Financial Methods in Business Valuation презентация

Содержание

Outline Business Valuation Introduction Reasons for a Business Valuation Valuation Process and Standards of Value Valuation Methodology Methods of Corporate Valuation Private Company Valuation Discounts and Premiums

Слайд 1 Financial Methods in Business Valuation


Tunlikbayeva Elzira

Слайд 2Outline

Business Valuation Introduction
Reasons for a Business Valuation
Valuation Process and Standards of

Value
Valuation Methodology
Methods of Corporate Valuation
Private Company Valuation
Discounts and Premiums

Слайд 3Business Valuations



“The act or process of determining the value of a

business enterprise or ownership interest therein.”



*International Glossary of Business Valuation.
*IRS Business Valuation Guideline 2006

Слайд 4 What are “Business Valuations?”

ASSET APPRAISAL
Real Estate
Machinery & Equipment
Intangible Assets

BUSINESS VALUATION
Complete Business

Enterprise Valuation

Слайд 5Reasons for Business Valuations

Sale of business or part interest
Ownership Disputes
Financing
Buy-Sell Agreements
Employee

Stock Ownership Plans
Condemnation
Divorce
Estate Planning
Change of Business Structure
Recapitalization
Life Insurance


Слайд 6Business Valuation: Common Uses of Business Valuation
Tax
Estate/Gifts
Buy/Sell Agreements
Bankruptcy and Litigation


Liquidation or Reorganization
Patent Infringement
Partner Disputes
Economic Damages
Financial Reporting
Purchase Price Allocation, Impairment Testing and Stock Options and Grants, etc.
Strategic Planning/Transaction
Value Enhancement
Business Plan/Capital Raising
Strategic Direction, Spin-Offs, Carve Outs, etc.
Acquisitions, Due Diligence

Employee Stock Ownership Plan (ESOP)
Internal Revenue Codes (IRC)
Solvency and Fairness Opinions
Damage Assessment
Dissenting Shareholder Actions
Dissolutions

Слайд 7MAIN VALUATION METHODS

Слайд 8



Standards of Value
and Valuation Process

Слайд 9Business Valuation: Standard of Value
Purpose
Establish Purpose of the Engagement
Estate/Gift,

Buy/Sell Agreements, etc.
Standards of Value (i.e. Fair Market Value, Fair Value, etc.)
Interest Being Valued (i.e. Enterprise, Equity, Marketable, Non-Marketable, Control, Minority, etc.)
Valuation Date
Agree on a Appropriate Valuation Date
Utilize Data Subsequent to the Valuation Date
Sometimes can Consider Data After the Valuation Date if it was Foreseeable as of the Valuation Date



Слайд 10Business Valuation: Standards of Value
Common Standards of Value
Fair Market Value (Tax):

Fair market value applies to virtually all federal and state tax matters, including estate, gift, inheritance, income and ad valorem taxes as well as many other valuation situations.
“The fair market value is the price at which the property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or to sell and both having reasonable knowledge of relevant facts.” – IRS Revenue Ruling 59-60
Liquidation Value: Orderly; forced.
Fair Value (Financial Reporting): Can vary but it is generally similar to Fair market value with some exceptions.
The amount at which an asset (or liability) could be bought (or incurred) or sold (or settled) in a current transaction between willing parties, that is, other than in a forced or liquidation sale.”-FASB (Financial Accounting Standards Board) 157
Fair Value (Litigation): Fair value may be the applicable standard of value in a number of different situations, including shareholder dissent and oppression matters, corporate dissolution and divorce.


Слайд 11Fair Value (FASB Definition)

Fair Value – is defined in this subtopic

as the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date.

Слайд 12Fair Value (Legal Definition)

Fair Value- is often used in court cases

to compensate a party for the involuntary use of an asset, such as eminent domain, where there is no reasonable assumption of a fair market value transaction.

Слайд 13General Valuation Objectives

There is no one right way to value an

asset, and in many cases, the process of assigning a single dollar value to a complex asset is as much art as it is science.
Business appraisers strive to achieve results that meet certain general requirements.
Consistency Ideally, different skilled appraisers should produce a similar valuation for a given asset.
Defensibility There is always the general possibility that any valuation could be subjected to legal challenges.
Suitability for purpose Valuations must be suitable to the purposes and circumstances of the individuals needing the information.

Слайд 14Misconceptions about Valuation
Myth 1: A valuation is an objective search for

“true” value
Truth 1.1: All valuations are biased. The only questions are how much and in which direction.
Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you.
Myth 2.: A good valuation provides a precise estimate of value
Truth 2.1: There are no precise valuations
Truth 2.2: The payoff to valuation is greatest when valuation is least precise.
Myth 3: . The more quantitative a model, the better the valuation
Truth 3.1: One’s understanding of a valuation model is inversely proportional to the number of inputs required for the model.
Truth 3.2: Simpler valuation models do much better than complex ones.

Слайд 15Professional Organizations: The Appraisal Foundation
The Appraisal Foundation comprises two independent boards.

The Appraiser Qualifications Board (AQB) and the Appraisal Standards Board, promulgates the widely recognized uniform standards of professional appraisal practice (USPAP). USPAP components include the following:
Standards and standards rules For example, Standard 10 deals with business appraisal reporting.
Statements on appraisal standards For example, Statement on Appraisal Standard 2 deals with discounted cash flow analysis.
Advisory opinions These opinions relate to specific subjects. For example, Advisory Opinion 10 deals with the appraiser-client relationship.

Слайд 16Standards

Business valuation appraisers follow the following standards and guidelines:
American Institute of

Certified Public Accountant’s Statements of Standards for Valuation Services No. 1 (“SSVS”);
The Appraisal Foundation’s Uniform Standards of Professional Appraisal Practice (“USPAP”);
The ethics and standards of the American Society of Appraisers; and
The Internal Revenue Service’s business valuation development and reporting guidelines.

Слайд 17Revenue Rulings

Revenue Ruling 59-60
Outlines the approaches, methods, and factors to be

considered in valuing shares of stock in closely-held corporations for federal tax purposes.
Revenue Ruling 65-192
Extended the concepts in Revenue Ruling 59-60 to income and other tax purposes as well as to business interests of any type.

