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In
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...
, valuation is the process of determining the
present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
(PV) of an
asset In financial accountancy, financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value ...
. In a business context, it is often the hypothetical price that a third party would pay for a given asset. Valuations can be done on assets (for example, investments in marketable securities such as companies' shares and related rights,
business Business is the practice of making one's living or making money by producing or Trade, buying and selling Product (business), products (such as goods and Service (economics), services). It is also "any activity or enterprise entered into for pr ...
enterprises, or
intangible asset An intangible asset is an asset that lacks physical substance. Examples are patents, copyright, franchises, goodwill, trademarks, and trade names, as well as software. This is in contrast to physical assets (machinery, buildings, etc.) and finan ...
s such as
patent A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A p ...
s,
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
and
trademark A trademark (also written trade mark or trade-mark) is a type of intellectual property consisting of a recognizable sign, design, or expression that identifies products or services from a particular source and distinguishes them from others ...
s) or on liabilities (e.g.,
bond Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
s issued by a company). Valuations are needed for many reasons such as
investment analysis In finance, valuation is the process of determining the present value (PV) of an asset. In a business context, it is often the hypothetical price that a third party would pay for a given asset. Valuations can be done on assets (for example, inve ...
,
capital budgeting Capital budgeting in corporate finance is the planning process used to determine whether an organization's long term capital investments such as new machinery, replacement of machinery, new plants, new products, and research development project ...
,
merger Mergers and acquisitions (M&A) are business transactions in which the ownership of companies, other business organizations, or their operating units are transferred to or consolidated with another company or business organization. As an aspect ...
and acquisition transactions,
financial reporting Financial statements (or financial reports) are formal records of the financial activities and position of a business, person, or other entity. Relevant financial information is presented in a structured manner and in a form which is easy to un ...
, taxable events to determine the proper
tax A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or n ...
liability.


Valuation overview

Common terms for the value of an asset or liability are
market value Market value or OMV (Open Market Valuation) is the price at which an asset would trade in a competitive auction setting. Market value is often used interchangeably with ''open market value'', ''fair value'' or ''fair market value'', although the ...
,
fair value In accounting and in most schools of economic thought, fair value is a rational and unbiased estimate of the potential market price of a good, service, or asset. The derivation takes into account such objective factors as the costs associated wi ...
, and intrinsic value. The meanings of these terms differ. For instance, when an analyst believes a stock's intrinsic value is greater (or less) than its market price, an analyst makes a "buy" (or "sell") recommendation. Moreover, an asset's intrinsic value may be subject to personal opinion and vary among analysts. The
International Valuation Standards The International Valuation Standards Council (IVSC) is an independent, not-for-profit, private sector standards organisation incorporated in the United States and with its operational headquarters in London, UK. IVSC develops international techn ...
include definitions for common bases of value and generally accepted practice procedures for valuing assets of all types. Regardless, the valuation itself is done generally using one or more of the following approaches; but see also, : #Absolute value models (" Intrinsic valuation") that determine the present value of an asset's expected future cash flows. These models take two general forms: multi-period models such as
discounted cash flow The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate devel ...
models, or single-period models such as the
Gordon model In finance and investing, the dividend discount model (DDM) is a method of valuing the price of a company's stock based on the fact that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In ...
(which, in fact, often "telescope" the former). These models rely on mathematics rather than price observation. See § Discounted cash flow valuation there. # Relative value models determine value based on the observation of market prices of 'comparable' assets, relative to a common variable like earnings, cashflows, book value or sales. This result will often be used to complement / revisit the intrinsic valuation. See § Relative valuation there. # Option pricing models, in this context, are used to value specific balance-sheet items, or the asset itself, when these have option-like characteristics. Examples of the first type are
warrants Warrant may refer to: * Warrant (law), a form of specific authorization ** Arrest warrant, authorizing the arrest and detention of an individual ** Search warrant, a court order issued that authorizes law enforcement to conduct a search for eviden ...
,
employee stock option Employee stock options (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are commonly viewed as an internal agreement prov ...
s, and
investment Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing i ...
s with
embedded option An embedded option is a component of a financial bond or other security, which provides the bondholder or the issuer the right to take some action against the other party. There are several types of options that can be embedded into a bond; common ...
s such as
callable bond A callable bond (also called redeemable bond) is a type of bond (debt security) that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity. In other words, on the call ...
s; the second type are usually
real options Real options valuation, also often termed real options analysis,Adam Borison (Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?'' (ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campbe ...
. The most common option pricing models employed here are the Black–Scholes- Merton models and
lattice models In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of cond ...
. This approach is sometimes referred to as
contingent claim valuation In finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset,Dale F. Gray, Robert C. Merton and Zvi Bodie. (2007). Contingent Claims Approach to Measuring and Managing Sovereign Credit Ri ...
, in that the value will be contingent on some other asset; see § Contingent claim valuation there.


