Tax%) + Equity/(Debt + Equity) * Cost of equity;***Unlevered Free Cash Flow (UFCF)**, because they are CF “adjusted” to run to the future. Some authors use NOPLAT or even EBITDA; here they are calculated as*Net income + Depreciation & amortization + Deferred taxes + Other non-cash items + Working capital changes – Capital expenditures + A/T Net interest expense*;**Terminal Value (TV)**, because it shifts the focus to the company value*after*the last projected year. It is calculated as*UFCF * (1 + g) / (r – g)*. Where r is WACC and g should represent the perpetual rate of cash flow growth. “g” is not easy to estimate. Some people suggest using the GDP growth rate (currently 2–3%) or the rate of inflation (1–2%), but remember this is supposed to represent the growth rate for many years, even if the current environment is sluggish (Pignataro, 2013).

## Rates, WACC, Beta and CAPM

Identifying the appropriate discount rate is a crucial phase: rates affect absolute and relative criteria, several calculation methods and the valuation reliability in general. Even though the appraiser adopts technical approaches, the rate selection is strongly dependent on **interpretation**.

Since every in/outflow represents **capital movements**, the appraiser has to estimate how much that capital costs the company in order to obtain a proper discount rate.

Cost of capital is the

Pratt, 1998expected rate of returnthat the market requires in order to attract funds to a particular investment.

Here, we are going to focus on the Weighted Average Cost of Capital (WACC), as a discount rate able to describe the capital structure in a percentage.

Let’s analyze WACC components.

### Cost of debt

The cost of debt (K^{d}) represents a normal *long-term* and *pre-tax* cost of debt, given by the sum of:

**Risk free rate**of return in the long period (based on the context where the company competes);**Default spread**, according to the firm’s creditworthiness.

Obviously, since payable interests are **deductible**, we have to multiply that by (1 – Tax%). So, if the Tax Rate is 35%, the after-tax K^{d} would be 5% * (1 – 35%) = 3,25%. This aspect is often underrated in business valuation with debt.

### Cost of equity

Guidelines suggest a number of cost of equity (K^{e}) estimation methods: CAPM, Build-up approach, Fama & French, Arbitrage Pricing Model (APM), Residual Income Model, Market Derived Capital Pricing Model (MCPM), LBO valuation and many more. Hereafter, we will discuss the **Capital Asset Pricing Model (CAPM)** as the main pillar in the international literature and as the most widely used today (Laghi & Di Marcantonio, 2016).

According to the CAPM, K^{e} is given by the sum of:

**Risk free rate**of return as the*“price of time”*(based on the context where the company competes). There are several proxies for risk free rate:- Government Bonds (e.g. yield-to-maturity 5,1% on US 10Y bonds benchmark, source: Datastream);
- Interbank rates (e.g. LIBOR, EURIBOR, EONIA, etc.);
- Swaps rates (e.g. USD swaps or Euro Interest Rate Swap).

**Comprehensive risk coefficient**as the*“price of risk”*, computed as*β * ERP*. Where:- β is the coefficient expressing how an asset moves compared to the moves of the overall stock market. But how to properly calculate Beta coefficient?
- Raw similar β identification: comparable public stock Betas are a good starting point (
*Ibbotson Associates*represent a respected data source in this field, as well as*Barra, Bloomberg*or*Thompson Capital*); - Adjusted β estimation: weighted average of historical raw Beta and market Beta (weights 2/3 and 1/3). This is the
**Blume technique**, useful to improve the raw estimator due to its historical point of view*[we need to look at the future in DCF analysis –Ed.].* - Unlevered β estimation: Betas represent the overall company risk: so, in order to distinguish
**inherent risk**and**systemic risk**, we have to “un-lever” Beta for each company adopting the so-called**Hamada formula**:*levered β / (1 + Debt/Equity * (1 – Tax%));* - Unlevered average β computation;
- Re-levered β computation: since we have to take into account Debts too, Beta has to be re-levered as follows:
*unlevered β * (1 + Debt/Equity * (1 – Tax%))*.

- Raw similar β identification: comparable public stock Betas are a good starting point (

- ERP is the
**Equity Risk Premium**: the differential between the*Market rate of return*and the risk free rate itself. Damodaran’s table provides updated ERP estimation for each country.

- β is the coefficient expressing how an asset moves compared to the moves of the overall stock market. But how to properly calculate Beta coefficient?

At this point, WACC limits are self-evident. That is why even CAPM has been often criticized. However, an expert and certified valuation analyst is surely able to **manage** these tool pondering pros and cons, knowing that he does not act as a crystal ball gazer. In this sense, the subjectivity elimination is unhelpful, especially if it needs **historical costs**‘ adoption: they are unsuitable both for market signals and exchange values (e.g. M&A purchase method). Moreover, the difference between historical and current values can be significant due to market trends and inflation.

## The contingency approach

Basically, the idea behind the contingency approach is to put the valuation into **context of space-time**: the method selection according to premises is not enough anymore, it is necessary that even the key drivers identification as well as the assumptions are declined into the particular case faced by the practitioner. It is no longer recommended to merely explain rates, risks and adjustments at the end in the opinion report, it is better to **reverse the process** and starting with cleaned data and a fundamental analysis *already aligned* to the business valuation space and the time.

In this sense, we can not hide behind math and formulas hoping to be in the *true side of valuation*. We cannot adopt DCF in every single case because of its pros: Kaplan & Ruback (1996) prefer multiplies methods than DCF in case of M&A, Leveraged Buyout, IPO and more. Nevertheless, neither do they consider future opportunities, goodwill externalities or investment plans’ suspensions, thus **dynamic approaches** come into play with real options valuation (Di Mascio, 2013). In conclusion, past mistakes tell us what not to do anymore while we are living in a superfast economy; on the other hand, machine learning and new business valuation tools could be a great help, so the appraiser’s mindset must necessarily be aligned to these challenges.

## Bibliography

DAMODARAN A. (2010). *The dark side of valuation: valuing young, distressed and complex businesses. *Upper Saddle River, New Jersey: Pearson Education, Inc.

DI MASCIO A. (2013). *Investire con l’analisi fondamentale. *Milano: Egea.

GUATRI L. & BINI M. (2007). *La valutazione delle aziende. *Milano: Egea.

KAPLAN S. N., RUBACK R.S (1996). The Market Pricing of Cash Flow Forecast: Discounted Cash Flow vs. the Method of Comparables. *Journal of Applied Corporate Finance*, 8, issue 4, p. 45-60. Available at: https://EconPapers.repec.org/RePEc:bla:jacrfn:v:8:y:1996:i:4:p:45-60.

LAGHI E., DI MARCANTONIO M. (2016). Beyond CAPM: estimating the cost of equity considering idiosyncratic risks, in *Quantitative Finance*, 16, 8: 1273-1296.

MARCELLO R. & POZZOLI M. (2019). Critical issues when valuing small businesses. Business valuation OIV journal spring 2019. 47-59. Available at: https://www.fondazioneoiv.it/wp-content/uploads/2019/06/Critical-issue-when-valuting-small-businesses.pdf

MASSARI M., GIANFRATE G., ZANETTI L. (2016). *Corporate Valuation. Measuring the Value of Companies in Turbulent Times.* Hoboken, NJ: John Wiley & Sons.

PIGNATARO P. (2013). *Financial Modeling and Valuation.* Hoboken, NJ: John Wiley & Sons.

PRATT S. P. (1998). *Cost of Capital. Estimation and Applications.* New York: John Wiley & Sons.