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1

GAAP Inputs Hierarchy: Level 1 Inputs

Level 1 Inputs: Quoted market prices in active markets for identical assets or liabilities. 

  • Used to value items traded in active markets. 
  • If there is a public, active market for the item being valued, that market is the best indicator of FV.
  • Active markets:
    • Stock markets
    • Bond markets
    • Commodities markets
    • Over-the-counter markets 
  • Since the quoted market price is for an identical asset or liab, adjustments to the quoted prices are NOT appropriate in establishing value. 

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GAAP Inputs Hierarchy: Level 2 Inputs

Level 2 Inputs: Directly or indirectly observable inputs, but not for identical item in active market, including:

  • Quoted prices for similar items, but not identical or in markets that are not active
  • Observable inputs other than quoted prices (int rates)

Market is not active when:

  • Few relevant transactions are available
  • Prices are not current or vary substantially
  • Little publicly available information

Examples of when used:

  • Stock restricted from trading, but similar to traded shares
  • Securities traded in brokered markets, rather than public markets
  • Residential and commericial property w comparable sales
  • Private debt securities for which there is publicly traded debt w comparable risks and terms
  • Inputs not directly observable, but derived principally from, or corroborated by, observable market data:
    • By correlation or other means to be useful in valuing an asset or liab
    • Use of multiple earnings, revenues, or similar performance measures to value a business enterprise.

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GAAP Inputs Hierarchy: Level 3 Inputs

Level 3 Inputs: Inputs are unobservable and based on entity's assumptions. Estimates are used for valuing item. 

Examples of Level 3 Inputs:

  • Expected cash flows
  • Expected life of an asset
  • Expected residual value
  • Likelihood of events occurring
  • And similar estimates

Examples of when used:

  • Asser retirement obligations
  • Financial asset servicing rights
  • Capital projects
  • Closely held businesses
  • And others

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Hierarchy/Inputs/Uses

  • Notice:
    • Some items valued directly
      • E.g. - share of stock or barrel of crude oil
    • Other items require more judgment and sue of valuation techniques. 

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Question: 

Which of the following levels of the U.S. GAAP hierarchy of inputs used for determining fair value can be based on inputs not directly observable for the item being valued?

 Level 1    Level 2    Level 3  

Level 1 = NO

Level 2 = YES

Level 3 = YES

Level 1 inputs in the U.S. GAAP hierarchy are based exclusively on observable quoted prices in active markets, not on unobservable inputs. Both level 2 and level 3 can include inputs not directly observable for the item being valued

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Question: 

Which of the following level(s) of input in the U.S. GAAP hierarchy of inputs for fair value determination is/are likely to be most appropriate for valuing basic agricultural commodities?

A.  Level 1, only.
B.  Level 2, only.
C.  Level 3, only.
D.  Level 1 and level 3.

Level 1, only

Level 1 inputs are quoted prices in active markets for identical assets or liabilities. Agricultural commodities of identical nature are widely traded in active commodities markets. The prices from those transactions would be the best measure of the value of identical agricultural commodities.

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Valuation Techniques: Capital Asset Pricing Model (CAPM):

CAPM: An economic model that determines a measure of relationship between risk and expected return. 

The general idea behind CAPM is that investors need to be compensated in two ways:

  1. Time value of money and
  2. Risk. 
  • The time value of money is represented by the risk-free (RFR) rate and compensates the investors for placing money in any investment over a period of time.
  • The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium.

CAPM Basic Formula:

RR=RFR + beta (ERR-RFR)

  • Where:
    • RR= Required Rate of Return
    • RFR= Risk-free rate of return -- Rate on US Gov't bonds
    • beta= Measure of volatibility of asset being measured (measure of risk)
    • ERR= Expected rate of return -- Benchmark rate for the class of asset being valued. 

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CAPM Illustration:

CAPM Formula and Illustration:

  • RR=RFR + beta (ERR-RFR)
  • Assume:
    • RFR: 3%
    • beta: 2
    • ERR: 10%
  • Then:
    • RR= .03+2(.10-.03)
    • RR= .03+2(.07)
    • RR= .03+.14=.17 = 17%

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CAPM beta:

beta: Measure of systematic risk as reflected by the volatibility of an investment or other asset.