Usage

In finance, valuation analysis is required for many reasons including tax assessment,
wills Wills may refer to: * Will (law) A will or testament is a legal document that expresses a person's (testator) wishes as to how their property ( estate) is to be distributed after their death and as to which person (executor) is to manage the pr ...
and estates,
divorce Divorce (also known as dissolution of marriage) is the process of terminating a marriage or marital union. Divorce usually entails the canceling or reorganizing of the legal duties and responsibilities of marriage, thus dissolving the ...
settlement Settlement may refer to: *Human settlement, a community where people live *Settlement (structural), the distortion or disruption of parts of a building *Closing (real estate), the final step in executing a real estate transaction *Settlement (fina ...
s, business analysis, and basic
bookkeeping Bookkeeping is the recording of financial transactions, and is part of the process of accounting in business and other organizations. It involves preparing source documents for all transactions, operations, and other events of a business. Tr ...
and
accounting Accounting, also known as accountancy, is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. Accounting, which has been called the "languag ...
. Since the value of things fluctuates over time, valuations are as of a specific date like the end of the accounting quarter or year. They may alternatively be
mark-to-market Mark-to-market (MTM or M2M) or fair value accounting is accounting for the "fair value" of an asset or liability based on the current market price, or the price for similar assets and liabilities, or based on another objectively assessed "fair" ...
estimates of the current value of assets or liabilities as of this minute or this day for the purposes of managing portfolios and associated financial risk (for example, within large financial firms including
investment bank Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing is ...
s and stockbrokers). Some balance sheet items are much easier to value than others. Publicly traded stocks and bonds have prices that are quoted frequently and readily available. Other assets are harder to value. For instance, private firms that have no frequently quoted price. Additionally, financial instruments that have prices that are partly dependent on theoretical models of one kind or another are difficult to value and this generates
valuation risk Valuation risk is the risk that an entity suffers a loss when trading an asset or a liability due to a difference between the accounting value and the price effectively obtained in the trade. In other words, valuation risk is the uncertainty ...
. For example, options are generally valued using the Black–Scholes model while the liabilities of
life assurance Life insurance (or life assurance, especially in the Commonwealth of Nations) is a contract between an insurance policy holder and an insurer or assurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death ...
firms are valued using the theory of
present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
. Intangible business assets, like goodwill and
intellectual property Intellectual property (IP) is a category of property that includes intangible creations of the human intellect. There are many types of intellectual property, and some countries recognize more than others. The best-known types are patents, cop ...
, are open to a wide range of value interpretations. Another intangible asset,
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
, is increasingly being recognized as a valuable asset in the information economy. It is possible and conventional for financial professionals to make their own estimates of the valuations of assets or liabilities that they are interested in. Their calculations are of various kinds including analyses of companies that focus on price-to-book, price-to-earnings, price-to-cash-flow and
present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
calculations, and analyses of bonds that focus on credit ratings, assessments of
default risk A credit risk is risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased c ...
, risk premia, and levels of
real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approx ...
s. All of these approaches may be thought of as creating estimates of value that compete for credibility with the prevailing share or bond prices, where applicable, and may or may not result in buying or selling by market participants. Where the valuation is for the purpose of a merger or acquisition the respective businesses make available further detailed financial information, usually on the completion of a
non-disclosure agreement A non-disclosure agreement (NDA) is a legal contract or part of a contract between at least two parties that outlines confidential material, knowledge, or information that the parties wish to share with one another for certain purposes, but wish ...
. It is important to note that valuation requires judgment and assumptions: * There are different circumstances and purposes to value an asset (e.g., distressed firm, tax purposes, mergers and acquisitions, financial reporting). Such differences can lead to different valuation methods or different interpretations of the method results * All valuation models and methods have limitations (e.g., degree of complexity, relevance of observations, mathematical form) * Model inputs can vary significantly because of necessary judgment and differing assumptions Users of valuations benefit when key information, assumptions, and limitations are disclosed to them. Then they can weigh the degree of reliability of the result and make their decision.


