Equity

Question 1

5.1 Equity Valuation : Applications and Processes

Answer 1

– Define valuation and intrinsic value and explain sources of perceived mispricing.
– Explain the going concern assumption and contrast a going concern value to a liquidation value.
– Describe definitions of value and justify which definition of value is most relevant to public company valuation.
– Describe applications of equity valuation.
– Describe questions that should be addressed in conducting an industry and competitive analysis.
– Contrast absolute and relative valuation models and describe examples of each type of model.
– Describe sum-of-the-parts valuation and conglomerate discounts.
– Explain broad criteria for choosing an appropriate approach for valuing a given company.

Question 2

Intrinsic Value and Mispricing

1- Definition of Intrinsic Value
– Intrinsic value is the “true” value of an asset, based on a complete understanding of its investment characteristics.
– It cannot be directly observed and must be estimated.

2- Market Efficiency and Intrinsic Value
– In perfectly efficient markets with perfect information, assets would trade at their intrinsic value.
– In reality, market prices often deviate from intrinsic value due to market inefficiencies, creating opportunities for mispricing.

3- Formula for Perceived Mispricing
– The formula for perceived mispricing is:
— “V_E - P = (V - P) + (V_E - V)”

4- Explanation of Variables
– V_E: Investor’s estimate of the security’s value.
– P: Current market price.
– V: Security’s “true” or intrinsic value.

5- Sources of Perceived Mispricing
– The first term “(V - P)” represents true mispricing, i.e., the difference between intrinsic value and market price.
– The second term “(V_E - V)” represents estimation error, i.e., the difference between the investor’s estimate of intrinsic value and the actual intrinsic value.

6- The Paradox of Market Efficiency (Grossman and Stiglitz, 1980)
– If prices perfectly reflect intrinsic value, investors would not expend resources to research companies, making market prices less meaningful.
– Investors must expect that active research and analysis will lead to profitable opportunities, ensuring intrinsic value is reflected in market prices.

Answer 2

Key Takeaways
– Market inefficiencies create opportunities for mispricing, allowing active investors to generate profits.
– Both true mispricing and estimation error contribute to perceived mispricing.
– The paradox of market efficiency highlights the need for active participation to maintain meaningful market prices.

Question 3

Going-Concern Value vs. Liquidation Value

1- Going-Concern Value
– The going-concern value assumes the company will continue to operate for the foreseeable future.
– It is typically used unless the company is facing financial distress, in which case liquidation value may be more appropriate.

2- Liquidation Value
– Liquidation value is the net amount that could be generated if the company’s assets were sold, after deducting liabilities.
– It is generally lower than the going-concern value because it reflects the value of assets sold under distressed conditions.

3- Orderly Liquidation Value
– If assets can be sold in an orderly manner (not under distress), the orderly liquidation value will be higher than the typical liquidation value.

Question 4

Fair Market Value vs. Investment Value

1- Fair Market Value
– Fair market value is the price agreed upon by a willing buyer and a willing seller under the following conditions:
— Both parties are informed about the asset.
— Neither party is compelled to trade.
– This concept is widely used across accounting standards, although definitions may vary.

2- Investment Value
– Investment value is subjective and varies based on individual circumstances.
– It reflects the value of an asset to a specific investor, considering factors such as synergies or strategic benefits.
— For instance, investment value may be higher for a buyer who can exploit potential synergies from the asset.

Question 5

Applications of Equity Valuation

1- Selecting Stocks
– Equity analysts use valuation to identify overpriced or underpriced stocks for investment decisions.

2- Inferring Market Expectations
– Market prices reflect assumptions that can be evaluated through valuation models to determine their reasonableness.

3- Evaluating Corporate Events
– Valuation tools help assess the impact of events like mergers, acquisitions, divestitures, spin-offs, and leveraged buyouts.

4- Rendering Fairness Opinions
– Third-party valuation is often required in mergers to determine the fairness of the proposed offer price.

5- Evaluating Business Strategies and Models
– Companies use valuation to measure the impact of strategies or business models on shareholder value.

6- Communicating with Analysts and Shareholders
– Valuation concepts support discussions regarding factors that influence a company’s value.

7- Appraising Private Businesses
– Private businesses need to be valued for transactions such as sales, mergers, or initial public offerings (IPOs).

8- Share-Based Payments
– Equity valuation determines the cost of compensating executives with stock grants and other share-based payments.

Question 6

Key Steps in the Valuation Process

1- Understand the Business
– Analyze the company’s industry, competitive position, and overall strategy to gain a clear understanding of its operations and value drivers.

2- Forecast Company Performance
– Project financial metrics such as revenue, expenses, and cash flows based on historical data, industry trends, and strategic plans.

3- Select an Appropriate Valuation Model
– Choose the valuation method that best fits the company’s characteristics and the purpose of the analysis (e.g., DCF, relative valuation).

4- Convert Forecasts to Valuation
– Use the selected model to calculate the company’s value based on the forecasted performance.

5- Apply Valuation Conclusions
– Interpret the results, compare them to market data, and make decisions based on the valuation outcomes (e.g., investment decisions or transaction pricing).

Question 7

Understanding the Business: Industry and Competitive Analysis

1- Importance of Industry Analysis
– Analyzing the industry is critical to forecasting a company’s financial performance.
– Industries are subject to specific risks and economic drivers (e.g., airlines face labor costs and fuel prices).

2- Michael Porter’s Five Forces Framework
– Factors that make an industry more attractive:
— 1- Low rivalry among industry participants.
— 2- High barriers to entry, reducing the threat of new competitors.
— 3- Few substitutes or high switching costs for customers.
— 4- Many suppliers competing for the business of a few producers.
— 5- Many customers with limited bargaining power compared to producers.

3- Assessing the Company’s Position
– Analysts must evaluate the company’s competitive strength within the industry.

4- Porter’s Three Corporate Strategies
– To achieve above-average performance, companies can:
— 1- Be the lowest-cost producer while offering comparable products or services (e.g., low-cost airlines).
— 2- Differentiate products or services to command premium prices (e.g., luxury goods).
— 3- Focus on specific segments within an industry (e.g., niche products tailored to specific user needs).

Question 8

Understanding the Business: Analysis of Financial Reports

1- Purpose of Financial Reports
– Financial reports provide critical insights into a company’s business model and strategic priorities.
– For instance, high advertising expenses may indicate a focus on building brand loyalty.

2- Importance of Financial Metrics
– Financial metrics are particularly significant when evaluating established companies in mature industries, where consistent data and trends are available.

3- Consideration for Younger Companies
– For younger companies or those in emerging industries, analysts may prioritize non-financial metrics, such as market share growth, user engagement, or product development progress.

Question 9

Understanding the Business: Sources of Information

1- Primary Sources of Information
– Companies provide critical disclosures through regulatory filings, press releases, and conference calls.
– These sources offer valuable insights into a company’s operations, strategy, and financial performance.

2- Supplementary Information
– Analysts should also use third-party sources, such as:
— Industry groups.
— Regulators.
— Data providers.
— Non-governmental organizations.

3- Ethical Considerations
– According to CFA Institute Standards, analysts must not act on or encourage others to act on material nonpublic information.

Question 10

Understanding the Business: Considerations in Using Accounting Information

1- Quality of Earnings
– Analysts should evaluate the quality of earnings by assessing:
— The accuracy of financial reporting.
— The sustainability of earnings over time.
– This involves a thorough analysis of financial statements, including the balance sheet and statement of cash flows.

2- Net Income vs. Operating Cash Flow
– Net income should align with operating cash flow over the long term.
– A high proportion of accruals relative to cash flows may indicate low-quality earnings, as cash earnings are generally more persistent.

3- Scrutiny of Footnotes and Disclosures
– Analysts should examine footnotes and other disclosures for potential red flags, such as:
— Inadequate or vague disclosures.
— Aggressive revenue recognition practices.
— Related-party transactions.
— Off-balance-sheet financing.
— High turnover rates among managers or directors.

Question 11

Forecasting Company Performance

1- Top-Down Approach
– Focuses on the broader economic environment, then narrows to the industry, and finally to the company.
– The company’s sales forecast is derived from:
— Overall industry sales.
— The company’s market share.

2- Bottom-Up Approach
– Begins with a micro-level analysis of the company’s operations.
– Details such as prices and unit costs are aggregated to create a company-level forecast of sales and profitability.

Question 12

Selecting the Appropriate Valuation Model: Absolute Valuation Models

1- Definition
– Absolute valuation models estimate a company’s intrinsic value, which is then compared to its market price to assess potential mispricing.

2- Present Value Models (Discounted Cash Flow Models)
– These models calculate intrinsic value based on future cash flows, discounted to the present. Commonly used metrics include:
— Dividends.
— Free Cash Flow to Equity (FCFE).
— Free Cash Flow to the Firm (FCFF).
— Residual Income (accrual accounting earnings exceeding opportunity costs).

– Challenges in equity valuation using present value models:
— Predicting future cash flows involves uncertainty.
— Estimating appropriate discount rates is complex.

3- Asset-Based Valuation
– This method estimates a company’s value based on the market value of its assets and the resources it controls.
– Often applied to natural resource companies, such as oil companies, where proven reserves are valued using market prices (e.g., oil futures contracts).

Question 13

Selecting the Appropriate Valuation Model : Relative Valuation Models

1- Definition
– Relative valuation models estimate an asset’s value by comparing it to the value of a similar asset or a benchmark.
– Common ratios used include price-to-earnings (P/E), price-to-book (P/B), and EV/EBITDA.
– A stock with a low P/E relative to peers or the industry average is considered relatively undervalued.
– Key assumption: Identical or comparable assets should sell for the same price.

2- Applications in Investment Strategies
– Portfolio Weighting: Investors may underweight high P/E stocks and overweight low P/E stocks compared to their benchmark weights.
– Pairs Trading: A more aggressive strategy where an investor:
— Goes long on a relatively undervalued stock.
— Takes an equivalent short position in an overvalued stock from the same industry.
— Profitability depends on the undervalued stock rising more (or falling less) than the overvalued stock.

3- Limitations
– Relative valuation models do not estimate intrinsic value.
– They only assess whether an asset is relatively undervalued or overvalued compared to another asset.

Question 14

Valuation of the Total Entity and Its Components

1- Sum-of-the-Parts Valuation
– This approach calculates the value of each business segment of an entity independently.
– It is especially useful for conglomerates, which operate in multiple, unrelated industries.

2- Conglomerate Discount
– A conglomerate discount occurs when investors perceive that:
— Capital is being inefficiently allocated across business units.
— The company is compensating for poor performance by acquiring unrelated businesses.
– It is possible that some observed conglomerate discounts are due to measurement errors rather than actual inefficiencies.

3- Breakup Value
– The sum-of-the-parts approach can reveal whether a company’s market price is lower than its breakup value, i.e., the value of its individual segments if sold separately.
– A conglomerate trading below its breakup value may present an investment opportunity.

Answer 14

Key Takeaways
– Sum-of-the-parts valuation is ideal for analyzing conglomerates with diverse business segments.
– The presence of a conglomerate discount may indicate inefficiencies or mispricing, but it could also result from valuation challenges.
– Investors can use this method to identify whether a company is undervalued relative to its breakup value.

Question 15

Issues in Model Selection and Interpretation

1- Consistency with the Company’s Characteristics
– The selected valuation model should align with the company’s specific attributes.
— Example: Asset-based models are suitable for banks due to their large share of marketable assets.

2- Data Availability and Quality
– The chosen model must be appropriate for the data available.
— Example: A dividend discount model is unsuitable for a company that does not plan to pay dividends in the near term.

3- Purpose of the Valuation
– The model should match the valuation’s objective.
— Example:
—- Free Cash Flow to Equity (FCFE) models are ideal for minority investments.
—- Free Cash Flow to the Firm (FCFF) models are better suited for acquisitions involving a controlling majority position.

Answer 15

Key Takeaways
– Analysts must ensure the valuation model fits the company’s characteristics, the data quality, and the purpose of the analysis.
– Choosing an inappropriate model can lead to inaccurate valuations and flawed decision-making.

Question 16

Steps in Converting a Forecast to a Valuation

1- Sensitivity Analysis
– Sensitivity analysis evaluates how changes in key inputs affect valuation outcomes.
— This is essential for uncertain parameters like growth rates or pricing strategies.

2- Situational Adjustments
– Adjustments are made based on investor circumstances and market conditions. Examples include:
— Control Premium: Investors may pay a premium for majority ownership compared to a minority share.
— Marketability Discount: Applied to private company shares to reflect the lack of a secondary market.
— Illiquidity Discount: For public companies with thinly traded shares.
— Blockage Factor: Discount to account for difficulties in executing large block trades without affecting market prices.

Answer 16

Key Takeaways
– Sensitivity analysis is crucial for assessing the robustness of valuations under different assumptions.
– Situational adjustments, including control premiums, marketability, and illiquidity discounts, address specific investor and market scenarios.
– These steps ensure the valuation reflects real-world considerations.

Question 17

Applying the Valuation Conclusion: The Analyst’s Role and Responsibilities // Roles of Analysts in Financial Markets

1- Sell-Side Analysts
– Employed at brokerage firms, sell-side analysts produce research reports for clients, such as:
— Pension funds.
— Investment management firms.

2- Buy-Side Analysts
– Work for investment management firms, trusts, and similar institutions.
– Their analysis directly supports investment decisions.

3- Corporate Analysts
– Focus on valuing potential investments and identifying merger or acquisition targets.

4- Analyst Contributions
– Analysts help clients make informed buy and sell decisions.
– They improve market efficiency by providing valuable insights.
– Analysts also monitor management performance, aiding capital suppliers in their assessments.

Question 18

Examining Financial and Operational Strategic Execution

1- Key Principles
– Do not solely rely on quantitative measures when assessing a company’s financial and operational performance.
– Avoid extrapolating past operating results as the sole basis for forecasting future performance.

2- Tendency to Regress to the Mean
– Successful companies may experience performance declines over time.
– Struggling companies may show improvements, moving closer to the industry average or mean.

Question 19

Analysis of Financial Reports

1- Use of Financial Ratios
– Financial ratio analysis is particularly valuable for established companies.
– Ratios can help indicate the strategy being pursued by the company (e.g., cost leadership or differentiation).

2- Relatively High Gross Margins
– Companies with high gross margins often focus on building and maintaining a strong brand.
– This strategy typically involves:
— Significant advertising expenses to reinforce brand value.

Question 20

Forecasting Company Performance

1- Top-Down Approach
– Begins with macroeconomic factors and narrows down to the company level.
— Step 1: Analyze the economic environment (e.g., GDP growth).
— Step 2: Project industry revenue based on GDP estimates.
— Step 3: Estimate the company’s revenue using its forecasted market share.

2- Bottom-Up Approach
– Starts with company-specific operational and financial data.
— Example: Use historical data from similar company operations to project performance.
— Step 1: Analyze the company’s operating characteristics, such as sales data.
— Step 2: Use micro-level inputs (e.g., revenue per store) to forecast total performance, like revenue at new retail locations.

Question 21

Valuation Models and Pairs Trading

1- Types of Valuation Models
– When using a going-concern assumption, two primary valuation models are applied:
— Absolute Valuation Models: Focus on intrinsic value based on cash flows or asset values.
— Relative Valuation Models: Use the method of comparables, which assesses an asset’s value relative to similar assets or benchmarks (e.g., price-to-earnings or price-to-book ratios).

2- Pairs Trading Strategy
– Involves taking a long position in a relatively undervalued stock and an equivalent short position in a relatively overvalued stock from the same industry.
– Benefits of pairs trading:
— Creates an investment profile that is neutral to overall market risk.
— Exploits relative mispricings between the two securities to generate profit.

Question 22

Research Reports: Contents, Format, and Responsibilities

1- Contents of a Research Report
– Key elements of a research report include:
— Investment recommendations with supporting key assumptions.
— Descriptions of valuation models and qualitative factors influencing the valuation.
— Discussion of uncertainties in intrinsic value estimates.
– Reports must be timely, clear, objective, and informative.
– Analysts must distinguish facts from opinions and disclose any actual or potential conflicts of interest.

2- Format of a Research Report
– While formats vary, most reports include:
— Table of contents.
— Investment conclusion.
— Business summary.
— Risks, valuation details, and historical data.

3- Research Reporting Responsibilities
– CFA Institute members are obligated to:
— Exercise reasonable care and independent professional judgment in their analysis.

Question 23

Characteristics of an Effective Research Report

1- Key Components of the Report
– Provide comprehensive background information, including:
— Key assumptions.
— Specific forecasts and valuation inputs.
— A clear description of the valuation model used.
– Address underlying uncertainties proactively.
– If a target price is included, specify the time frame for achieving it.

2- Characteristics of Effectiveness
– 1: Contains timely information.
– 2: Is clearly written.
– 3: Maintains objectivity, with key assumptions explicitly identified.
– 4: Distinguishes between facts and opinions.
– 5: Is internally consistent in its analysis and conclusions.
– 6: Provides sufficient information to enable readers to critique the conclusions.
– 7: Identifies key risk factors associated with the recommendation.
– 8: Discloses conflicts of interest that may affect objectivity.

Answer 23

Key Takeaways
– An effective research report ensures clarity, objectivity, and transparency while addressing risks and uncertainties.
– It empowers readers to evaluate the quality of intrinsic value estimates and assess the validity of the conclusions.

Question 24

Format of a Research Report

1- The Table of Contents
– Organizes the report structure.
– Essential for long research reports to help readers navigate the content.

2- The Summary and Investment Conclusions
– Provides a concise overview of key points and investment recommendations.
– Allows readers to grasp the overall message without reading the entire report.

3- The Business Summary
– Details the company’s operations, industry, and competitive landscape.
– Helps readers understand the company’s current position and strategic outlook.

4- The Risk Section
– Highlights potential risks that could impact the investment.
– Explains what could go wrong and how those risks may affect valuation or performance.

5- The Valuation Section
– Goes beyond the bottom-line valuation figure.
– Describes the valuation model used and key input assumptions that support the analysis.

6- Historical Data
– Provides factual data to substantiate the conclusions.
– Ensures the report is well-supported with evidence and trends.

Question 25

CFA Institute Standards of Professional Conduct Pertaining to Research Reports 1- Standard I(B): Independence and Objectivity -- Members and Candidates must maintain independence and objectivity in their professional activities. -- They must not offer, solicit, or accept any gift or benefit that could compromise their independence or objectivity. 2- Standard I(C): Misrepresentation -- Members and Candidates must avoid knowingly making any misrepresentations in investment analysis, recommendations, or other professional activities. 3- Standard V(A): Diligence and Reasonable Basis -- V(A)1: Members and Candidates must exercise diligence, independence, and thoroughness in their investment analysis and actions. -- V(A)2: They must have a reasonable and adequate basis for their recommendations, supported by appropriate research and investigation. 4- Standard V(B): Communication with Clients and Prospective Clients -- V(B)1: Members and Candidates must disclose to clients the principles of their investment processes and any material changes. -- V(B)2: They must use reasonable judgment in identifying factors important to investment decisions and include these in communications. -- V(B)3: Members and Candidates must distinguish between fact and opinion in their analyses and recommendations. 5- Standard V(C): Record Retention -- Members and Candidates must develop and maintain records to support their investment-related communications, analysis, and actions.

Question 26

Quiz - Understanding Mispricing: Difference Between Intrinsic Value and Market Price 1- Overview of the Question The question asks which source of perceived mispricing active investment managers attempt to identify, based on Statement 2. The goal is to determine the difference that leads to mispricing concerns. 2- Correct Answer A: Intrinsic value and market price. 3- Explanation 1- Understanding Mispricing: -- Mispricing occurs when there is a gap between the true intrinsic value of a security and its market price. -- Active managers aim to capture positive alpha by identifying and exploiting this gap. 2- Why A is Correct: -- 1- Intrinsic value refers to the "true" but unobservable value of a security, determined through fundamental analysis. -- 2- Market price is the observable price at which the security is traded in the market. -- 3- Mispricing results from the gap between true intrinsic value (unobservable) and the market price. This is the foundation of alpha generation for active managers. 3- Why B is Incorrect: -- 1- The estimated intrinsic value is an analyst's subjective approximation of the true intrinsic value. -- 2- While analysts may use estimates to identify potential mispricing, the mispricing itself arises from the deviation between true intrinsic value and market price, not from the estimated value. 4- Why C is Incorrect: -- 1- Comparing intrinsic value and estimated intrinsic value highlights potential analyst errors, which is unrelated to the mispricing active managers exploit. -- 2- This does not address the gap between true intrinsic value and market price, which is the focus of the question.

