Asset Valuation

Last Updated on 25 November 2025

Asset Valuation surveys the art and science of quantifying what an asset is worth. It starts by defining what we mean by value: fair, market and book, explaining that every asset carries a measurable worth. It then offers an in‑depth exploration of the methodologies and insights that drive asset valuation.

Next, the text examines the three core valuation methods: absolute, relative and asset‑based. Absolute valuation, via discounted cash flow analysis, estimates an asset’s worth by projecting its future cash flows and discounting them at the cost of capital. Relative valuation benchmarks the asset against peers using multiples such as price‑to‑earnings or EV/EBITDA to capture market sentiment. Asset‑based valuation calculates net asset value by summing the market values of all assets and subtracting liabilities.

For each method, Asset Valuation highlights key assumptions, advantages and limitations to help investors select the most appropriate valuation framework. Lastly, the text dives into the most common approach for valuing yielding assets: the Discounted Cash Flows (DCF) method.

It is meant to serve as guide to both practitioners and the curious.

Foreword

Asset Valuation is the practice of translating expectations about future economic benefits into a clear numerical worth. Whether we refer to fair value, market value or book value, every asset carries a promise to its stakeholders and often that promise must be made explicit.

Effective valuation traces an asset’s history, assesses its present condition and forecasts its future potential. It blends quantitative methods with qualitative insight and asks us to balance hard data with informed judgment. Strong valuation sharpens our view of the economic environment, guides efficient resource allocation and strengthens risk management.

Valuation underpins critical business activities such as mergers and acquisitions, capital raising and financial reporting. Investors use it to spot undervalued opportunities and guard against overpriced risks. Companies rely on it to set strategy and allocate capital. Regulators depend on it to ensure transparency and protect markets.

In this text we explore the leading valuation approaches: discounted cash flow analysis, relative multiples and asset based methods. For each framework we examine its key assumptions, strengths and common pitfalls so you can select the right tool for every situation.

Whether you are an investor, manager or advisor this compendium will deepen your understanding of worth and equip you to make more confident decisions.

Introduction

We value every asset that has a potential economic worth, which is some monetary benefit to its owner. This includes businesses, real-estate assets, infrastructure, art, data sets and much more. We can value any physical or non-physical entity that holds any economic benefit.

Valuation is not an exact science. There is often no single value for an entity or asset, but a range of values, since valuations are subjective, biased and based on many assumptions. A valuation is only as good as its assumptions, the information it uses to model reality and its methodology.

Why do we value assets?
Valuation is made to provide information to stakeholders, to support decision making such as an asset purchase or for regulatory requirements like financial reporting. Other reasons include debt financing, litigation, liquidation, due diligence and risk management.

Since value is such a basic and substantial part of society, investors need to be able to quantify it so they can calculate their perceived risk exposures and benefits. When investors look for a measure to help them choose between various opportunities to employ their capital, they need to be able to somehow discern between assets. Basically, they would like to choose those that offer them the highest benefit for a given level of risk. Monetary benefit can be measured by net present value (NPV), which quantifies future economic value in today’s terms.

Other types of value and benefit exist, such as diversification, historical cost or ESG. But when capital is the focus, valuation is the answer.

Valuation is the closest point to a price, and a price has an inverse relationship with return. Investors seeking to maximize their return will seek to lower the asset’s price as much as possible, and valuation provides the framework for educated discussions.

Most importantly, valuation models can allow investors to try different assumptions and see how they influence the value.

What do we value?
Whatever asset we study, we value the benefit coming from its ownership rights after payment to all other stakeholders and resources.

We can either value an entity, which is some kind of a legal structure that wraps an asset, such as in the case of a company or partnership, or a specific asset(s) such as the case of a house, a patent or a financial instrument that then pass the economic value they generated to some entity. When we value an entity, we will often deduct the amount of capital owed to debtors from our valuation to reach an equity value. Equity value is the economic benefit of being entitled to the economic value originating from the asset.

In this text, all types of valuable assets, be it business entities, physical assets or financial instruments are simply referred to as “assets” or “entities”.

What is the valuation result?
A quantified value. We reach valuations by looking into the future, into the past and at the present moment, and each resulting value serves for a different purpose. Each approach results in a different type of value:

Present value of future benefit- reached by the income approach. When we want to quantify the economic value an asset holds, meaning the true benefit an owner can get out of it, we will look into the future and calculate an Intrinsic Value, also called Fair Value. This is a forward-looking approach that holds reference to both the asset’s projected future benefit and the risks involved in waiting for this benefit to come.

This is the amount at which an asset should be bought and sold at arm’s length in a specific point in time, if everyone knew and shared all information. This value is often used to know the true, real quantifiable benefit an asset can hold for its owners based on assumptions about the future.
Adjusted historical value- reached by the book value method of the asset-based approach and the statistics method of the market approach. This is a backward-looking approach that includes Book Value, which combines cost and accounting principles to value assets and liabilities in an entity’s balance sheet. Book value is usually calculated as historical cost minus depreciation and amortization, and represents the total amount of capital remaining if the entity sold all its assets and repaid all its financial obligations. This value is often used for regulatory compliance in the form of an entity’s financial statements.

When we value complex financial instruments through past deal statistical analysis, we analyze the past and use it to try and draw some conclusions that will help us foresee the instrument’s future cash flow scenarios. The result is the instrument’s Fair Value.
Current market value- reached by the multiples method of the market approach or the replacement cost and adjusted NAV methods of the asset-based approach. This is basically an estimation of the cash we can get now by selling the asset or entity in the free market. This is a present-focused method, which is often used for a quick company valuation or real-estate. Its result is either a Market Value or a Replacement Value (Cost).

Each type of value serves a different need. Every valuation results in a value and may result in a price. It is true for the time of its completion and the information used for its preparation. New, material information will change its result.

What influences value?

Present value of future benefit is basically influenced by two things: everything that affects the amount of economic value we can expect to get from the asset, and the risk of this promise not fulfilling.
Adjusted historical value is basically influenced by the cost or accounting principles used.
Current market value is influenced by current market conditions.

In this text we will focus on economic value, the only method that quantifies true economic benefit. We will discuss the main approaches for asset valuation and dig deeper into the prevailing method for calculating fair value: Discounted Cash Flows (DCF).

Valuation and Accounting

Valuation is first and foremost an economic task, but sometimes it is required for regulatory compliance, such as for financial reporting. In such cases, it receives guidance from accounting principles such as the The Financial Accounting Standards Board’s (FASB) Generally Accepted Accounting Principles (GAAP) and the International Financial Reporting Standards (IFRS). These standards seek to simplify and standardize valuation so that market participants can adequately compare between different assets and different valuation performers in different periods in time.

What is an Asset

An asset, in an economic and investment meaning, can be defined as an object, contract or entity which grants its owner economic benefit. This benefit can be measured as periodic cash flows (also referred to as “yield”) and capital appreciation.

We can divide all assets by the way their value manifests into two main groups, yielding and non-yielding:

Yielding assets are expected to provide periodic cash flows at varying levels of certainty. For these types of assets, the main source of return is its periodic cash flows.

Yield- this refers to the periodic cash flows that an asset generates, which are available for use by its owners. This can be rent, interest payment, dividend payment and more. Yield is stated in periodic per-cent terms, whereby any period’s projected cash flows are divided by the asset’s current or historical value or price. If the asset is the tree, the yield is the fruit.
Non-yielding assets are not expected to provide periodic cash flows. Return is achieved through capital appreciation, and materialized through the act of selling an ownership stake.

Capital Appreciation- this refers to the change in an asset’s value over time. This term usually refers to the growth of our tree. The higher the periodic cash flows from the asset are, the higher its valuation for a given level of risk. A positive change in valuation over time is what’s called “capital appreciation”.

Yield and capital appreciation are objective concepts of capital efficiency, and serve to measure how well capital is used. Valuation is a subjective concept of value, and serves to bring together all relevant information into a single number that matches capital and need. Lastly, price is a subjective economic concept, which serves to point the maximum capital a party is willing to forgo to get ownership of an asset. It is also a legal concept, which refers to the amount of capital required to close a deal and transfer ownership.

Cost and return have an inverse relationship: the higher the amount paid for an asset, the lower the yield and capital appreciation potential, and vice-versa.

Both yield growth and capital appreciation can be influenced by various endogenic and exogenic factors:

Endogenic factors are ones that the owner has control over. These include all investments made to improve the asset, such as efforts to increase efficiency, enhance the asset’s condition, sustain a brand and more. If made correctly, any investment in the asset can result in higher yield. This happens when the yield from the investment in improvement is higher than the cost of capital used for the task.
Exogenic factors are ones that the owner has no control over, but they can influence the asset’s valuation, such as macro-economic conditions (interest rate changes, inflation, employment etc.), geopolitics, technological advancements, competitive landscape and more.

Assets can experience shifts in their valuation even if their yield remains unchanged. The reason is that investment decisions are made in the market between multiple opportunities and investors require to receive adequate return to compensate them for taking a given level of risk. If an asset becomes more lucrative relative to others, its valuation can increase in the market, just because the alternatives offer a worse return/risk ratio.

Assets can take two forms:

Tangible- having a physical form, such as real-estate, machinery, inventory, vehicles, computers, cash and more.
Intangible- having a non-physical, contractual form. These assets represent non-physical rights, benefits, and resources that have value such as intellectual property, goodwill, brand and trademarks, customer data, software and technology, research and development, contracts and agreements and even websites and domain names.

Every asset, be it tangible or intangible, can be defined by the set of responsibilities and benefits it carries. You buy this set when you get ownership of an asset:

Responsibilities- your responsibilities stem from your desire to maximize your benefit, and they are omnipresent: as owner of an asset, you need to operate it, maintain it, manage its risks, manage its financing, pay taxes, comply with rules and regulations, keep it relevant among the changing environment, understand how to get the most out of it and even grow it. You can pay someone to do it for you, but this must be done in order to sustainably extract value from the asset.
Benefits- if all goes well, you are entitled to receive the benefits. You get any cash flows remaining from your asset’s operations, you may enjoy capital appreciation and you may enjoy other, non-monetary gains as well.

When assets and investors meet, they interact in two ways:

Ownership– this refers to the legal right to possess and use an asset. The owner of an asset has the title to it, which means he has the legal claim to the asset and its unique set of responsibilities and benefits. Investors can own parts of assets, and the smaller their part is, the lower their control over the asset.
Control- this refers to the actual ability to direct the asset. This is where the investor influences the asset according to his world view, with the aim of maximizing his value from the asset. While his value is not always monetary, it is always measured from the point of view of his overall investment exposure and may conflict with other owners, if there are any.

Sometimes ownership and control come together, but not always. Beyond the benefits of owning an asset, controlling it has a value of its own, as we will discuss later.

Assets are the backbone of the economy. Together with skilled individuals, they hold and create value that spreads over society and improves people’s lives, and when they are held by free people, the true magic of capitalism happens. Private ownership of assets sits at the base of capitalist societies and is the best generator of value and wealth. The secret is that a private owner of an asset has the strongest incentive to invest and enhance it, the best information to do it right and the highest chance of increasing its efficiency- optimizing return on investment for both himself and the economy.

Model Bias

Like all models, all valuation methods are biased. A model is a controlled approximation of reality that comes to test various assumptions and their influence on a possible outcome. Valuation models do just that, with the goal of combining information and assumptions to create a figure of value.

As reality is the most complex system in existence, each method we use for valuation has to take some factors into consideration and neglect others while trying to reach a result.

The most complex valuation model is the Discounted Cash Flows (DCF) method for economic valuation, which we will thoroughly discuss in this text. While performing this economic valuation, we look far into the future and try to imagine the most probable turn of events that have yet to occur, and influence our asset.

Just like any model that tries to explain reality using a set of assumptions, asset valuation is also subject to the Bias-Variance Tradeoff. On one hand, the simple valuation methods are highly biased, in that they are far too simple to be able to catch the complexities that a specific asset holds. On the other hand, the complex DCF method can be too “flexible” and can be easily influenced by changing events. For a deeper discussion on a model’s ability to describe reality, see the Bias-Variance Tradeoff discussion in my text about Neural Networks.

If modeling a static, existing situation isn’t a challenging task by itself, attempting to model dynamic, future events within the complexity of reality is exponentially more difficult. It will always result in significant error.

But, it’s all good, since uncertainty about the future sits at the base of any economic activity. Investors accept uncertainty and expect to be properly compensated for dealing with it, so they use these valuations as a means of having a quantitative tool to work with in their decision making.