Business valuation

Business Business is the practice of making one's living or making money by producing or Trade, buying and selling Product (business), products (such as goods and Service (economics), services). It is also "any activity or enterprise entered into for pr ...
es or fractional interests in businesses may be valued for various purposes such as
mergers and acquisitions Mergers and acquisitions (M&A) are business transactions in which the ownership of companies, other business organizations, or their operating units are transferred to or consolidated with another company or business organization. As an aspect ...
, sale of
securities A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
, and taxable events. When correct, a valuation should reflect the capacity of the business to match a certain market demand, as it is the only true predictor of future cash flows. An accurate valuation of
privately owned companies A privately held company (or simply a private company) is a company whose shares and related rights or obligations are not offered for public subscription or publicly negotiated in the respective listed markets, but rather the company's stock is ...
largely depends on the reliability of the firm's historic financial information.
Public company A public company is a company whose ownership is organized via shares of stock which are intended to be freely traded on a stock exchange or in over-the-counter markets. A public (publicly traded) company can be listed on a stock exchange (l ...
financial statement Financial statements (or financial reports) are formal records of the financial activities and position of a business, person, or other entity. Relevant financial information is presented in a structured manner and in a form which is easy to un ...
s are audited by
Certified Public Accountant Certified Public Accountant (CPA) is the title of qualified accountants in numerous countries in the English-speaking world. It is generally equivalent to the title of chartered accountant in other English-speaking countries. In the United Sta ...
s (USA),
Chartered Certified Accountant Founded in 1904, the Association of Chartered Certified Accountants (ACCA) is the global professional accounting body offering the Chartered Certified Accountant qualification (ACCA). It has 240,952 members and 541,930 future members worldwid ...
s ( ACCA) or Chartered Accountants (UK), and
Chartered Professional Accountant Chartered Professional Accountant (CPA; french: comptable professionnel agréé) is the professional certification, professional designation which united the three Canadian accounting designations that previously existed: :* Canadian Institute ...
s (Canada) and overseen by a government regulator. Alternatively, private firms do not have government oversight—unless operating in a regulated industry—and are usually not required to have their financial statements audited. Moreover, managers of private firms often prepare their financial statements to minimize profits and, therefore,
taxes A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or ...
. Alternatively, managers of public firms tend to want higher profits to increase their stock price. Therefore, a firm's historic financial information may not be accurate and can lead to over- and undervaluation. In an acquisition, a buyer often performs
due diligence Due diligence is the investigation or exercise of care that a reasonable business or person is normally expected to take before entering into an agreement or contract with another party or an act with a certain standard of care. It can be a l ...
to verify the seller's information. Financial statements prepared in accordance with
generally accepted accounting principles Publicly traded companies typically are subject to rigorous standards. Small and midsized businesses often follow more simplified standards, plus any specific disclosures required by their specific lenders and shareholders. Some firms operate on th ...
(GAAP) show many assets based on their historic costs rather than at their current market values. For instance, a firm's
balance sheet In financial accounting, a balance sheet (also known as statement of financial position or statement of financial condition) is a summary of the financial balances of an individual or organization, whether it be a sole proprietorship, a business ...
will usually show the value of land it owns at what the firm paid for it rather than at its current market value. But under GAAP requirements, a firm must show the fair values (which usually approximates market value) of some types of assets such as financial instruments that are held for sale rather than at their original cost. When a firm is required to show some of its assets at fair value, some call this process "
mark-to-market Mark-to-market (MTM or M2M) or fair value accounting is accounting for the "fair value" of an asset or liability based on the current market price, or the price for similar assets and liabilities, or based on another objectively assessed "fair" ...
". But reporting asset values on financial statements at fair values gives managers ample opportunity to slant asset values upward to artificially increase profits and their stock prices. Managers may be motivated to alter earnings upward so they can earn bonuses. Despite the risk of manager bias, equity investors and creditors prefer to know the market values of a firm's assets—rather than their historical costs—because current values give them better information to make decisions. There are commonly three pillars to valuing business entities: comparable company analyses, discounted cash flow analysis, and precedent transaction analysis. Business valuation credentials include the Chartered Business Valuator (CBV) offered by the
CBV Institute The CBV Institute (french: L’Institut des CBV), formerly known as the Canadian Institute of Chartered Business Valuators (CICBV), is a Canadian business valuation organization. The CBV Institute is a not-for-profit valuation professional organiz ...
, ASA and CEIV from the
American Society of Appraisers The American Society of Appraisers (ASA) is an American nonprofit organization which serves as a professional affiliation of appraisers of all disciplines. The organization is the largest multi-discipline, voluntary membership, trade association ...
, and the CVA by the National Association of Certified Valuators and Analysts.


Discounted cash flow method

This method estimates the value of an asset based on its expected future cash flows, which are discounted to the present (i.e., the present value). This concept of discounting future money is commonly known as the
time value of money The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference. The t ...
. For instance, an asset that matures and pays $1 in one year is worth less than $1 today. The size of the discount is based on an
opportunity cost of capital In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new ...
and it is expressed as a percentage or discount rate. In finance theory, the amount of the
opportunity cost In microeconomic theory, the opportunity cost of a particular activity is the value or benefit given up by engaging in that activity, relative to engaging in an alternative activity. More effective it means if you chose one activity (for example ...
is based on a relation between the risk and return of some sort of investment. Classic economic theory maintains that people are rational and averse to risk. They, therefore, need an incentive to accept risk. The incentive in finance comes in the form of higher expected returns after buying a risky asset. In other words, the more risky the investment, the more return investors want from that investment. Using the same example as above, assume the first investment opportunity is a government bond that will pay interest of 5% per year and the principal and interest payments are guaranteed by the government. Alternatively, the second investment opportunity is a bond issued by small company and that bond also pays annual interest of 5%. If given a choice between the two bonds, virtually all investors would buy the government bond rather than the small-firm bond because the first is less risky while paying the same interest rate as the riskier second bond. In this case, an investor has no incentive to buy the riskier second bond. Furthermore, in order to attract capital from investors, the small firm issuing the second bond must pay an interest rate higher than 5% that the government bond pays. Otherwise, no investor is likely to buy that bond and, therefore, the firm will be unable to raise capital. But by offering to pay an interest rate more than 5% the firm gives investors an incentive to buy a riskier bond. For a valuation using the
discounted cash flow The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate devel ...
method, one first estimates the future cash flows from the investment and then estimates a reasonable discount rate after considering the riskiness of those cash flows and interest rates in the
capital markets A capital market is a financial market in which long-term debt (over a year) or equity-backed securities are bought and sold, in contrast to a money market where short-term debt is bought and sold. Capital markets channel the wealth of savers to ...
. Next, one makes a calculation to compute the present value of the future cash flows.


Guideline companies method

This method determines the value of a firm by observing the prices of similar companies (called "guideline companies") that sold in the market. Those sales could be shares of stock or sales of entire firms. The observed prices serve as valuation benchmarks. From the prices, one calculates price multiples such as the price-to-earnings or price-to-book ratios—one or more of which used to value the firm. For example, the average price-to-earnings multiple of the guideline companies is applied to the subject firm's earnings to estimate its value. Many price multiples can be calculated. Most are based on a financial statement element such as a firm's earnings (price-to-earnings) or book value (price-to-book value) but multiples can be based on other factors such as price-per-subscriber.