Answer 26

Key Takeaways -- Mispricing refers to the difference between intrinsic value and market price. -- Active managers aim to exploit this gap to generate positive alpha. -- True intrinsic value is unobservable, but its deviation from market price is the foundation of mispricing analysis. -- Answer A reflects this relationship, making it the correct choice.Key Takeaways -- Mispricing is defined as the gap between intrinsic value (unobservable) and market price (observable). -- Active investment managers generate positive alpha by identifying and exploiting this gap. -- The correct answer, A, reflects this relationship, while B and C misinterpret the focus of mispricing.

Question 27

Quiz - Understanding Measures of Value: Relevance for Core Equity Fund 1- Overview of the Question The question asks which measure of value is most relevant for the core equity fund described in Statement 4, focusing on companies expected to generate significant future free cash flows from core operations. 2- Correct Answer C: Going-concern value. 3- Explanation 1- Understanding Going-Concern Value: -- Going-concern value reflects a company's ability to continue operating and generating future cash flows. -- For companies in a core equity fund, future free cash flow from operations is a primary consideration, making this measure of value most relevant. 2- Why C is Correct: -- 1- The fund focuses on financially sound companies with sustainable business operations and the ability to generate future free cash flows. -- 2- The emphasis on future operations aligns directly with the going-concern value, which assumes the company will continue to operate indefinitely. 3- Why A is Incorrect: -- 1- Liquidation value is the value realized by selling off a company's assets, assuming operations cease. -- 2- This measure is not relevant for well-capitalized companies with strong future cash flow prospects, as they are not expected to be liquidated. 4- Why B is Incorrect: -- 1- Investment value is specific to a particular investor and reflects unique factors such as synergies or investor-specific objectives. -- 2- While investment value may be used in certain contexts, it is not the focus for selecting companies in a core equity fund based on their general ability to generate future cash flows.

Question 28

Market prices reflect the expectations of investors about the future performance of companies. The analyst can evaluate the reasonableness of the expectations implied by the market price by comparing the market’s implied expectations to his own expectations. This process assumes a valuation model, as discussed in the text.

Question 29

Quiz - Appropriateness of Asset-Based Valuation for Companies 1- Overview of the Question The question asks which company in Exhibit 1 is most appropriate for an asset-based valuation approach, based on Lacroix's notes. 2- Correct Answer B: NCF. 3- Explanation 1- Understanding Asset-Based Valuation: -- Asset-based valuation is most suitable for companies whose value is closely tied to their tangible assets, such as natural resource companies. -- The value is determined by applying the current market price of commodities to the proven reserves of the company, with adjustments for extraction costs. 2- Why B is Correct (NCF): -- 1- NCF is a pure-play natural resource company, deriving revenues from commodities such as iron, copper, zinc, and nickel. -- 2- Its assets can be valued using an asset-based approach by assessing the market price of its reserves and applying necessary discounts for extraction. 3- Why A is Incorrect (FTK): -- 1- FTK, a forest products company, also derives a significant portion of revenue from media operations, which are intangible in nature. -- 2- The mixed nature of FTK's revenue sources makes asset-based valuation less appropriate. 4- Why C is Incorrect (PSH): -- 1- PSH is a manufacturing company involved in machinery and industrial operations, which rely heavily on operational profitability rather than tangible asset valuation. -- 2- Asset-based valuation is generally inappropriate for such companies.

Question 30

Quiz - Identifying Overvalued Stocks Based on Holland's Criteria 1- Overview of the Question The question asks which company or companies from Exhibit 1 are most likely to be considered overvalued according to Holland's criteria. 2- Correct Answer A: FTK only. 3- Explanation 1- Holland's Overvaluation Criteria: -- A stock is overvalued if its P/E ratio is at least two standard deviations above the mean index P/E ratio. -- The mean index P/E ratio is 8.50, and the standard deviation is 0.20. -- The overvaluation threshold is calculated as: Threshold = Mean P/E + (2 × Standard Deviation) = 8.50 + (2 × 0.20) = 8.90. 2- Calculating P/E Ratios for the Stocks: -- 1- PSH: Share Price = Market Value ÷ Shares Outstanding = $620m ÷ 15m = $41.33. P/E Ratio = Share Price ÷ EPS = $41.33 ÷ $4.96 = 8.33. Below the threshold, not overvalued. -- 2- FTK: Share Price = Market Value ÷ Shares Outstanding = $1,240m ÷ 38m = $32.63. P/E Ratio = Share Price ÷ EPS = $32.63 ÷ $3.64 = 8.96. Above the threshold, overvalued. -- 3- NCF: Share Price = Market Value ÷ Shares Outstanding = $900m ÷ 20m = $45.00. P/E Ratio = Share Price ÷ EPS = $45.00 ÷ $5.15 = 8.74. Below the threshold, not overvalued. 3- Why A is Correct: -- FTK is the only stock with a P/E ratio above the overvaluation threshold of 8.90. 4- Why B is Incorrect: -- NCF's P/E ratio is 8.74, below the threshold. It is not overvalued. 5- Why C is Incorrect: -- PSH and NCF both have P/E ratios below the threshold. FTK is the only stock meeting the overvaluation criteria.

Question 31

Quiz - Identifying Companies Likely to Reflect a Conglomerate Discount 1- Overview of the Question The question asks which company is most likely to have a share price reflecting a conglomerate discount, based on the provided information. 2- Correct Answer A: FTK. 3- Explanation 1- Understanding Conglomerate Discounts: -- A conglomerate discount is applied when a company operates in multiple, unrelated sectors. -- Investors may perceive that conglomerates allocate capital less efficiently or fail to capture synergies compared to companies focused on a single sector. 2- Why A is Correct (FTK): -- 1- FTK derives 30% of its revenues from a media division, which is unrelated to its primary business of forest products. -- 2- This diversification across unrelated sectors makes FTK more likely to experience a conglomerate discount, as investors may view its capital allocation as inefficient. 3- Why B is Incorrect (NCF): -- NCF is a natural resource company with revenues tied to mining operations (iron and non-ferrous metals). -- It does not operate in unrelated sectors, making a conglomerate discount unlikely. 4- Why C is Incorrect (PSH): -- PSH is a manufacturing company producing machinery with applications in various industries. -- While the products are used across diverse sectors, PSH itself is not involved in multiple, unrelated businesses.

Question 32

5.2 Discount Dividend Valuation

Answer 32

-- Compare dividends, free cash flow, and residual income as inputs to discounted cash flow models and identify investment situations for which each measure is suitable. -- Calculate and interpret the value of a common stock using the dividend discount model (DDM) for single and multiple holding periods. -- Calculate the value of a common stock using the Gordon growth model and explain the model’s underlying assumptions. -- Calculate the value of non-callable fixed-rate perpetual preferred stock. -- Describe strengths and limitations of the Gordon growth model and justify its selection to value a company’s common shares. -- Calculate and interpret the implied growth rate of dividends using the Gordon growth model and current stock price. -- Calculate and interpret the present value of growth opportunities (PVGO) and the component of the leading price-to-earnings ratio (P/E) related to PVGO. -- Calculate and interpret the justified leading and trailing P/Es using the Gordon growth model. -- Estimate a required return based on any DDM, including the Gordon growth model and the H-model. -- Evaluate whether a stock is overvalued, fairly valued, or undervalued by the market based on a DDM estimate of value. -- Explain the growth phase, transition phase, and maturity phase of a business. -- Explain the assumptions and justify the selection of the two-stage DDM, the H-model, the three-stage DDM, or spreadsheet modeling to value a company’s common shares. -- Describe terminal value and explain alternative approaches to determining the terminal value in a DDM. -- Calculate and interpret the value of common shares using the two-stage DDM, the H-model, and the three-stage DDM. -- Explain the use of spreadsheet modeling to forecast dividends and to value common shares. -- Calculate and interpret the sustainable growth rate of a company and demonstrate the use of DuPont analysis to estimate a company’s sustainable growth rate.

Question 33

Broad Steps in Discounted Cash Flow (DCF) Analysis 1- Defining Cash Flows -- Identify the appropriate cash flows for valuation (e.g., dividends, free cash flow to equity, or free cash flow to the firm). 2- Forecasting Cash Flows -- Project the future cash flows based on assumptions about the company’s growth, profitability, and other key factors. 3- Choosing a Discount Rate Methodology -- Determine the appropriate discount rate to use, such as the cost of equity or the weighted average cost of capital (WACC). 4- Estimating a Discount Rate -- Calculate the specific discount rate that reflects the riskiness of the cash flows and the company’s cost of capital. Dividend Discount Models (DDMs) -- In cases where dividends are considered the appropriate measure of cash flows, DCF models are referred to as Dividend Discount Models (DDMs).

Question 34

Streams of Expected Cash Flows Stocks can be valued using different streams of cash flows: dividends, free cash flows, or residual income. This section focuses on dividends. 1- Dividends Overview -- Stock investors typically receive returns in the form of dividends. -- Earnings not distributed as dividends are reinvested earnings, expected to improve the company’s profitability over time. -- Dividends are generally less volatile than earnings, making dividend discount models (DDM) less sensitive to short-term earnings fluctuations and better suited for estimating long-term intrinsic value. 2- Reasons for Dividend Policies -- Companies may choose not to pay dividends: --- If they are unprofitable and lack cash to distribute. --- If they are highly profitable but prefer to reinvest cash into operations for growth. -- In recent decades, dividend-paying companies have declined as share repurchases have become more common. 3- Valuing Non-Dividend-Paying Companies -- DDM can still be used to value companies not currently paying dividends if future dividend timing and amounts are predictable. -- However, forecasting future dividends for non-dividend-paying firms is challenging. 4- Conditions for Using DDM The DDM is most appropriate when: -- The company pays dividends. -- The dividend policy aligns with the company’s profitability. -- The investor holds a non-control perspective (e.g., minority shareholder).

Question 35

Non-Control Perspective 1- Definition -- Investors with a non-control perspective are content to passively receive dividends rather than actively influencing a company's dividend policies or decision-making. 2- Relevance -- This perspective is typical of minority shareholders who do not seek to alter corporate policies but rely on management's judgment regarding dividend distributions.

Answer 35

Key Takeaways -- The non-control perspective aligns with valuation approaches like the Dividend Discount Model (DDM), which assumes dividends are the primary return to investors. -- Investors focus on receiving dividends as a reflection of the company's profitability and policy decisions.

Question 36

Free Cash Flows A company's cash flows are generated and utilized through operations, investments, and financing activities. For a going concern, cash flows are essential for reinvestment and new investments. Different measures of cash flows include: 1- Types of Cash Flows -- Cash Flow from Operations (CFO): Cash generated through day-to-day activities, including buying and selling products or services. -- Free Cash Flow to the Firm (FCFF): Cash flows available to all capital providers (bondholders and stockholders). --- Calculated as CFO minus capital expenditures. -- Free Cash Flow to Equity (FCFE): Cash flows available to shareholders only. --- FCFE ≈ FCFF - debt payments + funds raised from new debt issues. 2- When to Use Cash Flow-Based Valuation Models Cash flow-based models, such as those using FCFF or FCFE, are most appropriate when: -- The company is not dividend-paying. -- The company pays dividends that differ significantly from FCFE. -- Projected free cash flows align with the company’s profitability. -- The investor holds a control perspective or views the company as a potential merger target. 3- Limitations of Free Cash Flow Models -- Intense capital demands: Free cash flow models may undervalue companies reinvesting all cash flows into projects. -- Choice between FCFF and FCFE: --- FCFF is preferred when significant changes in capital structure are expected. --- FCFE is specific to shareholders and may not account for lender-related cash flows.

Answer 36

FCFE = CFO - FC_INV + Net debt (Net borrowing)

Question 37

Residual Income 1- Definition -- Residual income represents a company's earnings in excess of the investors' required return on common stock. -- The required rate of return reflects the opportunity cost for investors compared to other investments with equivalent risk. -- Stock Value Calculation: --- A stock's value is determined as: ---- Book value per share + Present value of expected future residual earnings. 2- Applications of Residual Income Models -- This approach can be used for both dividend-paying and non-dividend-paying stocks. -- It focuses on profitability relative to opportunity cost. 3- When to Use the Residual Income Approach This method is especially suitable when: -- The company does not pay dividends (as an alternative to free cash flow models). -- The company has negative expected free cash flows.

Answer 37

Key Takeaways -- Residual income provides a flexible valuation method that accounts for profitability exceeding required returns. -- It is particularly valuable for non-dividend-paying companies or firms with insufficient or negative free cash flows.

Question 38

Dividend Policies and Rationales 1- Reasons for Not Paying Dividends -- Companies may refrain from paying dividends due to: --- Lack of profitability: They have no cash to distribute. --- Profitability with reinvestment focus: Highly profitable companies may choose not to pay dividends to retain cash for reinvestment in growth opportunities. 2- Rationale for Paying Dividends -- Mature, profitable companies often pay consistent dividends because: --- They have limited investment opportunities. --- Returning cash to shareholders is viewed as a better use of funds.

Question 39

Example: Calculating Residual Income 1- Scenario -- Shareholders' initial investment: $150 million. -- Required rate of return: 6%. -- Company earns: $10 million during the year. 2- Calculations -- Required Return: --- $150 million × 6% = $9 million. -- Residual Income: --- $10 million (earnings) − $9 million (required return) = $1 million. 3- Conclusion -- Residual income represents the economic gain to shareholders, in this case, $1 million, which is the surplus after meeting the required return on investment.

Question 40

Residual Income Model 1- Formula for Stock’s Value -- Stock's value = Book value per share + Present value of expected future residual earnings. 2- Book Value Per Share -- Calculated as: --- Common stockholders’ equity ÷ Number of common shares outstanding.

Question 41

Expression for a Single Holding Period 1- Formula for Stock Value over One-Year Holding Period -- "V0 = (D1 + P1) ÷ (1 + r)^1". 2- Explanation of Variables -- D1: Dividend received at the end of the holding period. -- P1: Selling price of the stock at the end of the holding period. -- r: Required rate of return.

Question 42

Expression for Multiple Holding Periods 1- Formula for Stock Value Over Multi-Year Holding Period -- "V0 = T∑_t=1 (Dt ÷ (1 + r)^t) + (Pn ÷ (1 + r)^n)". 2- Explanation of Variables -- Dt: Dividends received at the end of period t. -- Pn: Selling price of the stock at the end of the holding period (n years). -- r: Required rate of return. -- n: Total number of holding periods. -- t: Time period for each dividend payment, ranging from 1 to n.

Question 43

Dividend Discount Model (DDM) for Infinite Dividends 1- Overview of the Concept -- The DDM calculates the value of a stock as the present value of all future dividends. If dividends are assumed to continue indefinitely, the following formula applies. 2- Formula -- Infinite Dividend Discount Model formula: --- "V0 = ∞∑_t=1 [Dt ÷ (1 + r)^t]" 3- Explanation of Variables -- V0: Current value of the stock. -- ∞∑_t=1: Summation from t=1 to infinity. -- Dt: Dividend expected in time period t. -- r: Required rate of return or discount rate. 4- Simplifications to the DDM -- Because forecasting infinite dividends is challenging, two common simplifications are used: --- 1- Assume future dividends follow a growth pattern: ---- Examples: Constant growth, two-stage growth, or three-stage growth. --- 2- Forecast a finite number of dividends and a terminal value: ---- The forecast horizon depends on the predictability or visibility of earnings.

Question 44

Gordon Growth Model 1- Overview of the Concept -- The Gordon Growth Model assumes that dividends grow at a constant rate indefinitely. This allows the calculation of a stock's present value based on the growth of future dividends. 2- Formula -- Gordon Growth Model formula: --- "V0 = [D0(1 + g) ÷ (r - g)] = [D1 ÷ (r - g)]" 3- Explanation of Variables -- V0: Present value of the stock. -- D0: Dividend paid in the current period. -- D1: Dividend expected in the next period (D1 = D0(1 + g)). -- r: Required rate of return. -- g: Constant dividend growth rate. 4- Assumptions and Conditions -- The model assumes that the required rate of return (r) is greater than the growth rate (g), ensuring a finite value. If r ≤ g, the value of the stock would be infinite or undefined. -- Both r and g should reflect long-term expectations for accuracy. Small changes in these parameters can lead to significantly different valuations. 5- Suitability -- The model is most appropriate when: --- Dividends exhibit a stable and predictable growth pattern. --- The relationship between profitability and dividends is consistent.

Question 45

Example: Gordon Growth Model 1- Problem Description -- A company’s most recent quarterly dividend (D0) is $0.24. Dividends are expected to grow at a constant rate of 5% per year (g = 0.05). The required return on equity (r) is 7% (0.07). -- Calculate the stock's current value (V0) using the Gordon Growth Model. 2- Solution -- First, calculate the annualized dividend for the next period (D1): --- "D1 = D0(1 + g)" --- "D1 = (4 × 0.24)(1.05)" --- "D1 = 1.05". -- Then, use the Gordon Growth Model formula to find the present value (V0): --- Formula: "V0 = D1 ÷ (r - g)" --- Calculation: "V0 = 1.05 ÷ (0.07 - 0.05)" --- Result: "V0 = 50.40".

Question 46

Example: Noncallable Fixed-Rate Perpetual Preferred Stock 1- Problem Description -- A noncallable 5% fixed-rate perpetual preferred stock has a par value of $25 per share. The required return on this issue (r) is 5.7% (0.057). -- Estimate the value of this issue (V0). 2- Solution -- Calculate the annual dividend (D1): --- Formula: "D1 = Dividend rate × Par value" --- Calculation: "D1 = 0.05 × 25" --- Result: "D1 = 1.25". -- Use the valuation formula for a perpetual stock: --- Formula: "V0 = D1 ÷ (r - g)" --- Substitution: "V0 = 1.25 ÷ (0.057 - 0)" --- Result: "V0 = 21.93".

Question 47

The Links Among Dividend Growth, Earnings Growth, and Value Appreciation 1- Overview of the Concept -- The Gordon growth model assumes a constant, proportional relationship between earnings and dividends, driven by a fixed payout ratio. 2- Key Relationships -- "g" represents both the dividend growth rate and the rate of capital appreciation. -- The stock's forward dividend yield, expressed as "D1 ÷ P0", remains constant. -- This constancy arises because both dividends and price grow at the same rate ("g").

Question 48

Share Repurchases 1- Overview of the Concept -- Share repurchases are becoming increasingly popular in developed markets and are often used alongside or in place of cash dividends. They have distinct features compared to cash dividends. 2- Key Features of Share Repurchases -- Share repurchases reduce the number of shares outstanding. -- Corporations feel a stronger commitment to maintaining dividend rates compared to share repurchase levels. -- Cash dividends are predictable in both amount and timing, while share repurchases are opportunistic and harder to predict. -- Share repurchases should have no impact on ongoing shareholders if the repurchases are made at market prices.

Question 49

Present Value of Growth Opportunities (PVGO) 1- Overview of the Concept -- The value of a stock can be expressed as the sum of two components: the value without earnings reinvestment and the present value of growth opportunities (PVGO). This separates the value derived from growth from the baseline no-growth value. 2- Formula -- Present value of the stock: "V0 = (E1 ÷ r) + PVGO" --- Where: --- V0: Current stock value. --- E1: Earnings per share expected in the next period. --- r: Required rate of return. --- PVGO: Present value of future growth opportunities. 3- Explanation of Components -- (E1 ÷ r): Represents the no-growth value per share, assuming constant EPS (E1) indefinitely without reinvestment. -- PVGO: Reflects the net present value of projects where earnings are reinvested, assuming returns exceed the opportunity cost of funds. 4- Key Implications -- Earnings growth influences shareholder wealth. --- If earnings return exceeds the opportunity cost (r), shareholder wealth increases as value is generated from positive NPV projects. --- Conversely, growth with returns below the cost of funds reduces value.

Answer 49

Key Takeaways -- PVGO highlights the importance of reinvestment decisions and their impact on shareholder value, distinguishing between no-growth intrinsic value and growth-driven value.

Question 50

Price-to-Earnings Ratio (P/E) and PVGO 1- Overview of the Concept -- The present value of growth opportunities (PVGO) is a key driver of a company’s valuation. Companies without positive NPV projects are considered no-growth companies and should distribute all earnings as dividends. PVGO reflects the value of potential growth opportunities or real options. 2- Formula for P/E Ratio with PVGO -- "P0 ÷ E1 = (1 ÷ r) + (PVGO ÷ E1)" 3- Explanation of Variables -- P0: Current stock price. -- E1: Expected earnings in the next period. -- r: Required rate of return. -- PVGO: Present value of growth opportunities. 4- Key Insights -- The formula separates the P/E ratio into two components: --- (1 ÷ r): Represents the P/E ratio of a no-growth company. --- (PVGO ÷ E1): Reflects the contribution of growth opportunities to the P/E ratio. -- Growth opportunities are valuable when the projects offer returns exceeding the cost of capital, while no-growth companies derive value only from existing earnings.

