Valuation (finance)
In finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset
In financial accounting, assets are economic resources. Anything tangible or intangible that is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset...

 or liability. Valuations can be done on assets (for example, investments in marketable securities such as stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...

s, option
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

s, business
A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...

 enterprises, or intangible asset
Intangible asset
Intangible assets are defined as identifiable non-monetary assets that cannot be seen, touched or physically measured, which are created through time and/or effort and that are identifiable as a separate asset...

s such as patent
A patent is a form of intellectual property. It consists of a set of exclusive rights granted by a sovereign state to an inventor or their assignee for a limited period of time in exchange for the public disclosure of an invention....

s and trademark
A trademark, trade mark, or trade-mark is a distinctive sign or indicator used by an individual, business organization, or other legal entity to identify that the products or services to consumers with which the trademark appears originate from a unique source, and to distinguish its products or...

s) or on liabilities (e.g., bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

s issued by a company). Valuations are needed for many reasons such as investment analysis, capital budgeting
Capital budgeting
Capital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...

, merger and acquisition
In business, a takeover is the purchase of one company by another . In the UK, the term refers to the acquisition of a public company whose shares are listed on a stock exchange, in contrast to the acquisition of a private company.- Friendly takeovers :Before a bidder makes an offer for another...

 transactions, financial reporting, taxable events to determine the proper tax
To tax is to impose a financial charge or other levy upon a taxpayer by a state or the functional equivalent of a state such that failure to pay is punishable by law. Taxes are also imposed by many subnational entities...

 liability, and in litigation.

Valuation overview

Valuation of financial assets is done using one or more of these types of models:
  1. Absolute value models that determine the present value of an asset's expected future cash flows. These kinds of models take two general forms: multi-period models such as discounted cash flow
    Discounted cash flow
    In finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...

     models or single-period models such as the Gordon model
    Gordon model
    The Gordon growth model is a variant of the discounted cash flow model, a method for valuing a stock or business. Often used to provide difficult-to-resolve valuation issues for litigation, tax planning, and business transactions that don't have an explicit market value. It is named after Myron J....

    . These models rely on mathematics rather than price observation.
  2. Relative value models determine value based on the observation of market prices of similar assets.
  3. Option pricing model
    Valuation of options
    In finance, a price is paid or received for purchasing or selling options. This price can be split into two components.These are:* Intrinsic Value* Time Value-Intrinsic Value:...

    s are used for certain types of financial assets (e.g., warrant
    Warrant (finance)
    In finance, a warrant is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed exercise price until the expiry date....

    s, put option
    Put option
    A put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...

    s, call option
    Call option
    A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...

    s, employee stock option
    Employee stock option
    An employee stock option is a call option on the common stock of a company, issued as a form of non-cash compensation. Restrictions on the option attempt to align the holder's interest with those of the business shareholders. If the company's stock rises, holders of options generally experience a...

    s, investments with embedded option
    Embedded option
    An Embedded option is a component of a financial bond or other security, and usually 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. Some common types of bonds with embedded options...

    s such as a callable bond
    Callable bond
    A callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches the date of maturity. In other words, on the call date, the issuer has the right, but not the obligation, to buy back the bonds from the bond...

    ) and are a complex present value model. The most common option pricing models are the Black–Scholes-Merton
    Robert C. Merton
    Robert Carhart Merton is an American economist, Nobel laureate in Economics, and professor at the MIT Sloan School of Management.-Biography:...

     models and lattice models
    Lattice model (finance)
    In finance, a lattice model can be used to find the fair value of a stock option; variants also exist for interest rate derivatives.The model divides time between now and the option's expiration into N discrete periods...


Common terms for the value of an asset or liability are fair market value
Fair market value
Fair market value is an estimate of the market value of a property, based on what a knowledgeable, willing, and unpressured buyer would probably pay to a knowledgeable, willing, and unpressured seller in the market. An estimate of fair market value may be founded either on precedent or...

, fair value
Fair value
Fair value, also called fair price , is a concept used in accounting and economics, defined as a rational and unbiased estimate of the potential market price of a good, service, or asset, taking into account such objective factors as:* acquisition/production/distribution costs, replacement costs,...