Technically, beta = 

  • (Asset std deviation) [a] / Benchmark std deviation [b] x Coefficient of correlation betwenn [a] and [b]

beta: Measure of volatibility of an asset when compared to a benchmark for the whole class of that asset. 

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beta Values:

There are three states of beta possible:

  • beta = 1
  • beta > 1
  • beta < 1

Beta = 1: Asset being valued moves in line with benchmark

  • Asset being valued has the same level of systematic risk as that class of asset; the investment has average systematic risk.

Beta > 1: Asset being valued moves greater than benchmark.

  • Asset being valued is more volatile (more systematic risk) than that class of asset
  • In earlier example:
    • ERR: 10%
    • beta = 2 = more risk than benchmark for class of asset being valued.
    • RR = 17% (greater)

Beta > 1: Asset being valued moves less than benchmark.

  • Asset being valued is less volatile (less systematic risk) than that class of asset.

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Plotting of CAPM:

The following graph shows the plotted slope of Beta under three assumptions as to its value:

  •  A. When B = 1, a percentage change in an asset class benchmark return (i.e., a market) produces the same percentage change in an individual asset (e.g., a stock) of the same asset class.
  • B. When B > 1, a percentage change in an asset class benchmark return produces a greater than equal change in an individual asset of the same asset class.
  • C. When B < 1, a percentage change in an asset class benchmark return produces a less than equal change in an individual asset of the same asset class.

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What are the Assumptions and Limitations of CAPM?

CAPM is based on a number of assumptions, some of which are more significant to the outcome than others. Some of the most significant assumptions and limitations of CAPM are:

  1. All investors are assumed to have equal access to all investments and all investors are assumed to be using a one period time horizon.
  2. It is assumed that asset risk is measured solely by its variance from the asset class benchmark.
  3. It is assumed that there are no external cost - commissions, taxes, etc.
  4. It is assumed that there are no restrictions on borrowing or lending at the risk-free rate of return; all parties are assumed to be able to do so.
  5. It is assumed that there is a market for all asset classes and, therefore, a market benchmark; to the extent there is not a market or a benchmark for a particular asset class, CAPM cannot be used.
  6. It uses historical data, which may not be appropriate in calculating future expected returns. 

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Uses of CAPM:

Uses of CAPM include:

  • Securities analysis: stocks, bonds, derivatives
  • Corporate investment in capital projects: establishing hurdle rates (or discount rates) for capital projects. 
  • Setting fair compensation for regulated monopolies. 

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Question:

A graph that plots beta would show the relationship between :

Asset return and benchmark return:

A graph which plots beta would show the relationship between the return of an individual asset and the return of the entire class of that asset, as reflected in a benchmark return for the class

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Valuation Techniques: Option Pricing Models -- Options Defined: 

Option: Contract that entitles the owner (holder) to buy (Call option) or sell (Put option) an asset at a stated price within a specified period. Financial options are a form of derivative instrument (contract).

  • American-Style -- Option permits exercise any time before expiration.
  • European Style -- Option permites exercise only at maturity date. 

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Valuing Option Factors:

Valuing Options:

  • An option may or may not have value.
  • Valuing an option, including determining it has no value, is based on six factors: 
    1. Current stock price relative to option price (exercise price).
      • The greater the stock price over the (call) option price the greater the value of option.
      • The greater the stock price over the (put) option, the lower the value of the option.
    2. Time expiration of option
      • Longer the time = greater value of option
    3. Risk-free Rate of Return
      • The higher the RFR = greater the value of option.
    4. Measure of risk of optioned asset
      • Standard deviation or beta
      • Larger std deviation = greater value of option
    5. Exercise price of option
    6. Dividend payments on optioned security
      • Smaller the dividends = greater the value of option (more earnings are being retained).

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What is the Black-Scholes option-pricing model?

The Black-Scholes model: is a mathematical formula for valuing stock options, which are derivative instruments (and certain other instruments).

  • The original model was developed to value European-style options, which permit exercise only at the expiration date of the option.   
  • It is developed to value options under specific cicumstances, including:
    • For European call options
    • Stock pays no dividends
    • Stock prices increase in small increments
    • Risk-free rate of return assumed constant

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What are some major advantages of the original Black-Scholes option pricing model?

