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In finance, the **terminal value** (continuing value or horizon 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 several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

**Finance** is a field that is concerned with the allocation (investment) of assets and liabilities over space and time, often under conditions of risk or uncertainty. Finance can also be defined as the art of money management. Participants in the market aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be split into three sub-categories: public finance, corporate finance and personal finance.

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 the term "security" is commonly used in day-to-day parlance to mean any form of financial instrument, even though the underlying legal and regulatory regime may not have such a broad definition. In some jurisdictions the term specifically excludes financial instruments other than equities and fixed income instruments. In some jurisdictions it includes some instruments that are close to equities and fixed income, e.g., equity warrants.

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 always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of the borrowed funds is less than the total amount of money paid to the lender.

- Perpetuity Growth Model
- Exit Multiple Approach
- Comparison of methodologies
- See also
- External links and references

Thus, the terminal value allows for the inclusion of the value of future cash flows occurring beyond a several-year projection period while satisfactorily mitigating many of the problems of valuing such cash flows. The terminal value is calculated in accordance with a stream of projected future free cash flows in discounted cash flow analysis. For whole-company valuation purposes, there are two methodologies used to calculate the Terminal Value.

In finance, **discounted cash flow** (**DCF**) analysis is a method of valuing a 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 development, corporate financial management and patent valuation. It was used in industry as early as the 1700s or 1800s, widely discussed in financial economics in the 1960s, and became widely used in U.S. Courts in the 1980s and 1990s.

In finance, **valuation** is the process of determining the present value (PV) of an asset. Valuations can be done on assets or on liabilities. Valuations are needed for many reasons such as investment analysis, capital budgeting, merger and acquisition transactions, financial reporting, taxable events to determine the proper tax liability.

The Perpetuity Growth Model accounts for the value of free cash flows that continue growing at an assumed constant rate in perpetuity; essentially, a geometric series which returns the value of a series of growing future cash flows (see Dividend discount model #Derivation of equation). Here, the projected free cash flow in the first year beyond the projection horizon (N+1) is used. This value is then divided by the discount rate minus the assumed perpetuity growth rate (see Sustainable growth rate #From a financial perspective ):

A **perpetuity** is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For example, the United Kingdom (UK) government issued them in the past; these were known as consols and were all finally redeemed in 2015. Real estate and preferred stock are among some types of investments that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity. Perpetuities are but one of the time value of money methods for valuing financial assets. Perpetuities are a form of ordinary annuities.

In mathematics, a **geometric series** is a series with a constant ratio between successive terms. For example, the series

The **discount window** is an instrument of monetary policy that allows eligible institutions to borrow money from the central bank, usually on a short-term basis, to meet temporary shortages of liquidity caused by internal or external disruptions. The term originated with the practice of sending a bank representative to a reserve bank teller window when a bank needed to borrow money.

- D
_{0}= Cash flows at a future point in time which is immediately prior to N+1, or at the end of period N, which is the final year in the projection period. - k = Discount Rate.
- g = Growth Rate.

T_{0} is the value of future cash flows; here dividends. When the valuation is based on free cash flow to firm then the formula becomes , where the discount rate is correspondingly 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 the external market and not by management. The WACC represents the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

To determine the present value of the terminal value, one must discount its value at T_{0} by a factor equal to the number of years included in the initial projection period. If N is the 5th and final year in this period, then the Terminal Value is divided by (1 + k)^{5} (or WACC). The Present Value of the Terminal Value is then added to the PV of the free cash flows in the projection period to arrive at an implied enterprise value.

**Enterprise value** (**EV**), **total enterprise value** (**TEV**), or **firm value** (**FV**) is an economic measure reflecting the market value of a business. It is a sum of claims by all claimants: creditors and shareholders. Enterprise value is one of the fundamental metrics used in business valuation, financial modeling, accounting, portfolio analysis, and risk analysis.

If the growth rate in perpetuity is not constant, a multiple-stage terminal value is calculated. The terminal growth rate can be negative, if the company in question is assumed to disappear in the future.

The Exit or Terminal Multiple Approach assumes a business will be sold at the end of the projection period. Valuation analytics are determined for various operating statistics using comparable acquisitions. A frequently used terminal multiple is Enterprise Value/EBITDA or EV/EBITDA. The analysis of comparable acquisitions will indicate an appropriate range of multiples to use. The multiple is then applied to the projected EBITDA in Year N, which is the final year in the projection period. This provides a future value at the end of Year N. The terminal value is then discounted using a factor equal to the number of years in the projection period. If N is the 5th and final year in this period, then the Terminal Value is divided by (1+k)^{5}. The Present Value of the Terminal Value is then added to the PV of the free cash flows in the projection period to arrive at an implied Enterprise Value. Note that if publicly traded comparable company multiples must be used, the resulting implied enterprise value will not reflect a control premium. Depending on the purposes of the valuation, this may not provide an appropriate reference range.