Net asset value method

The third-most common method of estimating the value of a company looks to the
asset In financial accountancy, financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value ...
s and liabilities of the business. At a minimum, a
solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
company could shut down operations, sell off the assets, and pay the
creditor A creditor or lender is a party (e.g., person, organization, company, or government) that has a claim on the services of a second party. It is a person or institution to whom money is owed. The first party, in general, has provided some property ...
s. Any cash that would remain establishes a floor value for the company. This method is known as the
net asset value Net asset value (NAV) is the value of an entity's assets minus the value of its liabilities, often in relation to open-end, mutual funds, hedge funds, and venture capital funds. Shares of such funds registered with the U.S. Securities and Exch ...
or cost method. In general the
discounted cash flow The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate devel ...
s of a well-performing company exceed this floor value. Some companies, however, are worth more "dead than alive", like weakly performing companies that own many tangible assets. This method can also be used to value heterogeneous portfolios of investments, as well as
nonprofit A nonprofit organization (NPO) or non-profit organisation, also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and operated for a collective, public or social benefit, in co ...
s, for which discounted cash flow analysis is not relevant. The valuation premise normally used is that of an orderly
liquidation Liquidation is the process in accounting by which a company is brought to an end in Canada, United Kingdom, United States, Ireland, Australia, New Zealand, Italy, and many other countries. The assets and property of the company are redistrib ...
of the assets, although some valuation scenarios (e.g.,
purchase price allocation Purchase price allocation (PPA) is an application of goodwill accounting whereby one company (the acquirer), when purchasing a second company (the target), allocates the purchase price into various assets and liabilities acquired from the transacti ...
) imply an " in-use" valuation such as
depreciated In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the a ...
replacement cost new. An alternative approach to the net asset value method is the excess earnings method. (This method was first described in the U.S.
Internal Revenue Service The Internal Revenue Service (IRS) is the revenue service for the United States federal government, which is responsible for collecting U.S. federal taxes and administering the Internal Revenue Code, the main body of the federal statutory ta ...
's ''Appeals and Review Memorandum'' 34, and later refined b
Revenue Ruling 68-609
) The excess earnings method has the appraiser identify the value of tangible assets, estimate an appropriate return on those tangible assets, and subtract that return from the total return for the business, leaving the "excess" return, which is presumed to come from the intangible assets. An appropriate capitalization rate is applied to the excess return, resulting in the value of those intangible assets. That value is added to the value of the tangible assets and any non-operating assets, and the total is the value estimate for the business as a whole. See
Clean surplus accounting The clean surplus accounting method provides elements of a forecasting model that yields price as a function of earnings, expected returns, and change in book value. Ohlson, J. A. (1995)"Earnings, Book Values and Dividends in Equity Valuation" Con ...
,
Residual income valuation Residual income valuation (RIV; also, residual income ''model'' and residual income ''method'', RIM) is an approach to equity valuation that formally accounts for the cost of equity capital. Here, "residual" means in excess of any opportunity costs ...
.


Specialised cases

In the below cases, depending on context, Real options valuation techniques are also sometimes employed, if not preferred; for further discussion here see and .


Valuation of a suffering company

investors in a suffering company, or in other "
distressed securities Distressed securities are securities over companies or government entities that are experiencing financial or operational distress, default, or are under bankruptcy. As far as debt securities, this is called distressed debt. Purchasing or holding ...
", may intend (i) to restructure the business, with the valuation reflecting its potential thereafter, or (ii) to purchase the company - or its debt - at a discount, as part of an Investment Strategy aimed at realizing a profit on recovery. Preliminary to the valuation, the
financial statements Financial statements (or financial reports) are formal records of the financial activities and position of a business, person, or other entity. Relevant financial information is presented in a structured manner and in a form which is easy to un ...
are initially recast, to "better reflect the firm's indebtedness, financing costs and recurring earnings". Here adjustments are made to
working capital Working capital (WC) is a financial metric which represents operating liquidity available to a business, organisation, or other entity, including governmental entities. Along with fixed assets such as plant and equipment, working capital is consi ...
, deferred
capital expenditure Capital expenditure or capital expense (capex or CAPEX) is the money an organization or corporate entity spends to buy, maintain, or improve its fixed assets, such as buildings, vehicles, equipment, or land. It is considered a capital expenditure ...
s,
cost of goods sold Cost of goods sold (COGS) is the carrying value of goods sold during a particular period. Costs are associated with particular goods using one of the several formulas, including specific identification, first-in first-out (FIFO), or average cost ...
, non-recurring professional fees and costs, above- or below-market leases, excess salaries in the case of private companies, and certain non-operating income/expense items. The valuation is built on this base, with any of the standard market-, income-, or asset-based approaches employed. Often these are used in combination, providing a "triangulation" or weighted average. Particularly in the second case above, the company may be valued using
real options analysis Real options valuation, also often termed real options analysis,Adam Borison ( Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?'' (ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campb ...
, serving to complement (or sometimes replace) this standard value; see and
Merton model The Merton model, developed by Robert C. Merton in 1974, is a widely used credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing ...
. As required, various adjustments are then made to this result, so as to reflect characteristics of the firm external to its profitability and cash flow. These adjustments consider any lack of marketability resulting in a discount, and re the stake in question, any
control premium A control premium is an amount that a buyer is sometimes willing to pay over the current market price of a publicly traded company in order to acquire a controlling share in that company. If the market perceives that a public company's profit and ...
or lack of control discount. Balance sheet items external to the valuation, but due to the new owners, are similarly recognized; these include excess (or restricted) cash, and other non-operating assets and liabilities.