A somewhat accurate projection is always better than no projection at all, because it gives us a starting point to plan and formulate strategies. A projection that is the result of a robust model, which lets us change assumptions and perform sensitivity analyses, is even better. Low accuracy projections are so important, they even help win wars^◆.

Valuation Definitions

Before we continue to discuss valuation, we should “level the field” and explain some key terms. Here we include some general concepts relating to valuation. Later in the text we will define concepts that specifically relate to discounting cash flows.

Fair Value- also known as Intrinsic Value, this represents the worth of all economic benefits an asset holds, based on as much information and true sources of value as possible. It is the result of a calculation that takes into account various assumptions about future business outcomes and the risk of reality deviating from our plans. This is an asset-specific, time-specific figure that may change together with its assumptions. This differs from book value, which is a calculation based on accounting principles.

Fair Market Value- interchangeable with “Market Value”. According to Oxford English Dictionary, this is “the amount for which something can be sold on a given market”. It is the price an asset gets in a given market by the market participants. In a world of imperfect information distribution, the asset’s market value will be different from its fair value because it is the last point where information that was not used for valuation is added into consideration. Different investors make their decisions based on various considerations that can’t be included in a valuation, such as their existing investment positioning, hidden benefit and their personal biases and preferences. The difference in market value from fair value is the manifestation of this information imbalance.

If all the possible information could have been included in valuation, its result would equal its market value. John Maynard Keynes acknowledged the difference between fair value and price by saying: “The market can stay irrational longer than you can stay solvent”. Important factors other than economic analysis affect asset prices and can create near-permanent distortions between fair values and their market variations.

Book value- this term refers to the accounting value of an item a balance sheet. This can include assets and liabilities, as reported in an entity’s financial statements. Basically, the book value is the historical cost of an asset minus any accumulated depreciation, or the current outstanding amount of a liability.

Book value is guided by accounting principles, making the value at which an item is carried on the balance sheet calculated under strict rules, that serve for reliable communication with investors (uniformity) and the government (regulation and taxation).

An entity or asset’s book value is disconnected from their fair value, in that book value includes different information in its computation and serve a different purpose. Book value brings high valuation accuracy for specific uses where true economic value is not important. It is different from fair value, which brings less valuation accuracy, but is able to catch true economic value.

To calculate book values, tangible assets such as buildings, machinery, and equipment are typically recorded on the balance sheet at their historical cost, less accumulated depreciation. Intangible assets like patents, trademarks, and goodwill are also included in book value minus amortization, and follow a different set of rules. This is where book value differs from fair value, since book value focuses on the past and individual assets, while fair value focuses on the future and takes into account synergies and future growth.

The book value of an entity’s liabilities (such as long term debt) is either the total amount that it owes to the other entities, or the remaining payment sum. The book value of equity value is all that’s left after subtracting the book value of liabilities from the book value of assets.

Replacement Value (Cost)- this is the value of an entity or asset which is derived from estimating the cost to replace it with an entity or asset similar in kind and quality, at current market prices. It is the result of the replacement cost method for valuation and takes only tangible assets into account. It is used as a quick indication of value and for situations when a replacement of an asset is required, such as insurance or real-estate. The replacement value, which often focuses on the tangible part of an entity or asset, is different than the market value which is reached in actual deals in the market, by rational investors that take all economic considerations into account.

Liquidation Value- this is the amount that would be realized when an asset or a group of assets are sold on a piecemeal basis^◆.

Price- this is the last step before executing an investment transaction, as each party needs to know the maximum amount of capital it is willing to pay for an asset in order to make a deal.

Price is also a legal term that signal what is required to execute a transaction. Communicating a price in negotiations can be considered a legal offer.

Financial Reports (Statements)- every business entity is periodically required, by law, to consolidate its financial information into a summary of its performance and position. These reports are important in order to communicate reliable financial data to the various stakeholders, including investors, debt holders and the government. These reports are created using accounting principles for uniformity and simplicity. They include necessary information for stakeholders to understand the business. The financial reports’ 3 main parts are:

Balance sheet- this document presents the entity’s assets, liabilities and equity at book value for a specific point in time, usually the end of a quarter and the end of a year. The balance sheet follows the accounting equation, which is a basic principle in accounting, and means that the Assets part is exactly equal Liabilities + Equity part. It is important to notice that as per accounting principles, not all assets and liabilities are included in the balance sheet, such as certain intangible assets and leases. The balance sheet is used for clarity and uniformity when describing an entity’s financial information.
Income statement- this document details the entity’s revenue and the various expenses made in order to achieve the revenue, including tax expenses and interest payments on debt. Its bottom line is the net profit for the period.
Cash flow statement- this document summarizes the movement of the business’s sources and uses, the cash and cash equivalents used during the given period. It is divided into three sections: operating activities, investing activities and financing activities.

Since stakeholders rely on the information presented in the financial statements, their preparation adheres to strict accounting principles. Valuation practitioners often use the information found in the financial reports to get more understanding about a business and make better informed projections.

Cash Flow- this is the net cash, or cash equivalents, that is transferred in and out of an asset.

Free Cash Flow- this is the cash that is left for an asset after all operating and business expenses are made. In other words, it is calculated assuming our entity is wholly equity financed. If positive, this cash is available for distribution to investors as dividend, debt service or reinvestment in the business. If negative, it shows the amount an entity needs to borrow to cover its expenses. It is called “free” because it is not earmarked for a specific purpose and can now be used at the discretion of the owners.

Free cash flow differs from net profit in 3 ways:

Free cash flow is calculated before debt service, while net profit is calculated after debt servicing payment, the interest rate.
Free cash flow doesn’t include non-cash expenses, but uses them to decrease tax payments. Net profit does include non-cash expenses.
Free cash flow is calculated after capital expenses and investment in working capital, while net profit ignores them.

While net profit comes from the world of accounting and contains various accruals, receivables and other accounting representations of financial obligations, free cash flow is an economic term that only includes hard cash only. Each serves a different need, and hence the difference in computation.

Control Premium^◆– there is additional value for a single investor who takes control of an asset, meaning they gain the power to direct its management and strategic path. This premium means that an asset is more valuable to a controlling investor, and such investor will be willing to pay a premium for the asset when they can get control over it. For example, private mergers and acquisitions of publicly traded companies frequently close at a higher price due to the control premium the buyer pays, together with an illiquidity premium.

This extra value naturally manifests in some types of asset valuation, such as the DCF, that assume a controlling interest. When using these asset valuation methods for a buyer of non-controlling shares, they will need to apply a discount to the valuation result. This is often referred to Discount for Lack of Control (DLOC) could span between 10% and 30%, depending on the various ownership rights and minority protection clauses in the entity’s Articles of Incorporation.

Valuation methods based on traded company equity do not include control premium, as they use information from publicly traded equity for valuation.

Marketability- this refers to the ease of trading an asset in a market without significantly influencing its price. This term is closely linked with liquidity, which refers to how quickly and easily an asset can be converted into cash without a significant influence on its price.

When we value entities or assets using DCF, we automatically assume high marketability since we often use publicly-traded comparable entity analysis for determining our discount rate. However, when our asset is illiquid, we should apply a discount on our valuation result to include a possible reduction in price in order to find a deal. This is called the Discount for Lack of Marketability (DLOM) and can span between 5% and 50%, depending on asset and market conditions.

Hurdle Rate- this is the minimum acceptable rate of return investors are willing to accept from their position in an asset. Projected return beneath this rate hints at a negative economic value for the investor in the specific transaction.

The Opportunity Cost of Capital- in a world of multiple investment opportunities, this term represents the fact that every investment option chosen means others are forgone. The Opportunity cost of Capital is simply the projected return of an asset when keeping other opportunities in mind. It is a standard of profitability that represents alternative uses of capital and a tool used to evaluate investment opportunities [Principles of Corporate Finance, 2019 (hereinafter: PoCF)]^◆.

When faced with a decision for how to allocate their capital, investors should always choose to invest their capital in assets that offer the highest return for a perceived level of risk.

Connecting this term with valuation, we use this cost as the interest rate to discount an investment’s projected cash flows, including its purchase, and reach its Net Present Value (NPV) terms. We will choose the opportunity that offers the highest NPV when compared with the other opportunities we face. Another angle to look at it is the IRR, we will choose investment opportunities that offer an opportunity cost higher than the IRR.

EBITDA- this is an entity’s earnings before interest, tax, depreciation and amortization, or in other words what earnings an entity generates before any external influence. It is a metric of an entity’s operational performance. By its definition, EBITDA is used for businesses and companies, and not other types of assets. Each asset type can have its own relevant multiples for use. It can also be viewed as EBIT plus any depreciated and amortized non-cash costs.

The Irrelevance theorem- this is a concept developed by Franco Modigliani and Merton Miller (1950s and 60s)^◆, which states that in a perfect and efficient market, an entity’s blend of capital sources do not influence its value. It doesn’t matter if financing is repaid by interest payments or dividends: what does influence an entity’s value is its investment policy and future growth opportunities. According to this concept, financing blend only regards the division of the cake, not its growth.

MM created two versions of this concept. The first version assumes a world without bankruptcy costs that add true costs to businesses in financial distress, and without income tax, which can be reduced by interest payments, creating value through the use of debt financing. The second version is more realistic.

The bottom line is that debt and equity are forms of an external claim on the value an entity holds and generates. In real life they do influence value through tax shields, financial distress costs, investors’ imperfect information and varying perceptions, market inefficiencies and the influence of macroeconomic factors on the various financing sources. In reality, Entities can draw value from their financing decisions.

Valuation Approaches

There are three main valuation approaches that sit on an endogenic-exogenic analysis axis: asset-based, income and market, with the asset-based method being mostly endogenic and the market method being mostly exogenic:

Endogenic methods for valuation look inside the asset for information about its value and exogenic methods look outside. The three main approaches can basically be summarized as:

Asset-based approach- this approach values an entity or asset by the worth of their underlying assets as independent parts. It focuses on an entity’s balance sheet, values each item individually and combines them to calculate the entity’s value. This approach assumes that the entity’s value is mostly based on the specific assets it owns and not its future economic potential. It includes the book value, adjusted NAV and replacement cost methods.
Income approach- this approach is based on the idea that an asset’s value manifests through the future economic benefit it promises to generate. This future benefit is not certain and thus needs to be discounted, meaning weighted, according to its risk profile. This approach includes various cash flow discounting methods, with the most deep and elaborate being the DCF.
Market approach- this approach uses information about deals from the immediate environment and uses their characteristics to draw conclusions about the asset or entity we are valuing. It usually relies on information about publicly-traded entities, similar assets in the physical market and publicly available statistical data- as guidance for fair value. This approach includes the multiples method for entities and real assets, but also statistical models for the valuation of more complex financial instruments.

Each approach includes several specific methods for use. Each method has its own benefits and drawbacks, and each serves for different assets or situations. Practitioners choose the best approach that suits their specific need and then judge them by the dimensions of speed, cost, complexity, and bias.

Each approach brings a different angle to valuing an entity’s enterprise value (which is the value of its operations), its asset value, liability value or equity value, which is the enterprise value minus debt and other non-operational financial liabilities.

We will discuss 6 methods for valuation in this text. For most cases, we can divide them according to their time focus as follows:

Notice that some methods look into the past in order to derive value, some stay in the present and some make predictions into the future. This is the one of the reasons why some of them are incomparable with others, such as book value and fair value that results from the DCF method, or multiples and replacement cost.

Which approach is better? The answer is neither. Each approach works best at some situations and poorly in others. But generally, for the calculation of true economic value, the DCF method provides the best answer. International tribunals agree- the following chart shows the results of a research made by PwC in 2017, showing the distribution of valuation methods used by international arbitration tribunals for dispute resolution:

^{Source: PwC, International Arbitration Damages Research, 2017 update, p. 6.}

The research found that tribunals prefer the forward-looking DCF method for valuation over the other options. Keep in mind that there is room for the other methods as well, as some situations require specific methods for the calculation of value, such as the case of company liquidation.

The following table is a good place to start. It summarizes some key characteristics of the 3 asset valuation approaches for most cases:

With going concern being the assumption that a business will continue to operate for the foreseeable future. Flexibility of Results relates to model bias from the field of statistical learning, and comes to emphasize how sensitive the model’s results can be to slight changes in inputs. Higher flexibility allows our model to tailor for specific cases at the cost of greater sensitivity to inputs that reduce its reliability.

There are some other methods for valuing assets, but they mostly stem from the methods we will discuss here and can therefore be neglected. We will now turn to discuss the 3 valuation approaches.