Слайд 18RR 59-60 Factors
The nature of the business and its history since

inception
The economic outlook in general and the condition and outlook of the specific industry in particular
The book value of the stock and the financial condition of the business
The earning capacity of the company
The dividend paying capacity
Whether or not the enterprise has goodwill or other intangible value
Sales of stock and the size of the block of stock to be valued
The market price of stocks of corporations engaged in the same or in a similar line of business having their stocks actively traded in a free and open market, either on an exchange or over- the-counter

Слайд 19National valuation standards of RK
1. Kazakhstan valuation Standard "Valuation of assets

acquired and disposed of by the state on separate grounds"
(Стандарт оценки "Оценка имущества, приобретаемого и отчуждаемого государством по отдельным основаниям")
2. Kazakhstan valuation Standard "Defining the cadastral value of real estate"
(Стандарт оценки Республики Казахстан "Определение кадастровой стоимости объектов недвижимости")
3. Kazakhstan valuation Standard of "Determination of fair value in accordance with IFRS"
(Стандарт оценки Республики Казахстан "Определение справедливой стоимости в соответствии с МСФО")
4. Kazakhstan valuation Standard "Valuation for lending purpose"
(Стандарт оценки Республики Казахстан "Оценка для целей кредитования" )

Слайд 20National valuation standards of RK
5. Kazakhstan valuation Standard "Valuation of Intellectual

Property and Intangible Assets" 
(Стандарт оценки Республики Казахстан "Оценка стоимости объектов интеллектуальной собственности и нематериальных активов")
6. Kazakhstan valuation Standard "Databases and the types of value" 
(Стандарт оценки Республики Казахстан "Базы и типы стоимости" )
7. Kazakhstan valuation Standard "Valuation of Report reliability"
(Стандарт оценки "Проверка достоверности отчета")
 8. Kazakhstan valuation Standard "Business Valuation"
(Стандарт оценки "Оценка стоимости бизнеса")
9.  Kazakhstan valuation Standard "Requirements for the form and content of the valuation report" 
(Стандарт оценки Республики Казахстан "Требования к содержанию и форме отчета об оценке")
 



Слайд 21National valuation standards of RK
10. Kazakhstan valuation Standard "Valuation of movable

property" 
(Стандарт оценки Республики Казахстан "Оценка стоимости движимого имущества")
 
11. Kazakhstan valuation Standard “Valuation of real estate’ 
(Стандарт оценки Республики Казахстан "Оценка стоимости недвижимого имущества")

Слайд 22Business Valuation: Valuation Process

1.1 Proposal and Engagement Letter


1.3 Establish Valuation Date


1.2

Establish Standard of Value and Define Purpose


Ongoing Internal Review and Discussion with Other Professionals and Client

Ongoing Internal Review and Discussion with Other Professionals and Client

Income, Market, Net Asset Approaches

Signed Engagement Letter with Retainer


1.4 Data Gathering


2.1 Company and Industry Analysis



2.3 Adjustments and Recasts (Control)



2.2 Analyze Historical Financial Statements



2.4 Financial Statements Analysis (Ratios, etc.)


3.1 Implement Selected Valuation Methodologies



3.3 Final Internal Review and QC Process



3.2 Narrative Write-up of the Report



3.4 Finalize

Слайд 23Elements of a Business Valuation Packet

Engagement Agreement
Checklist
Site Visit

Слайд 24Engagement Agreement


Rule 201A, Professional Competence, of the AICPA Code of Professional

Conduct, states that a member shall “undertake only those professional services that the member or the member’s firm can reasonably expect to be completed with professional competence.”

Слайд 25Engagement Agreement
In determining to accept an assignment, an evaluator considers, at

a minimum, the following:
Subject entity and its industry
Subject interest
Valuation date
Scope of the valuation engagement
Purpose of the valuation
Assumptions and limiting conditions
Applicable standard of value
Type of valuation report
Government regulations

Слайд 26Engagement Agreement
Other factors to be considered
Objectivity and Conflict of Interest
Independence and

Valuation
Establishing an Understanding with the Client
Assumptions and Limiting Conditions
Scope Restrictions and Limitations

Слайд 27Business Valuation: Analyzing Data
Researching Economic and Industry Information
Economy of Country

Local Economy
Target Industry
Financial Statements Analysis
Adjustments and Recasts (Control Value)
Extraordinary Items, Shareholders’ Perquisites (Personal Expenses), Fair Market Value Compensation and Rent, etc.
Ratio and Trend Analysis
Growth Rates, Liquidity, Leverage, Profitability, Efficiency, etc.

Слайд 28Business Valuation: Gathering Data
Gathering Company Data
Articles of Incorporation; Operating Agreement
History and

Background
Products and Services
Shareholders and Key Personnel Compensations and Responsibilities
Organization/Corporate Structure
Operations
Customers/Clients, Target Markets and Suppliers
Legal, Tax and Other Considerations
Five Year Historical and Latest Interim Financial Statements
Other Financial Information (A/R, A/P, Fixed Asset Ledger, etc. - if needed)
Adjustments
Projections (If applicable)

Слайд 29Checklist
A basic information checklist includes the following:
Historical financials of the company
Debt

schedule
Schedule of fixed assets
Lease agreements for facilities or equipment
Any existing contracts
List of shareholders with shares outstanding
Budgets or projections
Details on any transactions with a related party
Company documents
Other information including list of locations, customers, competitors, suppliers, contingent liabilities, and regulations

Слайд 30Checklist
Appraiser should try to derive an answer to the following:
How does

the company perceive itself?
Strengths, weaknesses, prospects, market, etc.
How does the company see the industry?
Influential factors, trends, growth, competition, etc.
Management and management compensation
Personal expenses, market rate compensation, etc.

Слайд 31Valuation Methodologies

Слайд 32Balance Sheet-Based Methods (Shareholders’ Equity)
These methods seek to determine the

company’s value by estimating the value of its net assets.
These are traditionally used methods that consider that a company’s value lies basically in its balance sheet.
They do not take into account factors that also affect the value such as:
the industry’s current situation
human resources or organizational problems
contracts,
company’s possible future evolution
money’s temporary value
accounting criteria are subject to a certain degree of subjectivity and differ from “market” criteria
all other factors that do not appear in the accounting statements.


Слайд 33Balance Sheet-Based Method on the basis of Book Value

A company’s book value, or net worth, is the value of the shareholders’ equity stated in the balance sheet (capital and reserves).
This quantity is also the difference between total assets and liabilities, that is, the surplus of the company’s total goods and rights over its total debts with third parties.