Answer 50

Key Takeaways -- PVGO helps distinguish between intrinsic value from earnings and value added by growth opportunities. -- The P/E ratio highlights the proportion of a company’s valuation attributable to growth.

Question 51

Example: Calculating PVGO and Percentage of Market Value Attributable to Growth 1- Problem Overview -- A company’s earnings per share (E1) is expected to be $0.85. The required rate of return (r) is 9.25%, and the current price of the stock (P0) is $18.60. The task is to determine what percentage of the stock’s market value is attributable to growth opportunities. 2- Formula and Solution -- Step 1: Calculate the no-growth value per share. --- "No-growth value = E1 ÷ r = 0.85 ÷ 0.0925 = 9.19" -- Step 2: Use the equation to find PVGO. --- "P0 = No-growth value + PVGO" --- "18.60 = 9.19 + PVGO" --- "PVGO = 9.41" -- Step 3: Calculate the percentage of market value attributable to growth. --- "Percentage = PVGO ÷ P0 = 9.41 ÷ 18.60 ≈ 51%" 3- Conclusion -- 51% of the stock’s market value is derived from growth opportunities, while the remaining 49% is attributable to current earnings without growth.

Question 52

Price-to-Earnings (P/E) Ratios Derived from the Gordon Growth Model 1- Overview of the Concept -- The Gordon growth model can be used to calculate the justified P/E ratio and determine the implied earnings growth rate from the stock price. P/E ratios can be calculated on a leading (forward) or trailing basis. -- Leading P/E uses forecasted earnings (E1), while trailing P/E uses the most recent earnings (E0). 2- Formulas (DDM) -- Leading (Justified forward) P/E ratio: --- Formula: "Leading P/E = P0 ÷ E1 = D1 ÷ E1 ÷ (r - g) = (1 - b) ÷ (r - g)" --- Explanation: "b" represents the retention rate, and (1 - b) is the dividend payout ratio. -- Trailing P/E ratio: --- Formula: "Trailing P/E = P0 ÷ E0 = D0(1 + g) ÷ E0 ÷ (r - g) = (1 + g)(1 - b) ÷ (r - g)" --- Explanation: "D0" is the dividend for the current period, and growth (g) adjusts dividends to the next period. 3- Explanation of Variables -- P0: Current stock price. -- E0: Current earnings per share. -- E1: Forecasted earnings per share. -- D0: Current dividend. -- D1: Expected dividend (D1 = D0(1 + g)). -- b: Retention rate. -- (1 - b): Dividend payout ratio. -- r: Required rate of return. -- g: Growth rate of dividends.

Answer 52

Key Insights -- Higher retention rates (b) lead to lower P/E ratios, assuming other factors remain constant. -- The P/E ratio is highly sensitive to differences between "r" and "g." -- Trailing P/E ratios are typically higher than leading P/E ratios due to the adjustment for growth (1 + g).

Question 53

Gordon Growth Model: Estimating the Required Rate of Return 1- Overview of the Concept -- The Gordon Growth Model can be rearranged to calculate a stock's required rate of return (r) by solving for it. This approach uses dividend expectations, the stock's price, and the growth rate of dividends. 2- Formula -- Formula for the required rate of return: --- "r = (D1 ÷ P0) + g" 3- Explanation of Variables -- r: Required rate of return. -- D1: Expected dividend in the next period. -- P0: Current stock price. -- g: Constant dividend growth rate. 4- Application and Assumptions -- The formula assumes that dividends grow at a constant rate (g) indefinitely. -- It also assumes that the relationship between dividends, stock price, and growth remains consistent over the long term.

Question 54

Multistage Growth Phases 1- Overview of the Concept -- The Gordon Growth Model's assumption of a single constant growth rate is often unrealistic. Many companies experience growth in distinct stages: growth, transition, and maturity. 2- Growth Phase -- Companies in this phase exhibit high growth and profit margins. -- Free cash flows are often negative due to high investment needs. -- Dividends are typically minimal or nonexistent. 3- Transition Phase -- Growth slows as competition increases, and profit margins decrease. -- Capital requirements decline, resulting in positive free cash flows and growing dividends. 4- Mature Phase -- Investments earn returns equivalent to the opportunity cost of capital. -- Growth rates stabilize, and dividend payout ratios become predictable. -- Companies in this phase are best suited for valuations using the Gordon Growth Model.

Question 55

Two-Stage Dividend Discount Model 1- Overview of the Concept -- This model assumes a company experiences a short-term phase of supernormal growth, denoted by gs, before transitioning to a long-term stable growth phase, denoted by gL. -- The total value of the company today (V0) includes the present value of dividends during the high-growth phase and the present value of the terminal value at the end of the high-growth period. 2- Formula for Present Value of the Stock (V0) -- Formula: --- "V0 = T∑_t=1 [D0(1 + gs)^t ÷ (1 + r)^t] + [Vn ÷ (1 + r)^n]" -- Where the terminal value (Vn) is: --- "Vn = [D0(1 + gs)^n(1 + gL)] ÷ (r - gL)" 3- Explanation of Variables -- V0: Present value of the stock. -- D0: Dividend paid in the current period. -- gs: Short-term growth rate during the high-growth phase. -- gL: Long-term stable growth rate after the high-growth phase. -- r: Required rate of return. -- T∑_t=1: Summation for dividends during the high-growth phase (t=1 to n). -- Vn: Terminal value at the end of the high-growth period. 4- Terminal Value Approaches -- The terminal value can be calculated using the Gordon Growth Model or estimated through a price multiple. -- The Gordon Growth Model assumes dividends grow at gL indefinitely. 5- Applicability -- This model is suitable for companies with a temporary phase of high growth, such as firms with expiring patents or first-mover advantages. -- More complex models can incorporate different discount rates for cash flows during different phases.

Answer 55

Key Takeaways -- The two-stage dividend discount model divides the valuation into a high-growth phase and a mature phase. -- The terminal value (Vn) significantly influences the valuation, especially for longer high-growth periods. -- The model uses a single discount rate (r) across all cash flows unless adapted for varying rates.

Question 56

Valuing a Non-Dividend-Paying Company 1- Overview of the Concept -- The two-stage method can be applied to value a company that does not currently pay dividends. In this case, dividends are assumed to be zero during the initial period, simplifying the valuation process. 2- Key Considerations -- The primary challenge is predicting when the company will initiate dividends and estimating the initial dividend amount.

Question 57

Example: Two-Stage Dividend Discount Model Starting with Zero Dividends 1- Problem Setup -- A company currently pays no dividends. -- It will begin paying an annual dividend of $2.00 in five years. -- After dividends begin, they are expected to grow at a rate of 5% per year. -- The required rate of return is 11%. 2- Objective -- Estimate the current stock value using the two-stage dividend discount model. 3- Solution and Formula -- Two-Stage Dividend Discount Model formula: --- "V0 = [Dn+1 ÷ ((1 + r)^n * (r - g))]" 4- Substitution and Calculation -- Inputs: --- Dn+1 = $2.00 (first dividend payment). --- r = 11% or 0.11 (required rate of return). --- g = 5% or 0.05 (growth rate after dividends start). --- n = 5 years (time until first dividend payment). -- Calculation: --- "V0 = 2.00 ÷ [(1.11)^4 * (0.11 - 0.05)] = 2.00 ÷ (1.4641 * 0.06) = 21.96"

Question 58

Example: Basic Two-Stage Dividend Discount Model (DDM) 1- Problem Setup -- Two analysts, Samuel Laviolette and Catherine Blanc, use the two-stage growth model to value Bloemfontein Minerals (BFM). -- Key inputs: --- BFM just paid an annual dividend of €0.80, based on €2.00 of earnings per share. --- A new mineral discovery allows the company to increase its dividend by 15% annually for the next three years. --- BFM's managers will maintain a 40% payout ratio over the long run. --- Investors require a 9% return on BFM shares. -- Laviolette uses the Gordon growth model for terminal value with a 6% long-term growth rate. -- Blanc applies a 13.5 trailing P/E ratio to terminal earnings. 2- Formula and Solution -- Both analysts calculate the value of dividends over the next three years: --- "Dividend Value = [(0.80)(1.15)/(1.09)] + [(0.80)(1.15)^2/(1.09)^2] + [(0.80)(1.15)^3/(1.09)^3] = 2.674" -- Laviolette's terminal value (Vn): --- Formula: "Vn = [(0.80)(1.15)^3(1.06)] / (0.09 - 0.06)" --- Substitution: "Vn = 42.990" --- Present value of Vn: "42.990 / (1.09)^3 = 33.194" --- Total value: "2.674 + 33.194 = 35.87" -- Blanc's terminal value (Vn): --- Formula: "Vn = [(0.80)(1.15)^3 / 0.40] * 13.5" --- Substitution: "Vn = 41.064" --- Present value of Vn: "41.064 / (1.09)^3 = 31.656" --- Total value: "2.674 + 31.656 = 34.38"

Question 59

H-Model 1- Overview of the Concept -- The H-model is an enhancement of the basic two-stage model. It assumes a smoother transition from a period of high growth (supernormal growth) to a long-term growth rate by gradually decreasing the growth rate over a specified time period. -- The model uses all inputs from the two-stage model but adds a variable, H, to represent the half-life of the supernormal growth period, which spans 2H years. 2- Formula -- H-model formula: --- "V0 = [D0(1 + gL) ÷ (r - gL)] + [D0H(gS - gL) ÷ (r - gL)]" 3- Explanation of Variables -- V0: Present value of the stock. -- D0: Current dividend per share. -- gS: Initial high (supernormal) growth rate. -- gL: Long-term sustainable growth rate. -- r: Required rate of return. -- H: Half-life of the supernormal growth period (H = half the number of years for the transition). 4- Key Characteristics and Suitability -- The H-model provides an approximate value for discounting future dividends when a company transitions gradually to a long-term growth rate. -- It is not suitable when the supernormal growth period is long or when there is a significant difference between gS and gL, as the approximation becomes less accurate in such cases.

Question 60

H-Model 1- Overview of the Concept -- The H-model is an enhancement of the basic two-stage model. It assumes a smoother transition from a period of high growth (supernormal growth) to a long-term growth rate by gradually decreasing the growth rate over a specified time period. -- The model uses all inputs from the two-stage model but adds a variable, H, to represent the half-life of the supernormal growth period, which spans 2H years. 2- Formula -- H-model formula: --- "V0 = [D0(1 + gL) ÷ (r - gL)] + [D0H(gS - gL) ÷ (r - gL)]" 3- Explanation of Variables -- V0: Present value of the stock. -- D0: Current dividend per share. -- gS: Initial high (supernormal) growth rate. -- gL: Long-term sustainable growth rate. -- r: Required rate of return. -- H: Half-life of the supernormal growth period (H = half the number of years for the transition). 4- Key Characteristics and Suitability -- The H-model provides an approximate value for discounting future dividends when a company transitions gradually to a long-term growth rate. -- It is not suitable when the supernormal growth period is long or when there is a significant difference between gS and gL, as the approximation becomes less accurate in such cases.

Answer 60

Key Takeaways -- The H-model addresses the abrupt transition issue in the two-stage model by introducing a gradual change in growth rates. -- It offers a simpler, approximate approach to valuation compared to more complex models.

Question 61

Example: Two-Stage Dividend Discount Valuation using the H-Model 1- Problem Setup -- Bloemfontein Minerals (BLM) has the following inputs: --- Most recent annual dividend (D0): €0.80. --- Dividends are initially expected to grow at 15% and then decline linearly to a long-term growth rate of 6% over three years. --- Required rate of return (r): 9%. 2- Formula Application -- H-Model formula: --- "V0 = [D0(1 + gL) ÷ (r - gL)] + [D0H(gS - gL) ÷ (r - gL)]" --- Substituting the values: --- "V0 = [(0.80)(1.06) ÷ (0.09 - 0.06)] + [(0.80)(1.5)(0.15 - 0.06) ÷ (0.09 - 0.06)]" 3- Solution Steps -- First Component: "0.80(1.06) ÷ (0.09 - 0.06) = 28.27". -- Second Component: "0.80(1.5)(0.15 - 0.06) ÷ (0.09 - 0.06) = 3.60". -- Summing both components: "V0 = 28.27 + 3.60 = 31.87". 4- Explanation of Results -- The estimated current stock value using the H-Model is €31.87. -- The H-Model valuation is lower compared to the basic two-stage model because the H-Model assumes that growth rates decline linearly rather than remaining constant during the high-growth phase.

Answer 61

The "H" represents half the time (in years) over which the dividend growth rate declines from its initial high growth rate to the long-term stable growth rate. Therefore: 3/2 = 1.5

Question 62

Three-Stage Dividend Discount Models (DDMs) 1- Overview of the Concept -- The three-stage DDM is designed to model a company's dividend growth through three distinct phases, capturing various growth patterns over time. 2- Versions of the Three-Stage DDM -- 1- General Version: --- Assumes three distinct stages of growth, with each stage having a constant growth rate. -- 2- H-Model-Like Version: --- The growth rate in the middle stage declines linearly to the mature growth rate in the third stage. --- The second and third stages resemble an H-Model structure.

Question 63

Example: Three-Stage Dividend Discount Model with Declining Growth Rates in Stage 2 1- Problem Statement -- A company’s most recent annual dividend is €0.80, with the following growth expectations: --- Dividends are expected to grow at 15% annually for the next three years (Stage 1). --- Dividends will transition to a long-term growth rate of 4% (Stage 3), declining linearly over ten years during Stage 2. --- The required rate of return (r) is 8%. 2- Solution Steps Stage 3 (Terminal Value): -- Formula for terminal value (V3): --- "V3 = [D3(1 + gL) ÷ (r - gL)] + [D3 * H * (gs - gL) ÷ (r - gL)]" --- Where: --- D3 = Dividend at the end of Stage 1. --- gL = Long-term growth rate (4%). --- gs = Growth rate at the end of Stage 1 (15%). --- H = Half-life of transition (10 ÷ 2 = 5). Calculations for V3: --- D3 = 0.80 * (1.15)^3 = 1.157. --- V3 = [1.157 * (1.04) ÷ (0.08 - 0.04)] + [1.157 * 5 * (0.15 - 0.04) ÷ (0.08 - 0.04)] = 48.36. Total Value (V0): -- Formula: --- "V0 = Σ {Dt ÷ (1 + r)^t} for t = 1 to n + V3 ÷ (1 + r)^n." --- Summing dividends for Stage 1 and Stage 3's discounted terminal value: --- V0 = [0.80(1.15) ÷ 1.08] + [0.80(1.15)^2 ÷ (1.08)^2] + [0.80(1.15)^3 ÷ (1.08)^3] + [48.36 ÷ (1.08)^3]. Final Calculation: --- V0 = 41.12.

Question 64

Estimating a Required Return Using Any DDM 1- Overview of the Concept -- Dividend Discount Models (DDMs) can be rearranged to estimate the required rate of return (r) implied by a stock’s current price. Different DDMs require different methods to solve for r. 2- Formula for Required Return Gordon Growth Model: -- Formula: "r = (D1 ÷ P0) + g" --- D1: Dividend expected in the next period. --- P0: Current stock price. --- g: Constant dividend growth rate. H-Model: -- Formula: "r = [(D0 ÷ P0) * (1 + gL + H(gs - gL))] + gL" --- D0: Most recent annual dividend. --- P0: Current stock price. --- gL: Long-term dividend growth rate. --- gs: Short-term dividend growth rate. --- H: Half-life of the transition period (e.g., H = n ÷ 2 for n years). 3- Application to Other Models -- For complex models, such as multi-stage DDMs, iterative calculations or computational tools may be required to estimate r.

Question 65

Sustainable Growth Rate 1- Overview of the Concept -- The sustainable growth rate (g) is the rate of dividend and earnings growth that a company can maintain given a constant return on equity (ROE) and capital structure. It reflects how quickly a firm can grow without altering its financial leverage. 2- Formula -- Sustainable growth rate formula: "g = b × ROE" --- b: Retention rate (the proportion of earnings retained, calculated as 1 - dividend payout ratio). --- ROE: Return on equity, representing the profitability relative to equity. 3- Key Insights -- A higher sustainable growth rate is achieved when both ROE and the retention rate increase. -- If ROE is held constant, an increase in the payout ratio will lower the sustainable growth rate. --- This effect is called the "dividend displacement of earnings," as more earnings paid out as dividends leave less for reinvestment in the business.

Question 66

Dividend Growth Rate, Retention Rate, and ROE Analysis 1- Overview of the Concept -- The sustainable growth rate formula can be enhanced by decomposing ROE (Return on Equity) using the DuPont analysis. This approach highlights how profit margin, asset turnover, and financial leverage contribute to growth. The expanded formula is called the PRAT model, focusing on Profit margin (P), Retention rate (R), Asset turnover (A), and Financial leverage (T). 2- Formula -- Formula for ROE: "ROE = (Net income ÷ Sales) × (Sales ÷ Total assets) × (Total assets ÷ Shareholders' equity)" -- Substituting into the sustainable growth rate: --- "g = (Net income - Dividends) ÷ Net income × (Net income ÷ Sales) × (Sales ÷ Total assets) × (Total assets ÷ Shareholders' equity)" 3- Key Variables -- P (Profit margin): Represents "Net income ÷ Sales". -- R (Retention rate): Equals "1 - Dividend payout ratio". -- A (Asset turnover): Defined as "Sales ÷ Total assets". -- T (Financial leverage): Expressed as "Total assets ÷ Shareholders' equity". 4- Insights -- The PRAT model connects a firm's operational efficiency, financial policies, and leverage to its growth potential. -- Increasing any component (e.g., higher profit margins, retention rates, or efficient use of assets) can boost the sustainable growth rate, provided the firm maintains consistent financial leverage.

Question 67

Financial Models and Dividends 1- Overview of the Concept -- Forecasting dividends often requires complex financial models that incorporate changes in a company's operating and financial environment. 2- Key Insights -- As competition increases, profit margins are likely to decline, requiring companies to adapt their payout strategies. -- To sustain dividend growth, firms may need to increase their payout ratios in response to lower profitability.

Question 68

Quiz - Calculating the Value of VZI's Growth on a Per Share Basis 1- Overview of the Question The question asks for the value of VZI's growth on a per share basis, assuming an efficient market, using the present value of growth opportunities (PVGO) formula. 2- Correct Answer A: $46.85. 3- Explanation 1- Understanding PVGO: -- PVGO measures the value of a company's growth opportunities. -- The formula for PVGO is: "PVGO = P0 - (E1 / r)". -- P0 is the stock price or intrinsic value, E1 is next year's earnings, and r is the required rate of return. 2- Steps to Solve: -- Step 1: Calculate the required rate of return (r) --- Formula: "r = rf + β × (rm - rf)". --- Substituting values: ---- rf = 2.3%, rm = 8.9%, β = 0.8. ---- "r = 2.3% + 0.8 × (8.9% - 2.3%) = 7.58%". -- Step 2: Calculate P0 using the Gordon growth model --- Formula: "P0 = D0 × (1 + g) / (r - g)". --- Substituting values: ---- D0 = 4.05, g = 5.1%, r = 7.58%. ---- "P0 = 4.05 × (1 + 0.051) / (0.0758 - 0.051) = 171.64". -- Step 3: Calculate E1 --- First, calculate E0: ---- Formula: "E0 = D0 / Payout ratio". ---- Substituting values: ----- D0 = 4.05, Payout ratio = 0.45. ----- "E0 = 4.05 ÷ 0.45 = 9". --- Next, calculate E1: ---- Formula: "E1 = E0 × (1 + g)". ---- Substituting values: ----- E0 = 9, g = 5.1%. ----- "E1 = 9 × 1.051 = 9.46". -- Step 4: Calculate PVGO --- Formula: "PVGO = P0 - (E1 / r)". --- Substituting values: ---- P0 = 171.64, E1 = 9.46, r = 7.58%. ---- "PVGO = 171.64 - (9.46 ÷ 0.0758) = 46.85". 4- Why A is Correct: -- The calculation shows that the PVGO for VZI is $46.85, which matches answer A. 5- Why B and C are Incorrect: -- B ($52.90) and C ($118.73) result from errors in applying the formulas for P0, E1, or PVGO.