The Asset-based Approach

The asset-based approach is used to value an asset or entity by summing the values of its individual assets and liabilities^◆. Its methods entail the following actions^◆:

Identifying each individual asset of an entity.
Using a specific valuation approach to value each such asset.
Aggregating the values to arrive at the value of the entity.

This approach calculates the value of an entity’s assets and financial liabilities as separate, independent components, and then adds them all up to achieve an overall value. It is based on the principle that an asset’s value can be derived by the sum of its components, and allows us to break an asset or entity into its components and value them individually, a valuable function for accounting needs.

The difference between various asset-based methods is only in the indicators used to value individual assets (Damages in International Investment Law, 2008, p. 218)^◆. This approach is endogenic, meaning it focuses on the individual analysis of the specific traits of an entity or asset, and focuses on the balance sheet^◆.

The asset-based can be used for both yielding and non-yielding assets. It is best suited for entities with significant tangible assets such as manufacturing activity, real-estate holdings and holding companies. It is used for when the entity’s future financial performance is not the primary focus, when it is in financial distress, or when other valuation methods are not appropriate. It provides a figure of minimum value, before considering future performance and synergies.

This approach has 3 main methods:

Book Value- an entity or asset’s equity book value is achieved through the application of accounting principles on their constituent parts as shown in the balance sheet.

We should differentiate between valuing the ownership stake of an entity or asset, their equity, or an individual asset in their balance sheet. Valuing the equity stake is achieved through calculating the difference of worth between their total assets and liabilities, as the fundamental accounting equation states: .

As defined above, the book value of an individual asset is basically its historical cost minus any accumulated depreciation or amortization.

Under the book value method, practitioners first calculate the value of individual assets and then sum them to reach a total asset or liability value.

Only assets and liabilities that have a clear cost and appear in an entity’s balance sheet are counted in book valuation. Items that do not appear in the balance sheet are ignored. For this reason, the book value method as a measure of valuation misses a significant amount of economic value. However, since its purpose is to provide clarity and consistency and not for economic decision making, this is not a problem.
Adjusted Net Asset Value (NAV)- this method is based on the latest book value figure and adjusts it to reach the current fair value of each asset. It starts from the latest book value of each item in the balance sheet and replaces it with its current fair value.

To calculate the fair value of a book-valued asset, practitioners perform an economic valuation of each asset separately using the market or income approaches. This adjustment is needed since practitioners now need to take into account factors that may not be accurately reflected in the historical cost or accounting measurements used in book value.

Under this approach, practitioners try to identify all relevant assets and liabilities, including those that aren’t recorded on the balance sheet, compute the fair value of each component and then add them all up to reach an overall valuation.

This approach is considered to be straightforward at assessing economic benefit. It is most suitable for cases when clarity is important and where the individual components have a significant influence on total asset valuation. For example, special custom-built assets, when there is a lack of comparable market transactions or generally for tangible assets that can be reproduced. It is also good for use with asset-intensive companies and distressed entities that aren’t worth more than their net tangible value.

However, since it still treats an entity or asset’s valuation as the sum of their (now fair valued) parts, it neglects to catch the value of synergies and overall growth.

Adjusted NAV is often used for investment vehicles such as hedge funds and mutual funds to provide a more accurate reflection of the vehicle’s fair value by adjusting the reported NAV for certain factors.
Replacement Cost- this method is based on the economic principle of substitution, which states that a rational buyer will only be willing to pay for an asset a cost similar or lower to that required to obtain an asset of equal characteristics. The opposite is true for a rational seller.

This method calculates an asset’s present-day “cost to replace” for tangible assets. It assumes that the value of an asset is equal to the cost of replacing or reproducing it with new one of similar functionality and condition, at current market prices. It is often used for equipment and real-estate assets, where assets are easily replaceable and the computation of the cost of reproducing a similar asset is relatively straightforward.

The replacement cost method is often considered a deficient method for valuing a business, as it assumes that it is possible to reconstruct the value of an entire investment by simply replacing its physical assets. It does not incorporate intangible assets such as a business’s “goodwill”^◆, as it typically focuses on tangible assets only. Its result is the replacement value, which for these reasons tends to be lower than fair value.

This method can constitute either a “floor” on the valuation of a business, since it ignores both intangible assets, synergies and entity-level growth, and a “ceiling” when a business is liquidating^◆.

Goodwill is an intangible asset that is created when an entity is acquired for more than the fair value of its assets. It represents all other elements that contribute to value but were not included in the entity’s valuation, such as brand reputation, market positioning, intellectual property and customer relationships. This is basically the value representation of all information that was not included in the entity’s valuation, but was included in the final deal.

The asset-based approach makes the following main assumptions:

Each asset and liability that is listed on the balance sheet was accurately valued based on prudent analysis with clear assumptions.
No balance sheet asset or liability was missed.
The individual valuation of assets and liabilities is a good approximation of an entity’s value. There is no synergy between the individual assets.
When trying to liquidate (sell) an asset in the free market, normal market conditions are assumed. This means that assets can be sold without significant discount or penalty due to illiquidity.

To summarize, the asset-based approach’s methods seek to value each component, be it an asset or a liability, separately, and then add the parts up. It is particularly useful when valuing holding companies, asset-intensive companies and distressed entities that are not assumed to continue maintaining business operations.

Generally, the asset-based approach produces a less reliable result for valuing business entities than the income or market approaches (Damages in International Investment Law, 2008, p. 219)^◆.

The Income Approach

The income approach is used to value yielding assets. It is based on the assumption that an asset’s present economic value represents all future expected benefits adjusted to risk. It is basically the linear combination of the projected, future cash flows that are associated with owning the asset, weighted by the time value of money.

This is a mainly endogenic approach that focuses on the asset or entity’s income, but also uses information about similar assets in the market in order to calculate the appropriate discount factor.

A major part of the income approach is the Discounted Cash Flows (DCF) method, which is the most elaborate and deep method for valuation. It is the only true, independent way to calculate economic value when there is relative certainty that periodic cash flows will come, and the best method for calculating fair value while allowing access to the underlying calculations and assumptions.

With DCF, practitioners formulate a full business plan for the asset starting from revenue, going through all expenses except debt service and derive projected periodic cash flows. They then discount them using the appropriate discount factor that adequately includes all risk aspects of a typical, similar asset.

Apart from this method being versatile, modular and thorough, it is based on deep research and business understanding, and the meticulous representation of small bits of information into a large model. It is also very versatile, allowing us to value every yield generating asset, as long as we can adequately assess its return potential and risk profile.

Other valuation methods that rely on future cash flows can be regarded as shortcuts to the DCF and share the same concepts, and can therefore be addressed within the DCF discussion. For example, the Gordon Growth Model for valuing dividend-distributing companies, the Direct Capitalization Cash Flow method for valuing real-estate assets, the Adjusted Present Value (APV) method (which is especially suitable for leveraged buyouts, LBOs) and more. They all share a common concept of assuming future cash flows and possible growth rates and discounting them at the appropriate discount factor.

Discounted Cash Flows (DCF) is the main method for valuing yield generating assets under the income approach. We will dive into it later in this text.

The income approach makes the following main assumptions:

We have a reasonable ability to project future cash flows. This assumption mainly holds for established, profitable businesses or assets that show a relatively sure cash flow trajectory.
The discount factor we use for discounting future cash flows adequately reflects the risks attached to the promise of said cash flows, as projected in our model. Risks can either come from outside, with events out of our control, but also from within. Risks and challenges facing our asset change over time and the single number we chose as our discount factor is able to catch all that.
The data we have about the asset we are valuing is true and accurate, and adequately describes its current condition and future prospects.

The Market Approach

This approach is suitable for any type of asset or entity, as long as there is public information about deals of similar assets in the near environment.

For valuation, it looks outside the asset or entity and into its surroundings, to find similar assets that were bought and sold in the free market where reliable data is easily accessible, in recent history.

When valuing financial instruments, this method includes the collection of trading data and making statistical computations. This method draws its information from the immediate physical environment or the stock market and is therefore regarded as exogenic.

This approach has 2 main methods:

Multiples- in this method we look for publicly available data on recent deals made for similar assets, take some readings, create an average multiple and use that to value our entity. The method is based on the assumption that identical assets should be worth the same and if not, arbitrage actions would make their price same.

We begin by creating a sample of deals of similar assets called “Comparables” and use this information to deduct insights for our own asset. Our sample group of Comparables should include “pure play” entities as much as possible, meaning entities that are similar and exclusively engaged in the same line of business or industry and share the same risks (Investment Banking- Valuation, Leveraged Buyouts and Mergers&Acquisitions, page 15)^◆.

Once we find a satisfactory group of 5-8 Comparables, we document the various data features, such as the deal price and each asset’s financial details. Based on the data we collected, we connect one of the features with each deal price through calculating a multiple. A feature can be revenue, EBITDA, net profit, net cash flow, number of users or book value- for a company, and number of rooms or square meters for a real-estate property.

The multiple is calculated by dividing some measure of value or price with a feature. For example, we can use the enterprise value (EV) or market capitalization as the numerator, and divide it by a feature of our choosing, creating multiples such as the revenue multiple (EV/full-year revenue), EV/EBIT multiple, EV/EBITDA multiple and others. For real-estate properties we can use price/room or price/area unit (such as square meter or square foot).

Once we calculated the multiple for each deal in our Comparables group, we calculate a simple or weighted average of the multiple we chose, and use that to value our asset by multiplying its relevant financial figure with the appropriate multiple, reaching a quick valuation.

The Multiples method is basically a quick shortcut, a derivative, that derives value from other people’s valuations. It brings speed at the cost of accuracy and can be used in situations when simple is better than deep. It can also be used in conjunction with the DCF method for providing external insight and checking our DCF result. It’s easy to do since DCF already employs the multiples method to calculate the WACC.

We won’t be wrong by saying that this method of valuation is highly biased and is very influenced by exogenic factors such as current supply and demand dynamics, and easily assists the creation of asset valuation bubbles. Due to its simplicity, it can be used in conjunction with other valuation methods as a means of sanity check.
Statistics- this method is used for valuing non-yielding complex financial instruments. It is based on the collection of various historical trading data in public markets and then the computation of ex-ante, potential future scenarios, using statistical analysis based on historical data.

Just like with the income approach, the assumption here is that present value is connected with future benefit. The difficulty here is that these assets are non-yielding, giving much weight to our assessment of the probability of future outcomes. These outcomes are not only dependent on our own asset’s dynamics, but often depend on another asset in a derivative manner.

Our best tool for this task is a lot of historical data, so under this method, valuation is derived from the mathematical relationship between the possible reward and the perceived risk, as computed using past trading data of similar assets. This method employs the Black-Scholes-Merton model, the Binomial model and Monte Carlo simulation methods, among others.

The market approach makes the following main assumptions:

Identical assets should have the same value, and that is not the case, arbitrage actions can close any pricing gaps.
Thought and effort was put into the valuation of the comparable deals, either by using proper DCF or by someone’s deep expertise. In other words, the published price is founded on well-thought-of assumptions and adequately represents fair value.
All Comparables and current price information were achieved from deals made “at arms length”, meaning between at least two free, independent, rational and reasonable parties that are free from conflicts of interest, undue influence or unfair advantages. Deals which were not made at arms length provide distorted pricing information.
The information that was provided about the deals valuation is true and accurate.
Enough deals on similar assets were made in recent history, and the practitioner was able to find them. If little deals were made in recent time, the practitioner goes further back and uses other similar deals. The further back we go, the more different the market conditions are and the less accurate our comparison becomes.
The differences between our asset and the comparable assets are minimal.

The market approach allows us to value both yielding and non-yielding assets, as long there is public information about similar assets being bought and sold.

Let’s now dive deep into the main method of valuation of true economic benefit, the DCF.

The Discounted Cash Flows (DCF) Method

The Discounted Cash Flow (DCF) method for valuation is implemented by looking deep into the asset, making assumptions about its operations into the future and weighting its free cash flow with risk^◆.

This is the most complex and thorough method for valuing cash flow generating assets, and this is why it is considered to be the most time consuming and expensive. It allows for the broad implementation of detailed assumptions and the preparation of a detailed business plan, as it uses an asset’s projected free cash flow to determine its valuation. Its added value is that it brings with it the ability to influence this plan and understand various future scenarios.