Balance Sheet of the Company A. Table 1.

Слайд 34Balance Sheet-Based Method on the basis of adjusted Book Value
This method

seeks to overcome the shortcomings that appear when purely accounting criteria are applied in the valuation.
When the values of assets and liabilities match their market value, the adjusted net worth is obtained.
Example:
Accounts receivable includes 2 million thousands of bad debt, this item should have a value of 8 million dollars.
Stock, after discounting obsolete, worthless items and revaluing the remaining items at their market value, has a value of 52 million dollars.
Fixed assets (land, buildings, and machinery) have a value of 150 million dollars, according to an expert.
The book value of accounts payable, bank debt and long-term debt is equal to their market value.

Слайд 35Book Value and Market Value
Figure 1
Evolution of the Price/Book Value Ratio

on the British, German and United States Stock Markets











































Слайд 36Adjusted Book Value
The adjusted balance sheet of the Company A.

Table 2.

Слайд 37Liquidation Value
This is the company’s value if it is liquidated, that

is, its assets are sold and its debts are paid off. This value is calculated by deducting the business’s liquidation expenses (redundancy payments to employees, tax expenses and other typical liquidation expenses) from the adjusted net worth.

Taking the example given in Table 2, if the redundancy payments and other expenses associated with the liquidation of the company A. were to amount to 60 million dollars, the shares’ liquidation value would be 75 million dollars (135-60).

Obviously, this method’s usefulness is limited to a highly specific situation, namely, when the company is bought with the purpose of liquidating it at a later date. However, Liquidation Value always represents the company’s minimum value as a company’s value.

Слайд 38Substantial Value
The substantial value represents the investment that must be made

to form a company having identical conditions as those of the company being valued.
It can also be defined as the assets’ replacement value, assuming the company continues to operate, as opposed to their liquidation value. Normally, the substantial value does not include those assets that are not used for the company’s operations (unused land, holdings in other companies, etc.).
Three types of substantial value are usually defined:
Gross substantial value: this is the assets’ value at market price (in the example of Table 2: 215).
Net substantial value or corrected net assets: this is the gross substantial value less liabilities.
It is also known as adjusted net worth, which we have already seen in the previous section (in the example of Table 2: 135).
Reduced gross substantial value: this is the gross substantial value reduced only by the value of the cost-free debt (in the example of Table 2: 175 = 215 - 40). The remaining 40 mln KZTs correspond to accounts payable.

Слайд 39Income Statement-Based Methods
Income Statement-Based Methods are based on the company’s income

statement. They seek to determine the company’s value through the size of its earnings, sales or other indicators.
This category includes the methods based on the PER: according to this method, the shares’ price is a multiple of the earnings.

Слайд 40Value of Earnings

According to this method, the equity’s value is obtained

by multiplying the annual net income by a PER (price earnings ratio), that is:
Equity value = PER x earnings
The PER (price earnings ratio) of a share indicates the multiple of the earnings per share that is paid on the stock market.
Thus, if the earnings per share in the last year has been $3 and the share’s price is $26, its PER will be 8.66 (26/3).
So Equity value = PER x earnings=8.66*32 mln KZT=277.12 mln KZT

The PER is the benchmark used predominantly by the stock markets. Note that the PER is a parameter that relates a market item (share price) with a purely accounting item (earnings).


Слайд 41
Sometimes, the relative PER is also used, which is simply the

company’s PER divided by the country’s PER.
Evolution of the PER of the German, English and United States Stock Markets markets in 1992 and 2002.


























































Слайд 42Value of the Dividends
Dividends are the part of the earnings effectively

paid out to the shareholder and, in most cases, are the only regular flow received by shareholders.
According to this method, a share’s value is the net present value of the dividends that we expect to obtain from it. In the perpetuity case, that is, a company from which we expect constant dividends every year, this value can be expressed as follows:
Equity value = DPS / Ke
Where: DPS = dividend per share distributed by the company in the last year; Ke = required return to equity.
If, on the other hand, the dividend is expected to grow indefinitely at a constant annual rate g, the above formula becomes the following:
Equity value = DPS1 / (Ke - g)

Where DPS1 is the dividends per share for the next year.

Слайд 43Business Valuation: Weighted Average Cost of Capital


Weighted Average Cost of Capital

(WACC)
WACC = Weight of Equity (Cost of Equity) + Weight of Debt (Cost of Debt * (1-Tax)) + Weight of Preferred Security (Cost of Preferred Security)
Provides Overall Cost of Capital to Whole Company
Assumes Constant Debt to Capital Over Time

Слайд 44Sales Multiples
This valuation method, which is used in some industries with

a certain frequency, consists of calculating a company’s value by multiplying its sales by a number.

For example, a pharmacy is often valued by multiplying its annual sales (in dollars) by 2 or another number, depending on the market situation. It is also a common practice to value a soft drink bottling plant by multiplying its annual sales in liters by 500 or another number, depending on the market situation.
The price/sales ratio can be broken down into a further two ratios:
 
Price/sales = (price/earnings) x (earnings/sales)
The first ratio (price/earnings) is the PER and the second (earnings/sales) is normally known as return on sales.

Слайд 45Other Multiples
In addition to the PER and the price/sales ratio, some

of the frequently used multiples are:
Value of the company / earnings before interest and taxes (EBIT).
Value of the company / earnings before interest, taxes, depreciation and amortization (EBITDA).
Value of the company / operating cash flow.
Value of the equity / book value.
Obviously, in order to value a company using multiples, multiples of comparable companies must be used.

Слайд 47

Business Valuation:
Cash Flow Discounting Approaches

Слайд 48Business Valuation: Cash Flow Discounting Approaches

Cash Flow Discounting-based methods seek to

determine the company’s value by estimating the cash flows it will generate in the future and then discounting them at a discount rate matched to the flows’ risk.


In these methods, the company is viewed as a cash flow generator and the company’s value is obtained by calculating these flows’ present value using a suitable discount rate.


Cash flow discounting methods are based on the detailed, careful forecasts, for each period, of each of the financial items related with the generation of the cash flows corresponding to the company’s operations.