Valuation of a startup company

Startup companies A startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship refers to all new businesses, including self-employment and businesses that never intend t ...
such as
Uber Uber Technologies, Inc. (Uber), based in San Francisco, provides mobility as a service, ride-hailing (allowing users to book a car and driver to transport them in a way similar to a taxi), food delivery (Uber Eats and Postmates), package ...
, which was valued at $50 billion in early 2015, are assigned
post-money valuation Post-money valuation is a way of expressing the value of a company after an investment has been made. This value is equal to the sum of the pre-money valuation and the amount of new equity. These valuations are used to express how much ownership ex ...
s based on the price at which their most recent investor put money into the company. The price reflects what investors, for the most part
venture capital Venture capital (often abbreviated as VC) is a form of private equity financing that is provided by venture capital firms or funds to startups, early-stage, and emerging companies that have been deemed to have high growth potential or which ha ...
firms, are willing to pay for a share of the firm. They are not listed on any stock market, nor is the valuation based on their assets or profits, but on their potential for success, growth, and eventually, possible profits. Many startup companies use internal growth factors to show their potential growth which may attribute to their valuation. The professional investors who fund startups are experts, but hardly infallible, see
Dot-com bubble The dot-com bubble (dot-com boom, tech bubble, or the Internet bubble) was a stock market bubble in the late 1990s, a period of massive growth in the use and adoption of the Internet. Between 1995 and its peak in March 2000, the Nasdaq Compo ...
.
Valuation using discounted cash flows Valuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money. The cash flows are made up of those within the “explicit ...
discusses various considerations here.


Valuation of intangible assets

Valuation models can be used to value
intangible asset An intangible asset is an asset that lacks physical substance. Examples are patents, copyright, franchises, goodwill, trademarks, and trade names, as well as software. This is in contrast to physical assets (machinery, buildings, etc.) and finan ...
s such as for
patent valuation Intellectual property assets such as patents are the core of many organizations and transactions related to technology. Licenses and assignments of intellectual property rights are common operations in the technology markets, as well as the use of t ...
, but also in
copyright A copyright is a type of intellectual property that gives its owner the exclusive right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time. The creative work may be in a literary, artistic, education ...
s,
software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...
,
trade secret Trade secrets are a type of intellectual property that includes formulas, practices, processes, designs, instruments, patterns, or compilations of information that have inherent economic value because they are not generally known or readily asc ...
s, and customer relationships. As economies are becoming increasingly informational, it is recognized that there is a need for new methods to value data, another intangible asset. Valuations here are often necessary both for
financial reporting Financial statements (or financial reports) are formal records of the financial activities and position of a business, person, or other entity. Relevant financial information is presented in a structured manner and in a form which is easy to un ...
and
intellectual property Intellectual property (IP) is a category of property that includes intangible creations of the human intellect. There are many types of intellectual property, and some countries recognize more than others. The best-known types are patents, cop ...
transactions. They are also inherent in securities analysis - listed and
private Private or privates may refer to: Music * " In Private", by Dusty Springfield from the 1990 album ''Reputation'' * Private (band), a Denmark-based band * "Private" (Ryōko Hirosue song), from the 1999 album ''Private'', written and also recorde ...
- in cases where analysts must estimate the incremental contribution of patents (etc) to equity value; see next paragraph. Since few sales of benchmark intangible assets can ever be observed, one often values these sorts of assets using either a present value model or estimating the costs to recreate it. In some cases, option-based techniques or
decision tree A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains condit ...
s may be applied. Regardless of the method, the process is often time-consuming and costly. If required, stock markets can give an indirect estimate of a corporation's intangible asset value; this can be reckoned as the difference between its
market capitalisation Market capitalization, sometimes referred to as market cap, is the total value of a publicly traded company's outstanding common shares owned by stockholders. Market capitalization is equal to the market price per common share multiplied by t ...
and its
book value In accounting, book value is the value of an asset according to its balance sheet account balance. For assets, the value is based on the original cost of the asset less any depreciation, amortization or impairment costs made against the asset. Tra ...
(including only hard assets), i.e. effectively its goodwill. As regards listed equity, the above techniques are most often applied in the biotech-, life sciences- and pharmaceutical sectors T. Segal (2020)
Biotech vs. Pharmaceuticals
investopedia.com
(see List of largest biotechnology and pharmaceutical companies). These businesses are involved in
research and development Research and development (R&D or R+D), known in Europe as research and technological development (RTD), is the set of innovative activities undertaken by corporations or governments in developing new services or products, and improving existi ...
(R&D), and testing, that typically takes years to complete (and where the new product may ultimately not be approved; see
Contingent value rights In corporate finance, Contingent Value Rights (CVR) are rights granted by an acquirer to a company’s shareholders, facilitating the transaction where some uncertainty is inherent. CVRs may be separately tradeable securities; they are occasiona ...
). Industry specialists thus apply the above techniques - and here especially
rNPV In finance, rNPV ("risk-adjusted net present value") or eNPV ("expected NPV") is a method to value risky future cash flows. rNPV is the standard valuation method in the drug development industry, where sufficient data exists to estimate success ...
- to the pipeline of products under development, and, at the same time,Aswath Damodaran (N.D.)
The Value of Intangibles
/ref> also estimate the impact on existing revenue streams due to expiring patents. For relative valuation, a specialized ratio is R&D spend as a percentage of sales. Similar analysis may be applied to options on films re the valuation of
film studios A film studio (also known as movie studio or simply studio) is a major entertainment company or motion picture company that has its own privately owned studio facility or facilities that are used to make films, which is handled by the productio ...
.