DCF is mainly used for valuing business entities, but its simpler variations can be used to value any yield-generating asset. The valuation of a yielding real-estate asset or a bond will be much simpler and straightforward than that of a company with many branches of activity. What’s different is the scope of the business plan that sits at the base of the valuation and the type of expenses we take into account. We control the level of sophistication and can choose when to simplify our model, and when to dig deep.

For these reasons, from this section onwards, I will refer to the assets we are valuing as an “entity” or a “business”. These terms represent any yield-generating asset of any type.

While DCF is usually considered a tool for valuing established business entities and assets that show predictable cash flows, it is also a great tool for valuing start-ups, despite initial thought. Although the uncertainty in young company cash flow projection is high, the added value of the business planning that sits at the core of DCF, together with the clear statement of assumptions and the ability to perform sensitivity analyses, can provide boundaries and make this method particularly useful even for this task.

Moreover, as valuing young start-up companies is more a task of story-telling and business planning that providing an indication, using DCF allows for a much smarter discussion that is based on prudent analysis. No one has a crystal ball that receives inputs and creates a valuation, so the better prepared you are for discussions of value, the stronger and more defendable your position will be.

Therefore, we notice that DCF doesn’t only focus on the bottom line, the free cash flow. It focuses on the path an entity or asset is projected to take and allows practitioners to alter the path and check for sensitivities.

DCF Definitions

Forecast Period- when performing DCF, we often project an entity’s future revenue, expenses and profits. We try to model how they may look like and base our forecasts on firm assumptions. We should create a forecast for several years, usually 5, or until the business stabilizes. We then calculate a Terminal Value that represents activity ad infinitum– where applicable, such the assumption of a going concern^◆. The period where we make specific assumptions and predictions before adding the Terminal Value is called the Forecast Period.

We discount the free cash flows our business is projected to generate during the Forecast Period in the following way:

Each periodic free cash flow is discounted using the asset’s Weighted Average Cost of Capital (WACC), I will explain it later in this text.

Terminal Value– for an asset that is projected to operate ad infinitum, we add a terminal value after our Forecast Period projections. The terminal value that encompasses the hypothetical annual results of activity to infinity, where applicable, such as for a company or a yielding asset.

We model the terminal value the same way we do with the Forecast Period- we do it explicitly in our model by adding another prediction column and start from the top. We apply a constant growth rate (referred to as G) to our revenue, while maintaining a fixed cost margins. We take the revenue figure from the last year of our Forecast Period and assume it is going to grow to infinity by the long-term growth rate G, which we assume is similar to the general growth of population, usually 2%. We then derive the various expenses based on the final Forecast Period year’s margins (expense to revenue).

Based on the Gordon Growth Model for discounting growing dividend payments, we discount the terminal value after our Forecast Period ends, in the following way:

When discounting our terminal value, we first assume an infinite growing perpetuity of cash flows from period T (our Terminal Year, at the end of our Forecast Period) onwards and discount them to time T. This is done by . We then discount this figure back to our present day, and add this figure to our Forecast Period DCF calculation. This is done by .

Another method for calculating terminal value can simply apply our long-term growth rate directly on the last Forecast Period year’s free cash flow (and not revenue), without adding another column to our model. In this case, we need to adjust the up-left nominator to , to account for this growth from our last Forecast Period year’s cash flow.

It’s worth mentioning another method for calculating the terminal value, the H-Model, which is basically a variation of the Gordon Growth Model that allows for the splitting of the long-term growth rate into two rates: one for the near-far period, factoring in still higher growth and the other for the very-far period, factoring in G. The goal is to allow for a still higher growth rate for an interim period, followed by G thereafter. This method is rarely used in practice.

It’s also worth mentioning that some practitioners apply a multiple to reach a terminal value, taking the last Forecast Period year’s financial figure and applying the appropriate multiple. This method is also rarely used in practice, mostly due to its reliance on exogenic information for an endogenic task.

The terminal value can have either a significant or a marginal influence on our valuation. There are two forces here that influence our valuation: first, due to the Time Value of Money, later cash flows are worth less in the terms of today’s money, since they are uncertain future promises. The further the period and the higher the Discount Rate, the lower the future cash flow is worth in today’s money.

Second, especially for young businesses or assets that are projected to show significant growth during the Forecast Period, the Terminal Value can have a significant effect on valuation, since it took the business or asset time to reach a high cash flow level. We should treat such cases with caution, since the Terminal Value is significantly affected by our assumptions.

The Time Value of Money- a dollar in our hands today is worth more than a dollar promised to us in the future. The reason is that there is a risk that the promise will not be kept, and also there is the missed return we could have gained if we invested that dollar today. The higher any of these factors is, the lower the promise is worth to us. We would prefer to receive payments as early as possible.

Discount Rate- this is the interest rate or cost, as expressed in per-cent terms, at which we discount or bring future cash flows to their present value. This rate quantifies the risk embedded in the promise of future cash flows, since many things can go wrong along the way. The Discount Rate represents this risk over time, and is comprised of two elements:

Risk-Free Rate- this rate represents the yield we can expect to get from holding the safest asset in the economy, usually non Consumer Price Index (CPI)-indexed, floating (non-fixed) interest rate government bonds. We will usually use a government bond with a maturity date similar to our projection term, or the generally accepted 10-year. Notice that the term “risk-free” is misleading in a sense that such bonds are still vulnerable to inflation and the slight-chance of a government default. It’s called “risk-free” but should be called “least-risky”.
Risk Premium- this rate accounts for the additional return investors require for exposing themselves to more risky assets. The risk premium is comprised of both systematic and asset-specific risks, for which investors expect to get compensated.

Discounting- this is the act of weighting future projected net cash flows with their appropriate risk, as quantified by the asset’s discount factor. As time goes by, risk naturally intensifies and therefore we account for the timing of the projected cash flow as well. The discounting action looks like this:

For each projected net cash flow in time t, apply a discount with the discount factor r (represented as %). The result of our discounting of future cash flows is their present value.

Present Value- this is the value in today’s terms of a future, projected cash flow. This value is reached by discounting a future cash flow with the appropriate risk, as measured by the discount factor.

Net Present Value (NPV)- this computation of present value includes our initial investment in an asset, and thus becomes a criteria for investment analysis. It is the difference between our initial investment in the asset the present value of its projected cash flows:

A positive NPV means that under our assumptions and including investment amount, the asset is projected to have a positive net value and is therefore a desirable investment, and vice-versa.

Internal Rate of Return (IRR)- is the specific discount rate that makes NPV equal to 0. It is another investment analysis criteria, a profitability measure, used for quantifying the required return on investment in per-cent terms. An asset’s projected return higher than IRR is considered a good investment and hints at a positive NPV, and vice-versa. The IRR is a volatile figure that depends on the amount and timing of the asset’s cash flows, among other assumptions.

Cost of equity- this is the annual return equity investors expect to receive for investing in an entity’s equity. It is their compensation for taking on the risks embedded with the entity and its operations. It is also the discount rate used to discount after-debt cash flows. Just like any other discount rate, it is comprised of a risk-free element and a risk premium element, which is in turn comprised of equity risk premium (systematic risk) and entity specific risk premium.

Cost of debt- this is the effective annual rate that an entity pays on its outstanding debt in the free market, and this is the cost for incurring new debt. It is also the discount rate used for discounting any future cash flows associated with debt of similar risk. Just like the cost of equity, it is comprised of a risk-free element and, a systematic risk premium element and a specific risk premium element.

Cost of Capital- this is the expected annual return (denoted in per-cent terms) on a portfolio of all the entity’s outstanding debt and equity securities. It is the opportunity cost of capital of an investment in an entity’s entire assets (Principles of Corporate Finance, page 229)^◆ that includes both debt and equity when applicable, and also the minimum return investment projects should offer the entity for a level of risk similar to its existing projects. In other words, it is the cost of financing all of an entity’s operations. Debt has a cost, equity has a cost and their blended weighted average, the WACC, is an entity’s cost of capital.

The History of DCF

DCF first lays on the combination of perceived benefit, risk and time. In order to use this tool, investors and economists first needed to recognize the need to quantify value, understand the difference between projected cash flows in different future periods and bridge both concept using quantified risk. These are not simple tasks and they lay on the work of many economists.

It was said that the DCF method for valuation originated at the beginning of the 19th century, with the prime motivation being economic, both in the United Kingdom^◆ and Germany^◆.

John Richard Edwards and Alison Warman, in the 1981 Fall issue of the “Accounting Historians Journal”^◆, share some information about the history of DCF through a case from 1889:

Two enterprises, Lord Granville’s Shelton Collieries and Ironworks (SCI) and the Shelton Iron and Steel Company Limited (SIS), agreed to join together to form the Shelton Iron, Steel and Coal Company Limited (SISC). To guide the contracting parties in negotiation the price to be paid for SCI, Messrs. Deloitte, Dever and Griffiths & Co., later appointed auditors of SISC, arranged for William Craig of Cheshire to value the property belonging to the former company. The detailed terms of reference given to Craig are represented in his report dated 16 July 1889 and include the requirements to advise on “the condition of the … [properties] … and on their present value.

According to the authors, Craig used the same DCF model we essentially use today: he forecast future cash flows based on recent past results, applied his assessment of the various factors which might be expected to alter these results in the future, and estimated a suitable discount rate which, when applied to the cash flows, produced a figure for the present value (page 3).

DCF sits on the combined work of many economists and researchers, among them:

Frank Knight (1920s)^◆– in his work, particularly in his book “Risk, Uncertainty and Profit”, connected the concepts of risk and uncertainty with economic behavior. He discussed how capital goods are valued and the role of time in their valuation.
Irving Fisher (1930s)^◆– he developed the “impatience and opportunity” theory of interest, and stated that the value of capital is the present value of the flow of (net) income that a capital asset generates.
John Burr Williams (1938)^◆– he presented the Theory of Investment Value and emphasized the importance of discounting future cash flows to determine the intrinsic value of an investment.
James Tobin (1950s)^◆– he extended the application of DCF to corporate finance and helped establish the method as a fundamental approach to valuing investments beyond individual securities.
Joel Dean (1951)^◆– he introduced the Discounted Cash Flow (DCF) as a method for valuation, motivated by an analogy with bond valuation^◆.
Franco Modigliani and Merton Miller (1958)^◆– they incorporated the DCF principles in their work on capital structure.
William Sharpe (1964)^◆– he developed the Capital Asset Pricing Model (CAPM) which is used to calculate the appropriate discount rate for applying to future projected cash flows.
Fischer Black and Myron Scholes (1970s)^◆– they invented the Black-Scholes-Merton model for valuing options, which shares the principle of discounting future cash flows.

Over the years, the model has become the “go-to” tool for valuing yielding assets, either when a deep business plan and scenario analysis are needed or when a simple discounting of cash flows is enough. It is based on a well founded methodology for computing value and allows stakeholders to make educated discussions about business and assumptions.

How We Value Using DCF

There are 7 main stages in creating a DCF model:

Business and environment analysis- we first need to collect information gain a deep understanding of the entity and its environment. In our DCF, we are going to be able to have smart foundations for our business projections and these need to be firmly based on research.

This includes an internal look into the business: what are its activities, what are its growth prospects, how the product or service is created etc. We analyze its past performance as shown in its financial statements.
We also make an external look: we identify the competition, alternatives and market conditions both in the past, the present and future projections.
Create a cash flow projection- we first decide on our Forecast Period, the number of years into the future for which we make detailed projections. Based on our understanding of the business and its environment, we create a detailed forecast, starting from revenue and going all the way down the various expenses towards periodic free cash flows.

Usually, we can create a monthly or quarterly forecast for the first 1-2 years and aggregate it to annual figures, which is always our output. We usually create a specified model of future cash flows for 5 years, but we can extend this period if there are significant actions in the business that will influence its operations in future years, such as a major investment in assets.
Calculate the discount factor- future projected cash flows are educated guesses. We therefore need to weight them by their perceived risk, that intensifies as we wander into the future. We use the Weighted Average Cost of Capital (WACC) to discount our projected cash flows.
Calculate Net Present Value- we discount our projected, periodic free cash flows using the appropriate discount factor and add the numbers up. When the business doesn’t have a set time to cease operations, we assume it will run to infinity and discount the last projected, periodic cash flow accordingly. At this stage we reached a business’s operational value, enterprise value or value of operations.
Value Surplus Assets- when we model a business’s activities, we focus on its operational assets and ignore all assets that it may own but are irrelevant to operations. The reason is that these assets do not belong under the business’s general discount factor and should be valued independently. Surplus assets include cash, vacant land, unused real-estate, unused patents or a collectible. We then add their fair value to our business’s operational value.
Deduct Financial Debt- after accounting for surplus assets, we need to account for any financial debt associated with our asset. For this, we calculate the remaining principle of any loan or bond and subtract that from our enterprise value as well. This figure should also include any underfunded pension fund or health care plans, or the expected cost of any contingent liability^◆.