Слайд 49Business Valuation: Cash Flow Discounting Approaches

Cash flow discounting-based valuation methods are

valuation techniques that provides an estimation of the value of an equity (net asset) based on the present value of expected cash flows.
The various forms:
Discounted Cash Flow Analysis (DCF)
Capitalization of Earnings
Dividend Discount Model (DDM)


Слайд 50Business Valuation: Cash Flow Discounting Approaches


Discounted Cash Flow Analysis
The different cash

flow discounting-based methods start with the following expression: more general and flexible than other capitalized earnings methods








Слайд 51Business Valuation: Cash Flow Discounting Approaches
Although at first sight it may

appear that the above formula is considering a temporary duration of the flows, this is not necessarily so as the company’s residual value in the year n (VRn) can be calculated by discounting the future flows after that period.
A simplified procedure for considering an indefinite duration of future flows after the year n is to assume a constant growth rate (g) of flows after that period. Then the residual value in year n is:
VRn = CFn (1 + g) / (k - g).
Although the flows may have an indefinite duration, it may be acceptable to ignore their value after a certain period, as their present value decreases progressively with longer time horizons. Furthermore, the competitive advantage of many businesses tends to disappear after a few years.

Слайд 52Business Valuation: Cash Flow Discounting Approaches
The main idea behind a DCF

approach is relatively simple: a companies' worth is equal to the present value of all its estimated future cash flows.
Many variables go into estimating cash flows, but among the most important are the company's future sales growth and profit margins. Projecting such variables doesn't involve simply extrapolating present trends into the future. It's important to consider a variety of factors, including:
the industry’s evolution and trends
economic data
market share of a company
a company's competitive advantages and future position
competitive position of the main competitors
identification of the value drivers
a company’s suppliers and customers
internal and external risks and etc

Слайд 53Business Valuation: Cash Flow Discounting Approaches
For example:
A company with strong competitive

advantages may grow faster than its competitors if it is stealing market share.

Chemical companies that are heavily reliant on oil and natural gas, for example, could see profit margins contract if these materials go up in price and they cannot pass these cost increases on to customer.

Some companies benefit from operating leverage. Operating leverage means that as a company grows larger, it is able to spread its fixed costs across a broader base of production. As a result, the company's operating profits should grow at a faster rate than revenue. It can add thousands of customers with only very modest investments to its existing computer systems.

Likewise, a software company sees most of its costs in development. Adding an additional customer doesn't change this key cost.

Слайд 54Business Valuation: Cash Flow Discounting Approaches
Main questions that must be asked

of any discounted cash-flow model is exactly what kind of cash flows are you going to be discounting and which discounting rate shall be applied?
There are three basic cash flows: the free cash flow, the equity cash flow, and the debt cash flow.
The free cash flow (FCF) enables the company’s total value (debt and equity: D + E) to be obtained.
The debt cash flow (DCF), which is the sum of the interest to be paid on the debt plus principal repayments. In order to determine the present market value of the existing debt, this flow must be discounted at the required rate of return to debt. In many cases, the debt’s market value shall be equivalent to its book value, which is why its book value is often taken as a sufficient approximation to the market value. (This is only valid if the required return to debt is equal to the debt’s cost)
The equity cash flow (ECF) enables the value of the equity to be obtained, which, combined with the value of the debt, will also enable the company’s total value to be determined.

Слайд 55Cash Flow Discounting Approaches: discount rates

In cash flow discounting-based valuations, a

suitable discount rate is determined for each type of cash flow. Determining the correct discount rate is one of the most important tasks and it shall take into account all risks, historic volatilities; in practice, the minimum discount rate is often set by the interested parties.


Слайд 56Cash Flow Discounting Approaches: The Free Cash Flow
The Free Cash Flow
The

free cash flow (FCF) is the operating cash flow, that is, the cash flow generated by operations, without taking into account borrowing (financial debt), after tax. It is the money that would be available in the company after covering fixed asset investments and working capital requirements, assuming that there is no debt and, therefore, there are no financial expenses.
In order to calculate future free cash flows, we must forecast the cash we will receive and must pay in each period. This is basically the approach used to draw up a cash budget.

Слайд 57Cash Flow Discounting Approaches: The Free Cash Flow
Company’s free cash flow

must not include any payments to fund providers. Therefore, dividends and interest expenses must not be included in the free cash flow.

In order to calculate the free cash flow, we must ignore financing for the company’s operations and concentrate on the financial return on the company’s assets after tax, viewed from the perspective of a going concern, taking into account in each period the investments required for the business’s continued existence.

Finally, if the company had no debt, the free cash flow would be identical to the equity cash flow.

Слайд 58Cash Flow Discounting Approaches: The Free Cash Flow
For example the below

table gives the income statement for the company X. Using this data, we shall determine the company’s free cash flow.

Слайд 59Cash Flow Discounting Approaches: The Free Cash Flow
Free cash flow can

be obtained from earnings before interest and tax (EBIT). The tax payable on the EBIT must be calculated directly; this gives us the net income without subtracting interest payments, to which we must add the depreciation for the period because it is not a payment but an accounting entry. We must also consider the sums of money to be allocated to new investments in fixed assets and new working capital requirements (WCR), as these sums must be deducted in order to calculate the free cash flow.


Слайд 60Cash Flow Discounting Approaches: The Free Cash Flow
WCR = Cash +

Accounts Receivable + Inventories - Accounts Payable



Слайд 61Cash Flow Discounting Approaches: The Free Cash Flow
Balance sheet of a

Company X at 01/01/2010.






Balance sheet of a Company X at 31/12/2010.












Слайд 62Cash Flow Discounting Approaches: The Free Cash Flow
WCR = Cash +

Accounts Receivable + Inventories - Accounts Payable



Слайд 63Cash Flow Discounting Approaches: The Free Cash Flow
The below table shows

how the free cash flow is obtained from earnings before interest and tax (EBIT).
















Слайд 64Cash Flow Discounting Approaches: The Free Cash Flow
Calculating the Value of

the Company Using the Free Cash Flow
In order to calculate the value of the company using this method, the free cash flows are discounted (restated) using the weighted average cost of debt and equity or weighted average cost of capital (WACC):
V(E + D) = present value [FCF; WACC]
V = FCF1/(1+ wacc) + FCF2 (1+ wacc)^2+CF3 (1+ wacc) ^3+..
+ FCFn/(1+wacc) ^n
WACC = E*Ke + D*Kd *(1 - T )/ (E + D)
D = market value of the debt. E = market value of the equity.
Kd = cost of the debt before tax = required return to debt.
T = tax rate, Ke = required return to equity, which reflects the equity’s risk.
The WACC is calculated by weighting the cost of the debt (Kd) and the cost of the equity (Ke) with respect to the company’s financial structure. This is the appropriate rate for this case as, since we are valuing the company as a whole (debt plus equity), we must consider the required return to debt and the required return to equity in the proportion to which they finance the company.