Advantages of Original Black-Scholes Option pricing model:

  1. Assigns probability factor to the likelihood that the price of the stock will pay off within the time to expiration;
  2. Assigns probability factor to the likelihood that the option will be exercised;
  3. Discounts the exercise price to present value.

 

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What are some major limitations of the original Black-Scholes option pricing model?

Limitations:

  1. Appropriate only for European call options, which permit exercise only at the expiration date;
  2. Assumes options are for stocks that pay no dividends;
  3. Assumes options are for stocks whose price increases in small increments;
  4. Assumes the risk-free rate of return remains constant during life of the option;
  5. Assumes there are no transaction costs or taxes associated with the options.

Modified Black-Scholes Models overcome most original limitations. 

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What is the Binomial Option Pricing Model (BOMP)?

Binomial Option Pricing Model: Another method for determining the value of an option.

  • Uses "tree' diagram to estimate values at a number of time points between the valuation date and the expiration date. 
  • It is more versatile than Black-Scholes Model.

Binomial Option Pricing Model Steps:

  1. Generate price tree diagram--Use a branch for each desired period until expiration.
  2. Calculate option value at each tree end node as of the expiration date
  3. Calculate option value at each preceding node back to present valuation date.

Example: 

  • Assume an option for a share of stock that expires in one year and has an exercise price of $100. An evaluation estimates that at the end of the year the underlying stock could have a price as high as $120 and as low as $80. 
  • Assume that a .60 probability is assigned to the $120 high value and a .40 probability (1.00 - .60) is assigned to the $80 low value.
  • The entity's cost of funds is 10%.
    • Expected Value = [(.60 x $20) + ( .40 x $0)]/1.10
    • = [ $12 + $ 0 ]/1.10
    • Option Value = $12/1.10 = $10.91

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Question: Binomial Model

Charles Allen was granted options to buy 100 shares of Dean Company stock. The options expire in one year and have an exercise price of $60.00 per share. An analysis determines that the stock has an 80% probability of selling for $72.50 at the end of the one-year option period and a 20% probability of selling for $65.00 at the end of the year. Dean Company's cost of funds is 10%. Which one of the following is most likely the current value of the 100 stock options?

$1,000

The stock has an 80% chance of selling at $72.50 at the end of the option period. That is $12.50 above the option price. The stock has a 20% chance of selling at $65.00 at the end of the option period. That is $5.00 above the option price. Therefore, the value of the option is:

  • [(.80 x $12.50) + (.20 x $ 5.00)]/1.10, or
  • [($10.00) + ($1.00)]/1.10, or
  • $11.00/1.10 = $10.00 x 100 shares = $1,000

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Question: Black Scholes

Which one of the following characteristics is not an advantage of the Black-Scholes option pricing model?

A.  Incorporates the probability that the price of the stock will pay off within the time to expiration.
B.  Incorporates the probability that the option will be exercised.
C.  Discounts the exercise price.
D.  Accommodates options when the price of the underlying stock changes significantly and rapidly.

D.  Accommodates options when the price of the underlying stock changes significantly and rapidly.

The Black-Scholes option pricing model does not accommodate options when the price of the underlying stock changes significantly and rapidly. The Black-Scholes model assumes that the stock for which the option is being valued increases in small increments. 

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Valuation Techniques: Business Entity -- Business Valuation Defined: 

Business Valuation: The estimation of the economic value of a business entity or portion thereof.

  • When entity is publicly traded in an active market, its value can be determined by its market capitalization, its total value in the market.
  • Uses of business valuation:
    • Buying or selling a business
    • Developing a buy/sell agreement
    • Estate purposes
    • And others 

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Business Valuation Process (Overview): 

Business Valuation Process Involves:

  1. Establishing standards and premise of the valuation;
  2. Assessment of the economic environment of the business;
  3. Analysis of financial statements
  4. Formulation of valuation

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Business Valuation Process: Establishing Standards and Premises:

Establishing Standards and Premises: 

  • Identifies reasons for and circumstances of valuation
  • Standards of value -- Establish conditions of valuation:
    • Is valuation legally or otherwise mandated?
    • Is valuation at request of or for owners?
    • Is valuation for prospective buyer?
  • Premise of value -- Establishes assumptions to be used:
    • ​Will business continue as single going concern?
    • Will business be separated into separate units?
    • Will assets be sold separately?