Valuation of mining projects

In
mining Mining is the extraction of valuable minerals or other geological materials from the Earth, usually from an ore body, lode, vein, seam, reef, or placer deposit. The exploitation of these deposits for raw material is based on the economic via ...
, valuation is the process of determining the value or worth of a mining property - i.e. as distinct from a listed mining corporate. Mining valuations are sometimes required for
IPO An initial public offering (IPO) or stock launch is a public offering in which shares of a company are sold to institutional investors and usually also to retail (individual) investors. An IPO is typically underwritten by one or more investment ...
s,
fairness opinion A fairness opinion is a professional evaluation by an investment bank or other third party as to whether the terms of a merger, acquisition, buyback, spin-off, or privatization are fair. It is rendered for a fee. They are typically issued when ...
s, litigation, mergers and acquisitions, and shareholder-related matters. In valuing a mining project or mining property,
fair market value The fair market value of property is the price at which it would change hands between a willing and informed buyer and seller. The term is used throughout the Internal Revenue Code, as well as in bankruptcy laws, in many state laws, and by several ...
is the standard of value to be used. In general, this result will be a function of the property's "reserve" - the estimated size and grade of the deposit in question - and the complexity and costs of extracting this.Andrew Beattie (2020)
A Beginner's Guide to Mining Stocks
/ref>
"CIMVal"
generally applied by the
Toronto Stock Exchange The Toronto Stock Exchange (TSX; french: Bourse de Toronto) is a stock exchange located in Toronto, Ontario, Canada. It is the 10th largest exchange in the world and the third largest in North America based on market capitalization. Based in t ...
, is widely recognised as a "standard" for the valuation of mining projects. (CIMVal:
Canadian Institute of Mining, Metallurgy and Petroleum The Canadian Institute of Mining, Metallurgy and Petroleum (CIM) is a not-for-profit technical society of professionals in the Canadian minerals, metals, materials and energy industries. CIM's members are convened from industry, academia and go ...
on Valuation of Mineral Properties ) The
Australasian Australasian is the adjectival form of Australasia, a geographical region including Australia Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continen ...
equivalent i
''VALMIN''
the
Southern African Southern Africa is the southernmost subregion of the African continent, south of the Congo and Tanzania. The physical location is the large part of Africa to the south of the extensive Congo River basin. Southern Africa is home to a number of ...
is ''SAMVAL''. These standards stress the use of the
cost approach In real estate appraisal, the cost approach is one of three basic valuation methods.Uniform Standard of Professional Appraisal Practice, 2008, Appraisal Foundation, Standards Rule 1-4(b) p. U18 The others are market approach, or sales comparison ap ...
, market approach, and the
income approach The income approach is one of three major groups of methodologies, called valuation ''approaches'', used by appraisers. It is particularly common in commercial real estate appraisal and in business appraisal. The fundamental math is similar to the m ...
, depending on the stage of development of the mining property or project. See for further discussion and context, as well as
Mineral economics Mineral economics is the academic discipline that investigates and promotes understanding of economic and policy issues associated with the production and use of mineral commodities. Mineral economics min·rəl ‚ek·ə′näm·iksis specially ...
in general, and
Mineral resource estimation Mineral resource estimation is used to determine and define the ore tonnage and grade of a geological deposit, from the developed block model. There are different estimation methods used for different scenarios dependent upon the ore boundaries, ge ...
and
Mineral resource classification There are several classification systems for the economic evaluation of mineral deposits worldwide. The most commonly used schemes base on the International Reporting Template, developed by the CRIRSCO - Committee for Mineral Reserves International ...
. Analyzing listed mining corporates (and other resource companies) is also specialized, as the valuation requires a good understanding of the company’s overall assets, its operational business model as well as key market drivers, and an understanding of that sector of the stock market. Re the latter, a distinction is usually made based on size and financial capabilities; see . *The price of a “Junior” mining stock, typically having one asset, will at its early stages be linked to the result of its
feasibility study A feasibility study is an assessment of the practicality of a project or system. A feasibility study aims to objectively and rationally uncover the strengths and weaknesses of an existing business or proposed venture, opportunities and threats pr ...
; later, the price will be a function of that mine's viability and value, largely applying the above techniques. *A “Major”, on the other hand, has numerous
properties Property is the ownership of land, resources, improvements or other tangible objects, or intellectual property. Property may also refer to: Mathematics * Property (mathematics) Philosophy and science * Property (philosophy), in philosophy and ...
, and the contents of any single deposit will impact stock value in a limited fashion; this due to diversification, access to funding, and, also, since the share price inheres goodwill. Typically, then, the exposure is more to the market value of each mineral in the portfolio, than to the individual properties.