Слайд 65

Cash Flow Discounting Approaches
The Free Cash Flow

Слайд 66Cash Flow Discounting Approaches: The Equity Cash Flow
The Equity Cash Flow
The

equity cash flow (ECF) is calculated by subtracting from the free cash flow the interest and principal payments (after tax) made in each period to the debt holders and adding the new debt provided. In short, it is the cash flow remaining available in the company after covering fixed asset investments and working capital requirements and after paying the financial charges and repaying the corresponding part of the debt’s principal (in the event that there exists debt).
 
ECF = FCF - [interest payments x (1- T)] - principal repayments + new debt
When making projections, the dividends and other expected payments to shareholders must match the equity cash flows.

Слайд 67Cash Flow Discounting Approaches: The Equity Cash Flow
The Equity Cash Flow

Слайд 68Cash Flow Discounting Approaches: The Equity Cash Flow
Example:

Слайд 69Cash Flow Discounting Approaches: The Equity Cash Flow

This cash flow assumes

the existence of a certain financing structure in each period, by which the interest corresponding to the existing debts is paid, the installments of the principal are paid at the corresponding maturity dates and funds from new debt are received. After that there remains a certain sum which is the cash available to the shareholders, which will be allocated to paying dividends or buying back shares.

When we restate the equity cash flow, we are valuing the company’s equity (E), and, therefore, the appropriate discount rate will be the required return to equity (Ke). To find the company’s total value (D + E), we must add the value of the existing debt (D) to the value of the equity (E).
 

Слайд 70Cash Flow Discounting Approaches: The Equity Cash Flow
Calculating the Value of

the Company’s Equity by Discounting the Equity Cash Flow
The market value of the company’s equity is obtained by discounting the equity cash flow at the rate of required return to equity for the company (Ke).

VE = ECF1/(1+ Ke) + ECF2 (1+ )^2+CF3 (1+ Ke) ^3+.. + (ECFn +Vn)/(1+Ke) ^n

When this value is added to the market value of the debt, it is possible to determine the company’s total value.
V=VE+VD


Слайд 71Cash Flow Discounting Approaches: The Equity Cash Flow
The required return to

equity can be estimated using any of the following methods:

1. Gordon and Shapiro’s constant growth valuation model:
Ke = [Div1 / P0] + g.
Div1 = dividends to be received in the following period
P0 = share’s current price
g = constant, sustainable dividend growth rate.
Div1 = Div0(1 + g).


Слайд 72Cash Flow Discounting Approaches: The Equity Cash Flow
For example,
if a

share’s price is 200 KZT
dividend received last year is 8.62 KZT
dividend’s expected annual growth rate is 11%:

Ke = (10/200) + 0.11 = 0.16 = 16%




Слайд 73Cash Flow Discounting Approaches: The Equity Cash Flow
2. Cost of Equity:

Capital Asset Pricing Model (CAPM)
The capital asset pricing model (CAPM) defines the required return to equity in the following terms
For larger publicly-traded companies:
Ke = RF + ß (RM - RF)
RF = rate of return for risk-free investments (Treasury bonds).
ß = share’s beta (a systematic risk measure)
(The beta measures the systematic or market risk of a share. It indicates the sensitivity of the return on a share held in the company to market movements. If the company has debt, the incremental risk arising from the leverage must be added to the intrinsic systematic risk of the company’s business, thus obtaining the levered beta)
RM = expected market return.
RM – RF = equity risk premium
Thus, given certain values for the equity’s beta, the risk-free rate and the market risk premium, it is possible to calculate the required return to equity.

Слайд 74Cash Flow Discounting Approaches: The Equity Cash Flow


Cost of Equity: Capital

Asset Pricing Model (CAPM). Example:
For example, if
RF =4%
ß =1.3
RM=10%
Growth rate =5%





Слайд 75Cash Flow Discounting Approaches: The Equity Cash Flow
Cost of Equity: Capital

Asset Pricing Model (CAPM). Example:
Ke=0,04+1,3*(0,1-0,04)=0,118 (11.8%)

Vn = CFn (1 + g) / (k - g) – residual value of the company after year n

V(3)=(57,51*(1+0,05))/(0,118-0,05=888,02 - residual value of the company after year 3

Слайд 76Cash Flow Discounting Approaches: The Equity Cash Flow


Cost of Equity and

Leverage
Companies with more debt relative to equity are Riskier and have higher costs of equity
Beta (B)
Beta is a measure of the sensitivity of the movement in returns on a particular stock to movements in returns on some measure of the market (i.e. S&P 500, etc.)
Published and calculated betas typically reflect the capital structure of each respective company at market values
Unlevered beta is the beta a company would have if it had no debt
Lever the beta for the subject company based on one more assumed capital structure



The result will be a market-derived beta specifically adjusted for the degree of financial leverage of the subject company

Wd = Weight of Debt
We = Weight of Equity
Wc = Weight of Capital

Слайд 77Cash Flow Discounting Approaches: The Equity Cash Flow


Cost of Equity: Build-up


For smaller closely-held companies
Inputs are same as CAPM except for the application of industry risk premium instead of Beta coefficient
Industry risk premium based on Morningstar (Ibbotson) Yearbook





Generally similar to CAPM after adjustments for size and specific risks

Слайд 78

Cash Flow Discounting Approaches
The Capital Cash Flow

Слайд 79Cash Flow Discounting Approaches: The Capital Cash Flow
The Capital Cash Flow
Capital

cash flow (CCF) is the term given to the sum of the debt cash flow plus the equity cash flow. The debt cash flow is composed by the sum of interest payments plus principal repayments. Therefore:
 
CCF = ECF + DCF = ECF + I - ∆D
I = D*Kd
It is important to not confuse the capital cash flow with the free cash flow.

Слайд 80Cash Flow Discounting Approaches: The Capital Cash Flow
Calculating the Company’s Value

by Discounting the Capital Cash Flow
According to this model, the value of a company (market value of its equity plus market value of its debt) is equal to the present value of the capital cash flows (CCF) discounted at the weighted average cost of capital before tax (WACCBT):
E + D = present value [CCF; WACCBT]

V = CCF1/(1+ WACC(BT) ) + CCF2 (1+ WACC(BT) )^2+CCF3 (1+ WACC(BT) ) ^3+.. + CCFn+Vn /(1+ WACC(BT) ) ^n
WACC(BT) =(E*Ke + D*Kd)/(E + D)
CCF = (ECF + DCF)
.