After this is done we need to subtract this value from our operational value. This introduces our entity’s debt into the valuation.
Valuation- the last stage of our valuation model is to reach a final equity (ownership) valuation at the most probable scenario. Next, we perform sensitivity analyses on some of the main parameters that affect valuation, such as the discount factor and the long-term growth rate.

With DCF, our goal is to create some kind of trajectory for the asset’s financial behavior in the future. We begin by modeling its revenue into the future and then go down its various expense sections and model them as well, with the goal of generating a free cash flow projection into the future. We then discount each annual free cash flow with the appropriate discount factor to account for the time value of money, and add them all up to reach an asset’s enterprise value.

When valuing simple businesses or assets, the task is relatively easy. It gets tougher as the business gets more complex and includes many activities.

For every case, what we do is we model each profit and loss part separately, based on clear assumptions, and input the bottom line into our DCF model.

What Makes a Good DCF

A good DCF has the following qualities:

Since a valuation is only as good as its assumptions and technique, both need to be consistent and clear. A good DCF clearly shows the assumptions that lay below it and allow for an easy change in assumptions value. The technique needs to be spotless.
It is based on a good and thorough business plan that makes a projection years into the future. The business plan should be based on verifiable information and achieved by directly speaking with people that are highly familiar with the asset and have control over its trajectory. They need to be able to tell if our assumptions are reasonable.
Our assumptions and predictions need to show the most probable business outcome. Sellers will be too optimistic in their valuations while in reality they may be pessimistic and buyers will push for a more pessimistic valuation, while in reality they may be more optimistic. They want to buy the asset since they are optimistic about its prospects. A lower price will give them a higher “cushion” for error.

The Tools we Use For DCF

In the world of DCF, Microsoft Excel is king. This is because Excel allows us the precision at the smallest level and makes our technique easily visible. For this reason it is the work-horse for virtually all financial projection tasks. It allows us a clear view into the relationship between model’s assumptions and predictions, which is something a “black-box” machine learning model cannot do. By the way, this is why we are somewhat far from an AI-based valuation model, since it is very important to know exactly how each assumption or value affect the model’s result.

We need to have a lot of information on the asset we valuing. We need to ask its stakeholders for the following items:

Historical financial reports- we should see the balance sheet and profit and loss reports for several years back, if applicable. This is important because at least the annual reports have been audited by a certified accountant, making them reliable.
Business plan- any existing business plan made by stakeholders, if applicable. We can use it to have a quicker and deeper understanding on the entity’s activity and learn about its stakeholders’ perception.
Market information- usually, stakeholders will have information about the relevant markets the asset operates in. This can be anywhere from internal work to paid reports.
Operational information- for both the present and several years back, we need to know about employee count and distribution, among other inputs, if applicable.

The Challenges in DCF analysis

While DCF is a powerful tool for calculating and presenting fair value, it brings with it several challenges:

Difficulty in predicting the future- when performing DCF analysis, we find ourselves predicting two difficult variables: future cash flows and risk level, which are based on forward looking assumptions. Predicting the future with absolute accuracy is not practical, and we are therefore left with the quality of our assumptions and the information we use, as measures for the quality of our work. The further we go into the future, the less able we are to accurately predict any outcome.

Predicting cash flows- any prediction above several months is prone to quickly-increasing levels of uncertainty, that result in higher variability of possible true outcomes. The further we step into the future, the lower our expected prediction accuracy diminishes. Practitioners should use the most probably, well-founded scenario in their prediction and perform sensitivity analyses on the result.

Predicting the discount rate- if predicting cash flows is difficult, predicting the appropriate discount rate introduces a new level of difficulty. This calculation uses historical industry information that while more stable than company-level information, is still influenced by market perceptions and biases. Also, the need to create a sample of comparable companies or assets adds a layer of practitioner judgement.

Further complexity is added when practitioners add specific risk premiums to the cost of equity. Slight changes in the discount rate can have a significant influence on valuation.

Lastly, it’s important to remember that the discount rate tries to catch two effects with one factor: the time value of money and the embedded uncertainty in predicted cash flows. There is inherent bias in trying to put so much responsibility on a single number.
Cognitive bias and information overload- practitioners often encounter a plethora of internal cognitive biases when valuing assets. They can also find themselves overwhelmed by information overload, as the amount of information they deal with can be quite significant. However, this diminishes with experience.

Often times, stakeholders may try to influence the valuation as well, so users of valuations should always understand who ordered the valuation, who prepared it and who gains from each scenario.

While not human, AI models suffer from biases as well^◆. Furthermore, they are mostly good at interpolating, meaning they work well within the scope of their training dataset, often repeating versions of cases they have already witnessed. This can come as a disadvantage to young, growing companies, that often predict strong and unique growth path.
Overestimation of growth- revenue growth is the most fluid variable in DCF analysis, even more than the cost of equity (as part of the WACC calculation). Oftentimes, practitioners create a detailed forecast for the first 12-24 months or 4-8 quarters and move to annual projections thereafter. While forecasting the next 2 years is prone to some bias, longer periods introduce much room for error. It’s easy to become too optimistic with our entity’s prospects. However, success brings competition, which will eventually lead our entity to show slower growth. Over time, most entities’ growth rates will probably revert to their industry means within several years, unless they hold unique assets and make significant investment in assets.

Furthermore, since we usually model our projections of future periods based on their preceding periods, changes in the early periods have a cascading effect on the later periods as well. This is often the case when we project future revenue as a per-cent growth over previous periods. This increases the variance of our cash flow projections and valuations as well.
Sensitivity to assumptions- DCF is very sensitive to its underlying assumptions. Sometimes, assumptions can be so fundamental that they cause high variability of valuation results. Practitioners should therefore present sensitivity analyses for different values of their main assumptions.
Reliance on specific company beta- single company betas usually have large standard errors. Beta, when used for WACC, should reflect the industry an entity operates in, its risks and debt levels. We should use industry betas as more stable and better representing figures for sector sensitivity to systematic risks.
Use of multiples to calculate terminal value- some practitioners apply a multiple on the last predicted cash flow in the DCF in order to calculate the terminal value. This multiple is taken from available data of similar deals and brings exogenic influence to an endogenic analysis. It is preferred to use a stable growing dividend discount model like the Gordon Growth Model to estimate the terminal value.
Use of risk-free rate- we should use a risk-free rate that is suitable in term to our projected cash flows. Usually, a government bond that matures in between 10 and 20 years.
Not enough emphasis on capital expenses- like investors themselves, entities employ capital today to get value in the future. When this investment is made in monthly employee salaries, it is considered a part of the “Cost of Goods Sold” or “Operational Costs”. When it is made as investment in physical assets, it is referred to as “Capital Expenses”, and entities must make this investment in order to support growth, among investment in working capital.

It usually takes some time between investment and return, but the two are closely related. Practitioners often ignore the direct connection between these investments and future revenue, and treat it as another cash expense with a vague connection to revenue growth. I elaborate on this topic hereunder in Connecting Investments with Growth.
Influence by exogenic factors- macroeconomic and other external factors, such as interest rates, inflation, employment and even industry-specific conditions can affect both cash flows and the discount rate. There is no way of predicting these factors, only try to model their influence.

In the beginning, DCF was used for valuing bonds. This is performed by discounting the bond’s future cash flows using a discount rate determined by the market, which in turn is a rate determined primarily by the credit risk associated with the issuer. In 1951, economist Joel Dean introduced DCF as a method for valuing business entities, in his book “Capital Budgeting”. Joel based his practice on bond valuation, which was well established by that time^◆.

Recall that the method for discounting future cash flows puts the projected cash flows in the nominator and the discount factor in the denominator. This works well for bonds due to their nature, but when extended to valuing business entities, it can be asserted that DCF “shoots in the dark”. Here are the differences between the two types of assets:

Cash flows from bonds (and some yielding assets) are well-defined and upward capped. Their manifestation chances can adequately be caught by the borrower’s credit risk, which in turn influences their discount rate for valuation and decision making. The probabilistic distribution of cash flows is one-sided, meaning it only includes downside scenarios.
Cash flows from business entities are different. Their manifestation is unknown and representation in the DCF is prone to bias. Unlike bonds, their life spans are usually not capped and their probabilistic distribution is two-sided, meaning there is both upside and downside potential.

The amount of unknowns when implementing DCF for business entities that offer hard-to-predict future cash flows (this can be referred to as the “stochastic nature of predicted cash flows”)- is high.

However, while we can conclude by saying that DCF is highly biased, it is still much better than the other methods for valuation, at least in the transparency it creates for the estimation of economic value and the ability to alter the assumptions to check for sensitivities. This is as valuable as the valuation itself. The uncertainties should be tackled with firm assumptions and an elaborate use of information by the practitioner.

DCF Sections

We will now discuss each part of the DCF, from top to bottom.

Revenue

Revenue (or sales) is the money, either in cash or obligation, that the entity generates during its operation, providing value for someone in exchange for a payment. This is the first section to predict. We start from the present, understanding the sources of the asset’s revenues: we try to understand what activities generate the revenue, what is the service(s). We then go back into the past, by studying the entity’s historical revenue from its financial reports. This can serve as the base for our projection.

The result is a several-year revenue forecast which is based on a deep understanding of the entity’s business and clear assumptions. When the business is projected to operate for many years (i.e. it is not a project with a fixed term), we add another column to our analysis and call it the “Terminal Value” column. We use some kind of an estimate of the long-term growth in revenue, usually pegged to the projected long-tern population growth of 2%.

Later in the model we also forecast long-term values for the various expenses, and we usually do it by either using the latest forecast period expense margin or an average of more than one period. Lastly, when we generate a free cash flow figure for this column, we will treat this figure differently when discounting cash flows at the end of our valuations. This estimated long-term growth in revenue is usually marked by a capital G.

During our work, we will connect the various expenses with the entity’s revenue, since the creation of revenue requires investment in tools, resources and personnel. Growth in revenue brings to higher employee costs, higher need for long term investment in assets and higher investment in working capital (all explained hereunder). We need to understand the relationship between the entity’s revenue and its expenses in order to model it into the future. We need to clearly state these connections and use them to proportionally increase costs as our entity grows.

It’s also important to mention that most of the time, our projections within the DCF model are stated in nominal terms, meaning our cash flows assume embedded inflation while not dealing with it directly. Inflation can significantly erode our asset’s performance, and this risk is accounted for in our discount factor, the nominal WACC. We usually don’t need to include a specific analysis of inflation in our model, since the nominal WACC, which is based on nominal costs that are valued by market participants, discounts this risk as well.

Market Research

In free economies, almost every business or asset operate within a market with significant competition. When we come to value an entity we must understand its main functions of value generation and from that derive its market of activity. Once we identified the main market(s), we need to spot the main competitors and try to collect data on them, such as financial data from public sources or management assumptions. This information can be used as a guidance for us when modeling our entity’s business trajectory.

We also need to understand the market size: this is the total annual revenue generated within all market participants. For many global markets, we can find market analysis papers online that give these top-level figures for free. For more local markets or for markets where there is not enough data, we will need to derive the size ourselves.

Once we reached the current size and projected growth several years forward, we can use this figure as a tool for scrutinizing our revenue projections. Our asset or business will most likely not take a significant part of the market during the Forecast Period, so this helps us spot if we were too optimistic with our revenue growth projections. Our competitors’ financial information can also hint at the probably profit margins in the industry. In the long term, we assume our entity will not show a significant shift from these figures.

The competition serves as a limiting force on our projections. In most cases, our entity’s competitors will not let it enjoy overly-high profit margins in the long term, as they will increase efficiency in order to survive and put a cap on our entity’s pricing.

Cost of Goods Sold (COGS)

COGS is the direct expense made to create the service or product. Every economic value needs inputs to materialize and this section captures those direct expenses in labor and raw materials, when applicable.

This is the first expense we meet and it’s directly related with the nature of our product or service.

Gross Profit

This is the first profit section in our model. We calculate it by subtracting a period’s COGS from its revenue. We then go ahead and measure the Gross Profit Margin, which is the ratio between the gross profit and revenue. The higher it is, the better and shows greater efficiency in creating the product.