Valuing financial services firms

There are two main difficulties with valuing
financial services Financial services are the Service (economics), economic services provided by the finance industry, which encompasses a broad range of businesses that manage money, including credit unions, banks, credit-card companies, insurance companies, acco ...
firms.Aswath Damodaran (2009)
''Valuing Financial Service Firms''
Stern, NYU
Doron Nissim (2010
''Analysis and Valuation of Insurance Companies''
Columbia Business School Columbia Business School (CBS) is the business school of Columbia University, a Private university, private research university in New York City. Established in 1916, Columbia Business School is one of six Ivy League business schools and is one ...
The first is that the cash flows to a financial service firm cannot be easily estimated, since
capital expenditure Capital expenditure or capital expense (capex or CAPEX) is the money an organization or corporate entity spends to buy, maintain, or improve its fixed assets, such as buildings, vehicles, equipment, or land. It is considered a capital expenditure ...
s,
working capital Working capital (WC) is a financial metric which represents operating liquidity available to a business, organisation, or other entity, including governmental entities. Along with fixed assets such as plant and equipment, working capital is consi ...
and debt are not clearly defined: "debt for a financial service firm is more akin to raw material than to a source of capital; the notion of
cost of capital In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new ...
and
enterprise value Enterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value of a business (i.e. as distinct from market price). It is a sum of claims by all claimants: creditors (secured and unsecured) ...
(EV) may be meaningless as a consequence." (See related discussion re. the risk management of financial- vs non-financial firms.) The second is that these firms operate under a highly regulated environment, and valuation assumptions ( and model outputs) must incorporate regulatory limits, at least as "bounds". The approach taken for a DCF valuation, is to then "remove" debt from the valuation, by discounting
free cash flow to equity In corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or stock buybacks—after all expenses, reinvestments, and debt repayments are taken care o ...
at the
cost of equity In finance, the cost of equity is the return (often expressed as a rate of return) a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire cap ...
(or equivalently to apply a modified
dividend discount model In finance and investing, the dividend discount model (DDM) is a method of valuing the price of a company's stock based on the fact that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In ot ...
). This is in contrast to the more typical approach of discounting free cash flow to the ''Firm'' where
EBITDA A company's earnings before interest, taxes, depreciation, and amortization (commonly abbreviated EBITDA, pronounced , , or ) is a measure of a company's profitability of the operating business only, thus before any effects of indebtedness, stat ...
less capital expenditures and working capital is discounted at the
weighted average cost of capital The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Importantly, it is dictated by ...
, which incorporates the
cost of debt In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new ...
. For a multiple based valuation, similarly, price to earnings is preferred to EV/EBITDA. Here, there are also industry-specific measures used to compare between investments and within sub-sectors; this, once normalized by market cap, and recognizing regulatory differences: *
Insurance companies Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...
:
embedded value The Embedded Value (EV) of a life insurance company is the present value of future profits plus adjusted net asset value. It is a construct from the field of actuarial science which allows insurance companies to be valued. Background Life insura ...
and
actuarial reserves In insurance, an actuarial reserve is a reserve set aside for future insurance liabilities. It is generally equal to the actuarial present value of the future cash flows of a contingent event. In the insurance context an actuarial reserve is the p ...
* Banking sector:
net interest margin Net interest margin (NIM) is a measure of the difference between the interest income generated by banks or other financial institutions and the amount of interest paid out to their lenders (for example, deposits), relative to the amount of their (in ...
and provision for credit losses * Wealth- and
investment management Investment management is the professional asset management of various securities, including shareholdings, bonds, and other assets, such as real estate, to meet specified investment goals for the benefit of investors. Investors may be institut ...
firms: assets under management *
Investment bank Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing is ...
s: price to tangible book value and
return on tangible equity Return on tangible equity (ROTE) (also return on average tangible common shareholders' equity (ROTCE)) measures the rate of return on the tangible common equity. ROTE is computed by dividing net earnings (or annualized net earnings for annualized ...
.


Mismarking

Mismarking Mismarking in securities valuation takes place when the value that is assigned to securities does not reflect what the securities are actually worth, due to intentional fraudulent mispricing. Mismarking misleads investors and fund executives about ...
in securities valuation takes place when the value that is assigned to securities does not reflect what the securities are actually worth, due to intentional
fraudulent In law, fraud is intentional deception to secure unfair or unlawful gain, or to deprive a victim of a legal right. Fraud can violate civil law (e.g., a fraud victim may sue the fraud perpetrator to avoid the fraud or recover monetary compensa ...
mispricing. Mismarking misleads investors and fund executives about how much the securities in a securities portfolio managed by a trader are worth (the securities'
net asset value Net asset value (NAV) is the value of an entity's assets minus the value of its liabilities, often in relation to open-end, mutual funds, hedge funds, and venture capital funds. Shares of such funds registered with the U.S. Securities and Exch ...
, or NAV), and thus misrepresents performance.Kent Oz (2009)
"Independent Fund Administrators As A Solution for Hedge Fund Fraud,"
''Fordham Journal of Corporate & Financial Law''.
When a
rogue trader A rogue trader is person who makes financial trades in an unauthorised manner. Rogue trader may also refer to: * ''Rogue Trader'' (book), the autobiography of (and later a movie about) Nick Leeson, the man who caused the collapse of Barings Bank * ...
engages in mismarking, it allows him to obtain a higher
bonus Bonus commonly means: * Bonus, a Commonwealth term for a distribution of profits to a with-profits insurance policy * Bonus payment, an extra payment received as a reward for doing one's job well or as an incentive Bonus may also refer to: Place ...
from the financial firm for which he works, where his bonus is calculated by the performance of the securities portfolio that he is managing.