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Business Valuation Process: Economic Environment Assessment:

Economic Environment Assessment: 

It should consider:

  • General economic environment
  • Specific operating economic environment
  • Economic nature of environment
  • Economic conditions of physical location

Economic assessment provides framework for valuing specific entity. 

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Business Valuation Process: Financial Statement Analysis:

Financial Statement Analysis: They include:

  • Common size-analysis -- Converting dollar amlunts to percentages for comparison over time and with other entities.
    • Common size Income Statement: would show all individual items of revenue, expense, gain, and loss as a percentage to total revenues (or net revenues)
    • Common size Balance Sheet: would show all indiv items of assets, liab, and equity as a percentage of total assets. 
  • Trend Analysis -- Determining changes in important measures over time.
  • Ratio Analysis -- Determining important ratios to assess change and compare with other entities.
  • Adjustments -- Making adjustments to statements to better reflect normal, on-going operations.

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Business Valuation Process: Formulation of Valuation:

Business Valuation Approaches:

The Alternative Approaches to Business Valuation are:

  • Market Approach
  • Income Approach
  • Asset Approach

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Business Valuation Approaches: Market Approach:

Market Approach (also Guideline Public Company Method): Determines value of a business by comparing it with highly similar entities for which there is a readily determinable value. 

  • Example:
    • Market value of publicly-traded company could be used as basis for determining value of highly comparable non-public company.
  • Use of Market Approach may require adjustments to get final value for business. Adjustments may include:
    • Premium for controlling interest in business being valued
    • Discount for lack of controlling interest in business being valued
    • Discount when business being valued is not as markeatable as entity on which its value is based.
  • Market Approach Disadvantages:
    • Difficulty in identifying highly comparable entities for which there is a ready and objetive market value. 
    • Difficulty in determing appropriate "liquidity" ("sellability") and other discounts in valuing comparable entity.

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Business Valuation Approaches: Income Approach:

Income Approach: Determines value by calculating net present value of the benefit stream generated by the entity being valued. 

  • Net present value = Entity value
  • Net present value is calculated using discount rate or capitalization rate
  • Discount rate should be based on rate of return needed to attract investor funding given level of risk.

Alternative Income Approach Methods:

  1. Discounted Cash Flows: Uses discounted future cash flows to get present value.
    • Future cash flows consist of both expected future inflows and outflows.
    • The discount rate may be based on: WACC, CAPM, or both.
  2. The Capitalization of Earnings: Applies capitalization or interest rate to earnign to get value.
    • Net income (or other measure of earning) is divided by an assumed or desired rate of return to obtain value of the entity that generated the earnings.
    • Example:This example assumes no future growth and disregards inflation. 
      • An entity expects to earn $100,000 and the rate of return required for the level of risk is 20%.
      • Capitalized value = $100,000/.20 = $500,000
      •  The value of the business would be $500,000.
      • Notice that a $500,000 investment earning at the rate of 20% would provide a $100,000 return. 
    • ​Example: This example assumes a 4% growth rate and a 3% inflation rate.

      • An entity expects to earn $100,000 and the rate of return required for the level of risk is 20%

      • Capitalized value = Expected Earnings/[Discount Rate - (Growth Rate + Inflation Rate)]

      • Capitalized value = $100,000/[.20 - (.04 + .03)]

      • Capitalized value = $100,000/.13 = $769,231

      • The value of the business would be $769,231

  3. Earnings Multiples: Applies a multiples factor to earnings to get a value. 

    • The multiple is, in effect, the same as the rate used above to capitalize earnings.

      • A capitalization rate of 20% would be the same as a multiple of 5 (100%/20% = 5).

      • When using the capitalization rate, as show above, the rate is divided into earnings to get a value; when using the multiple, the multiple is multiplied by the earnings to get a value. 

    • Enterprise multiples provide a value for the entity as a whole, not just the value of the common shareholders interest.

    • Equity multiples provide a value for the equity holders interest, not for the enterprise as a whole. 

    • The P/E ratio (multiple) is computed as: Market Price/Earnings per Share. 

  4. Free Cash Flow: Applies discount rate to free cash flows to get present value. 

    • Free cash flow is the cash that an entity generates after the cash flow expended or amortized to maintain or expand its capital asset base.