, and intrinsic value
Intrinsic value
Intrinsic value can refer to:*Intrinsic value , of an option or stock.*Intrinsic value , of a coin.*Intrinsic value , in ethics and philosophy.*Intrinsic value , in philosophy....

. The meanings of these terms differ. For instance, when an analyst believes a stock's intrinsic value is greater (less) than its market price, an analyst makes a "buy" ("sell") recommendation. Moreover, an asset's intrinsic value may be subject to personal opinion and vary among analysts.

Business valuation

A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...

es or fractional interests in businesses may be valued for various purposes such as mergers and acquisitions, sale of securities, and taxable events. An accurate valuation of privately owned companies largely depends on the reliability of the firm's historic financial information. Public company
Public company
This is not the same as a Government-owned corporation.A public company or publicly traded company is a limited liability company that offers its securities for sale to the general public, typically through a stock exchange, or through market makers operating in over the counter markets...

 financial statements are audited by Certified Public Accountant
Certified Public Accountant
Certified Public Accountant is the statutory title of qualified accountants in the United States who have passed the Uniform Certified Public Accountant Examination and have met additional state education and experience requirements for certification as a CPA...

s (US), Chartered Certified Accountant
Chartered Certified Accountant
Chartered Certified Accountant was historically seen as a British qualified accountant designation awarded by the Association of Chartered Certified Accountants . However, although ACCA is UK based, it is a global body for professional accountants with 147,000 qualified members and 424,000...

Association of Chartered Certified Accountants
Founded in 1904, the Association of Chartered Certified Accountants is the global body for professional accountants offering the Chartered Certified Accountant qualification . it is one of the largest and fastest-growing global accountancy bodies with 147,000 members and 424,000 students in 170...

) or Chartered Accountant
Chartered Accountant
Chartered Accountants were the first accountants to form a professional body, initially established in Britain in 1854. The Edinburgh Society of Accountants , the Glasgow Institute of Accountants and Actuaries and the Aberdeen Society of Accountants were each granted a royal charter almost from...

s (UK and 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. 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
"Due diligence" is a term used for a number of concepts involving either an investigation of a business or person prior to signing a contract, or an act with a certain standard of care. It can be a legal obligation, but the term will more commonly apply to voluntary investigations...

 to verify the seller's information.

Financial statements prepared in accordance with generally accepted accounting principles
Generally Accepted Accounting Principles
Generally Accepted Accounting Principles refer to the standard framework of guidelines for financial accounting used in any given jurisdiction; generally known as accounting standards...

 (GAAP) show many assets based on their historic costs rather than at their current market values. For instance, a firm's balance sheet
Balance sheet
In financial accounting, a balance sheet or statement of financial position is a summary of the financial balances of a sole proprietorship, a business partnership or a company. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A...

 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." 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.

Discounted cash flows 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. 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
Opportunity cost of capital
The opportunity cost of capital is the expected rate of return forgone by bypassing of other potential investment activities for a given capital.It is a rate of return that investors could earn in financial markets....

 and it is expressed as a percentage. Some people call this percentage a discount rate.

The idea of opportunity cost can be illustrated in an example. A person with only $100 to invest can make just one $100 investment even when presented with two or more investment choices. If this person is later offered an alternative investment choice, the investor has lost the opportunity to make that second investment since the $100 is spent to buy the first opportunity. This example illustrates that money is limited and people make choices in how to spend it. By making a choice, they give up other opportunities.

In finance theory, the amount of the opportunity cost 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 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. 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 (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 value ratios. Next, one or more price multiples are 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 common method of estimating the value of a company looks to the assets and liabilities of the business. At a minimum, a solvent company could shut down operations, sell off the assets, and pay the creditors. Any cash that would remain establishes a floor value for the company. This method is known as the net asset value or cost method. Normally, the discounted cash flows of a well-performing exceed this floor value. However, some companies are "worth more dead than alive", such as weakly performing companies that own many tangible assets. This method can also be used to value heterogeneous portfolios of investments, as well as non-profit companies for which discounted cash flow analysis is not relevant. The valuation premise normally used is that of an orderly liquidation of the assets, although some valuation scenarios (e.g. purchase price allocation) imply an "in-use" valuation such as depreciated replacement cost new.

An alternative approach to the net asset value method is the excess earnings method. This method was first described in ARM34, and later refined by the U.S. Internal Revenue Service's 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.