See also

*
Appraisal (disambiguation) Appraisal may refer to: Decision-making * Appraisal (decision analysis), a decision method * Archival appraisal, process for determining which records need to be kept, and for how long * Project appraisal, comparing options to deliver an objectiv ...
*
Asset price inflation Asset price inflation is the economic phenomenon whereby the price of assets rise and become inflated. A common reason for higher asset prices is low interest rates. When interest rates are low, investors and savers cannot make easy returns using l ...
*
Business valuation Business valuation is a process and a set of procedures used to estimate the economic value of an owner's interest in a business. Here various valuation techniques are used by financial market participants to determine the price they are willing t ...
*
Business valuation standard Business Valuation Standards (BVS) are codes of practice that are used in business valuation. Examples of business appraisal standards are as follows: * CICBV Practice Standards. Published by the CBV Institute. * Uniform Standards of Professional ...
*
Control premium A control premium is an amount that a buyer is sometimes willing to pay over the current market price of a publicly traded company in order to acquire a controlling share in that company. If the market perceives that a public company's profit and ...
*
Depreciation In accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wear, and second, the a ...
*
Earnings response coefficient In financial economics, finance, and accounting, the earnings response coefficient, or ERC, is the estimated relationship between equity returns and the unexpected portion of (i.e., new information in) companies' earnings announcements. Developme ...
*
Efficient-market hypothesis The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted bas ...
*
Enterprise value Enterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value of a business (i.e. as distinct from market price). It is a sum of claims by all claimants: creditors (secured and unsecured) ...
*
Equity value Equity value is the value of a company available to owners or shareholders. It is the enterprise value plus all cash and cash equivalents, short and long-term investments, and less all short-term debt, long-term debt and minority interests. Equity ...
*
Film finance Film finance is an aspect of film production that occurs during the development stage prior to pre-production, and is concerned with determining the potential value of a proposed film. In the United States, the value is typically based on a fo ...
*
Fundamental analysis Fundamental analysis, in accounting and finance, is the analysis of a business's financial statements (usually to analyze the business's assets, liabilities, and earnings); health; and competitors and markets. It also considers the overall state ...
*
Intellectual property valuation An intellectual property valuation - or economic appraisal - is prepared, for example, for transactions -merger and acquisition - pricing and strategic purposes, financing securitization and collateralization, tax planning and compliance, and li ...
*
Investment management Investment management is the professional asset management of various securities, including shareholdings, bonds, and other assets, such as real estate, to meet specified investment goals for the benefit of investors. Investors may be institut ...
*
Lipper average Lipper Average also known as Lipper Index are a series of indices produced by Lipper, a subsidiary of Thomson Reuters, that establish benchmarks to measure the performance of a portfolio, or of various mutual funds and exchange-traded funds. They al ...
*
Market-based valuation A Market-based valuation is a form of stock valuation that refers to market indicators, also called extrinsic criteria (i.e. not related to economic fundamentals and account data, which are intrinsic criteria). Examples of market valuation methods ...
*
Minority discount Minority discount is an economic concept reflecting the notion that a partial ownership interest may be worth less than its proportional share of the total business. The concept applies to equities with voting power because the size of voting positi ...
*
Paper valuation Paper Valuation is the Valuation (finance), value of privately held Share (finance), shares that is not directly tradeable at an exchange. This notional value, though, is as yet untested on real buyers. The opposite of paper value is exchangeable ...
*
Patent valuation Intellectual property assets such as patents are the core of many organizations and transactions related to technology. Licenses and assignments of intellectual property rights are common operations in the technology markets, as well as the use of t ...
*
PEG ratio The 'PEG ratio' ( price/earnings to growth ratio) is a valuation metric for determining the relative trade-off between the price of a stock, the earnings generated per share ( EPS), and the company's expected growth. In general, the P/E ratio is h ...
*
Present value In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
* Present value of growth opportunities *
Price discovery In economics and finance, the price discovery process (also called price discovery mechanism) is the process of determining the price of an asset in the marketplace through the interactions of buyers and sellers. Overview Price discovery is diff ...
*
Pricing Pricing is the process whereby a business sets the price at which it will sell its products and services, and may be part of the business's marketing plan. In setting prices, the business will take into account the price at which it could acqui ...
*
Real options valuation Real options valuation, also often termed real options analysis,Adam Borison (Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?'' (ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campbe ...
*
Real estate appraisal Real estate appraisal, property valuation or land valuation is the process of developing an opinion of value for real property (usually market value). Real estate transactions often require appraisals because they occur infrequently and every pro ...
*
Standard cost accounting Standard cost accounting is a traditional cost accounting method introduced in the 1920s, as an alternative for the traditional cost accounting method based on historical costs. Adolph Matz (1962) ''Cost accounting.'' p. 584. Overview Standard c ...
*
Stock valuation In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit fr ...
*
Sum-of-the-parts analysis Sum of the parts analysis (SOTP), or break-up analysis, is a method of valuation of a multi-divisional company, holding company, or a conglomerate. The essence of the method is to determine what divisions would be worth if the conglomerate is br ...
* Terminal value *
Valuation risk Valuation risk is the risk that an entity suffers a loss when trading an asset or a liability due to a difference between the accounting value and the price effectively obtained in the trade. In other words, valuation risk is the uncertainty ...
*Specific pricing models **
Capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into accou ...
**
Arbitrage pricing theory In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, it is widely beli ...
** Black–Scholes (for
options Option or Options may refer to: Computing *Option key, a key on Apple computer keyboards *Option type, a polymorphic data type in programming languages * Command-line option, an optional parameter to a command *OPTIONS, an HTTP request method ...
) **
Fuzzy pay-off method for real option valuation The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzz ...
**
Single-index model The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expres ...
**
Markov switching multifractal In financial econometrics (the application of Statistics, statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent-Emmanuel Calvet, Laurent E. Calvet and Adlai J. Fisher that in ...
**
Multiple factor models In mathematical finance, multiple factor models are asset pricing models that can be used to estimate the discount rate for the valuation of financial assets. They are generally extensions of the single-factor capital asset pricing model (CAPM). M ...
**
Chepakovich valuation model The Chepakovich valuation model is a specialized discounted cash flow Valuation (finance), valuation model, originally designed for the valuation of “growth stocks” (ordinary/common shares of companies experiencing high revenue growth rates), a ...


References

{{Authority control Financial markets Financial economics