    •  Free Cash Flow Calculation: Net income + Depreciation/Amortization - Capital expenditures +/- Changes in Working Capital = Free Cash Flow

    • Its a variation of discounted cash flows. 

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What are the Alternative Income Approach Methods?

Alternative Income Approach Methods:

  1. Discounted Cash Flows: Uses discounted future cash flows to get present value.
    • Future cash flows consist of both expected future inflows and outflows.
    • The discount rate may be based on: WACC, CAPM, or both.
  2. The Capitalization of Earnings: Applies capitalization or interest rate to earnign to get value.
    • Net income (or other measure of earning) is divided by an assumed or desired rate of return to obtain value of the entity that generated the earnings.
    • Example:This example assumes no future growth and disregards inflation. 
      • ​An entity expects to earn $100,000 and the rate of return required for the level of risk is 20%.
      • Capitalized value = $100,000/.20 = $500,000
      • The value of the business would be $500,000.
      • Notice that a $500,000 investment earning at the rate of 20% would provide a $100,000 return. ​
    • Example: This example assumes a 4% growth rate and a 3% inflation rate.

      • An entity expects to earn $100,000 and the rate of return required for the level of risk is 20%

      • Capitalized value = Expected Earnings/[Discount Rate - (Growth Rate + Inflation Rate)]

      • Capitalized value = $100,000/[.20 - (.04 + .03)]

      • Capitalized value = $100,000/.13 = $769,231

      • The value of the business would be $769,231

  3. Earnings Multiples: Applies a multiples factor to earnings to get a value. 
    • The multiple is, in effect, the same as the rate used above to capitalize earnings.
    • A capitalization rate of 20% would be the same as a multiple of 5 (100%/20% = 5).
    • When using the capitalization rate, as show above, the rate is divided into earnings to get a value; when using the multiple, the multiple is multiplied by the earnings to get a value. 
    • Enterprise multiples provide a value for the entity as a whole, not just the value of the common shareholders interest.
    • Equity multiples provide a value for the equity holders interest, not for the enterprise as a whole. 
    • The P/E ratio (multiple) is computed as: Market Price/Earnings per Share. 
  4. Free Cash Flow: Applies discount rate to free cash flows to get present value. 
    • Free cash flow is the cash that an entity generates after the cash flow expended or amortized to maintain or expand its capital asset base.
    • Free Cash Flow Calculation: Net income + Depreciation/Amortization - Capital expenditures +/- Changes in Working Capital = Free Cash Flow
    • Its a variation of discounted cash flows. 

32

Business Valuation Approaches: Asset Approach:

Asset Approach: Determines value by adding values of individual assets that comprise the entity being valued. 

  • Fair value of each indiv asset (and liab) is determined.
  • Sum of net assets is value of entity.

Valuation of indiv assets requires used of specific valuation techniques:

  • Income Approach
  • Market Approach
  • Cost Approach

Certain assets like intangible ones are difficult to value alone.

Asset Approach Appropriateness:

  • Less appropriate for valuing going concern
  • Less appropriate for valuing non-controlling interest
  • More appropriate for valuing entity in liquidation
  • More appropriate for entity with little or no cash flows or earnings.

33

Question: 

 

Which one of the following is least likely to be the reason an entity would seek a valuation of the entity as a going concern?

A.  In connection with a planned sale of the entity.

B.  In connection with a property tax determination.

C.  In connection with developing a buy-sell agreement among the owners.

D.  In connection with developing a settlement with the estate of a recently deceased owner.

B.  In connection with a property tax determination.

An entity would not seek to determine the value of an entity as a going concern in connection with a property tax determination. Valuation for property tax purposes would be concerned only with the value of the separate taxable assets of the entity, not with the value of the entity as a going concern.

34

Question:

A business with a net book value of $150,000 has an appropriate fair value of $120,000. Charles Harvey, one of three owners, has decided to sell his 10% interest in the business. Which one of the following is most likely the amount at which Harvey can sell his interest?

A.  $40,000
B.  $15,000
C.  $12,000
D.  < $12,000

D.  < $12,000

Harvey would likely receive less than $12,000 upon sale of his interest. While Harvey has a claim to 10% of the fair value of the business, because his ownership interest is very minor, the value of his interest upon sale would likely be less than $12,000 due to a noncontrolling interest discount.

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