Question 69

Quiz - Calculating the Maximum Price Sewell Would Pay for APH 1- Overview of the Question The question asks for the maximum price Sewell would be willing to pay today for a share of APH, given his expectations and required return. 2- Correct Answer B: $86.37. 3- Explanation 1- Understanding the Valuation: -- The maximum price Sewell would pay is the present value (P0) of all future cash flows: Future dividends (D1, D2, D3). Sale price (P3). -- These cash flows are discounted to today using Sewell's required rate of return, 10.9%. 2- Steps to Solve: -- Step 1: Calculate future dividends --- Dividend formula: "D_t = D0 × (1 + g1)^t". --- Substituting values: ---- D1 = 5.00 × (1 + 0.068) = 5.34. ---- D2 = 5.00 × (1 + 0.068)^2 = 5.70. ---- D3 = 5.00 × (1 + 0.068)^2 × (1 + 0.036) = 5.91. -- Step 2: Calculate sale price in 3 years --- Sale price: P3 = $99. -- Step 3: Calculate present value of future cash flows --- Formula: "P0 = D1 / (1 + r)^1 + D2 / (1 + r)^2 + (D3 + P3) / (1 + r)^3". --- Substituting values: ---- P0 = (5.34 ÷ 1.109) + (5.70 ÷ 1.109^2) + [(5.91 + 99) ÷ 1.109^3]. ---- P0 = 4.81 + 4.63 + 76.93 = 86.37. 3- Why B is Correct: -- The correct application of the dividend growth formula and discounting future cash flows gives a present value of $86.37, matching answer B. 4- Why A and C are Incorrect: -- Both A ($82.04) and C ($86.50) arise from incorrect rounding or misuse of the discounting formula.

Question 70

Quiz - Calculating the Required Return for PTM 1- Overview of the Question The question asks for the required return (r) that Sewell calculates for PTM, using the H-model. 2- Correct Answer A: 11.3%. 3- Explanation 1- Understanding the H-model: -- The H-model is used to calculate the required return (r) when a stock's growth transitions gradually from a high initial rate (gs) to a lower long-term rate (gL). -- Formula: "r = (D0 / P0) × [(1 + gL) + H × (gs - gL)] + gL". Where: D0 = current dividend. P0 = current stock price. gL = long-term growth rate. gs = supernormal growth rate. H = half-life of the growth transition period. 2- Steps to Solve: -- Step 1: Identify the inputs --- D0 = $3.00 (derived from $3.27 ÷ 1.09, given 9% growth for the next year). --- P0 = $56.69 (current price). --- gL = 4.6% (long-term growth rate). --- gs = 9.0% (supernormal growth rate). --- H = 10 ÷ 2 = 5 (half-life of 10 years). -- Step 2: Apply the H-model formula --- Substitute the inputs into the formula: "r = (3.00 ÷ 56.69) × [(1 + 0.046) + 5 × (0.09 - 0.046)] + 0.046". --- Calculate step-by-step: ---- Dividend yield: "3.00 ÷ 56.69 = 0.0529". ---- Growth adjustment: "(1 + 0.046) + 5 × (0.09 - 0.046) = 1.046 + 5 × 0.044 = 1.046 + 0.22 = 1.266". ---- Multiply: "0.0529 × 1.266 = 0.0669". ---- Add gL: "0.0669 + 0.046 = 0.113 or 11.3%". 3- Why A is Correct: -- The required return is calculated as 11.3%, matching answer A. 4- Why B and C are Incorrect: -- B (11.9%) and C (12.5%) result from errors in applying the formula, such as incorrect adjustments to growth rates or dividend yield.

Question 71

Quiz - Calculating the Capitalization Rate for CTI's Preferred Stock 1- Overview of the Question The question asks for the capitalization rate (r) for Carthage Industries' (CTI) preferred stock, which is non-callable. 2- Correct Answer C: 7.0%. 3- Explanation 1- Understanding the Capitalization Rate for Preferred Stock: -- The capitalization rate (r) represents the return required by investors for preferred stock. -- Formula: "r = D / P", where: D = Preferred dividend. P = Current market price of the preferred shares. 2- Steps to Solve: -- Step 1: Identify the inputs --- Preferred dividend (D) = $7.68. --- Market price (P) = $110. -- Step 2: Calculate r using the formula --- Substituting values: ---- "r = 7.68 ÷ 110 = 0.0698 or 6.98%". -- Step 3: Round the result --- The result, 6.98%, rounds to 7.0%, which matches answer C. 3- Why C is Correct: -- The calculation gives a capitalization rate of approximately 6.98%, which rounds to 7.0%, matching answer C. 4- Why A and B are Incorrect: -- A (5.8%) is too low and not supported by the formula or inputs. -- B (6.4%) does not match the actual result of the calculation.

Question 72

Quiz - Estimating USC's Intrinsic Value 1- Overview of the Question The question asks for USC's estimated intrinsic value, using a three-stage dividend discount model with projected dividends and discounted cash flows. 2- Correct Answer C: $43.27. 3- Explanation 1- Understanding the Three-Stage Valuation: -- The three-stage model includes: High-growth phase (18% growth for five years). Transition phase (growth declines to long-term rate). Stable phase (constant long-term growth of 6%). -- The intrinsic value is the present value of all expected future dividends, including terminal value calculated at the end of the high-growth period. 2- Steps to Solve: -- Step 1: Project dividends during the high-growth period --- The first dividend (D1) is given as $1.82. --- Subsequent dividends are calculated using the formula: "D_t = D_t-1 × (1 + g_s)". --- High-growth rate (g_s) = 18%. --- Dividends: ---- Year 1: $1.82. ---- Year 2: "1.82 × 1.18 = 2.1476". ---- Year 3: "2.1476 × 1.18 = 2.5342". ---- Year 4: "2.5342 × 1.18 = 2.9903". ---- Year 5: "2.9903 × 1.18 = 3.5286". -- Step 2: Calculate the terminal value at the end of Year 5 using the H-model --- Formula: "V_0 = [D_H × (1 + g_L)] / (r - g_L) + [D_H × H × (g_s - g_L)] / (r - g_L)". --- Inputs: ---- D_H = $3.5286, g_L = 6%, g_s = 11%, H = 5 ÷ 2 = 2.5, r = 13%. --- Terminal value (V_0 at Year 5): ---- "V_0 = [(3.5286 × (1 + 0.06)) / (0.13 - 0.06)] + [(3.5286 × 2.5 × (0.11 - 0.06)) / (0.13 - 0.06)]". ---- "V_0 = [3.5286 × 1.06 / 0.07] + [3.5286 × 2.5 × 0.05 / 0.07]". ---- "V_0 = 53.5144 + 10.0000 = 63.5144". -- Step 3: Discount the cash flows and terminal value to present value --- Discount rate (r) = 13%. --- Discount the projected dividends and terminal value: ---- Present value of dividends: ----- Year 1: "1.82 ÷ 1.13 = 1.6106". ----- Year 2: "2.1476 ÷ 1.13^2 = 1.6819". ----- Year 3: "2.5342 ÷ 1.13^3 = 1.7563". ----- Year 4: "2.9903 ÷ 1.13^4 = 1.8340". ----- Year 5: "3.5286 ÷ 1.13^5 = 1.8340". ---- Present value of terminal value: ----- "63.5144 ÷ 1.13^5 = 36.3882". --- Total present value: ---- "1.6106 + 1.6819 + 1.7563 + 1.8340 + (3.5286 ÷ 1.13^5) + (63.5144 ÷ 1.13^5) = 43.2710". 3- Why C is Correct: -- The calculated intrinsic value of $43.2710 matches answer C ($43.27). 4- Why A and B are Incorrect: -- Both A ($39.31) and B ($39.68) result from errors in projecting dividends, calculating the terminal value, or discounting cash flows.

Question 73

5.3 Free Cash Flow Valuation

Answer 73

-- Compare the free cash flow to the firm (FCFF) and free cash flow to equity (FCFE) approaches to valuation. -- Explain the ownership perspective implicit in the FCFE approach. -- Explain the appropriate adjustments to net income, earnings before interest and taxes (EBIT), earnings before interest, taxes, depreciation, and amortization (EBITDA), and cash flow from operations (CFO) to calculate FCFF and FCFE. -- Calculate FCFF and FCFE. -- Describe approaches for forecasting FCFF and FCFE. -- Explain how dividends, share repurchases, share issues, and changes in leverage may affect future FCFF and FCFE. -- Compare the FCFE model and dividend discount models. -- Evaluate the use of net income and EBITDA as proxies for cash flow in valuation. -- Explain the use of sensitivity analysis in FCFF and FCFE valuations. -- Explain the single-stage (stable-growth), two-stage, and three-stage FCFF and FCFE models and justify the selection of the appropriate model given a company’s characteristics. -- Estimate a company’s value using the appropriate free cash flow model(s). -- Describe approaches for calculating the terminal value in a multistage valuation model. -- Evaluate whether a stock is overvalued, fairly valued, or undervalued based on a free cash flow valuation model.

Question 74

Dividends and Free Cash Flows 1- Overview of the Concept -- Dividends represent the cash flows actually paid to stockholders, whereas free cash flows (FCFF and FCFE) represent the cash available for distribution. These metrics require detailed interpretation and are not always readily available. 2- When FCFF or FCFE is Preferred -- Analysts favor FCFF or FCFE instead of dividends in the following scenarios: --- The company does not pay dividends. --- Dividends do not reflect the company’s true dividend capacity. --- Forecasted free cash flows align with the company’s profitability. --- The investor adopts a control perspective in the valuation.

Question 75

[Equity Valuation: Preference for FCFF vs FCFE and Their Formulas] 1- When FCFF is Preferred Over FCFE -- FCFF (Free Cash Flow to the Firm) is preferred when the capital structure is unstable or expected to change significantly. -- It is also favored when the firm has negative or unpredictable FCFE due to inconsistent debt repayments or large financing activities. -- Analysts use FCFF when valuing the entire firm (enterprise value), especially for firms with high leverage or where debt/equity decisions are made at the corporate level. -- FCFF is also suitable when clean data on net borrowing or interest expense is unavailable or unreliable. 2- FCFF Formula: **FCFF = NI + NCC + Int(1 - tax_rate) - FCInv - WCInv** Where: --- NI = Net income --- NCC = Non-cash charges (e.g., depreciation, amortization) --- Int = Interest expense --- tax_rate = Effective tax rate --- FCInv = Capital expenditures (fixed capital investment) --- WCInv = Working capital investment 3- FCFE Formula: **FCFE = NI + NCC - FCInv - WCInv + Net Borrowing** Where: --- Net Borrowing = New debt issued – debt repayments Key Notes: -- FCFF is discounted using the **WACC** (weighted average cost of capital) to find **firm value**, then subtract net debt to get equity value. -- FCFE is discounted directly using the **cost of equity** to obtain **equity value**.

Question 76

Equity Value and Weighted Average Cost of Capital (WACC) 1- Equity Value -- Equity value is calculated as: --- Formula: "EquityValue = FirmValue - MarketValueOfDebt" -- Firm value is derived from discounting FCFF at WACC, and equity value is obtained by subtracting the market value of debt. 2- WACC Formula -- WACC represents the average cost of capital for the firm, weighted by the proportions of debt and equity in the capital structure: --- Formula: "WACC = [MV(Debt) ÷ (MV(Debt) + MV(Equity))] × rd × (1 - TaxRate) + [MV(Equity) ÷ (MV(Debt) + MV(Equity))] × re" 3- Explanation of Variables -- MV(Debt): Market value of the firm's debt. -- MV(Equity): Market value of the firm's equity. -- rd: Cost of debt. -- re: Cost of equity. -- TaxRate: Corporate tax rate.

Answer 76

Key Takeaways -- MV(Debt) and MV(Equity) must reflect current market values, not book values. -- WACC reflects the firm's blended cost of capital and is used to discount FCFF to derive firm value.

Question 77

Single-Stage (Constant-Growth) FCFF and FCFE Models 1- Overview of the Concept -- These models assume that free cash flows grow at a constant rate, denoted as "g". FCFF and FCFE are discounted to determine the value of the firm or equity, respectively. 2- Constant-Growth FCFF Valuation Model -- The FCFF formula with growth is: --- Formula: "FCFFt = FCFFt-1 × (1 + g)" -- The firm's value is calculated as: --- Formula: "FirmValue = FCFF1 ÷ (WACC - g)" 3- Constant-Growth FCFE Valuation Model -- The FCFE formula with growth is: --- Formula: "FCFEt = FCFEt-1 × (1 + g)" -- The equity value is calculated as: --- Formula: "EquityValue = FCFE1 ÷ (r - g)" 4- Explanation of Variables -- FCFFt: Free cash flow to the firm at time t. -- FCFEt: Free cash flow to equity at time t. -- g: Constant growth rate of free cash flows. -- WACC: Weighted average cost of capital, used for FCFF valuation. -- r: Required rate of return on equity, used for FCFE valuation. -- FCFF1 and FCFE1: Expected free cash flows in the first year.

Answer 77

Key Takeaways -- FCFF and FCFE models differ in discount rates (WACC for FCFF, r for FCFE) and what they value (firm vs. equity).

Question 78

Free Cash Flow (FCF) 1- Overview of the Concept -- Free cash flow measures the cash available for distribution after accounting for expenses, reinvestment, and financing obligations. FCFE (Free Cash Flow to Equity) is derived from FCFF (Free Cash Flow to the Firm) by adjusting for net payments to debtholders. 2- Formulas -- FCFE formula: --- "FCFE = FCFF - NetPaymentsToDebtholders" -- Net payments to debtholders formula: --- "NetPaymentsToDebtholders = (InterestAndPrincipalPaymentsMade - CashFromNewDebtIssues)" 3- Explanation of Variables -- FCFE: Free cash flow available to equity holders. -- FCFF: Free cash flow available to all capital providers. -- NetPaymentsToDebtholders: The net cash paid to or raised from debt providers. --- InterestAndPrincipalPaymentsMade: Payments for interest and repayment of principal on debt. --- CashFromNewDebtIssues: Cash raised from issuing new debt.

Question 79

Distinction Between FCFF, FCFE, and Cash Flow from Operations 1- Overview of the Concept -- Free Cash Flow to the Firm (FCFF) is used to calculate the value of the entire firm, while Free Cash Flow to Equity (FCFE) calculates the value of equity only. -- Cash flow from operations is a critical financial metric but cannot be used directly to calculate FCFF or FCFE as it may lead to double-counting or omitting cash flows. 2- Key Insights -- FCFF: Represents cash available to all capital providers (both debt and equity holders). -- FCFE: Represents cash available to equity holders after accounting for payments to and receipts from debtholders. 3- Potential Errors in Valuation -- Using cash flow from operations or net income in place of FCFF or FCFE risks double-counting or omitting important cash flows. --- For instance, net income includes only equity-related cash flows and ignores cash paid to debtholders.

Question 80

In the WACC, ALWAYS use Market Values, not Book values !!!

Answer 80

In the WACC, ALWAYS use Market Values, not Book values !!!

Question 81

Calculating FCFF from Net Income 1- Formula -- Free Cash Flow to the Firm (FCFF) is calculated as follows: --- Formula: "FCFF = NI + NCC + Int(1 - Tax rate) - FCInv - WCInv" 2- Explanation of Variables -- NI: Net income to common shareholders. -- NCC: Net non-cash charges (e.g., depreciation and amortization). -- Int(1 - Tax rate): After-tax interest expense, reflecting funds available to lenders. -- FCInv: Investment in fixed capital (e.g., PP&E or intangible assets). -- WCInv: Investment in working capital (changes in A/R, A/P, inventory, etc.). 3- Adjustments -- Depreciation is added back as it is a non-cash charge. -- After-tax interest expense is added back because it was subtracted during net income calculation. -- Investments in fixed capital (e.g., property, equipment) are subtracted as they reduce cash available to all capital providers. -- Changes in working capital (excluding cash and short-term debt) are subtracted to account for changes in operational funding requirements.

Answer 81

Key Takeaways -- The formula adjusts net income to reflect cash flows available to both debt and equity holders by accounting for non-cash items, capital expenditures, and changes in working capital. -- FCFF is crucial for valuing the firm as it represents cash flows available to all capital providers.

Question 82

Computing FCFF from the Statement of Cash Flows 1- Overview of the Concept -- Free Cash Flow to the Firm (FCFF) can be computed starting from operating cash flow (CFO), as it already includes adjustments for non-cash items and changes in working capital. 2- Formula -- Formula (using CFO): --- "FCFF = CFO + Int(1 - Tax rate) - FCInv" -- Alternative Formula (using Net Income): --- "CFO = NI + NCC - WCInv" --- Substitute CFO: "FCFF = NI + NCC + Int(1 - Tax rate) - WCInv - FCInv" 3- Explanation of Variables -- CFO: Cash flow from operations, derived from net income adjusted for non-cash expenses and changes in working capital. -- Int(1 - Tax rate): After-tax interest expense to include cash flows available to debt holders. -- FCInv: Investment in fixed capital, such as purchases of PP&E. -- NCC: Net non-cash charges, included in CFO when starting from net income. -- WCInv: Investment in working capital, already factored into CFO under direct computation. 4- Key Adjustments -- Under US GAAP: After-tax interest expense must be added back if included in CFO. -- Non-cash charges, such as depreciation, do not need further adjustment when using CFO as a starting point. -- No further adjustments for working capital investments are necessary if CFO is already provided.

Answer 82

Key Takeaways -- When CFO is available, computing FCFF becomes simpler as adjustments for non-cash charges and working capital are pre-accounted for. -- The formula aligns cash flows to reflect availability to all capital providers by reconciling operating activities with financing and investing activities.

Question 83

Calculating CFO Using Adjustments to Net Income 1- Overview of the Concept -- Cash Flow from Operations (CFO) can be calculated starting from Net Income (NI) by adding back non-cash expenses (e.g., depreciation) and adjusting for changes in working capital components. 2- Formula -- CFO formula: --- "CFO = NI + Dep - ΔA/R - ΔInventory + ΔA/P" 3- Explanation of Variables -- NI: Net income. -- Dep: Depreciation expense, a non-cash charge added back to NI. -- ΔA/R: Change in accounts receivable (subtract increase or add decrease). -- ΔInventory: Change in inventory (subtract increase or add decrease). -- ΔA/P: Change in accounts payable (add increase or subtract decrease). 4- Key Adjustments -- Non-cash charges like depreciation increase CFO as they do not represent cash outflows. -- Increases in assets like accounts receivable or inventory reduce CFO, as they represent cash not yet received or cash used for purchases. -- Increases in liabilities like accounts payable increase CFO, reflecting cash conserved by delaying payments.

Question 84

Classification of Certain Items on the Statement of Cash Flows 1- Overview of the Concept -- IFRS and US GAAP differ in the classification of interest and dividends on the cash flow statement, providing varying degrees of flexibility. 2- Key Differences Between IFRS and US GAAP -- Interest Received: --- IFRS: Classified as either operating or investing activities. --- US GAAP: Classified as operating activities. -- Interest Paid: --- IFRS: Classified as either operating or financing activities. --- US GAAP: Classified as operating activities. -- Dividends Received: --- IFRS: Classified as either operating or investing activities. --- US GAAP: Classified as operating activities. -- Dividends Paid: --- IFRS: Classified as either operating or financing activities. --- US GAAP: Classified as financing activities.

Answer 84

Key Takeaways -- IFRS offers more flexibility in classifying cash flows, allowing companies to better align classifications with the nature of their business. -- US GAAP provides stricter guidelines, ensuring uniformity but limiting flexibility.

Question 85

Adjustments to Derive Operating Cash Flow from Net Income 1- Overview of the Concept -- When calculating Free Cash Flow to the Firm (FCFF) using net income as the starting point, adjustments are made to account for non-cash items, changes in working capital, and other income statement entries that impact net income but not cash flows. 2- Items Added Back to Net Income -- These items are non-cash expenses or adjustments: --- Depreciation expense. --- Amortization expense. --- Impairment of intangibles. --- Restructuring charges. --- Amortization of long-term bond discounts. --- Losses on non-operating activities. --- Increases in accounts payable. 3- Items Subtracted from Net Income -- These items reduce cash flows: --- Income from the reversal of restructuring charges. --- Amortization of long-term bond premiums. --- Gains on non-operating activities. --- Increases in accounts receivable. --- Increases in inventory.

Question 86

Adjustments to Derive Operating Cash Flow from Net Income That May Merit Additional Attention from an Analyst 1- Overview of the Concept -- Certain adjustments to net income for FCFF calculations require specific judgment due to their complexity or the potential for misrepresentation of cash flows. 2- Key Considerations for Adjustments -- Deferred Taxes: --- Deferred taxes arise from differences between reported income and taxable income. --- Typically, deferred tax charges are not added back unless they are unlikely to reverse in the near future, such as in a fast-growing company that may defer liabilities indefinitely. -- Share-Based Compensation: --- Employee stock options create expenses recorded on the income statement without immediate cash outflows. --- Cash received from exercised stock options is considered a financing cash flow. Analysts must adjust for their tax treatment and impact on operating cash flow. -- Non-Recurring Items: --- Restructuring charges or similar items may have significant, temporary effects on financial statements. --- Analysts should adjust these to ensure baseline amounts reflect sustainable operations and not one-time events.