**Future value** is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function. The value does not include corrections for inflation or other factors that affect the true value of money in the future. This is used in time value of money calculations.

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.

There are several important differences between the two approaches.

The Perpetuity Growth Model has several inherent characteristics that make it intellectually challenging. Because both the discount rate and growth rate are assumptions, inaccuracies in one or both inputs can provide an improper value. The difference between the two values in the denominator determines the terminal value, and even with appropriate values for both, the denominator may result in a multiplying effect that does not estimate an accurate terminal value. Also, the perpetuity growth rate assumes that free cash flow will continue to grow at a constant rate into perpetuity. Consider that a perpetuity growth rate exceeding the annualized growth of the S&P 500 and/or the U.S. GDP implies that the company's cash flow will outpace and eventually absorb these rather large values. Perhaps the greatest disadvantage to the Perpetuity Growth Model is that it lacks the market-driven analytics employed in the Exit Multiple Approach. Such analytics result in a terminal value based on operating statistics present in a proven market for similar transactions. This provides a certain level of confidence that the valuation accurately depicts how the market would value the company in reality.

On the other hand, the Exit Multiple approach must be used carefully, because multiples change over time. Simply applying the current market multiple ignores the possibility that current multiples may be high or low by historical standards. In addition, it is important to note that at a given discount rate, any exit multiple implies a terminal growth rate and conversely any terminal growth rate implies an exit multiple. When using the Exit Multiple approach it is often helpful to calculate the implied terminal growth rate, because a multiple that may appear reasonable at first glance can actually imply a terminal growth rate that is unrealistic.

In practice, academics tend to use the Perpetuity Growth Model, while investment bankers favor the Exit Multiple approach. Ultimately, these methods are two different ways of saying the same thing. For both terminal value approaches, it is essential to use a range of appropriate discount rates, exit multiples and perpetuity growth rates in order to establish a functional valuation range. For related discussion, see Valuation using discounted cash flows #Determine the continuing value.

- Closure in Valuation: Estimating Terminal Value, Prof. Aswath Damodaran, Stern School of Business
- Terminal Value (Columbia Business School Research Paper No. 18-12), Prof. Doron Nissim, Columbia Business School

**Fundamental analysis**, in accounting and finance, is the analysis of a business's financial statements ; health; and competitors and markets. It also considers the overall state of the economy and factors including interest rates, production, earnings, employment, GDP, housing, manufacturing and management. There are two basic approaches that can be used: bottom up analysis and top down analysis. These terms are used to distinguish such analysis from other types of investment analysis, such as quantitative and technical.

In finance, the **net present value** (**NPV**) or **net present worth** (**NPW**) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

The **time value of money** is the greater benefit of receiving money now rather than an identical sum later. It is founded on time preference.

**Adjusted present value** (APV) is a valuation method introduced in 1974 by Stewart Myers.

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 *undervalued* are bought, while stocks that are judged *overvalued* are sold, in the expectation that undervalued stocks will overall rise in value, while overvalued stocks will generally decrease in value.

**Rational pricing** is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

**Bond valuation** is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.

**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 effect a sale of a business. In addition to estimating the selling price of a business, the same valuation tools are often used by business appraisers to resolve disputes related to estate and gift taxation, divorce litigation, allocate business purchase price among business assets, establish a formula for estimating the value of partners' ownership interest for buy-sell agreements, and many other business and legal purposes such as in shareholders deadlock, divorce litigation and estate contest. In some cases, the court would appoint a forensic accountant as the joint expert doing the business valuation.

**Valuation using discounted cash flows** 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 the cash flows within the forecast period together with a continuing or terminal value that represents the cash flow stream after the forecast period.

In economics, **valuation using multiples**, or “relative valuation”, is a process that consists of:

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 analysis, or bond pricing. However, there are some significant and important modifications when used in real estate or business valuation.

**Earnings growth** is the annual compound annual growth rate (CAGR) of earnings from investments. For more general discussion see: Sustainable growth rate #From a financial perspective; Stock valuation #Growth rate; Valuation using discounted cash flows #Determine the continuing value; Growth stock; PEG ratio.

The **First Chicago Method** or **Venture Capital Method** is a business valuation approach used by venture capital and private equity investors that combines elements of both a multiples-based valuation and a discounted cash flow (DCF) valuation approach.

**Residual income valuation** is an approach to equity valuation that formally accounts for the cost of equity capital. Here, "residual" means in excess of any opportunity costs measured relative to the book value of shareholders' equity; **residual income** (RI) is then the income generated by a firm after accounting for the true cost of capital. The approach is largely analogous to the EVA/MVA based approach, with similar logic and advantages. Residual Income valuation has its origins in Edwards & Bell (1961), Peasnell (1982), and Ohlson (1995).

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 of. Whereas dividends are the cash flows actually paid to shareholders, the FCFE is the cash flow simply available to shareholders. The FCFE is usually calculated as a part of DCF or LBO modelling and valuation. The FCFE is also called the levered free cash flow.

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