Professional sports has a different net asset value method which sometimes can break down and cause team to make horrible decisions while signing players (see Buffalo Sabres/Ville Leino).


In finance, valuation analysis is required for many reasons including tax assessment, wills and estates, divorce settlements, business analysis, and basic bookkeeping and accounting. Since the value of things fluctuates over time, valuations are as of a specific date e.g., the end of the accounting quarter or year. They may alternatively be mark-to-market 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 banks 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. For example, options are generally valued using the Black–Scholes model while the liabilities of life assurance firms are valued using the theory of present value
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

. Intangible business assets, like goodwill
Goodwill (accounting)
Goodwill is an accounting concept meaning the value of an entity over and above the value of its assets. The term was originally used in accounting to express the intangible but quantifiable "prudent value" of an ongoing business beyond its assets, resulting perhaps because the reputation the firm...

 and intellectual property
Intellectual property
Intellectual property is a term referring to a number of distinct types of creations of the mind for which a set of exclusive rights are recognized—and the corresponding fields of law...

, are open to a wide range of value interpretations.

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 calculations, and analyses of bonds that focus on credit ratings, assessments of default risk, risk premia and levels of real interest rates. 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
Mergers and acquisitions
Mergers and acquisitions refers to the aspect of corporate strategy, corporate finance and management dealing with the buying, selling, dividing and combining of different companies and similar entities that can help an enterprise grow rapidly in its sector or location of origin, or a new field or...

 the respective businesses make available further detailed financial information, usually on the completion of a non-disclosure agreement
Non-disclosure agreement
A non-disclosure agreement , also known as a confidentiality agreement , confidential disclosure agreement , proprietary information agreement , or secrecy agreement, is a legal contract between at least two parties that outlines confidential material, knowledge, or information that the parties...


It is important to note that valuation is part art and science because it requires judgment and assumptions:
  1. There are different circumstances and purposes to value an asset (e.g. distressed firm, tax purposes, mergers & acquisitions, financial reporting). Such differences can lead to different valuation methods or different interpretations of the method results.
  2. All valuation models and methods have limitations (e.g., degree of complexity, relevance of observations, mathematical form).
  3. 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.

Valuation of a suffering company

Additional adjustments to a valuation approach, whether it is market-, income- or asset-based, may be necessary in some instances. These involve:
  • excess or restricted cash
  • other non-operating assets and liabilities
  • lack of marketability discount of shares
  • control premium or lack of control discount
  • above or below market leases
  • excess salaries in the case of private companies.

There are other adjustments to the financial statements that have to be made when valuing a distressed company. Andrew Miller identifies typical adjustments used to recast the financial statements that include:
  • working capital
    Working capital
    Working capital is a financial metric which represents operating liquidity available to a business, organization or other entity, including governmental entity. Along with fixed assets such as plant and equipment, working capital is considered a part of operating capital. Net working capital is...

  • deferred capital expenditures
  • cost of goods sold
    Cost of goods sold
    Cost of goods sold refers to the inventory costs of those goods a business has sold during a particular period. Costs are associated with particular goods using one of several formulas, including specific identification, first-in first-out , or average cost...

  • non-recurring professional fees and costs
  • certain non-operating income/expense items.

Valuation of intangible assets

Valuation models can be used to value intangible assets such as patents, copyrights, software, trade secrets, and customer relationships. 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. Regardless of the method, the process is often time consuming and costly.

Valuations of intangible assets are often necessary for financial reporting and intellectual property transactions.

Stock markets give indirectly an estimate of a corporation's intangible asset value. It can be reckoned as the difference between its market capitalisation and its book value
Book value
In accounting, book value or carrying 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. Traditionally, a company's book value...

 (by including only hard assets in it).

Valuation of mining projects

In mining
Mining is the extraction of valuable minerals or other geological materials from the earth, from an ore body, vein or seam. The term also includes the removal of soil. Materials recovered by mining include base metals, precious metals, iron, uranium, coal, diamonds, limestone, oil shale, rock...

, valuation is the process of determining the value or worth of a mining property.

Mining valuations are sometimes required for IPOs, fairness opinions, litigation, mergers & acquisitions and shareholder related matters.