Слайд 81Cash Flow Discounting Approaches: The Capital Cash Flow


Cost of Debt
Cost

of Debt Based on Subject Company’s Credit Rating and Borrowing Rate (i.e. Prime rate + 1%, BBB, BB, B-, Prime Rate, etc.) at Valuation Date
After Tax Cost of Debt
Cost of Debt x (1 – Target Company’s Tax Rate)
Debt to Capital Ratio
Control Value: Target/Optimal or Industry Average Debt to Capital Ratio
Lack of Control/Minority Value: Company Specific Debt to Capital Ratio


Слайд 82Cash Flow Discounting Approaches: The Free Cash Flow
Balance sheet of a

Company X at 01/01/2010.






Balance sheet of a Company X at 31/12/2010.












Слайд 84Business Valuation: Cash Flow Discounting Approaches



The DCF model that we will

talk about in this article discounts free cash flow, which is defined as operating cash flow minus capital expenditures. Free cash flow represents the cash a company has left over after spending the money necessary to keep the company growing at its current rate. It's important to estimate how much the company reinvests in itself each year via capital expenditures. Reinvestment can take the form of a company purchasing machinery to start up a new production line, or retail companies opening new stores to expand their reach.

Note: There are actually two types of DCF models: "free cash flow to equity" and "cash flow to the firm." The first involves counting just the cash flow available to shareholders and is a bit easier to understand.
The second involves counting the cash flow available to both debt and equity holders and has several additional steps. We will talk about just the first method here, though both methods should give you roughly the same result for any given company. -







Слайд 85Business Valuation: Cash Flow Discounting Approaches


Capitalization of Earnings Approach
Single Period Discounted

Cash Flow Analysis
Simplest for Companies with Stable Growth
Next Year Free Cash Flow to Firm (FCFF)
Next Year Free Cash Flow to Equity (FCFE)
Apply Appropriate Discount Rate



Слайд 86Business Valuation: Market Approach


Publicly-Traded (Guideline) Comparable Company Analysis
The Guideline Publicly Traded

Company Method indicates the value of the subject company by comparing it to publicly-traded companies in similar lines of business
Valuation Multiples Vary Based on Industry and States of Growth
Problem is that there are rarely perfect matches
Equity Multiples
Fair Market Value of Equity (Stock Price x Outstanding Number of Shares)
Common Equity Level Multiples
Price / Earnings (P/E)
Price / Tangible Book Value (P/B)

Слайд 87Business Valuation: Market Approach


Publicly-Traded (Guideline) Comparable Company Analysis
Enterprise Multiples
Enterprise

Value = (Stock Price x Outstanding Number of Shares) + Total Debt/Preferred Securities – Cash and Short-Term Investments
Common Enterprise Level Multiples
EV / Revenue
EV / EBITDA
EV / EBIT

Слайд 88Business Valuation: Market Approach


Publicly-Traded (Guideline) Comparable Company Analysis
Other Multiples
EV / R&D

Expenses; # of Phase I, Phase II and Phase III products in pipeline – Early Stage Biotechnology
EV / # of Licenses and Rights – Shell Company, etc
Appropriate Multiple Depends on Company Characteristics




Слайд 89Business Valuation: Market Approach


Market Transaction (M&A) Approach
In the Guideline Merged and

Acquired Company Method, the value of the business is indicated based on multiples paid for entire companies or controlling interests.
Public Market Transaction Approach
Public Buyer or Seller Transactions
Control Value
Private Market Transaction Approach
Private to Private Transactions
Control Value
Common Transaction Database
MergerStat, Pratts’ Stat, Biz Comps, Capital IQ






Слайд 90Business Valuation: Market Approach


Market Approach Adjustments
Most Companies Differ from the

Subject Company
Need to Adjust for Differences between Market Comparables and Subject Company
Common Adjustments are Based on:
Size
Growth Rate
Profitability
Leverage
Other Company Specific Factors
Discounts and Premiums


Слайд 91Business Valuation: Reconciling Items
Reconciling Items and Adjustments
Appropriate Weighting Value Conclusions

from Different Approaches
Non-Operating Assets/Liabilities and Excess Working Capital/Cash
Pass-Through Entity Tax Adjustments
Adjustment for Discounted Cash Flow Analysis and Publicly-Traded Guideline Comparable Company Analysis
Depends on Hypothetical Buyer (C-Corp.? S-Corp.?, etc.)
Interest-Bearing Debt and Contingent Liabilities
Discounts and Premiums
Apply to Equity Level
Lack of Marketability and Minority Discounts, Key Person Discount and Control Premium, etc.





Слайд 92Discounts and Premiums



Control Premium
Lack of Control/Minority Discounts
Lack of Marketability/Illiquidity Discounts
Others Discounts

Слайд 93Business Valuation: Lack of Marketability Discounts
Let the Fireworks Begin!!
Often subject to

wide disparity among practitioners
Determination based on analogy
Data sources problematic
Reasonable range




Слайд 94Business Valuation: Lack of Marketability Discounts
Lack of Marketability Discounts (LOM)
Marketability (liquidity)

is valuable. Other things equal, investors will pay more for the more liquid (marketable) asset
The discount for lack of marketability is the largest money issue in many, if not most, disputed valuations of minority interests in closely-held, private companies
The U.S. Tax Court normally allows discounts for lack of marketability for non-controlling interests in closely held companies, but the size of the discounts varies greatly from one case to another
Need to carefully study the recent case law in the relevant jurisdiction
The quality of the expert evidence and testimony presented in the Tax Court makes a big difference in the outcome
The Tax Court expects good empirical evidence, relevant to the subject at hand; simple averages are insufficient




Слайд 95Business Valuation: Lack of Marketability Discounts
Lack of Marketability Discounts
The highest discount

that the Tax Court has allowed purely for lack of marketability is 45%, and most discounts have been considerably less
The ESOP discounts for lack of marketability are generally low because most ESOP stock has a “put” right to sell the stock back to the sponsoring company, thus enhancing its liquidity and value.
Dissenting shareholder and shareholder oppression cases are quite mixed on the matter of discount for lack of marketability
There is little case law on discount for lack of marketability in divorce cases, and what exists is also quite mixed
If the standard of value is clearly stated as fair market value, then a discount for lack of marketability is appropriate