Question 87

Calculating FCFE from FCFF, Net Income, and CFO 1- Overview of the Concept -- Free Cash Flow to Equity (FCFE) reflects the cash flow available to equity holders after covering all operating costs, reinvestments, and servicing debt. 2- Formulas -- FCFE from FCFF: --- "FCFE = FCFF - [Int(1 - Tax rate)] + Net borrowing" -- FCFE from Net Income: --- "FCFE = NI + NCC - FCInv - WCInv + Net borrowing" -- FCFE from CFO: --- "FCFE = CFO - FCInv + Net borrowing" 3- Explanation of Variables -- FCFE: Free Cash Flow to Equity. -- FCFF: Free Cash Flow to the Firm. -- Int: Interest expense. -- Tax rate: Corporate tax rate. -- Net borrowing: New debt raised minus debt repayments. -- NI: Net income. -- NCC: Non-cash charges (e.g., depreciation, amortization). -- FCInv: Investments in fixed capital. -- WCInv: Investments in working capital. -- CFO: Cash flow from operations. 4- Comparison with FCFF -- FCFE directly relates to equity valuation, while FCFF captures the cash flow available to all capital providers (debt and equity). -- FCFF includes interest payments (net of tax benefits) and does not adjust for debt financing, making FCFE more equity-specific.

Question 88

Calculating FCFF Using EBIT or EBITDA 1- Overview of the Concept -- Free Cash Flow to the Firm (FCFF) can also be derived using EBIT or EBITDA as the starting point, bypassing the need for net income or CFO. This method ensures consistency when analyzing firms at different levels of profitability. 2- Formulas -- FCFF from EBIT: --- "FCFF = EBIT(1 - t) + Dep - FCInv - WCInv" -- Formula for EBIT: --- "EBIT = [NI + Interest(1 - t)] ÷ (1 - t)" -- FCFF from EBITDA: --- "FCFF = EBITDA(1 - t) + Dep(t) - FCInv - WCInv" 3- Explanation of Variables -- FCFF: Free Cash Flow to the Firm. -- EBIT: Earnings before interest and taxes. -- EBITDA: Earnings before interest, taxes, depreciation, and amortization. -- t: Marginal corporate tax rate. -- Dep: Depreciation expense. -- FCInv: Fixed capital investment. -- WCInv: Working capital investment. -- NI: Net income. -- Interest: Interest expense. 4- Key Points on Usage -- Using EBIT or EBITDA simplifies calculations by eliminating adjustments for noncash charges and tax impacts. -- When starting with EBIT, after-tax interest is excluded as it is not deducted in EBIT. -- EBITDA adjusts for tax effects on depreciation, ensuring accurate results.

Question 89

Calculating FCFF and FCFE Using Different Approaches 1- Overview of the Concept -- Free Cash Flow to the Firm (FCFF) and Free Cash Flow to Equity (FCFE) can be calculated using different starting points, including CFO, EBIT, EBITDA, or the uses of cash flows. These calculations provide a comprehensive view of cash flows available for both the firm and equity holders. 2- FCFF Calculation Using CFO -- CFO Formula: "CFO = NI + Dep - ΔA/R - ΔInventory + ΔA/P" -- FCFF Formula: "FCFF = CFO + Int(1 - t) - FCInv" --- Substituting values: --- CFO = 133.70 + 45.00 - 135.00 - 6.00 + 50.00 = 87.70 --- FCFF = 87.70 + (14.00)(1 - 0.30) - 0.00 = 97.50 3- FCFE Calculation from FCFF -- Formula: "FCFE = FCFF - Int(1 - t) + Net borrowing" --- Substituting values: --- FCFE = 97.50 - (14.00)(1 - 0.30) + 21.22 = 108.92 4- FCFF Calculation Using EBIT or EBITDA -- From EBIT: --- Formula: "FCFF = EBIT(1 - t) + Dep - FCInv - WCInv" --- Substituting values: FCFF = (205)(1 - 0.30) + 45.00 - 0.00 - 91.00 = 97.50 -- From EBITDA: --- Formula: "FCFF = EBITDA(1 - t) + Dep(t) - FCInv - WCInv" --- Substituting values: FCFF = (250)(1 - 0.30) + (45)(0.30) - 0.00 - 91.00 = 97.50 5- FCFF and FCFE from Uses of Free Cash Flow -- FCFF Calculation: --- Formula: "FCFF = ΔCash + Int(1 - t) - New borrowing + Dividends paid + Share repurchases" --- Substituting values: FCFF = 108.92 + (14.00)(1 - 0.30) - (-21.22) + 0.00 + 0.00 = 97.50 -- FCFE Calculation: --- Formula: "FCFE = ΔCash + Dividends paid + Share repurchases" --- Substituting values: FCFE = 108.92 + 0.00 + 0.00 = 108.92

Answer 89

Exercise: FCFF and FCFE Calculations from the Uses of Free Cash Flow 1- Calculate FCFF -- Formula: --- "FCFF = ΔCash + Int(1 - t) - New borrowing + Dividends paid + Share repurchases" -- Calculation: --- ΔCash = 108.92 --- Int(1 - t) = 14.00 × (1 - 0.3) = 9.8 --- New borrowing = -21.22 --- Dividends paid = 0.00 --- Share repurchases = 0.00 FCFF = 108.92 + 9.8 - 21.22 + 0.00 + 0.00 = 97.5 2- Calculate FCFE -- Formula: --- "FCFE = ΔCash + Dividends paid + Share repurchases" -- Calculation: --- ΔCash = 108.92 --- Dividends paid = 0.00 --- Share repurchases = 0.00 FCFE = 108.92 + 0.00 + 0.00 = 108.92

Question 90

Calculating FCFF and FCFE from the Uses of Free Cash Flow 1- Overview of the Concept -- Free Cash Flow to the Firm (FCFF) and Free Cash Flow to Equity (FCFE) can be calculated from the uses of free cash flow. This method verifies cash flow by analyzing how funds are allocated between retaining cash, paying debt providers, and paying equity holders. 2- FCFF from Uses -- Formula: --- "FCFF = Increase in cash balance + Interest expense × (1 - Tax rate) + Repayment of principal in excess of new borrowing + Cash dividends + Share repurchases in excess of share issuance" -- Key Components: --- Retained funds: Represented by the increase in the cash balance. --- Debt capital providers: Includes interest (net of taxes) and repayment of principal beyond new borrowing. --- Equity capital providers: Includes dividends and share repurchases beyond new share issuance. 3- FCFE from Uses -- Formula: --- "FCFE = Increase in cash balance (including new borrowing) + Cash dividends + Share repurchases in excess of share issuance" -- Simplified Components: --- Focuses on equity holder transactions and cash flow changes, excluding lender-specific transactions apart from their impact on cash balance.

Answer 90

Key Takeaways -- Calculating FCFF and FCFE from uses provides a consistency check with the sources of cash flow. -- FCFF addresses both debt and equity transactions, while FCFE is limited to equity-related cash flows.

Question 91

Sales-Based Forecast of Free Cash Flows 1- Overview of the Concept -- A basic forecast of free cash flows assumes a constant growth rate but may not capture all components. A more robust forecast incorporates individual elements of free cash flow. 2- Inputs for a Sales-Based Forecast -- 1- Sales growth rates. -- 2- After-tax operating margin (used for FCFF). -- 3- Net profit margin (used for FCFE). -- 4- Relationship of incremental fixed capital investments (FCInv) to sales increases. -- 5- Relationship of working capital investments (WCInv) to sales increases. -- 6- Debt ratio (DR).

Question 92

Sales-Based Forecast of FCFF and FCFE 1- Overview of the Concept -- Sales-based forecasts of FCFF and FCFE require modeling incremental capital expenditures and working capital expenditures relative to sales growth. 2- Formula -- For FCFF: "FCFF = EBIT(1 - Tax rate) - (FCInv - Dep) - WCInv" -- For FCFE under a target debt ratio: "FCFE = NI - (1 - DR)(FCInv - Dep) - (1 - DR)(WCInv)" 3- Explanation of Variables -- FCInv - Dep: Incremental fixed capital expenditures net of depreciation. -- WCInv: Incremental working capital expenditures. -- DR: Target debt ratio. -- EBIT: Earnings before interest and taxes. -- NI: Net income. 4- Steps to Estimate (FCInv - Dep) and WCInv -- 1- Forecast a constant growth rate for sales using historical data. -- 2- Calculate proportions based on historical data: --- For FCInv - Dep: "Capital expenditures - Depreciation expense ÷ Increase in sales". --- For WCInv: "Increase in working capital ÷ Increase in sales". -- 3- Apply the calculated proportions to the forecasted sales growth to estimate future incremental expenditures.

Answer 92

Key Takeaways -- Sales-based forecasts consider historical relationships between expenditures and sales, offering more precision. -- The target debt ratio allows for more nuanced FCFE calculations, assuming adjustments to capital structure.

Question 93

Free Cash Flow Versus Dividends and Other Earnings Components 1- Overview of the Concept -- Free cash flow models are often more appropriate than dividend discount models (DDMs), especially for companies that do not pay dividends. They provide flexibility for analyzing profitability and allocation of resources, such as during takeover bids. 2- Key Free Cash Flow Formulas -- FCFF: "FCFF = NI + NCC + Int(1 - Tax rate) - FCInv - WCInv" -- FCFE: "FCFE = NI + NCC - FCInv - WCInv + Net borrowing" -- FCFF (from EBITDA): "FCFF = EBITDA(1 - Tax rate) + Dep(Tax rate) - FCInv - WCInv" 3- Differences Between Free Cash Flow and Dividends -- Dividends and share repurchases are discretionary and may not reflect a company’s ability to generate cash. -- FCFE and dividends are not equal, but they often trend in the same direction due to shared economic drivers. 4- Analyst Adjustments to CFO -- CFO calculations may need adjustments to reconcile inconsistencies, particularly for multinational companies or subsidiaries. -- Financing and investing activities must be excluded from CFO to ensure accuracy.

Answer 93

Key Takeaways -- Free cash flow models offer greater flexibility than DDMs, especially for companies with inconsistent dividend policies or growth-focused reinvestments. -- EBITDA, while sometimes used as a proxy for FCFF, requires adjustments for depreciation, working capital, and tax effects for accurate free cash flow analysis.

Question 94

Free Cash Flow and Complicated Capital Structures 1- Overview of the Concept -- Companies may have more complex capital structures, including preferred stock, in addition to debt and equity. While the issuance of preferred stock is treated as net borrowing (increasing FCFE), it does not affect FCFF. 2- Adjusted FCFF Formula for Preferred Dividends -- FCFF: "FCFF = NI + NCC + Int(1 - Tax rate) + Preferred dividends - FCInv - WCInv" -- Adjustments are necessary when using net income as a starting point to calculate FCFF, as net income typically does not include preferred dividends. 3- Treatment in FCFE Calculations -- No adjustments for preferred dividends are needed in FCFE if net income already reflects their deduction.

Question 95

International Application of the Single-Stage Model 1- Overview of the Concept -- When inflation is high or volatile, real values may be used for international stock valuation instead of nominal values. This approach requires the use of a real discount rate. 2- Modified Real Discount Rate Formula -- "Country (real) return ± Industry adjustment ± Size adjustment ± Leverage adjustment" -- Adjustments account for differences in industry, size, and leverage to refine the real rate of return for a country. 3- Valuation Formula Using Real Values -- "V0 = [FCFE0(1 + g_real)] ÷ (r_real - g_real)" -- This formula determines the equity value of a company in real terms, reflecting the growth rate and discount rate adjusted for inflation. Sensitivity Analysis of FCFF and FCFE Valuations 1- Overview of Sensitivity Analysis -- Sensitivity analysis helps evaluate the impact of varying inputs, such as FCFF, FCFE, growth rate (g), and the risk-free rate, on the valuation model. 2- Modified Valuation Formula -- "V0 = [FCFE0(1 + g)] ÷ [(Risk-free rate + β(Equity risk premium)) - g]" -- This formula incorporates the sensitivity of equity valuation to changes in risk-free rate, beta (β), equity risk premium, and growth rate. 3- Key Implications -- Valuations increase with higher initial FCFE and growth rates. -- Valuations decrease with higher risk-free rates, beta, or equity risk premiums.

Answer 95

Key Takeaways -- Real terms and adjusted discount rates are vital for international valuation under volatile inflation conditions. -- Sensitivity analysis identifies the most impactful variables in equity valuation and helps mitigate uncertainty in financial models.

Question 96

Two-Stage FCFF Valuation Model 1- Overview of the Concept -- The two-stage FCFF model incorporates changes in growth rates for free cash flow, reflecting different stages of a firm's lifecycle. Growth rates can vary for variables such as sales, profitability, and financing costs. 2- General Valuation Formula -- "Firm value = T∑_t=1 [FCFFt ÷ (1 + WACC)^t] + [FCFFn+1 ÷ (WACC - g)] × [1 ÷ (1 + WACC)^n]" 3- Explanation of Components -- "T∑_t=1": Summation of FCFF discounted by the WACC for each year in stage one. -- "FCFFn+1 ÷ (WACC - g)": Terminal value of FCFF at the end of stage one using a constant growth model. -- "[1 ÷ (1 + WACC)^n]": Present value adjustment for the terminal value. 4- Important Notes -- FCFF or FCFE must be calculated individually for each year during the first stage, as the growth rate may differ annually. -- Terminal value assumes a stable growth rate (g) beyond stage one.

Answer 96

Key Takeaways -- The two-stage FCFF model is more complex than dividend discount models, accommodating varying growth rates. -- Proper estimation of growth rates, WACC, and terminal value is critical for accurate valuation.

Question 97

Three-stage models are logical extensions of two-stage models. A common assumption is a constant growth rate in all three stages. Alternatively, a constant growth rate could be assumed in the first and third stages, with a declining growth rate in stage two.

Question 98

Environmental, social, and governance (ESG) considerations can have a material impact on the valuation model. Both quantitative and qualitative assumptions can be incorporated into valuation models. Specifically, the cost of equity could be adjusted to account for qualitative factors.

Answer 98

ESG Considerations in Free Cash Flow Models 1- Impact of ESG on Valuation -- Environmental, Social, and Governance (ESG) factors can materially influence valuations in free cash flow models. 2- Quantitative vs. Qualitative Factors Quantitative Factors: -- Examples: Expected environmental fines or penalties. -- These factors are straightforward and can be easily incorporated into valuations. Qualitative Factors: -- More challenging to model. -- One approach is to adjust the cost of equity by including a risk premium to account for ESG risks. -- This requires significant judgment and subjective evaluation.

Question 99

Valuing Non-Operating Assets 1- Overview of the Concept -- Free cash flow valuations focus on assets that generate operating cash flows. However, firms with significant non-operating assets must include these in their total valuation. 2- Examples of Non-Operating Assets -- "Excess" cash and marketable securities (amount beyond what is needed for ordinary operations). -- Non-current investments in stocks and bonds. -- Land held for investment purposes. -- Pension surplus. 3- Valuation Adjustment -- Non-operating assets carried at book value should be adjusted to their market value for accurate valuation purposes.

Question 100

Nonoperating Assets and Firm Value 1- Components of Firm Value -- The total value of the firm equals the sum of the value of operating assets and nonoperating assets. -- Operating assets are calculated using Free Cash Flow (FCF) models. 2- Treatment of Nonoperating Assets -- Nonoperating assets should be reflected at their current market value rather than their book value.

Answer 100

Key Examples of Nonoperating Assets: -- Excess cash and marketable securities. -- Non-current investments in stocks and bonds. -- Land held for investment. -- Pension surplus.

Question 101

Explanation of the Correct Answer: Correct Answer: A (€35 million). 1- Why Your Answer Was Incorrect: If you selected an incorrect option (such as B: €40 million), you may have misunderstood the treatment of current liabilities. Specifically: -- Working capital investment involves current assets minus current liabilities. -- Failing to subtract both accounts payable (€25 million) and accrued taxes and expenses (€20 million) would overstate the working capital investment. 2- Theory Behind the Correct Answer: -- Working capital investment is defined as: Increase in current assets (excluding cash) less increase in current liabilities. -- The calculation here involves: Increase in accounts receivable (€40 million) and inventory (€40 million). Less increase in accounts payable (€25 million) and accrued taxes and expenses (€20 million). 3- Steps to Identify the Correct Answer: -- Add increases in relevant current assets: €40 (accounts receivable) + €40 (inventory) = €80. -- Subtract increases in relevant current liabilities: €25 (accounts payable) + €20 (accrued taxes) = €45. -- Working capital investment = €80 - €45 = €35 million.

Answer 101

Key Takeaways: -- Always exclude cash and notes payable from the calculation of working capital changes. -- Include only operational current assets and liabilities that are directly tied to the company's operations. -- The correct answer, A (€35 million), aligns with these principles.

Question 102

Quiz - Assessing the Impact of Dividends and Share Repurchases on FCFE 1- Overview of the Question The question asks whether Grenier’s comment about the impact of dividends and share repurchases on FCFE is correct. 2- Correct Answer B: No, because a share repurchase would not have affected FCFE. 3- Explanation 1- Why Grenier’s Comment is Partially Incorrect: -- Grenier correctly states that a higher dividend payment would not have affected FCFE. -- However, his claim that a share repurchase would have reduced FCFE is incorrect. 2- Key Theory: -- Free Cash Flow to Equity (FCFE) represents the cash flow available to equity holders after accounting for: --- Operating expenses. --- Fixed capital investment. --- Working capital investment. --- Interest and debt repayments. -- FCFE is calculated before dividends or share repurchases are distributed. Both are merely allocations of FCFE and do not affect its calculation. 3- How to Identify the Correct Answer: -- Focus on the distinction between cash flow available to equity holders (FCFE) and how that cash is used (e.g., paying dividends or buying back shares). -- Since share repurchases are a use of FCFE, they do not reduce the amount calculated as FCFE.

Answer 102

Key Takeaways -- Dividends and share repurchases are allocations of FCFE, not components of its calculation. -- Grenier was wrong to claim that a share repurchase would reduce FCFE. -- The correct answer, B, reflects that FCFE remains unaffected by share repurchases.

Question 103

Quiz - Valuation of Bern Under Scenario 2 1- Overview of the Question The question involves determining the intrinsic value of Bern’s shares under Scenario 2 using a two-stage valuation model and comparing it to the market value of the shares. 2- Correct Answer A: Undervalued. 3- Step-by-Step Calculations Step 1: Calculate the Weighted Average Cost of Capital (WACC) WACC formula: WACC = (w_d × r_d × (1 - Tax rate)) + (w_p × r_p) + (w_e × r_e) Inputs: Debt (D) = €15,400 million. Preferred stock (P) = €4,000 million. Equity (E) = €18,100 million. Total value = €37,500 million. Required returns: -- r_d (debt) = 6%. -- r_p (preferred stock) = 5.5%. -- r_e (equity) = 11%. Corporate tax rate = 26.9%. Weights: w_d = D / Total value = 15,400 ÷ 37,500 = 0.4107. w_p = P / Total value = 4,000 ÷ 37,500 = 0.1067. w_e = E / Total value = 18,100 ÷ 37,500 = 0.4827. Substitute into the WACC formula: WACC = (0.4107 × 0.06 × (1 - 0.269)) + (0.1067 × 0.055) + (0.4827 × 0.11). WACC = 0.0181 + 0.0059 + 0.0531 = 0.0770 or 7.70%. Step 2: Project FCFF for the Growth Period (Years 1 to 3) Inputs: Starting FCFF (Year 0) = €3,226 million. Growth rate for Years 1–3 = 1.5%. Yearly FCFF calculations: Year 1: FCFF_1 = 3,226 × (1 + 0.015) = €3,274.39 million. Year 2: FCFF_2 = 3,274.39 × (1 + 0.015) = €3,323.51 million. Year 3: FCFF_3 = 3,323.51 × (1 + 0.015) = €3,373.36 million. Step 3: Calculate Terminal Value (End of Year 3) Terminal value formula: TV_3 = FCFF_4 / (WACC - g_L). Inputs: FCFF_4 = FCFF_3 × (1 + g_L), where g_L = 0.75%. FCFF_4 = 3,373.36 × (1 + 0.0075) = €3,398.66 million. WACC = 7.70%, g_L = 0.75%. Substitute into the terminal value formula: TV_3 = 3,398.66 ÷ (0.0770 - 0.0075) = 3,398.66 ÷ 0.0695 = €48,901.58 million. Step 4: Discount FCFF and Terminal Value to Present Value Discount formula: PV = FCFF_t / (1 + WACC)^t. Discount each year's FCFF: Year 1: PV_1 = 3,274.39 ÷ (1 + 0.0770)^1 = 3,274.39 ÷ 1.0770 = €3,040.37 million. Year 2: PV_2 = 3,323.51 ÷ (1 + 0.0770)^2 = 3,323.51 ÷ 1.1608 = €2,865.42 million. Year 3: PV_3 = 3,373.36 ÷ (1 + 0.0770)^3 = 3,373.36 ÷ 1.2518 = €2,700.53 million. Discount the terminal value: PV_TV = 48,901.58 ÷ (1 + 0.0770)^3 = 48,901.58 ÷ 1.2518 = €39,144.95 million. Step 5: Calculate Total Value of Operating Assets Sum of discounted values: Total operating assets = PV_1 + PV_2 + PV_3 + PV_TV. Total operating assets = 3,040.37 + 2,865.42 + 2,700.53 + 39,144.95 = €47,751.27 million. Step 6: Calculate Value of Bern’s Equity Equity value formula: Equity value = Total operating assets + Non-operating assets - Debt - Preferred stock. Inputs: Non-operating assets (land value) = €50 million. Debt = €15,400 million. Preferred stock = €4,000 million. Substitute: Equity value = 47,751.27 + 50 - 15,400 - 4,000 = €28,401.27 million. Step 7: Compare Intrinsic Value to Market Value Intrinsic value of equity = €28,401.27 million. Market value of equity = €18,100 million. Since intrinsic value > market value, Bern’s shares are undervalued.