Operational Expenses

Once we finished modelling the entity’s revenue and direct cost of its generation, we go ahead and include the operational expenses, which are all the expenses made to support its productive place in the market. It is divided into three groups of expenses:

General and Administrative (G&A) costs- this part includes all the management salaries, office expenses, accountancy and legal support, utilities, city tax, insurance, social events and more, when applicable.
Sales and Marketing (S&M) costs- this part includes all expenses relating to marketing a product or a service and getting new customers. It includes the active selling efforts made by sales people, advertising and public relations, but also customer support and social media activity.
Research and Development (R&D) costs- this part includes all the expenses made to research new product or service features to support a sustainable future growth. It includes all costs relating to investment in medium to long-term revenue generation. The market is constantly developing, new technology enters it and may cause existing solutions to become obsolete.

Earnings Before, Interest Tax, Depreciation and Amortization (EBITDA)

This is the second profit section in our model. We calculate it by subtracting the three operational cost groups from our gross profit, and then go ahead and calculate the EBITDA Margin, which is the ratio between the EBITDA and revenue. The higher it is, the better and shows greater efficiency in running a productive organization.

EBITDA is considered to be an indicator of an entity’s operating performance without the impact of several non-operating expenses such as financing decisions, tax consideration and expenses related to depreciation and amortization. It offers us a clean window into the entity’s operating performance.

While EBITDA is used when valuing businesses, there are similar concepts in other types of assets, such as the Net Operating Income for real-estate. They both come to serve the same purpose: a base for operational efficiency and a financial metric for comparison between similar assets.

Depreciation and Amortization

This section represents a non-cash expense, meaning it reduces the value of an asset in the balance sheet. It is often used to depreciate tangible and intangible operating assets such as manufacturing equipment, office furniture or computers.

While this expense is mentioned in the profit and loss statement, it doesn’t involve an actual outflow of cash. Its purpose is to reduce corporate income tax and incentivizes companies to invest. It appears on an profit and loss statement because accounting principles requires it to be recorded, despite not actually involving cash payment. Other examples of non-cash expenses include stock-based compensation, unrealized gains and losses, deferred income taxes and more^◆.

During our Forecast Period, we model the depreciation according to our projected periodic capital investments according to fixed rules, such as 3-year depreciation for 5-10 years, computers for 3-10 years etc. Over the long term, we assume that depreciation equals capital investments and we implement it in the Terminal Year of our model.

Operating Profit (EBIT)

The third profit section in our model, operational profit includes all expenses up to the operating level, including depreciation and amortization. It is basically EBITDA + depreciation and amortization. We calculate Operating Profit Margins as well.

Tax

This section captures the payment to the government as a share of accumulated operating profit or loss as of the beginning of the period. It’s basically income tax that is collected from operating profit where past loss serves as a “cushion”. In many jurisdictions, an asset should only start paying tax on its net operating profit after all past operating losses of several years are recovered. The exact lookback window may change between jurisdictions.

Profit After Tax

The fourth profit section in our model, this is basically operating profit minus tax expenses. As with all other profit sections we can calculate its margin that can tell us something about the influence on tax on our profit.

Adjustment of Net Profit into Cash Flow

Up until this point we modeled our entity’s predicted revenue and various expenses which may include non-cash sections, such as depreciation and amortization or some other accounting concepts. However, we need to calculate the net, hard cash generated by our entity. This is called the free cash flow and we discount that in order to reach an estimation of fair value. This is what’s important to the owner, so we need to make adjustments to our after tax profit and add some important expenses in order to convert it to cash terms. We therefore add 3 main sections to our model:

Depreciation and Amortization- we add back these non-cash expenses which were used to reduce our operating profit and thus the tax expense. These are not true expenses and therefore need to be accounted for when moving to work with cash terms (i.e. cash flows).
Capital Expenses (CAPEX)- we subtract any capital that was spent on investing in new assets or maintaining existing ones. For example: the purchase of machinery, construction, building renovations or equipment purchases such as computers and furniture. We model this investment separately and connect it with our entity’s projected operations, such as x employees per machine or y furniture pieces per programmer. We need to connect this investment with our entity’s projected growth, as we discuss hereunder at Connecting Investments with Growth.
Changes in Working Capital- these money flows affect the entity’s cash flows. When an entity grows, it often needs to invest in additional working capital to support its growing operations. As an entity matures and becomes more efficient, it can release cash tied up in working capital. “Changes in working capital” accounts for the impact of fluctuations in current assets and liabilities on the projected cash flows.

We model our working capital needs for every period in our forecast and measure the difference from the previous period. This difference is what we include in our DCF model. We can either reach the periodic working capital through the balance sheet using days outstanding, or through per-cent of sales, both based on historical and forward-looking analysis. We should use the most suitable method for each case.

Working Capital is the cash available to meet a business’ short-term obligations. An entity’s net working capital can be calculated by subtracting current (short term) liabilities from current assets in book value, which describes the bottom line economic rights and obligations an entity has. Remember that in accounting, a promise to pay is considered as payment, but in valuation only hard cash counts. Adjusting our after tax profit into cash flow requires the closing of this gap through the actual transfer of funds.

Current assets are assets that are expected to be converted to cash or used up within one year. This includes cash, accounts receivable and inventory.

Current liabilities are obligations that are expected to be settled within one year. This includes accounts payable, short-term debt and other short-term liabilities.

Connecting Investments with Growth

It’s important to keep revenue/operating profit/FCF growth connected with capital investments. In order to grow, entities need to continuously invest in the business, either by using Retained Earnings, which are profits that are retained within the entity and not distributed to investors, or by raising new capital.

The Reinvestment Rate measures how much capital an entity is investing back into its business to generate future growth^◆. It is a measure of how efficiently an entity can convert its investments into additional future earnings. It is often measured using the most recent financial statements or throughout the Forecast Period in our model, and used to estimate the amount of capital that needs to be reinvested in the business in order to support future growth. It is calculated for a single period as follows:

Where each section is the expense and profit during the period.

A higher reinvestment rate implies that the entity makes more investments and thus reduces its free cash flows in the short term, but potentially increasing them in the long term if the investments yield a higher return than the entity’s WACC. It’s important to base our growth rate on the investments made and accurately estimate the reinvestment rate, in order to strengthen the reliability of our valuation. Underestimating the reinvestment rate will lead to an overvaluation of our entity, since we assume too little investments for the growth we anticipated, and vice versa.

After estimating our entity’s reinvestment rate, we should estimate our entity’s after tax Return on Invested Capital (ROIC) throughout our Forecast Period:

Where Invested Capital is the accumulated capital invested in the entity since its inception, all the equity and debt financing put in its activity as measured in its balance sheet, plus this period’s total adjustment for cash flow. This helps in understanding how efficiently our entity employs its capital and quantifies the any return on its invested capital.

We should then use our estimated reinvestment rate and ROIC to see what our entity’s sustainable operating profit growth rate should look like:

The reason is that both the reinvestment rate and ROIC are often calculated using the entity’s operating income after tax and reflects this figure’s relation with invested capital. Operating profit is a measure of an entity’s earnings from its core business operations, excluding financing and tax expenses, which makes it a useful metric for assessing capital available for investment. It is usually not applied to revenue, as a high revenue growth does not necessarily translate to higher operating profits or FCF. The growth rate could serve as a barometer to either operating profit or free cash flow growth, either is ok as long as it’s consistent.

We should calculate these figures for each year of our Forecast Period. We should check if they look logical, compare them with the competition and let them guide us towards a more true projected operating profit growth rate.

Growth comes from both reinvestment of profits in new assets and from increased efficiency in utilizing existing assets^◆, and we should always have that in mind.

Notice that these calculations directly take invested capital into account, but any expense related to the monthly wages of employees that influence the operating profit is only taken indirectly. The reason is that in finance, these two sources of growth are treated differently: while capital assets are usually physical and in control of the entity, periodically depreciated and are projected to generate a return over time, employees provide value based on monthly payments and are generally less stable than physical assets. There’s also a different tax treatment for these two revenue generators.

Free Cash Flow

As explained above, this is the cash flow generated by an entity after all required expenses and obligations are met.

We should discern between two types of free cash flows:

Free Cash Flow to the Firm (FCFF)- this is the cash flow that is generated and is free for the owners to decide about its use, be it for reinvestment into the business, debt service or dividend distribution. It is the result of modelling an entity’s free cash flows solely from its business activity, without accounting for any debt, reaching an enterprise value. We discount these cash flows using WACC.
Free Cash Flow to Equity (FCFE)- this is the cash flow that is available for shareholders after all expenses, including debt service, have been accounted for. It is the result of modelling an entity’s free cash flows where we do take debt and its servicing into account in our model. Interest payments will appear right before tax, and principle repayment and borrowing will appear as another adjustment of net profit into cash flow. The result of discounting these cash flows is the equity value for the entity’s shareholders. We discount these cash flows using the entity’s cost of equity.

We usually prefer to work with FCFF since it is simpler to ignore debt and its servicing in our planning, and focus on operations. This also allows for a cleaner comparison between the operations of other investment opportunities, not having to include financing strategy in the mix.

Discounted Cash Flow

After calculating our entity’s free cash flows during the Forecast Period and Terminal Year, we can go ahead and discount them by the appropriate discount rate, and thus incorporate the risk and time value of money into our valuation.

Before discounting, we need to define the exact periods of our projected cash flows and understand their distribution over each period. We need to decide on two more parameters- the date of valuation and the timing of cash flow generation:

Date of valuation- this is our , the time when our value is calculated and true according to our assumptions. DCF valuations can either be made fixed for the beginning of a quarter, or floating at any point in time. If we choose to fix our valuation at the beginning of a quarter, as is often the case for regulatory compliance, we use specific periods for our model such as FY 2024, FY 2025 etc. If we choose any other point in time, we can project annual cash flows and label them as FY 1, FY 2 etc. Either way, our valuation is true to .

If we need our Forecast Period years to start on January 1^st but our is some time within the year, we can model our first cash flow from to the nearest year-end, and start the next period at the next January 1^st. In this case, we make a partial projection of cash flow for the time between and the nearest year-end, and time our discount periods accordingly. We need to take into account the time between our and the next January 1^st. For example, if our is June 30^th and we want our Forecast Period years to begin on January 1^st, we model the first period of 6 months and discount that by 0.25. The next year will be a full year projection, discounted by 1.25, etc. It’s ok to round our to the nearest beginning of month or quarter for simplicity.
Timing of cash flow generation- are the cash flows projected to be generated relatively evenly over the year, such as the case for stable companies and rented real-estate, or are they generated at the end of the year, such as the case for some bonds?

For the first case, and most cases, we will assume that the cash flows are generated at the middle of the year and we will therefore use mid-year discount periods of 0.5 that increase at intervals of 1. So we will discount the cash flow generated in the first year using 0.5, the second with 1.5 etc.

For the second case, we will just discount the cash flows at the end of the year, meaning 1 for the first year, 2 for the second etc.

After discounting our Forecast Period years, we are often left with discounting our Terminal Year to reach the Terminal Value. For that, we will use the period of our last year from the Forecast Period. This is because we discount our Terminal Year’s representation of infinite cash flows to the end of our last Forecast Period year, and then need to also discount it back to .

Reaching a Valuation

After we were able to discount our projected cash flows, we add the discounted Forecast Period and Terminal Year figures up to reach our entity’s operational value. We then subtract the book value of the the entity’s debt to reach its equity value. The book value represents the total amount owed so we use that do extract the total value left for equity holders. The equity value is the value of the remaining stake after all debts are paid. We can divide this figure with the entity’s share count to reach a “per share” equity valuation.

After reaching our valuation, it is good practice to ask ourselves how sure we are of this figure. Our model is always biased, but we can make it a bit more realistic by taking a look at our competitors’ profit margins and equity to book ratios. As we mentioned above, our projection results can’t be too far from the competition, especially in the long-term. In free markets, our competitors will not let us maintain incredible profit margins over time. Consistent figures that are way outside the normal in the market are most probably inaccurate overestimations.

Finally, we must take a deep look into our assumptions and make sure they are well founded and that we can explain them.

Sensitivity Analysis

This is a very important part of a valuation. Since we are making projections into the future, we must leave space for things to not go as planned and show how this can affect our valuation. What we do in practice, is we take pairs of parameters that we believe influence valuation, such as the WACC, the long-term growth rate (G) or any other parameter we used to achieve a valuation, and then use Excel’s “What-If Analysis”, “Data Table” feature to calculate and show our valuation under various parameter values.

This is a good place to include any possible Discount for Lack of Marketability (DLOM) or Discount for Lack of Control (DLOC) in the form of sensitivity analysis on value.