Слайд 96Business Valuation: Lack of Marketability Discounts
Lack of Marketability/Illiquidity Discount for Minority

Interest
Restricted Stock Studies
Restricted stocks are, by definition, stocks of public companies that are restricted from public trading under SEC Rule 144
Although they cannot be sold on the open market, they can be bought by qualified institutional investors. Thus, the “restricted stock studies” compare the price of restricted shares of a public company with the freely-traded public market price on the same date
Price differences are attributed to liquidity
Many feel the discounts are a reliable guide to discounts for LOM
Empirical Studies: McConaughy, SEC Institutional Investor, Gelman, Trout, Moroney, Maher, Standard Research Consultants, Siber, FMV Opinion, Management Planning, Johnson, Columbia Financial Advisors Studies











Слайд 97Business Valuation: Lack of Marketability Discounts
Restricted Stock Studies
General Findings
Show

that restricted shares are worth less than unrestricted shares – generally ranging from 10 to 30%. Discounts as high as 55% have been observed
Discounts are larger for smaller companies and companies with more volatile stocks and more debt
These data are most appropriate for valuing restricted stocks and are difficult to apply to private companies
The value of the studies is that the comparisons are apples to apples (i.e. liquid stock value vs. illiquid stock value of the same company at the same time).
Restrictions have been relaxed and discounts have dropped
Statistical studies can explain at best 1/3 of the discount











Слайд 98Business Valuation: Lack of Marketability Discounts
Pre-IPO Stock Studies
A pre-IPO transaction is

a transaction involving a private company stock prior to an Initial Public Offering (IPO)
The pre-IPO studies compare the price of the private stock transaction with the public offering price. The percentage below the public offering price at which the private transaction occurred is a proxy for the discount for lack of marketability
The application of pre-IPO studies heavily debated and criticized because comparisons are apples to oranges
The dates of the transaction differ at a time when the company is changing rapidly (in the year before the IPO)
Discounts are very large
Discounts/premium should be based on specific to the subject case and not past court cases










Слайд 99Business Valuation: Lack of Marketability Discounts
Other Studies
Modified put option model (i.e.

Finnerty and Chaffee)
Modified cost of capital – total beta (McConaughy and Covrig)
“Private Company Discount” by Koeplin, Sarin & Shapiro, Journal of Applied Corporate Finance Winter 2000.
Find approximately a 30% discount. Perhaps the best study, but limited sample size makes it difficult to apply to a specific case.










Слайд 100Business Valuation: Lack of Marketability Discounts
Factors Affecting Discounts for Lack of

Marketability
Company’s Financial Performance and Growth
Size of Distributions
Prospects for Liquidity (Expected Liquidity Event)
Restrictions on Transferability
Company’s Redemption Policy
Costs Associated with a Public Offering
Pool of Potential Buyers
Nature of the Company, Its History, Other Risk Factors
Amount of Control in Transferred Shares
Company’s Management






Слайд 101Business Valuation: Lack of Marketability Discounts
Lack of Marketability/Illiquidity Discounts for Controlling

Interests
Still a controversial concept
A company with control can be marketable, but illiquid
More marketable and liquid than the minority interest; Higher lack of marketability discount for smaller blocks (for closely held companies)
Super majority requirement for certain States
Typically, private companies sell in 6 months which is shorter than the restriction period of restricted stocks







Слайд 102Business Valuation: Control Premium and Minority Discount
Control Premium
Other things equal, an

interest with control is worth more than one that lacks control
An amount by which the pro rata value of a controlling interest exceeds the pro rata value of a noncontrolling interest in a business enterprise that reflects the power of control often associated with takeovers of public companies
Some suggest that valuations of controlling interests be adjusted upward if they are based on publicly-traded stock prices which are minority interests
Hubris and synergy may explain premia
Not needed if cash flows are estimated at the control level





Слайд 103Business Valuation: Control Premium and Minority Discount
Control Premium
Common Prerogatives of Control
Elect

directors and appoint management
Determine management compensation and perquisites
Set policy and change the course of business
Acquire or liquidate assets
Select people with whom to do business and award contracts
Make acquisitions
Liquidate, dissolve, sell, leverage or recapitalize the company
Sell or acquire treasury shares
Register the company’s stock for a public offering
Declare and pay dividends
Change the articles of incorporation or bylaws or operating agreement





Слайд 104Business Valuation: Control Premium and Minority Discount
Control Premium Database
Control Premia Based

on Market Transactions
Identify one month to six months control premium prior to announcement date for public and private transactions from Mergerstat, Capital IQ, etc.
Control premia should exclude potential synergies associated with selected transactions, but this is extremely difficult
Appropriately adjust for other qualitative factors based on control prerogatives




Слайд 105Business Valuation: Control Premium and Minority Discount
Lack of Control/Minority Discount
Some feel

that the control premium and the minority discounts should have the relationship as shown below:



This is overly simplistic. Ignores hubris and synergy and other factors that impact take-over premia
Must deal with negative “premia” in databases






Слайд 106Business Valuation: Control Premium and Minority Discount
Lack of Control/Minority Discount
Supermajority Requirement

– About a quarter of the states require something more than 50% plus 1 share vote to approve certain major corporate actions, such as selling out or merging. Thus, a discount for a lack of supermajority may be appropriate
Swing Vote Potential – Depending on distribution of the stock, a minority, swing block could have the potential to gain a premium price over a pure minority value
Interest of 50% - Discount from lack of control value should be less for the interest with some control prerogatives and a little greater for the interest without the control prerogatives
Many experts feel that publicly-traded stocks generally sell at a control value






Слайд 107Business Valuation: Other Discounts
Other Discounts
Key Person Discount
Measure potential negative impact

to the projected cash flows in the absence of Key Personnel
Trapped-in Capital Gains
A company holding an appreciated asset would have to pay a capital gains tax on the sale of the asset. If ownership of the company were to change, the liability for the tax on the sale of the appreciated asset would not disappear
Use with Caution, it depends on expected time of liquidity event (usually applied when liquidity event is imminent
Consult a tax expert to analyze the situations
Block Discount
A large interest may be less liquid than a smaller one