Question 104

5.4 Market-Based Valuation: Price and Entreprise Value Multiples

Answer 104

-- Contrast the method of comparables and the method based on forecasted fundamentals as approaches to using price multiples in valuation and explain economic rationales for each approach. -- Calculate and interpret a justified price multiple. -- Describe rationales for and possible drawbacks to using alternative price multiples and dividend yield in valuation. -- Calculate and interpret alternative price multiples and dividend yield. -- Calculate and interpret underlying earnings, explain methods of normalizing earnings per share (EPS), and calculate normalized EPS. -- Explain and justify the use of earnings yield (E/P). -- Describe fundamental factors that influence alternative price multiples and dividend yield. -- Calculate and interpret a predicted P/E, given a cross-sectional regression on fundamentals, and explain limitations to the cross-sectional regression methodology. -- Calculate and interpret the justified price-to-earnings ratio (P/E), price-to-book ratio (P/B), and price-to-sales ratio (P/S) for a stock, based on forecasted fundamentals. -- Calculate and interpret the P/E-to-growth (PEG) ratio and explain its use in relative valuation. -- Calculate and explain the use of price multiples in determining terminal value in a multistage discounted cash flow (DCF) model. -- Evaluate whether a stock is overvalued, fairly valued, or undervalued based on comparisons of multiples. -- Evaluate a stock by the method of comparables and explain the importance of fundamentals in using the method of comparables. -- Explain alternative definitions of cash flow used in price and enterprise value (EV) multiples and describe limitations of each definition. -- Calculate and interpret EV multiples and evaluate the use of EV/EBITDA. -- Explain sources of differences in cross-border valuation comparisons. -- Describe momentum indicators and their use in valuation. -- Explain the use of the arithmetic mean, the harmonic mean, the weighted harmonic mean, and the median to describe the central tendency of a group of multiples.

Question 105

Price and Enterprise Value Multiples 1- Price Multiples -- These are ratios of a stock's market price to a fundamental measure of value per share, such as: --- Earnings per Share (EPS). --- Net assets. 2- Enterprise Value Multiples -- These relate the total market value of the company’s capital to a fundamental value for the entire company, such as: --- EBITDA. --- Sales. 3- Momentum Indicators -- Momentum indicators analyze a stock's price or a fundamental metric relative to its past values over time. -- They are used to identify patterns and trends in prices.

Question 106

Price and Enterprise Value Multiples in Valuation 1- Methods of Valuation -- There are two main methods for using price and enterprise value multiples: --- The method of comparables. --- The method based on forecasted fundamentals. 2- Method of Comparables -- Values an asset based on multiples of similar assets. --- Example: Multiplying a company’s EPS by a benchmark P/E ratio to determine if it is undervalued or overvalued. -- Key Assumptions: --- Stock prices should align with a consistent measure of value (e.g., earnings). --- Relies on the "law of one price," which assumes identical assets should trade at the same price. -- Limitations: Multiples do not reveal whether the stock price reflects its intrinsic value. -- If the benchmark group is mispriced, conclusions about fair, under, or overvaluation can be misleading. -- Applications: --- Used for relative valuations (e.g., determining mispricing based on comparable securities). --- Can be applied to enterprise value metrics like EBITDA. 3- Method Based on Forecasted Fundamentals -- Uses multiples linked to business profitability, growth, or financial strength. --- Premise: Cash flows are driven by a company’s fundamentals. -- Approach: --- Start with a DCF model to calculate the ratio of DCF value to forecasted EPS. --- Compare the actual multiple (e.g., price-to-book) to a justified multiple. -- Example: --- A stock is overvalued if its actual P/B exceeds its justified P/B.

Question 107

[Price to Earnings] 1- Overview of the Concept: -- The price-to-earnings ratio (P/E) is a widely used price multiple that measures a company's stock price relative to its earnings per share (EPS). 2- Popularity of P/E Ratio: -- 1- Earnings power is a key determinant of investment value. -- 2- The P/E ratio is widely recognized and frequently utilized by investors. -- 3- It may reflect the long-run average returns in stock investments. 3- Drawbacks of the P/E Ratio: -- 1- EPS can be zero, negative, or very small, making the ratio less meaningful. -- 2- It is challenging to determine if earnings are sustainable. -- 3- Reported EPS can be distorted by differences in accounting standards.

Question 108

[Alternative Definitions of P/E] 1- Overview of the Concept: -- The P/E ratio is calculated by dividing the current stock price (numerator) by the earnings per share (EPS, denominator). Different definitions of EPS and P/E are used depending on the context. 2- Types of P/E Ratios: -- 1- Trailing P/E: Uses EPS from the trailing 12 months. -- 2- Forward P/E: Uses next year’s expected EPS. 3- Considerations for P/E Calculations: -- Other definitions of EPS can be used, such as median P/E over multiple years (e.g., Value Line methodology). Consistency is key for comparability across companies. -- Forward-looking P/E ratios are more relevant for valuation, but trailing P/E may not reflect significant recent changes. 4- Normalized P/E: -- Adjusted P/E ratios are based on normalized earnings to remove the impact of nonrecurring items, enhancing comparability.

Question 109

[Calculating the Trailing P/E] 1- Key Considerations for EPS Calculation: -- Potential dilution of EPS: Basic EPS is based on the weighted average number of shares outstanding, while diluted EPS includes the effect of exercised options and warrants. Diluted EPS allows analysts to compare companies with differing amounts of dilutive securities. -- Nonrecurring items: Adjustments are needed to remove one-time events that do not reflect core, sustainable earnings. These adjustments are crucial but challenging, especially when companies use non-IFRS measures. -- Business-cycle influences: Earnings fluctuate with the business cycle, creating high P/E ratios at the bottom and low P/E ratios at the top (Molodovsky effect). Trailing P/E may need normalization using one of the following: --- Historical average EPS: Averages EPS over the most recent business cycle. --- Average return on equity (ROE): Multiplies the average ROE by the current book value per share. 2- Challenges in Comparability: -- Accounting standards and assumptions can lead to difficulties in comparing P/E ratios across companies. Adjustments may be necessary, such as for inventory valuation methods. 3- Handling Extremely Low, Zero, or Negative Earnings: -- Traditional P/E ratios become undefined or meaningless. Alternatives include forward P/E or normalized P/E ratios. -- The inverse price-to-earnings ratio (earnings yield, E/P) can rank companies consistently, even when earnings are low or negative.

Question 110

[Forward P/E] 1- Definition: -- Forward P/E is calculated based on next year’s expected earnings, which may represent the next four quarters, the next 12 months, or the next fiscal year. 2- Forecasted EPS Calculation: -- Typically, the forecasted EPS is the sum of the next four quarter-end EPS estimates, including the current quarter. --- Example: If the date is February 1st, the forecasted EPS would include the quarters ending on March 31st, June 30th, September 30th, and December 31st. -- For the next 12 months (NTM) definition, EPS is generally calculated as the weighted average of the expected EPS for the next two fiscal years.

Question 111

[Example: Forward P/E] 1- Formula for Forward P/E Based on Next Four Quarters of Forecasted EPS: -- Formula: "P/E = Price / EPS_forecasted". -- Usage: This formula calculates the forward price-to-earnings ratio using the sum of the forecasted EPS for the next four quarters, including the current quarter. 2- Formula for Next Twelve Months (NTM) P/E: -- Formula: "P/E = Price / EPS_NTM". -- Usage: This formula determines the forward P/E by using a weighted average of the expected EPS over the next twelve months. It accounts for the portion of earnings from the current fiscal year and the next fiscal year based on the time remaining. 3- Formula for Fiscal-Year Forward P/E: -- Formula: "P/E = Price / EPS_fiscal-year". -- Usage: This version calculates the forward P/E ratio using the forecasted EPS for the entire next fiscal year. It provides a clear picture based on a full fiscal year’s earnings expectation.

Answer 111

[Finding Variables in the Forward P/E Example] 1- Variable: EPS_forecasted (Next Four Quarters) -- Explanation: To calculate EPS for the next four quarters, sum the forecasted quarterly EPS from the table. This includes the current quarter (March 31, 20X5) and the next three quarters (June 30, September 30, and December 31, 20X5). -- Example Calculation: --- EPS_forecasted = 0.00 (March) + 0.04 (June) + (-0.05) (September) + 0.14 (December) = 0.13. 2- Variable: EPS_NTM (Next Twelve Months) -- Explanation: Calculate EPS over the next 12 months using a weighted average of the current fiscal year (20X5) and the next fiscal year (20X6) based on time proportions. --- 8 months of the 20X5 EPS = (8 ÷ 12) * 20X5 EPS. --- 4 months of the 20X6 EPS = (4 ÷ 12) * 20X6 EPS. -- Example Calculation: --- 20X5 EPS: 0.01 × (8 ÷ 12) = 0.0067. --- 20X6 EPS: 0.30 × (4 ÷ 12) = 0.10. --- Total EPS_NTM = 0.0067 + 0.10 = 0.1067. 3- Variable: EPS_fiscal-year (Next Fiscal Year) -- Explanation: Use the annual forecasted EPS for 20X6 from the table. -- Example Calculation: --- EPS_fiscal-year = 20X6 EPS = 0.30. 4- Variable: Price (Stock Price) -- Explanation: The stock price is given in the example as $25.30 (as of May 7, 20X5).

Question 112

[Justified P/E Ratios] 1- Overview of Justified P/E Ratios -- Justified P/E ratios help determine the market value per dollar of EPS using DCF models. -- Based on the Gordon growth model, they provide fundamental values for forward and trailing P/E ratios. 2- Formula Justified Forward P/E: "JustifiedForwardP/E = P0/E1 = (D1/E1) ÷ (r - g) = (1 - b) ÷ (r - g)" Justified Trailing P/E: "JustifiedTrailingP/E = P0/E0 = [(D0 * (1 + g)) ÷ E0] ÷ (r - g) = [(1 - b) * (1 + g)] ÷ (r - g)" 3- Explanation of Variables -- P: Share price. -- E: Earnings per share (E1 is for the next period, E0 is for the current period). -- D: Dividends per share (D1 is for the next period, D0 is for the current period). -- r: Required rate of return. -- g: Dividend growth rate. -- b: Retention rate (proportion of earnings retained by the firm). 4- Key Observations -- Justified P/E ratios are inversely related to the required rate of return (r). -- They are positively related to the growth rate (g).

Answer 112

Key Takeaways -- Use forward P/E to focus on future earnings, while trailing P/E reflects past performance adjusted for growth. -- The formulas provide insights into the valuation based on fundamental drivers such as growth, dividends, and retention.

Question 113

[Predicted P/E Based on Cross-Sectional Regression] 1- Overview of Cross-Sectional Regression -- A cross-sectional regression method predicts P/E ratios using independent variables such as earnings growth rate, payout ratio, and earnings volatility. -- This method aggregates data into a single regression equation for analysis. 2- Limitations of the Method -- The analysis is based on a sample of stocks over a specific time period, limiting generalizability. -- Parameters often lack stability over time, leading to fluctuating explanatory power. -- Multicollinearity is common, where independent variables are highly correlated, affecting reliability.

Answer 113

Key Takeaways -- While useful, this method faces challenges in stability and multicollinearity. -- Analysts often prioritize studying the relationship between stock prices (or returns) and economic variables over direct P/E multiple relationships.

Question 114

[Valuation Using the P/E Approach] 1- Overview of the Method -- The P/E approach involves comparing a company’s actual forecasted earnings to a benchmark multiple. -- The goal is to compare the company’s actual price multiple to a benchmark multiple derived from comparable assets. 2- Steps in Using the Method of Comparables -- Select and calculate the relevant price multiples for the company. -- Determine the benchmark value of the multiple, often the mean or median from comparison assets. -- Use the benchmark multiple to estimate the company’s stock value. -- Analyze differences between the estimated value and the current stock price. 3- Selection of Comparison Assets -- Comparisons can be made with peer groups, industries, sectors, equity indices, or past company stock values. -- Aggregated data from multiple companies generally provides better insight than comparisons with a single company. 4- Classification Systems for Grouping Companies -- Widely used systems include: --- The Global Industry Classification System (GICS). --- The Industrial Classification Benchmark (ICB). -- Narrow groupings, such as industry-specific groupings, are effective for identifying comparable firms. 5- Financial Ratio Analysis -- Ratios can help explain differences between a company’s price multiple and the benchmark value. -- Examples of ratios used include those for liquidity, asset turnover, leverage, and profitability.

Question 115

[Peer-Company and Industry Multiples] 1- Peer-Company Multiples -- Peer-company multiples compare companies within the same peer group, assuming they share similar business characteristics. -- Adjustments should account for differences in factors such as expected growth rates. --- For example, companies with higher-than-average growth rates should have higher P/E ratios compared to the peer group average. 2- P/E-to-Growth (PEG) Ratio -- The PEG ratio incorporates earnings growth into the P/E ratio, calculated as P/E ÷ expected earnings growth rate. -- Stocks with lower PEG ratios are generally considered more attractive. -- Limitations of the PEG ratio: --- The PEG assumes a linear relationship between P/E and growth, which may not align with models like the dividend discount model. --- It does not consider risk or the duration of growth. PEG = [P/E] / g 3- Industry and Sector Multiples -- These use mean or median P/E ratios across industries or sectors for relative valuation. -- The median P/E is often preferred as it minimizes sensitivity to outliers. -- A broader comparison group may identify systematic mispricing within peer groups.

Answer 115

Key Takeaways -- Peer-company and industry multiples provide a framework for assessing relative valuation but require adjustments for specific company characteristics and growth expectations.

Question 116

Quiz - Metric 2: Five-Year PEG Ratio 1- Overview of the Concept -- The five-year P/E-to-growth (PEG) ratio evaluates how much investors are paying for each unit of growth. A lower PEG ratio indicates better pricing relative to growth. 2- Formula -- Name of Formula: Five-Year PEG Ratio. -- Formula: "PEG = (Forward P/E Ratio ÷ Earnings Growth Rate)"

Question 117

[Overall Market Multiple] 1- Overview of the Concept -- The overall market multiple uses equity market indexes as comparison assets. Adjustments are often necessary to account for size differences between companies in the index, as most indexes are market-cap weighted. 2- Application -- A stock's P/E ratio can be compared as a percentage of the index's P/E to the historical average of this ratio. -- For example: --- If a stock’s P/E has historically been 20% greater than the index’s P/E, it is maybe not considered undervalued if the current ratio is around 20% greater than the index. 3- Fed Model -- This model evaluates the overall market valuation by comparing the index’s earnings yield (the reciprocal of the P/E ratio) to the yield on 10-year US Treasury bonds. --- If the earnings yield is lower than the Treasury yield, the market may be overvalued. -- Limitations: --- It does not account for growth rates, equity risk premiums, or inflation effects. --- The relationship between interest rates and earnings yields is not linear, especially when interest rates are low. 4- Yardeni Model -- This model modifies the Fed Model by incorporating expected earnings growth rates. --- Formula: "CEY = CBY - b * LTEG + Residual" --- Where: ---- CEY: Current earnings yield on the market index. ---- CBY: Current corporate bond yield (Moody’s A-rated). ---- LTEG: Consensus five-year earnings growth rate. ---- b: Weight investors assign to growth, usually between 0.10 and 0.25. -- The justified P/E ratio based on the Yardeni Model is: "Justified P/E = 1 / (CBY - b * LTEG)".

Answer 117

Key Takeaways -- The Fed Model assesses valuation relative to Treasury yields but omits growth and risk factors. -- The Yardeni Model improves upon this by integrating earnings growth expectations, offering a more comprehensive view of market valuation.

Question 118

[Equity Index and Price-to-Earnings (P/E) Ratios] 1- Overview of the Concept: The equity index may not always be efficiently priced, requiring a comparison of the current P/E ratio of the index to its historical P/E ratios. 2- Factors for Analysis: -- 1- A higher current P/E ratio could be justified in specific situations: --- Lower interest rates can support higher valuations. --- Higher-than-average expected growth rates may explain elevated P/E ratios. -- 2- A higher current P/E ratio may also indicate that the overall market is overvalued, signaling caution. 3- Additional Consideration: -- The time frame used to compare average multiples is critical for meaningful analysis, as it affects the interpretation of valuation metrics.

Question 119

[Own Historical P/E and P/Es in Cross-Country Comparisons] 1- Own Historical P/E -- A company's stock valuation can be assessed by comparing its P/E ratio to its own historical values. -- Justification: The stock’s P/E is expected to revert to historical averages, and the justified price is calculated by multiplying the historical average P/E by the most recent EPS. -- Adjustments: --- May be required if the business mix, leverage, interest rates, or macroeconomic conditions have changed during the analysis period. 2- P/Es in Cross-Country Comparisons -- Comparing P/E ratios across countries can be affected by different accounting standards and macroeconomic factors like inflation. -- Companies that can pass on higher prices to customers are less exposed to inflation, supporting a higher P/E ratio. -- Formula for Justified Forward P/E: --- "P0 / E1 = 1 / [ρ + (1 - λ)I]" --- Where: ---- P0: Current price. ---- E1: Next year’s EPS. ---- ρ: Real rate of return (ρ = r - I). ---- r: Nominal rate of return. ---- I: Inflation rate. ---- λ: Proportion of inflation passed on to pricing.

Answer 119

Key Takeaways -- Historical P/E provides a baseline by referencing a company’s historical valuation trends. -- Cross-country comparisons highlight the influence of inflation and macroeconomic factors on P/E ratios. The formula accounts for inflation-adjusted earnings growth and real return expectations.

Question 120

[Using P/Es to Obtain Terminal Value in Multistage Dividend Discount Models] 1- Overview -- P/E ratios are commonly used to estimate terminal values in dividend discount models (DDMs). These are referred to as terminal price multiples. -- By applying a P/E ratio, terminal value becomes a function of key factors such as the required rate of return and growth rate. 2- Approaches to Determine Terminal Price Multiples -- Fundamental Models: --- The Gordon growth model can be reformulated to calculate a P/E ratio, linking terminal value to financial estimates like return requirements and growth. -- Comparable-Based Models: --- Use the mean or median P/E ratios of industry peers. --- P/E ratios can be derived using trailing or forward EPS, with forward multiples being preferred in many cases. --- Advantages: The use of market data ensures the terminal value reflects the industry environment. --- Disadvantages: The benchmark P/E may be mispriced, leading to inaccuracies in terminal value estimation.

Answer 120

Key Takeaways -- P/E ratios simplify the calculation of terminal values in DDMs by leveraging growth, return, and comparables. -- The choice of approach depends on the availability of reliable market data and the assumptions about growth and required returns.

Question 121

[Basic and Diluted EPS] 1- Basic EPS Formula -- Formula: "Basic EPS = (Net Income - Preferred Dividends) ÷ Weighted Average of Shares Outstanding" -- Explanation: Basic EPS measures earnings per share based on the current shares outstanding. It does not account for potential shares from convertible securities. 2- Diluted EPS Formula -- Formula: "Diluted EPS = (Net Income - Preferred Dividends + Convertible Preferred Dividends + Convertible Debt Interest × (1 - Tax Rate)) ÷ (Weighted Average Shares + Shares From Preferred Shares + Shares From Convertible Debt + Shares Issuable From Stock Options)" -- Explanation: Diluted EPS includes adjustments for securities that could convert into common shares, such as stock options, convertible preferred shares, and convertible debt. Key Adjustments: -- Convertible Debt: Add back interest expense (net of tax) to net income since interest payments would not occur if the debt is converted. -- Stock Options and Warrants: Add the potential shares issuable under these instruments to the denominator.