Key Performance Indicators (KPIs) and Presentation

After we made our detailed and educated guesses into the future, we should go ahead and try to decipher what they mean. We should look at our model and use various KPIs to measure our entity’s future performance, business activity and cost structure, and start examining the reasonability of our assumptions.

This is where the DCF analysis meets business planning. A proper use of KPIs and the presentation of some important features that come up in our projection can add true value to the entity’s management.

The quickest way to do that is to look at our profit and cost margins and try to spot any irregularities.

Advanced practitioners, which also understand the business and strategic aspect of their work, may want to do the following:

Use the multiples method for valuation- calculate the last Forecast Period year’s valuation multiples and compare that to industry-prevalent figures as visible from the competition and various statistics sources from the web. Good multiples to examine are the revenue multiple, EBITDA multiple and free cash flow multiple. This can also be an indication of the right discount factor range to use.
Compare the entity’s profit margin with the competition once it stabilizes, and explain why there are any differences.
Chart the projected change in our entity’s periodic projected revenue to see any exaggerated figures.
Chart the different types of revenue sources across the years, either in absolute terms or in 100% stacked columns. This will show us where managerial attention should be put, and is also good for comparing with the management’s plans. It can clearly show is whether we projected a different trajectory for entity than its owner would want to take.
Chart the different types of revenue sources and their direct costs across the years. This can be done using regular bar charts, and help us spot activities that are less profitable, as based on our assumptions. We can use that to make our projection better and more accurate as we share that with management.
Chart the total periodic projected revenue in each activity and compare that with the total projected market size. This is a good sanity checks for the cases when we lost touch with the market and projected a large market share within a few years, without noticing.

There are many more KPIs to analyze, whether by plotting or a numerical analysis, but this look at the strategic meaning of our work is very important for its quality and value.

The Weighted Average Cost of Capital (WACC)

WACC is an entity’s average cost of financing, stated in annual per-cent (%) terms. It is the return capital providers are willing to receive for dealing with an entity, and the cost at which an entity is able to finance itself. To calculate the WACC, we take the average cost of each of its financing sources, its debt and equity, and weight them by their proportion in the entity’s total outstanding funding amount. It is an entity’s “cost of capital”, based on all financing sources.

WACC has 2 main uses, depending on the need:

Corporate finance- when used for corporate management and financial modelling, the entity’s own WACC is used as the discount rate for calculating the net present value of (NPV) projects that share the same general risk as the corporation. It serves for capital budgeting and decisions about project investment, as only investments offering an IRR higher than WACC should be pursued, as they offer positive value.
Valuation- when used for valuation, WACC is the discount factor we use to discount our projected cash flows. Unlike in corporate finance, for valuation we use the industry WACC, since we need to use a general, typical cost of capital for a similar entity in the same industry. The industry WACC is a less volatile and idiosyncratic figure, which better represents the most probable trajectory for our entity when it comes to financing its operations. When using industry WACC, we assume that our entity shares the same risk profile and financing blend as its general industry. Riskier industries will have a higher average WACC.

Either way, the higher the WACC, the higher the discount rate and the lower the value of our asset will be. If an entity’s or industry’s risk profile changes, so should the WACC.

We will focus on the use of WACC for entity valuation purposes. In order to calculate WACC for entity valuation, we follow these steps:

Examine the environment- we first create a sample of similar entities or from the public markets (called “Comparables”) that operate in the same sector and are similar in size. We collect their market capitalization, their total financial debt and cash, their respective marginal corporate tax rate and leveraged beta (explained hereunder). Our goal is to create a fair sample that adequately represents our entity’s operating environment.
Debt and equity financing proportions- we need to figure out what is the mean proportion of debt and equity financing in the relevant industry. We examine our Comparables observations and use their average figures: for each observation, we subtract cash from financial debt as it appears on the balance sheet to calculate its net debt, and collect each observation’s current market capitalization, which is the total fair value of its equity.

Together, as per the fundamental accounting equation, they form the fair value of each publicly-traded company’s assets: . We then calculate the following financing ratios for each observation: and . We then calculate a simple average for each.

We need to include all types of debt in our debt financing proportion, both short and long term, unless some short term debt is taken temporarily, is uncharacteristic of the entity’s operations and is balanced with cash equivalents. Generally, if short term debt forms at least 10% of the total liabilities and net working capital is negative, this means that it is probably used to finance long term assets and should thus be included in the WACC (PoCF, page 518)^◆.

The reader probably noticed that we use the book values of debt and not its fair value. Debt is often stated in the balance sheet at its historical cost, the face value when it was issued, minus repayments or amortizations made up to the balance sheet date. For financially-healthy companies, the book value of debt is not far from its fair value, so it’s not a far approximation to use the figure stated in the latest balance sheet. The reasons we settle for this approximation are first, that often there is not enough publicly traded debt we can draw a fair price from and second, that debt is repaid at face value and using the latest book figures adequately states how much debt financing our entity has taken.

We use current fair values of each financing source because we are dealing with a fair value estimation of our own.
Pre-tax cost of debt^◆– this is the effective annual rate that an entity pays on its long term debt as of the time of assessment. It is also the cost at which the entity can now borrow. This is the effective, pre-tax cost of debt, meaning this doesn’t take into account the value of interest rate tax shield. In our valuation, we use the after-tax cost of debt that does account for the tax shield associated with interest payments, and we add that by adjusting the average cost of debt we calculate from our Comparables.

For entities with publicly traded debt it is easy, we use the current yield of their outstanding, long-term (longest maturity as possible) publicly traded debt. For entities without publicly traded debt, we can either use their credit rating and calculate a default spread above risk-free return, or look for this cost in the financial statements and calculate the average interest payment on the entity’s debt. We collect this data for each of our observations and calculate its simple mean.

Default spread also known as “credit spread”, is the debt risk premium, which is the extra return investors require as compensation for taking on more risk above a risk-free debt security such as government bonds of the same maturity.
Cost of equity- as mentioned above, this is the annual return equity investors expect to receive for investing in an entity’s equity. It is their compensation for taking on the risks embedded with the entity and its operations.

In DCF, we often use a model to compute this figure. The prevailing model is the CAPM, which calculates a cost of equity for a diversified investor. Practitioners then add some specific risk premiums to this figure to make the cost of equity more realistic and representative of their client.
Calculate the WACC.

The following figure shows the WACC and its parts:

^{Source: Corporate Finance Institute.}

Calculating the WACC

For an entity financed by both debt and equity, WACC is calculated in the following way:

See hereunder an explanation about the formula’s parts:

is the cost of debt for a typical entity of a similar size in the same sector.

is the complement to the marginal corporate tax rate an entity is subject to. The marginal corporate tax rate is the cash tax paid as a percentage of each dollar of additional income generated by an entity. We need to use a figure that will best represent the true tax cost of an entity’s future operations, including entities that operate in several geographies.

is the typical proportion of debt financing out of total financing (equal to total assets) for a typical entity of a similar size in the sector, the .

is the cost of equity for a typical entity of a similar size in the same sector, as calculated using a model.

is the typical proportion of equity financing out of total financing (equal to total assets) for a typical entity of a similar size in the sector, .

Recall that for entity valuation purposes, the WACC parts are derived from a set of comparable entities that represent the typical entity of a similar size that operates in the same sector. Also note that the WACC should bring into account all types of financing and its proportion. For example, when preferred stock is involved, we should treat it as a factor in our calculation as well, find its cost and weight it by its part of the entity’s total financing. However, it is not recommended to break down debt into individual pieces by seniority and attach different costs to each one^◆.

When an entity is wholly financed by equity, its WACC is equal to its cost of equity, which represents both the price it has to pay for its equity financing and the opportunity cost of capital for its equity investors, the return they forgo on alternative investment opportunities with a similar risk profile.

Notice that we calculate an after-tax WACC, because usually interest is a tax deductible expense and this tax shield has real value. Also remember that we did not account for interest payments in our cash flow prediction, as if our entity was entirely equity financed. WACC is our way of introducing the effect of debt financing into our business’s enterprise valuation and to account for the value in the interest rate tax shield. The second half of the recognition of debt into our valuation is made when we deduct the remaining financial debt from our enterprise value.

After we calculate the WACC, we can perform a quick sensitivity analysis using each of its main parameters: cost of debt, tax rate, risk-free rate, beta and market return. We can achieve that using Excel’s “Data Table” capability. We create a row of several values for each parameter and see how it affects the WACC in a row below. This can give us a range of possible WACCs and teach us how each parameters affect the number.

WACC includes the weighted average of an entity’s financing costs, and so it adequately covers and quantifies the risk of a typical entity’s operations as judged by its debt holders and owners, in a market full of investment opportunities. For this reason we use the WACC we calculated in order to discount our projected cash flows and reach its valuation.

Nominal Vs. Real WACC

The difference between nominal and real cash flow projections lies in the inclusion or exclusion of the effects of inflation.

Nominal cash flow projections reflect the current value of goods and services in each period, and thus include the impact of inflation. In other words, nominal cash flows use each period’s prices. Nominal cash flows relate to modelling the cash quantity with disregard to purchasing power.

Real cash flow projections are adjusted to exclude the effects of inflation, using the prices of throughout the forecast. They show the value of future cash flows in constant prices, stripping them of the inflation component, which is any shift in prices that stems from the overall change in prices in the economy (also called “constant prices”). Real cash flows relate to modelling the entity’s real purchasing power over time.

Converting cash flows from nominal to real terms can be made as follows:

We take the projected nominal cash flow for period t and divide it by (1 + the average periodic inflation rate up to period t) raised to the power of t.

This formula assumes that inflation rates are compounded, which is an accurate reflection of economic reality over multiple periods. By using this method, we account for the cumulative effect of inflation on the purchasing power of money over time. When converting, we must make sure we are using rates and cash flows for the same time periods.

Just like cash flows, WACC can also be stated in either nominal or real terms. We use a nominal WACC as the discount factor for nominal cash flows, and a real WACC to discount real cash flows.

Nominal WACC is based on nominal costs of debt and equity, in that it its based on the market values of publicly-traded debt that is not CPI-indexed, and therefore already includes the risk of inflation in its price. This is the WACC most DCF valuations use in normal times, when inflation is within a healthy range.

Real WACC includes adjustment to the nominal WACC, as we need to strip the influence of inflation from our discount factor. We can do that by removing inflation from the cost of debt and risk-free rate as follows:

Real cost of debt– to convert our nominal cost of debt to real terms, we subtract from it the predicted annual inflation or use the more accurate Fisher equation, shown hereunder.
Real cost of equity- when we use CAPM as our model to value the cost of equity, we use the yield to maturity of non-CPI-indexed government bonds, that already include a premium for expected inflation. We convert this figure into real terms by subtracting the predicted annual inflation rate from the nominal risk-free rate, or use the the more accurate Fisher equation shown hereunder.

Basically:

Approximated by:

This is an adjustment to the Fisher equation, as part of the Fisher Effect^◆. Remember to make sure to use same-period rates. Interest rates are usually stated in annual terms, so we use either the projected or actual annual inflation rate for the same year as well.

Notice that we don’t use the Fisher equation to adjust nominal WACC into a real WACC, since doing so assumes inflation affects all its parameters, while in reality it only affects some of them. We spot the parameters that are influenced by inflation and only adjust them.

Prof. Aswath Damodaran

Prof. Damodaran is a Professor of Finance at the Stern School of Business at New York University^◆. He runs a website where he shares many resources related to finance and valuation, that are the results of his studies. Practitioners often use his work to quickly get accurate country and sector-specific figures of cost of debt, beta and equity market risk premiums for our WACC calculation. This is a great free service that saves time and maintains methodic depth. It is especially beneficial for cases when there are not enough “pure play” Comparables. I will put links to the main data we can use from Prof. Damodaran’s website in the “Resources” part of this text.

Where business entities and investors meet

Looking at the WACC formula, we may think that an entity’s average cost of capital can be reduced by substituting expensive equity with cheaper debt, since debt is always cheaper than equity. But this is not the case, since as an entity’s debt financing ratio increases, so do its risks regarding debt servicing, which brings to an increase in its cost of equity. As Modigliani and Miller suggest in their Irrelevance Theorem, the two effects cancel each other out, not including the value of the interest rate tax shield on one side the the extra costs of financial distress on the other.

Behind every asset or entity there are owners, who study the market, provide capital and make strategic decisions. Their goal is to get the highest return for given risk, as much as the environment allows, creating economic value in their path. Business entities are tools for an efficient use of capital and its conversion into true economic value.