Слайд 108Business Valuation: Other Discounts
Other Discounts
Voting vs. Non-Voting
If a company has both

voting and nonvoting classes of stock, there may be a price difference between the two, usually in favor of the voting stock
Based on level of influence by the voting shareholders, restrictive agreements, state laws and policies and the total number of block of shares between voting and non-voting
Empirical studies indicates premium for voting shares
Lease, McConnell and Mikkelson Study – 5.4%
Robinson, Rumsey and White Study – 3.5% ~ 4.5%
O’Shea and Siwicki Study – 3.5%
Houlihan Lokey Howard & Zukin Study – 3.2% (average), 2.7% (median)




Слайд 109Business Valuation: Discounts and Premiums
Common Errors in Applying Discounts and Premiums
Greed

produces inconsistencies with economic reality
Low value desired
Conservative projections
High discount rate
Large DLOM, etc.
Higher value desired
Aggressive projections
Low discount rate
Small DLOM, etc.
Conservative projections should be accompanied by a lower discount rate
Aggressive projections should be accompanied by a higher discount rate




Слайд 110Business Valuation: Discounts and Premiums
Common Errors in Applying Discounts and Premiums
Using

synergistic acquisition premia to quantify premiums for control
Assuming that the discounted cash flow valuation method always produces a minority value
Assuming that the guideline public company method always produces a minority value
Valuing underlying assets instead of the stock or partnership interests
Using minority interest marketability discount data to quantify marketability discounts for controlling interests
Using only pre-initial public offering studies and not restricted stock studies as benchmark for discounts for lack of marketability
Indiscriminate use of average discounts or premiums applying (or omitting) a premium or discount inappropriately for the legal context
Applying discounts or premiums to the entire capital structure
Quantifying discounts or premiums based on past court cases
Using a tangible (real property, fixed assets, etc.) appraiser to quantity discounts and premiums




Слайд 111References
Brealey, R.A. and S.C. Myers (2000), “Principles of Corporate Finance,” 6th

edition, McGraw- Hill, New York.

Copeland, T. E., T. Koller and J. Murrin (2000), “Valuation: Measuring and Managing the Value of Companies”, 3rd edition, Wiley, New York.

Copeland and Weston (1988), “Financial Theory and Corporate Policy,” 3rd edition, Addison- Wesley, Reading, Massachusetts.

Faus, Josep (1996), “Finanzas operativas,” Biblioteca IESE de Gestión de Empresas, Ediciones Folio.

Fernández, Pablo (2001a), “Internet Valuations: The Case of Terra-Lycos”, SSRN Working Paper n. 265608.
Fernandez, Pablo (2001b), “Valuation using multiples. How do analysts reach their conclusions?,” SSRN Working Paper n. 274972.
 
 
 

Слайд 112References
Fernández, Pablo (2001c), “Valuing real options: frequently made errors,” SSRN Working

Paper n. 274855.

Fernández, Pablo (2002), “Valuation Methods and Shareholder Value Creation,” Academic Press, San Diego, CA.

Miller, M.H. (1986), “Behavioral Rationality in Finance: The Case of Dividends,” Journal of Business, No. 59, october, pp. 451-468.

Sorensen, E. H. and D.A. Williamson (1985), “Some evidence on the value of the dividend discount model,” Financial Analysts Journal, 41, pp. 60-69.

Слайд 113termins


Patent infringement is the commission of a prohibited act with respect

to a patented invention without permission from the patent holder. Permission may typically be granted in the form of a license.

A buy–sell agreement, also known as a buyout agreement, is a legally binding agreement between co-owners of a business that governs the situation if a co-owner dies or is otherwise forced to leave the business, or chooses to leave the business.

An employee stock ownership plan (ESOP) is an employee-owner scheme that provides a company's workforce with an ownership interest in the company. In an ESOP, companies provide their employees with stock ownership, often at no up-front cost to the employees. ESOP shares, however, are part of employees' compensation for work performed. Shares are allocated to employees and may be held in an ESOP trust until the employee retires or leaves the company. The shares are then sold.
 
 


Слайд 114
An engagement letter defines the legal relationship (or engagement) between a

professional firm (e.g., law, investment banking, consulting, advisory or accountancy firm) and its client(s). This letter states the terms and conditions of the engagement, principally addressing the scope of the engagement and the terms of compensation for the firm.

Equity carve-out (ECO), also known as a split-off IPO or a partial spin-off, is a type of corporate reorganization, in which a company creates a new subsidiary and subsequently IPOs it, while retaining management control. Only part of the shares are offered to the public, so the parent company retains an equity stake in the subsidiary. Typically, up to 20% of subsidiary shares is offered to the public.

Corporate spin-off, a type of corporate transaction forming a new company or entity



Слайд 115
Corporate spin-off, a type of corporate transaction forming a new company

or entity

Слайд 116Everything You Should Know
Understand the Standard of Value
Involve the Appraiser Early

on
Distinguish Between a Business Appraisal and a Real Estate Appraisal
Establish a Reasonable Time Frame
Insist on an Appraisal Firm with Experience and Credentials
Know the Primary Business Valuation Methods
Consider the Appraisal as a First Line of Defense
Litigation Support Issues

Слайд 117СРСП
Define the Company for your Project , give the below

description
Articles of Incorporation; Operating Agreement
History and Background
Products and Services
Shareholders
Organization/Corporate Structure
Operations
Customers/Clients, Target Markets and Suppliers
Legal, Tax and Other Considerations
Five Year Historical and Latest Interim Financial Statements
Other Financial Information (A/R, A/P, Fixed Asset Ledger, etc. - if needed)

Похожие презентации

Учет и анализ основных средств на ООО ДСУ Ново - Деревенское 236
Корректировка плана МТО ООО Таргин 262
Формирование себестоимости 245
Институт управления имуществом должника 210
Типы организации и построения финансовых структур российских компаний 261
Опыт реализации RAB-регулирования 342

Обратная связь

Если не удалось найти и скачать презентацию, Вы можете заказать его на нашем сайте. Мы постараемся найти нужный Вам материал и отправим по электронной почте. Не стесняйтесь обращаться к нам, если у вас возникли вопросы или пожелания:

Email: Нажмите что бы посмотреть 

Что такое ThePresentation.ru?

Это сайт презентаций, докладов, проектов, шаблонов в формате PowerPoint. Мы помогаем школьникам, студентам, учителям, преподавателям хранить и обмениваться учебными материалами с другими пользователями.

Для правообладателей

Яндекс.Метрика