Answer 121

Key Takeaways -- Basic EPS focuses on actual shares outstanding, while diluted EPS accounts for the dilutive effects of potential shares from other securities. -- Adjustments in diluted EPS ensure comparability by reflecting the potential dilution's impact on earnings per share.

Question 122

[Methods to Normalize Earnings] 1- Historical Average EPS -- Explanation: This method calculates the average earnings per share (EPS) over the most recent full business cycle. -- Usage: It accounts for fluctuations in earnings caused by the business cycle, providing a normalized EPS measure. 2- Average Return on Equity (ROE) -- Explanation: This method uses the average ROE from the most recent full business cycle, multiplied by the current book value per share, to normalize earnings. -- Usage: It adjusts for changes in company size by incorporating the current book value.

Answer 122

Key Takeaways -- Historical Average EPS is simple but may not account for changes in company size or structure. -- Average ROE considers company size through the book value per share, offering a more dynamic approach to normalizing earnings.

Question 123

[Price-to-Book (P/B) Ratio] 1- Overview of the Concept: The P/B ratio compares the market price per share to the book value per share (BV). BV represents the shareholders' equity minus preferred stock, divided by the common shares outstanding. 2- Formula: -- Book value per share formula: "BV per share = (Shareholders' equity - Preferred stock portion) / Common shares outstanding". 3- Rationale for Using P/B: -- 1- The book value remains positive even if earnings per share (EPS) is negative. -- 2- BV is more stable than EPS across a business cycle. -- 3- BV may align with market values for companies with liquid assets, such as insurance firms. -- 4- Useful when a company is not expected to continue as a going concern. -- 5- Differences in P/B ratios relate to long-run average returns. 4- Possible Drawbacks of P/B: -- 1- Critical assets, like human capital or brand reputation, may not appear on the balance sheet. -- 2- Accounting effects (e.g., internally generated intangibles vs. acquired assets) can distort BV. -- 3- Historical cost valuation of assets on financial statements may differ from market values. -- 4- Share repurchases can distort the book value of equity.

Answer 123

Key Takeaways -- P/B is a valuable metric for evaluating companies but must be interpreted alongside its limitations. -- The stability of BV and its limitations (e.g., unrecorded intangible assets) must be considered in analysis.

Question 124

[Determining Book Value] 1- Overview of the Concept: Book value per share is based on the balance sheet and represents the equity available to common shareholders. It is calculated by subtracting equity claims senior to common stock from total shareholders' equity and dividing by the number of common shares outstanding. 2- Formula: -- Common shareholders' equity formula: "Common shareholders' equity = Shareholders' equity - Equity claims senior to common stock". -- Book value per share formula: "BV per share = Common shareholders' equity / Number of common shares outstanding" ; Or "BV = Shareholders' Equity - Preferred Stock / Number of common shares outstanding". 3- Adjustments to Book Value: Adjustments are often needed to: -- 1- Better reflect the value of shareholder investment. -- 2- Facilitate comparisons between different stocks. 4- Common Adjustments Include: -- 1- Eliminating intangible assets, such as goodwill, to provide a clearer financial picture. -- 2- Switching from LIFO (Last-In, First-Out) to FIFO (First-In, First-Out) inventory accounting to ensure comparability of the P/B ratio. -- 3- Including significant off-balance-sheet assets and liabilities for a more comprehensive valuation. 5- Additional Considerations: Some assets and liabilities are recorded at historical cost, while others may be recorded at market value, depending on accounting standards. These differences should be considered when calculating the P/B ratio.

Answer 124

Key Takeaways -- Accurate adjustments to book value improve the reliability of P/B ratio analysis. -- Awareness of accounting methods is crucial for meaningful comparisons and insights.

Question 125

[Valuation Based on Forecasted Fundamentals] 1- Overview of the Concept: Fundamentals can be used to calculate a stock’s justified price-to-book (P/B) ratio. Two models are commonly used: the Gordon growth model and the residual income model. 2- Formulas: -- 1- Justified P/B using the Gordon growth model: "P0/B0 = (ROE - g) / (r - g)" --- Where: --- P0: Current stock price. --- B0: Book value per share. --- ROE: Return on equity. --- g: Growth rate of earnings. --- r: Required rate of return. -- 2- Justified P/B using the residual income model: "P0/B0 = 1 + (Present value of expected future residual earnings / B0)" 3- Explanation of the Gordon Growth Model: -- The justified P/B ratio is determined by the relationship between ROE and the required rate of return (r). -- A larger ROE relative to r generates a greater justified P/B. -- Among stocks with the same P/B, the one with higher ROE is relatively undervalued. 4- Explanation of the Residual Income Model: -- The justified P/B ratio incorporates the present value of expected future residual earnings. -- This model emphasizes earnings that exceed the required return on equity.

Answer 125

Key Takeaways -- The Gordon growth model emphasizes the relationship between ROE, growth, and the required rate of return. -- The residual income model highlights the role of future residual earnings in determining justified P/B. -- A higher justified P/B indicates better stock valuation fundamentals.

Question 126

Valuation Based on Comparables A P/B ratio can be used for a peer comparison-based valuation in the same way as a P/E ratio or other price multiples. Forecasted book values are not readily available in financial statements, so most analysts use trailing book values to compute P/B.

Question 127

[Price-to-Sales (P/S) Ratio] 1- Overview of the Concept: The P/S ratio evaluates a company’s valuation relative to its annual revenue. It has gained popularity for valuing both privately held and public companies. 2- Rationale for Using P/S: -- 1- Sales are less prone to distortion or manipulation compared to EPS or book value. -- 2- Sales are positive even when earnings per share (EPS) is negative. -- 3- Sales are more stable over time than EPS. -- 4- P/S is particularly useful for mature, cyclical, or zero-income companies. 3- Possible Drawbacks of Using P/S: -- 1- A company may exhibit high sales growth without corresponding profits. -- 2- Share price incorporates the effects of debt financing on profitability and risk, which sales alone do not reflect. -- 3- Sales do not account for a company’s cost structure, limiting insight into profitability. -- 4- Revenue recognition practices may distort the P/S ratio, depending on accounting policies. 4- Relationship Between P/S and P/E: The P/S ratio has a direct relationship with the P/E ratio and net profit margin: -- Formula: "P/S = (P/E) × (Net profit margin)".

Answer 127

Key Takeaways -- The P/S ratio is a useful alternative valuation measure when earnings or book value data are unreliable. -- Its limitations, such as ignoring cost structures and profitability, require careful interpretation alongside other metrics.

Question 128

[Price-to-Sales (P/S) Ratio Derived from the Gordon Growth Model] 1- Overview of the Concept: The P/S ratio can be derived from the Gordon growth model by incorporating profitability and growth factors. 2- Formula: "P0/S0 = (E0/S0) × (1 - b) × (1 + g) / (r - g)" -- Where: --- P0: Current stock price. --- S0: Sales per share. --- E0/S0: Profit margin (earnings-to-sales ratio). --- b: Retention ratio (proportion of earnings retained for reinvestment). --- g: Growth rate of earnings. --- r: Required rate of return. 3- Explanation of Key Variables: -- E0/S0 represents the profit margin, capturing the earnings generated per unit of sales. -- (1 - b) reflects the portion of earnings distributed as dividends. -- (1 + g) adjusts for expected earnings growth. -- The denominator (r - g) accounts for the difference between required return and growth rate, a key element of valuation.

Answer 128

Key Takeaways -- The P/S ratio derived from the Gordon growth model links sales to profitability, growth, and required returns. -- Higher profit margins and growth rates result in higher justified P/S ratios, while a higher required return lowers the ratio.

Question 129

[Valuation Based on Comparables] 1- Overview of the Concept: The P/S ratio is often used in valuation by comparing companies. Analysts typically report it on a trailing basis but may adjust it using forecasted sales. 2- Key Considerations: -- Analysts can use forward-looking sales estimates from data vendors to improve the relevance of P/S comparisons. -- The quality of a company’s financial reporting and accounting practices must be evaluated when comparing P/S ratios. -- Differences in accounting rules between companies can impact the comparability of P/S ratios.

Question 130

[Reporting of Assets and Liabilities] 1- Overview of the Concept: The reporting of assets and liabilities can differ based on whether they are recorded at historical cost or market value (fair value). This distinction impacts the interpretation of valuation metrics like the price-to-book (P/B) ratio. 2- Reporting Categories: -- Financial Assets: --- Typically reported at market value. --- "Held to maturity" financial assets are an exception, as they are recorded at historical cost. -- Non-Financial Assets: --- Usually reported at historical cost. --- Accumulated depreciation is subtracted from historical cost. --- Market value reporting applies under accounting rules related to impairment, preventing companies from reporting values higher than the current value. 3- Implications for P/B Ratio: -- The P/B ratio is more suitable for companies with predominantly financial assets, as these are often reported at fair value. -- Non-financial asset-heavy companies pose challenges for P/B comparisons due to the use of historical cost and depreciation.

Answer 130

Key Takeaways -- The P/B ratio is effective for valuing financial asset-based companies but is less reliable for firms with significant non-financial assets. -- Understanding the basis of asset valuation (historical cost vs. market value) is essential when analyzing P/B ratios.

Question 131

[Relationship Between Price-to-Earnings (P/E) and Price-to-Sales (P/S)] 1- Overview of the Concept: The relationship between the P/E ratio and the P/S ratio is directly influenced by the net profit margin. This connection allows analysts to compare valuation metrics across companies. 2- Formula: "P/S = P/E × Net Profit Margin" 3- Key Insights: -- If two stocks have the same P/E ratio: --- The stock with a higher net profit margin will have a higher P/S ratio. --- A lower net profit margin results in a lower P/S ratio. -- Example Comparison: --- Stock A and Stock B have equal P/E ratios. --- Stock A has a higher P/S ratio because its net profit margin is greater than Stock B’s.

Question 132

[Price-to-Cash-Flow (P/CF) Ratio] 1- Overview of the Concept: The price-to-cash-flow (P/CF) ratio is a widely used valuation measure that compares a company’s market price to its cash flow. It is considered less susceptible to accounting manipulation compared to earnings-based metrics. 2- Reasons for Using P/CF: -- 1- Cash flow is less prone to manipulation than earnings. -- 2- Cash flow is more stable over time than earnings. -- 3- Using cash flow helps address variations caused by accounting conservatism in reported earnings. 3- Drawbacks of Using P/CF: -- 1- Non-cash revenue items are excluded, potentially limiting the completeness of the metric. -- 2- Free cash flow to equity (FCFE), while more accurate, can be volatile and sometimes negative. -- 3- Accounting methods, particularly for operating cash flow, can inflate cash flow values. -- 4- Differences in cash flow allocation under IFRS and US GAAP (among operating, investing, and financing activities) create comparability challenges.

Answer 132

Key Takeaways -- P/CF is a reliable alternative to earnings-based metrics but requires careful consideration of how cash flow is defined. -- Differences in accounting practices and the choice of cash flow measure (e.g., FCFE vs. operating cash flow) can significantly impact the ratio's interpretation.

Question 133

[Determining Cash Flow] 1- Overview of the Concept: Cash flow can be approximated or calculated using several methods, each with varying degrees of accuracy and relevance for valuation. Commonly used concepts include cash flow from operations, free cash flow to equity (FCFE), and EBITDA. 2- Approximations for Cash Flow: -- A common approximation is "EPS plus depreciation, amortization, and depletion per share," referred to as the earnings-plus-noncash-charges definition. 3- Accurate Cash Flow Measures: -- 1- Cash Flow from Operations (CFO): --- Found in the statement of cash flows. --- Requires adjustments for nonrecurring items and differences in accounting standards when comparing companies. -- 2- Free Cash Flow to Equity (FCFE): --- Strongly linked to valuation theory. --- More volatile than CFO due to sensitivity to investment and financing decisions. -- 3- EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization): --- Can be calculated by adjusting reported earnings to exclude interest, taxes, and noncash charges like depreciation.

Answer 133

Key Takeaways -- CFO is a reliable measure of ongoing operations but requires adjustments for cross-company comparisons. -- FCFE is most closely tied to valuation but is more volatile. -- EBITDA serves as a proxy for cash flow but omits important cash outflows, like taxes and interest.

Question 134

[Valuation Based on Forecasted Fundamentals and Comparables] 1- Valuation Based on Forecasted Fundamentals: The justified price-to-cash-flow (P/CF) ratio depends on the required rate of return and growth rate. It is inversely related to the required rate of return and positively related to the growth rate. 2- Formula for Valuation: -- Intrinsic value assuming FCFE grows perpetually at a constant rate: "V0 = [(1 + g) × FCFE0] / (r - g)" -- Where: --- V0: Intrinsic value. --- g: Growth rate of free cash flow to equity (FCFE). --- FCFE0: Current free cash flow to equity. --- r: Required rate of return. -- Justified P/FCFE is calculated as: "Intrinsic value ÷ FCFE estimate". 3- Valuation Based on Comparables: -- Cash flow multiples (P/CF) can be used for relative valuations. -- For companies with negative FCFE, using operating cash flow or free cash flow to the firm in the denominator may provide a more meaningful comparison.

Answer 134

Key Takeaways -- The justified P/CF ratio reflects the relationship between growth, required return, and cash flow. -- Comparables-based valuation requires care when cash flows are negative, and alternative cash flow measures may be needed.

Question 135

[Dividend Yield in Valuation] 1- Overview of the Concept: Equity returns consist of capital appreciation and dividends. Dividend yield, a commonly reported metric, plays a key role in valuation by representing the income portion of total return. 2- Rationale for Using Dividend Yields: -- 1- Dividends are a tangible component of total return. -- 2- Dividends are considered less risky compared to capital appreciation, providing stability to investors. 3- Drawbacks of Using Dividend Yields: -- 1- Dividends are only one part of total return and do not capture capital gains. -- 2- Dividends paid reduce retained earnings and may displace earnings in future periods. -- 3- Dividends may not always be less risky, as companies can reduce or eliminate dividends during financial stress. 4- Calculation of Dividend Yield: -- It is preferable to calculate D/P (Dividend/Price) rather than P/D, as some companies do not pay dividends. -- Trailing Dividend Yield: --- Computed as the annualized amount of the most recent quarterly per-share dividend divided by the current market price. --- If the final dividend for the year differs from interim dividends, use the most recent annual dividend per share.

Answer 135

Key Takeaways -- Dividend yield is a useful valuation metric, emphasizing income stability. -- It should be used alongside other metrics, as it does not account for total equity returns or company reinvestment potential.

Question 136

[Trailing and Leading Dividend Yield] 1- Overview of Dividend Yield: Dividend yield measures the annual dividend income relative to the current stock price. It is used to evaluate income-generating potential. There are two primary types: trailing dividend yield and leading (forward) dividend yield. 2- Trailing Dividend Yield: -- Formula: "Trailing Dividend Yield = Dividend Rate / Current Market Price". --- Dividend Rate: Annualized amount of the most recent dividend. --- For quarterly dividends: "Dividend Rate = 4 × Quarterly Dividend per Share". --- Assumes quarterly dividends remain constant throughout the year. 3- Leading Dividend Yield: -- Formula: "Forward Dividend Yield = Forecasted Dividends per Share / Current Market Price". --- Reflects expected dividends, which may differ from past dividends. --- The forward yield could be higher or lower than the trailing yield, depending on dividend changes. .

Answer 136

Key Takeaways -- Trailing Yield focuses on historical dividend payments, providing a backward-looking measure. -- Leading Yield is forward-looking, incorporating expected changes in dividend payments. -- Investors should use both measures to assess a stock’s dividend performance and growth potential

Question 137

[Valuation Based on Dividend Yield] 1- Valuation Based on Forecasted Fundamentals: The dividend yield can be derived using the Gordon growth model. It reflects the relationship between required rate of return and growth rate. -- Formula: "D0 / P0 = (r - g) / (1 + g)" --- Where: --- D0: Current dividend. --- P0: Current stock price. --- r: Required rate of return. --- g: Growth rate of dividends. -- Insights: --- Dividend yield is positively correlated with the required rate of return (r). --- Dividend yield is negatively correlated with the growth rate (g). 2- Valuation Based on Comparables: When comparing dividend yields across companies, analysts should: -- 1- Attribute differences to other factors, such as expected growth rates. -- 2- Examine payout ratios to assess dividend safety. --- A high payout ratio indicates that a company may have limited capacity to increase future dividends. -- 3- Consider coverage ratios and leverage ratios for insights into the sustainability of dividends.

Answer 137

Key Takeaways -- Dividend yield is a valuable metric for assessing return and safety but requires adjustment for growth and payout sustainability. -- Comparables analysis should consider company-specific factors like payout and leverage ratios.

Question 138

[Enterprise Value to EBITDA (EV/EBITDA)] 1- Overview of the Concept: Enterprise value (EV) represents the total company value minus cash and short-term investments. The EV/EBITDA multiple compares EV to EBITDA, a pre-interest, pretax operating cash flow measure. EV multiples are less sensitive to leverage compared to price multiples. 2- Definition of EBITDA: EBITDA is the sum of net income, interest expenses, taxes, depreciation, and amortization. It serves as a measure of operating performance, excluding non-operational items. 3- Reasons for Using EV/EBITDA: -- 1- Useful for comparing companies with varying degrees of leverage. -- 2- Controls for differences in depreciation and amortization across firms. -- 3- EBITDA is often positive, even when earnings per share (EPS) are negative. 4- Drawbacks of EV/EBITDA: -- 1- EBITDA overestimates cash flow from operations if working capital is growing. -- 2- It ignores the impact of revenue recognition policies on cash flow from operations (CFO). -- 3- Free cash flow to the firm (FCFF) is more aligned with valuation theory than EBITDA.

Answer 138

Key Takeaways -- EV/EBITDA is a versatile valuation metric, especially for leveraged companies, but it has limitations in reflecting true cash flows. -- Alternative measures like FCFF should be considered for a more accurate valuation.

Question 139

[Enterprise Value and EV/EBITDA Valuation] 1- Determining Enterprise Value: Enterprise value (EV) represents the total market value of a company, adjusted for cash and short-term investments. -- Formula: "EV = Debt + Common equity + Preferred equity - Cash and short-term investments". --- Cash is subtracted because an acquirer would gain control of these assets when buying the company and use them to repay debt. 2- Valuation Based on Forecasted Fundamentals: The justified EV/EBITDA multiple depends on growth, returns, and costs: -- Positively related to the expected growth rate. -- Positively related to the return on invested capital (ROIC). -- Negatively related to the weighted average cost of capital (WACC). 3- Valuation Based on Comparables: -- A low EV/EBITDA multiple suggests a company may be undervalued compared to peers. -- An alternative measure is Total Invested Capital (TIC), which includes the market value of invested capital without subtracting cash and short-term investments.

Answer 139

Key Takeaways -- EV accounts for both equity and debt, making it suitable for leveraged companies. -- The EV/EBITDA multiple is influenced by growth, efficiency, and funding costs. -- TIC provides another perspective when cash holdings distort EV comparisons.

Question 140

[Enterprise Value Multiples] 1- Overview of EV Multiples: EV/EBITDA is the most widely used enterprise value multiple, but others such as EV/FCFF, EV/EBITA, and EV/EBIT are also common. These multiples adjust the denominator to include interest, ensuring cash flows reflect availability to all providers of capital. 2- Use of Nonfinancial Measures: -- Nonfinancial metrics can be included in the denominator for industry-specific valuations. --- Example: EV/proven reserves is a common metric for oil companies. 3- Enterprise Value to Sales (EV/S): -- EV/S is a common alternative to the price-to-sales (P/S) ratio. -- Particularly useful for comparing companies with different capital structures, as it incorporates both debt and equity financing.

Answer 140

Key Takeaways -- EV multiples are versatile and adjust for capital structure differences. -- EV/S is a useful alternative to P/S, especially for industries where debt plays a significant role in financing. -- Nonfinancial denominators allow for industry-specific valuations, such as EV/proven reserves in the energy sector.

Question 141

[Challenges in International Relative Valuation] 1- Overview of the Concept: Relative valuation is more complex in an international setting due to differences in economic conditions, accounting standards, and financial reporting practices. 2- Key Challenges: -- P/E ratios and other valuation multiples can vary significantly for companies in the same industry but based in different countries. -- Accounting data often require adjustments to facilitate meaningful comparisons. --- For example, restating financial statements from IFRS to US GAAP (or vice versa). --- Common adjustments include pensions and goodwill accounting. 3- Impact on Price Multiples: -- Cash flow-based metrics, such as P/CFO and P/FCFE, are the least affected by accounting differences. -- P/E, P/B, and EBITDA-based multiples are more influenced by variations in accounting rules.

Answer 141

Key Takeaways -- International valuation requires careful adjustments to align accounting standards. -- Cash flow-based multiples are more reliable for cross-country comparisons due to their reduced sensitivity to accounting rule differences. -- P/E, P/B, and EV/EBITDA multiples should be interpreted cautiously in global contexts.