A business has the right to exist if it can generate a net return that is higher than what its owners can generate elsewhere using their capital, for the same level of perceived risk. For example, a business may be able to get cheaper financing than what its investors can get, or create value better than what the owners can create elsewhere. If owners can create better net return elsewhere, they will seek to liquidate the business and transfer their capital to where it can be used best.

The efficiency of capital use is measured by the return on risk a business entity can generate. Therefore, a business entity’s main function is to be the best at utilizing capital and create the maximum return for every capital investment, in a sustainable way.

WACC is sensitive to value creation. Since financing becomes more expensive the more of it is used, an entity should always use its capital for value creation. If an entity starts using its capital for purposes other than value creation, its WACC will increase because no new value will come to offset the higher cost of financing. The better use the entity makes of its financing sources, the lower its WACC will become and the higher its value will be.

The Capital Markets Theory (CAPM)

The Capital Markets Theory (CAPM)^◆ was developed in the early 1960s by William Sharpe and on parallel by Jack Treynor, John Lintner and Jan Mossin. The model provided the first coherent framework for relating the required return on an investment to its perceived risk^◆. It can be considered as an extension to the earlier work of the Modern Portfolio Theory^◆, which was developed by Harry Markowitz and published in 1952.

We often use the CAPM in our valuations as a methodical model to calculate the asset’s fair cost of equity in normal times, which is a part of the Weighted Average Cost of Capital (WACC) calculation. The CAPM is fit for the task since it offers a clear framework for connecting market risk and asset return through its formula, under various assumptions that we can live with.

The CAPM is based on the ideas developed within the Modern Portfolio Theory, which hypothesized that some risks do not affect asset prices. It distinguishes between idiosyncratic risks, risks that are asset-specific and can be diversified away, and systematic risks, risks that are embedded in the economic environment, and can’t be diversified away. It is a single-factor model, as it only accounts for systematic risk as a source of expected return to investors. For this reason, the fair cost of equity according to the CAPM should always be calculated from the point of view of a diversified investor. According to this model, diversified investors can act more efficiently in the market, since they are only concerned with systematic risks, and thus require lower compensation in the form of return.

While this model offers a relatively simple explanation of the relationship between expected return and risk, the empirical record of the model is poor enough to invalidate the way it is used in applications^◆, as it makes several simplifying and unrealistic assumptions about the markets. However, due to its simplicity and coherence, it is still widely used for both portfolio construction and the valuation of assets.

The CAPM provides a mathematical representation of the relationship between an asset’s expected return, the economy’s risk-free rate, the asset’s beta (or that of similar assets) and the market’s expected return in the following way:

Where:

is the expected annual return on an asset, its cost of equity.

is the risk-free rate in the economy, as manifests in the current yield to maturity (or just “yield”, as expressed in annual per-cent terms) of a government bond, usually of 10 or 20 years, or an average of both. Care should be taken when reading this figure in periods when the yield curve is skewed. In such cases we should take the appropriate risk-free rate of normal times and apply a sensitivity analysis.

is the asset’s “beta”. Beta measures the systematic risk an asset is exposed to, relative to the market’s systematic risk. I will elaborate on this shortly.

is the expected return on the “market portfolio”, which is a portfolio consisting of all traded securities in a market, as weighted by each asset’s projected return and relative value within the market. The theory states that we should include all assets, but in practice this parameter is represented by the expected return of the main value-based index in the market, such as the S&P 500, so the work is made for us.

is the expected “market portfolio”‘s excess return over the economy’s risk-free rate. This is a market’s equity risk premium (ERP), which quantifies the return above the risk-free rate investors in the market accepted in the past year.

Notice that the E(.), which stands for “expected”. When we perform ex-ante analysis and look into the future with a projection, we will use projected figures. When we perform ex-post analysis and explain past phenomena, we use past figures. In the second case we don’t need to use the E(.) notation.

The Security Market Line and Capital Market Line

The relationship between a single asset’s return, the risk-free rate, beta and market premium can be graphically represented as the Security Market Line (SML), which is a linear, visual representation of the said relationship in a plot depicting publicly-traded assets’ expected beta (x) and return (y). This is CAPM’s solution for an entity’s cost of equity based on systematic risk only, meaning it assumes its user is a diversified investor.

It’s worth mentioning another important CAPM term, the Capital Market Line (CML), which is the SML’s version for portfolios of assets. It tangents the Efficient Frontier on an expected standard deviation (x) and return (y) plot. Since the CML relates to diversified portfolios of assets and non-diversified investors it is avoided when valuing a specific asset.

The SML can suggest when an asset offers higher return than it should for its perceived risk and is therefore undervalued, and when the opposite happens. It looks like this:

^{Source: Wikipedia.}

The SML is our CAPM cost of equity for a diversified investor under different values of asset beta, asset return and the risk free rate. When our entity is not publicly traded, we use data from publicly-traded Comparables to approximate its fair cost of equity.

It’s worth noting that while the CAPM is the generally accepted method for calculating the fair value of an entity’s cost of equity for valuation, other methods exist for this task, such as the Arbitrage Pricing Theory (Stephen A. Ross, 1976)^◆ and the Three Factor Model (Fama and French, 1992)^◆. While these are multi-factor models, the CAPM is considered to be a single-factor model- an asset’s exposure to systematic risk, as measured by beta. CAPM found the lead due to its simplicity and the ability it grants us to get the equity cost we need from a few basic, publicly available parameters.

As we will soon find, CAPM is a bit too simple and practitioners often add two risk factors to its result: the size and specific risk premiums. Before discussing those, let’s focus on beta.

The Beta Coefficient

The beta coefficient (beta for short) measures, ex-post, how the general market behavior affects an asset’s price, and is calculated as follows:

Beta is calculated through regression, as it is the slope of the least-squares line (the regression line) of a plot depicting the market’s periodic return (x, explanatory variable) and the asset’s periodic return (y, dependent variable). By the way, another regression parameter, , measures the proportion of the total variance in the stock’s returns that can be explained by market movements (PoCF, page 232)^◆.

Notice that the calculation is made ex-post, on past trading data, and focuses on publicly traded assets that have daily or weekly price figures. This is one of the reasons we use the sample of Comparables for our valuation of privately-owned entities, since the observations are all publicly-traded and have daily data for calculating their betas. We then calculate an average and use that as our entity’s beta in the WACC calculation.

The data used for calculation is typically daily price change data for 1-3 years past. The same can be done for weekly or monthly data for up to 5 years. Daily data is more noisy but more statistically significant. Longer frequencies reduce noice and capture significant trends, but require a longer historical dataset which may already be irrelevant.

The beta calculations show us that the market’s beta is always 1. If an asset’s beta is lower than the market’s, it is showing a lower volatility than the market. This hints that when the market moves by 1%, a publicly-traded asset with a beta lower than 1 will move by less than 1%, and the opposite for .

Beta Significance Testing

For our valuation needs, we should also perform a significance testing by calculating the t-test of each beta calculation in our Comparables group, and only use betas that we find to be statistically significant. This makes sure that we use betas that indicate a true relationship between the explanatory variable (market) and dependent variable (the traded security).

Therefore, in cases when we calculate betas by ourselves, we should divide each beta with its standard error to reach its t-statistic. The t-statistic describes how far our observed data is from the null hypothesis of no relationship between the variables. Values greater than 1.96 show a significant relationship between the two variables, and those are the betas we should use.

The standard error is a statistical measure that provides an indication of the accuracy of predictions made by a regression model. It estimates how closely the data points fit the regression line. The smaller the standard error, the lower the variability around the coefficient estimate for the regression slope and the more we can be sure of our regression line as adequately explaining the sample.

The beta of a single security is an inaccurate estimation that has a significant standard error. This error can be mitigated when considering portfolios of securities, and thus practitioners turn to industry betas, that are more robust.

Unleveraged Beta

When we calculate the beta on publicly traded assets, we calculate a leveraged beta, the beta of the equity stake in an entity that often takes on debt as well. In valuation of privately-held entities, we value an entity’s operational assets without regard to debt financing and therefore need to use unleveraged beta for the CAPM.

The inclusion of debt financing increases the equity holders’ returns (ROE) when the cost of debt is lower than the return on assets (ROA). All beta in the stock market is leveraged since it is calculated on traded equity of companies that mostly use debt financing.

We can convert the leveraged beta into its unleveraged form based on the after-tax debt to equity financing ratio:

Where:

is the unleveraged beta, meaning the beta of the entity’s entire balance sheet. This is the beta we use in our cost of equity calculation, since it represents an asset’s systematic risk without the influence of debt financing.

is the leveraged beta, meaning the beta of the entity’s equity after debt financing has been included.

is the entity’s debt to equity financing ratio, comprised of the value of (preferably) the fair value of net after tax debt and equity.

is the entity’s marginal corporate tax rate.

The leveraged to unleveraged beta conversion formula shows us that leveraged beta is always higher than unleveraged beta. It is also intuitive, since higher debt means higher risk, and investors expect more compensation for taking on more risk. When an entity takes on more debt, more cash is being transferred to interest payments and there is less left for payment to investors.

Adjustments to the CAPM’s Cost of Equity

In asset valuation, we often complement the CAPM’s computation of an entity’s cost of equity with other risk factors that connect the theoretic, general computation result of the CAPM that is only based on systematic risk and thus relates to a diversified investor, towards our own privately-owned asset, here and now.

The adjustment we make include the linear addition of several specific risk factors to the cost of debt:

Size risk premium- often, publicly traded entities have a larger volume of activity than the privately-held entity we are valuing. In such cases, the information we get from our Comparables is skewed towards larger entities, and we need to compensate for that by adding to the cost of equity of our entity, to compensate for its small size.

This is often done by using a third party service that makes statistical calculations and suggest what size premiums to add for every entity size in each geography. For example: Ibbotson and Kroll (previously Duff & Phelps).

In the Duff & Phelps “Risk Premium Report 2013”^◆, the company stated that this calculation is the result of a study that was performed on historical data and observed different excess return than the CAPM suggests, for different companies of different sizes.

It’s important to mention that while 94% of valuation practitioners use size premium to adjust the cost of capital in valuation, not everyone agrees with this practice. Prof. Damodaran himself stated his objection for this practice^◆, which in his view brings to an exaggeration of the true cost of equity for small companies. Others say that adding a size premium in excess of CAPM is no different than adding an arbitrary number to the cost of equity^◆.
Specific risk premium- this is an additional rate of return that investors expect to earn for bearing the unique, non-systematic risks associated with a particular entity^◆. Practitioners use this figure to play around with the WACC and influence it if it seems too low for the entity they value compared to industry averages, especially in low interest-rate environments where the cost of debt is historically low, bringing to a reduced WACC. This premium should not include anything relating to size, since this was accounted for with the size risk premium.

Resources

Here are some resources that can help my readers with making better valuations:

A template DCF model- since Excel works with tiny tabs, I find it easier to have most important sub-calculations in one sheet. This lets us only scroll to reach our section of interest. This is my format for a business DCF valuation:
Prof. Damodaran’s data links-
– This link directs to the Professor’s cost of equity and capital calculation results for the US, where we can find various WACC related typical figures by industry.

– This link directs to the Professor’s beta calculation results for the US, where we can find various beta and other risk figures by industry.

– This link directs to the Professor’s market premium calculation results. Notice that he calculates two types of equity market premiums: one based on credit rating and the other based on the latest Credit Default Swap (CDS) spreads over US CDS. The latter data is more current but is only available for some countries. All data can also be downloaded as an Excel file.

– This link directs to the Professor’s statistics about profit margins for the different US industries.

– This link directs to the Professor’s current data page, where he shares a plethora of data and statistics.
WACC calculation services- there are free online services that show you the WACC of publicly-traded companies, such as valueinvesting.io’s platform, which also calculates the cost of debt and cost of equity.

Conclusion

As I hopefully demonstrated, the measuring of an asset’s worth is a multifarious, intricate and fascinating endeavor. It requires us to look both back into the past, explore our present surroundings and venture into the future of a complex and dynamic environment. It entails domain expertise, business acumen and the true understanding of the environment in which our entity or asset is operating.

In this text, we learned about the 3 main approaches to valuation, their various methods and their assumptions, and then dove deep into the Discounted Cash Flows (DCF) method for the valuation of yielding assets. We went over its history, its benefits, its characteristics and challenges, before elaborating about its expert use.

Valuation sits at the core of every investment decision and when done right, it can bring abundant business and strategic benefits.

I hope this text serves as a window for my readers, a source of information and a beacon of expertise.

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