In valuation of a mining project or mining property, fair market value is the standard of value to be used. The CIMVal Standards are a recognised standard for valuation of mining projects and is also recognised by the Toronto Stock Exchange (Venture). The standards spearheaded by Spence & Roscoe, stress the use of the cost approach, market approach and the income approach
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 methods used for financial valuation, securities...

, depending on the stage of development of the mining property or project.

Asset pricing models

See also Modern portfolio theory
Modern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...

  • Capital asset pricing model
    Capital asset pricing model
    In finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...

  • Arbitrage pricing theory
    Arbitrage pricing theory
    In finance, arbitrage pricing theory is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a...

  • Black–Scholes (for options
    Option (finance)
    In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

  • Single-index model
  • Markov switching multifractal
    Markov switching multifractal
    In financial econometrics, the Markov-switching multifractal is a model of asset returns that incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory-like volatility persistence and power variation of financial returns...

See also

  • Applied information economics
    Applied information economics
    Applied information economics is a decision analysis method developed by Douglas W. Hubbard and partially described in his book How to Measure Anything: Finding the Value of Intangibles in Business . AIE is a method for the practical application of several proven methods from decision theory and...

  • Appraisal
    Economic appraisal is a type of decision method applied to a project, programme or policy that takes into account a wide range of costs and benefits, denominated in monetary terms or for which a monetary equivalent can be estimated. Economic Appraisal is a key tool for achieving value for money and...

  • Asset price inflation
    Asset price inflation
    Asset price inflation is an economic phenomenon denoting a rise in price of assets, as opposed to ordinary goods and services. Typical assets are financial instruments such as bonds, shares, and their derivatives, as well as real estate and other capital goods.-Price inflation and assets...

  • Business valuation
    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. Valuation is used by financial market participants to determine the price they are willing to pay or receive to consummate a sale of a business...

  • Business valuation standard
    Business valuation standard
    Business Valuation Standards are codes of practice that are used in business valuation. Each of the three major United States valuation societies — the American Society of Appraisers , , and the National Association of Certified Valuation Analysts — has its own set of Business...

  • Depreciation
    Depreciation refers to two very different but related concepts:# the decrease in value of assets , and# the allocation of the cost of assets to periods in which the assets are used ....

  • Earnings response coefficient
    Earnings response coefficient
    -Introduction:The earnings response coefficient, or ERC, is the estimated relationship between equity returns and the unexpected portion of companies' earnings announcements....

  • Efficient market hypothesis
    Efficient market hypothesis
    In finance, the efficient-market hypothesis asserts that financial markets are "informationally efficient". That is, one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information available at the time the investment is made.There are...

  • Equity investment
  • Intellectual property valuation
    Intellectual property valuation
    Valuation is considered as one of the most critical areas in finance; it plays a key role in many areas of finance such as buy/sell, solvency, merger and acquisition...

  • Investment management
    Investment management
    Investment management is the professional management of various securities and assets in order to meet specified investment goals for the benefit of the investors...

  • Market-based valuation
    Market-based valuation
    Market-based valuation is a form of stock valuation that refers to market indicators, also called "extrinsic" criteria .- Examples of market valuation methods :...

  • Present value
    Present value
    Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

  • Pricing
    Pricing is the process of determining what a company will receive in exchange for its products. Pricing factors are manufacturing cost, market place, competition, market condition, and quality of product. Pricing is also a key variable in microeconomic price allocation theory. Pricing is a...

  • Real estate appraisal
    Real estate appraisal
    Real estate appraisal, property valuation or land valuation is the process of valuing real property. The value usually sought is the property's Market Value. Appraisals are needed because compared to, say, corporate stock, real estate transactions occur very infrequently...

  • Stock valuation
    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 from price movement – stocks that are judged...

  • Price discovery
    Price discovery
    The price discovery process is the process of determining the price of an asset in the marketplace through the interactions of buyers and sellers ....

  • Terminal value
    Terminal value (finance)
    In finance, the terminal value of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most often used in multi-stage discounted cash flow analysis, and allows for the limitation of cash flow projections to a...

  • Chepakovich valuation model
    Chepakovich valuation model
    The Chepakovich valuation model uses the discounted cash flow valuation approach. It was first developed by Alexander Chepakovich in 2000 and perfected in subsequent years...

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