Question 142

[Momentum Valuation Indicators and Earnings Surprise] 1- Overview of Momentum Indicators: Momentum valuation indicators compare a stock’s price or fundamental metric (e.g., earnings) to its historical values. These are commonly used to identify trends and potential future performance. -- Price-Based Momentum Indicators: Referred to as technical indicators. -- Fundamental Momentum Indicators: Examples include earnings surprise, standardized unexpected earnings, and relative strength. 2- Earnings Surprise: Earnings surprise measures the difference between reported earnings and expected earnings. -- Formula: "UE_t = EPS_t - E[EPS_t]" --- Where: --- UE_t: Unexpected earnings at time t. --- EPS_t: Reported earnings per share at time t. --- E[EPS_t]: Expected earnings per share at time t. -- Scaled Earnings Surprise: The unexpected earnings are divided by the standard deviation of analysts’ earnings forecasts. 3- Rationale for Using Earnings Surprise: -- Positive earnings surprises often signal the potential for future abnormal returns (alpha). -- Investors use earnings surprise as an indicator of a company's ability to exceed expectations, influencing market sentiment and stock valuation.

Answer 142

Key Takeaways -- Momentum indicators, such as earnings surprise, highlight trends and deviations from expectations. -- Positive earnings surprises may indicate a company's potential to deliver higher returns, serving as a leading indicator for future performance.

Question 143

[Standardized Unexpected Earnings (SUE) and Relative Strength] 1- Standardized Unexpected Earnings (SUE): SUE measures unexpected earnings adjusted for historical volatility, allowing for a scaled comparison of surprises. -- Formula: "SUE_t = [EPS_t - E(EPS_t)] / σ(EPS_t - E(EPS_t))" --- Where: --- EPS_t: Reported earnings per share at time t. --- E(EPS_t): Expected earnings per share at time t. --- σ: Standard deviation of unexpected earnings over past quarters. -- Purpose: SUE scales unexpected earnings by past volatility, making it a robust metric for evaluating earnings surprises across time or companies. 2- Relative Strength (RS): Relative strength compares a stock's performance to its past performance, peer group, or an index over a specified period. -- Usage: --- Patterns of persistence (momentum) or reversals are monitored by technical analysts. --- RS is typically scaled to 1.0 at the beginning of a period. --- A value below 1.0 at the end of the period indicates underperformance relative to the benchmark. -- Interpretation: --- High RS values suggest a stock is outperforming its peers or the index. --- Low RS values indicate underperformance and may signal caution.

Answer 143

Key Takeaways -- SUE accounts for earnings surprise volatility, making it valuable for cross-company or time-series analysis. -- Relative strength identifies performance trends, with higher RS values signaling momentum and lower values indicating lagging performance.

Question 144

[Averaging Multiples and Using Multiple Valuation Indicators] 1- Averaging Multiples: The Harmonic Mean The harmonic mean and weighted harmonic mean are commonly used for averaging valuation multiples to mitigate the impact of outliers. -- Harmonic Mean Formula: "X_H = n / ∑_i=1^n (1 / X_i)" --- Where: --- X_H: Harmonic mean. --- X_i: Individual values. --- n: Number of observations. -- Weighted Harmonic Mean Formula: "X_WH = 1 / ∑_i=1^n w_i (1 / X_i)" --- Where: --- X_WH: Weighted harmonic mean. --- w_i: Weights assigned to each value. -- Applications: --- The weighted harmonic mean is particularly useful for calculating the weighted average P/E ratio, effectively reducing the impact of extreme values (outliers). 2- Using Multiple Valuation Indicators -- Investors often use multiple valuation indicators, such as P/E, EV/EBITDA, and P/B, to make more informed decisions. -- Institutions may employ up to 10 factors when evaluating stocks. 3- Key Considerations in Using Multiples: -- Look-Ahead Bias: --- Occurs when decision-making uses information that was not available at the time of the analysis, such as financial reporting lags. --- It can lead to unrealistic results and should be avoided. -- Screening Process: --- Screening involves filtering investments based on valuation multiples and fundamental metrics. --- It helps narrow the selection of potential investments by applying criteria like valuation ratios, growth rates, or profitability.

Answer 144

Key Takeaways -- The harmonic mean is an effective method for averaging multiples while minimizing the effect of outliers. -- Using multiple valuation indicators reduces reliance on a single metric, improving decision accuracy. -- Investors should be cautious of biases like look-ahead bias and use screening to refine their investment universe.

Question 145

Quiz - Evaluation of Statement 1: Forward P/E Ratios vs. Earnings Yields 1- Overview of the Question This question assesses the accuracy of Hassan’s claim that using forward P/E ratios or earnings yields will always produce a meaningful ranking of comparable companies. 2- Correct Answer C: Incorrect with respect to forward P/E ratios. 3- Explanation 1- Why C is Correct (Forward P/E Ratios are Not Always Meaningful) -- Forward P/E ratios can become negative when a company is expected to report negative earnings in the future. -- A negative P/E ratio does not carry meaningful interpretative value for comparison or ranking purposes, as the relationship between price and negative earnings is not intuitive. 2- Why Earnings Yields Are Meaningful -- Earnings yield (Earnings ÷ Price, or the inverse of the P/E ratio) is always meaningful, as it produces a positive or zero value regardless of whether earnings are positive, negative, or zero. -- Earnings yields allow consistent ranking of companies from lowest to highest values, even in cases of financial distress.

Answer 145

Key Takeaways -- Forward P/E ratios can be misleading or meaningless when earnings are expected to be negative, as these result in a negative ratio. -- Earnings yields are more robust and provide meaningful comparisons in all scenarios, making them preferable in such cases. -- The correct answer, C, identifies the limitation of forward P/E ratios.

Question 146

[PEG Ratio and its Assumptions] 1- Overview of the PEG Ratio: The Price-to-Earnings-to-Growth (PEG) ratio assumes a linear relationship between the P/E ratio and growth. It is calculated as: "PEG = P/E ÷ Growth Rate". 2- Implications of the Assumption: -- Doubling the growth rate reduces the PEG ratio by half, assuming all other factors remain constant. --- Example: A stock with a P/E of 20 and a growth rate of 5% has a PEG of 4. If the growth rate increases to 10%, the PEG falls to 2. 3- Limitations of the Linear Relationship Assumption: -- The linear relationship implied by the PEG ratio does not hold in all valuation models, such as the Dividend Discount Model (DDM). --- Doubling the growth rate in the DDM formula does not result in a justified P/E ratio that is exactly half of its previous level.

Answer 146

Key Takeaways -- The PEG ratio provides a quick, simplified measure of valuation relative to growth, but its reliance on a linear relationship may oversimplify real-world scenarios. -- For more accurate valuation, models like the DDM, which account for nonlinear dynamics, should be considered.

Question 147

[Insights on Price-to-Book (P/B) Ratio] 1- Impact of Share Repurchases on P/B Ratio: -- Share repurchases and secondary issuances can distort the P/B ratio, complicating comparisons across time periods. --- Example: If shares are repurchased at prices above book value, the P/B ratio increases, even though the intrinsic value of the company might not have changed. 2- Stability of Book Value vs. Earnings: -- A company’s book value is generally more stable than its earnings over the business cycle. -- As a result, the P/B ratio provides a more meaningful and consistent measure of relative value compared to the P/E ratio during different phases of the cycle.

Answer 147

Key Takeaways -- When using P/B ratios, be cautious of distortions caused by share repurchases or issuances. -- The P/B ratio is a more reliable valuation tool for assessing long-term value, especially in cyclical industries or during periods of earnings volatility.

Question 148

Understanding Valuation Using P/E Ratios with an Example 1- Overview of the Concept -- Price-to-earnings (P/E) ratios are widely used to assess the relative valuation of a stock. A stock's P/E can be compared to historical averages or benchmarks to determine whether it is overvalued or undervalued. 2- Framework for Analysis -- To evaluate a stock’s valuation: --- Compare its current P/E to a relevant index or benchmark. --- Compare its current P/E to its historical average, accounting for any consistent discount or premium relative to the benchmark. 3- Metric 3 Calculations: P/E Relative to Historical Average -- Assume a stock's historical P/E has been 97% of the benchmark average. -- Formula for implied P/E: "Implied P/E = Benchmark P/E × Historical Discount Factor" --- Example Calculation: "Implied P/E = 15.72 × 0.97 = 15.25" -- Comparison: --- Current P/E = 15.67 --- Historical fair P/E = 15.25 --- Result: The stock is trading at a higher P/E than its historical fair value, making it overvalued under this analysis. 4- Metric 1 Calculations: P/E Relative to a Benchmark -- Formula for benchmark comparison: "P/E = Stock Price ÷ Earnings per Share" --- Example Calculation: "P/E = 60.34 ÷ 3.85 = 15.67" --- Benchmark P/E = 15.72 -- Result: The stock has a lower P/E than the benchmark, indicating it is undervalued when compared to the index.

Answer 148

Key Takeaways -- P/E ratios can provide insights into valuation, but results may differ depending on whether the comparison is to a benchmark or historical average. -- In this example, the stock appears undervalued relative to the index but overvalued relative to its historical fair value.

Question 149

5.5 Residual Income Valuation

Answer 149

-- Calculate and interpret residual income, economic value added, and market value added. -- Describe the uses of residual income models. -- Calculate the intrinsic value of a common stock using the residual income model and compare value recognition in residual income and other present value models. -- Explain fundamental determinants of residual income. -- Explain the relation between residual income valuation and the justified price-to-book ratio based on forecasted fundamentals. -- Calculate and interpret the intrinsic value of a common stock using single-stage (constant-growth) and multistage residual income models. -- Calculate the implied growth rate in residual income, given the market price-to-book ratio and an estimate of the required rate of return on equity. -- Explain continuing residual income and justify an estimate of continuing residual income at the forecast horizon, given company and industry prospects. -- Compare residual income models to dividend discount and free cash flow models. -- Explain strengths and weaknesses of residual income models and justify the selection of a residual income model to value a company’s common stock. -- Describe accounting issues in applying residual income models.

Question 150

[Residual Income and its Use in Equity Valuation] 1- Overview of Residual Income (RI): Residual income is the net income remaining after deducting the cost of equity capital (the shareholders’ opportunity cost). It is also referred to as economic profit, abnormal earnings, or economic value added. 2- Calculation of Residual Income: Residual income explicitly accounts for the cost of equity capital. Two approaches can be used: -- 1- Subtract the equity charge from net income. -- 2- Subtract the capital charge (for both debt and equity) from net operating profit after tax (NOPAT). 3- Use of Residual Income in Equity Valuation: -- Value Creation: --- A company with positive residual income is creating value. --- A company with negative residual income is destroying value. -- Relation to Earnings Yield (E/P): --- If the earnings yield equals the required rate of return for a no-growth company, the stock is just covering its cost of equity. -- Applications: --- Residual income models are used for valuing individual stocks and stock indexes. --- RI is also applied to measure goodwill impairment.

Answer 150

Key Takeaways -- Residual income provides a more accurate measure of value creation by incorporating the cost of equity. -- It is particularly useful for evaluating whether a company is earning above its required rate of return. -- RI models are valuable for equity valuation and assessing goodwill impairment.

Question 151

[Commercial Implementations of Residual Income] 1- Economic Value Added (EVA): EVA is a commercial implementation of residual income and measures a company’s economic profit. -- Formula: "EVA = NOPAT - (WACC × TC)" --- Where: --- NOPAT: Net operating profit after taxes. --- TC: Total capital. -- Adjustments to Accounting Data for EVA Calculation: --- Capitalizing research and development expenses. --- Expensing only cash taxes (not deferred taxes). --- Adding back the LIFO reserve. --- Treating operating leases as capital leases. 2- Market Value Added (MVA): MVA represents the difference between the market value of a company and the accounting book value of its total capital. -- Formula: "MVA = Market value of company - Accounting book value of total capital" "MVA = (DMV + EMV) - (DBV + EBV)" --- Where: --- DMV: Market value of debt. --- EMV: Market value of equity. --- DBV: Book value of debt. --- EBV: Book value of equity. 3- Applications: -- Companies with positive residual income should have a positive MVA, as they are creating value beyond the cost of capital. -- EVA and MVA are widely used to: --- Measure internal corporate performance. --- Determine executive compensation. --- Assess economic profit rather than equity valuation.

Answer 151

Key Takeaways -- EVA focuses on economic profit after accounting for the cost of capital and requires adjustments to financial data. -- MVA evaluates value creation by comparing market and book values. -- These metrics are critical for assessing performance and aligning management incentives.

Question 152

[Residual Income Model for Intrinsic Valuation] 1- Residual Income (RI) Formula: The residual income measures the earnings above the cost of equity capital. -- Formula: "RI_t = E_t - rB_t-1" --- Where: --- RI_t: Residual income in period t. --- E_t: Company’s net income for period t. --- r: Company’s cost of equity. --- B_t-1: Book value of equity at the beginning of period t. 2- Intrinsic Value Using Residual Income Model: The intrinsic value (V_0) of a company is the sum of its current book value (B_0) and the present value of all future residual income. -- Formula: "V_0 = B_0 + ∑_t=1^∞ [RI_t ÷ (1 + r)^t]" -- Substituting RI_t: "V_0 = B_0 + ∑_t=1^∞ [(E_t - rB_t-1) ÷ (1 + r)^t]" 3- Key Insights of the Residual Income Model: -- Value Creation and Book Value: --- Companies earning more than their cost of capital sell for more than their book value. --- Companies earning less than their cost of capital sell for less than their book value. -- Relation to Dividend Discount Model (DDM): --- Under consistent assumptions, the residual income model provides the same intrinsic value as the DDM. --- However, value recognition in RI models often occurs earlier.

Answer 152

Key Takeaways -- The residual income model is particularly useful for valuing companies with inconsistent or no dividend payouts. -- It integrates the cost of equity, emphasizing whether the company is adding value beyond its equity capital costs. -- The RI model highlights the importance of current book value and future earnings in valuation.

Question 153

Companies that earn more than the cost of capital should sell for more than their book value. Similarly, companies that earn less than the cost of capital should sell for less than their book value.

Question 154

[General Residual Income Model Derived from the Clean Surplus Relationship] 1- Assumption of Clean Surplus Accounting: Clean surplus accounting assumes that changes in the book value of equity (B_t) are only due to earnings (E_t) and dividends (D_t): "B_t = B_t-1 + E_t - D_t". 2- Substitution of Dividends: Using the clean surplus relationship, intrinsic value (V_0) can be expressed in terms of earnings and book value changes: "V_0 = [E1 + B0 - B1] / (1 + r)^1 + [E2 + B1 - B2] / (1 + r)^2 + [E3 + B2 - B3] / (1 + r)^3 + …". 3- Residual Income Model Formula: The above expression simplifies into the residual income model: "V_0 = B_0 + ∑_t=1^∞ RI_t / (1 + r)^t". --- Substituting "RI_t = E_t - rB_t-1", we get: "V_0 = B_0 + ∑_t=1^∞ [(ROE × E_t - r)B_t-1] / (1 + r)^t". 4- Interpretation: -- Residual Income Model (RI): It expresses intrinsic value as the sum of: --- Current book value of equity (B_0). --- Present value of future residual income, which measures earnings exceeding the cost of equity.

Answer 154

Key Takeaways -- The RI model is useful for valuing companies with inconsistent or no dividend payments but stable book value or earnings. -- Clean surplus accounting ensures the consistency of residual income computations. -- The RI model incorporates book value and profitability, linking them directly to intrinsic valuation.

Question 155

[Fundamental Determinants of Residual Income] 1- Justified Price-to-Book (P/B) Ratio: The residual income model determines the justified P/B ratio based on fundamental drivers, including ROE, growth, and required return. -- Formula: "P/B = (ROE - g) / (r - g)" --- Alternatively expressed as: "P/B = 1 + [(ROE - r) / (r - g)]" -- Where: --- ROE: Accounting return on equity. --- g: Sustainable growth rate. --- r: Required return on equity. 2- Single-Stage Residual Income Model with Constant Growth: For a constant growth rate (g), the residual income model simplifies the intrinsic value formula: "V_0 = B_0 + [(ROE - r) / (r - g)] × B_0" --- Where: --- V_0: Intrinsic value. --- B_0: Book value of equity. 3- Relation to Tobin’s q: Tobin’s q is similar to the P/B ratio but uses total capital instead of equity: "Tobin’s q = Market value of debt and equity / Replacement cost of total assets". 4- Key Insights: -- A high justified P/B ratio indicates a company is earning returns (ROE) above its cost of equity (r), suggesting value creation. -- Tobin’s q assesses the relationship between a company’s market value and the replacement cost of its total assets, offering a broader perspective.

Answer 155

Key Takeaways -- The residual income model connects P/B ratios to fundamental drivers like ROE, growth, and required return, emphasizing the importance of profitability relative to equity costs. -- Tobin’s q extends this analysis to total capital, making it useful for assessing overall asset efficiency and valuation.

Question 156

It is normally not appropriate to assume a constant perpetual growth rate and ROE spread over the cost of equity. Eventually, the ROE will revert to the cost of equity and the residual income will be zero. This leads to the multistage residual income model.

Answer 156

The terminal value of residual income often approaches zero because the ROE approaches the cost of equity.

Question 157

[Multistage Residual Income Model] 1- Overview of the Multistage Residual Income Model: This model estimates residual income over a finite time horizon and includes a terminal value, known as continuing residual income. As the return on equity (ROE) approaches the cost of equity, the residual income often declines toward zero. The book value captures a significant part of the valuation. 2- Assumptions for Continuing Residual Income: -- Residual income may continue indefinitely. -- Residual income may be zero starting in the terminal year. -- Residual income may gradually fade to zero over time. 3- Formulas for Valuation: With a Terminal Premium at Time T: "V_0 = B_0 + ∑_t=1^T [(E_t - rB_t-1) / (1 + r)^t] + [(P_T - B_T) / (1 + r)^T]" --- Where: --- P_T: Price or terminal value at time T. --- B_T: Book value at time T. With Fading Residual Income Over Time: "V_0 = B_0 + ∑_t=1^(T-1) [(E_t - rB_t-1) / (1 + r)^t] + [(E_T - rB_T-1) / ((1 + r - ω)(1 + r)^(T-1))]" --- Where: --- ω: Persistence factor (0 ≤ ω ≤ 1). --- ω = 1: Residual income persists without fading. --- ω = 0: Residual income ends at T. 4- Key Insights for the Persistence Factor (ω): -- A higher persistence factor is justified if: --- The company has a low dividend payout ratio. --- Historical persistence levels in the industry are high. -- A lower persistence factor is recommended for: --- Companies with significant nonrecurring items or accruals. --- Industries with high ROE volatility.

Answer 157

Key Takeaways -- The multistage RI model balances short-term earnings with assumptions about terminal value and persistence. -- Proper estimation of the persistence factor (ω) is critical to accurately valuing companies with varying residual income sustainability. -- Book value forms a strong base for valuation, complemented by future residual income forecasts.

Question 158

The total present value is consistent using expected dividends, expected free cash flow, or book value plus expected residual income. However, residual income models recognize value sooner than dividend discount models because much of the value is in the initial book value. This is advantageous because there is more uncertainty in forecasting dividends or cash flow far into the future.

Question 159

[Strengths and Weaknesses of the Residual Income Model] 1- Strengths of the Residual Income Model: -- Terminal values constitute a smaller portion of the total present value, reducing reliance on long-term assumptions. -- Uses readily available accounting data, making it practical and accessible. -- Applicable to companies with no dividends or negative cash flows in the near term. -- Can be employed when cash flows are unpredictable or volatile. -- Focuses on economic profitability, directly tying valuation to excess returns over equity costs. 2- Weaknesses of the Residual Income Model: -- Relies on accounting data, which may be subject to manipulation. -- Accounting data often require adjustments to align with economic realities. -- Requires clean surplus accounting, which may not always hold. -- Assumes that the cost of debt capital is correctly reflected in net income, which may not be accurate in all cases.

Answer 159

Key Takeaways -- The RI model is particularly useful for valuing firms with inconsistent cash flows or no dividends. -- However, care must be taken to ensure the reliability and accuracy of accounting inputs. -- Clean surplus violations or improper cost-of-capital assumptions can undermine its effectiveness.

Question 160

[Guidelines for Using the Residual Income Model] 1- When the Residual Income (RI) Model is Most Appropriate: -- The company does not pay dividends, or dividend payments are unpredictable. -- Near-term free cash flows are negative, making traditional cash flow models less reliable. -- There is significant uncertainty in forecasting terminal values, as the RI model reduces reliance on terminal value assumptions. 2- When the RI Model is Least Appropriate: -- Clean surplus accounting does not hold, meaning changes in book value are not fully captured by net income and dividends. -- Book value and return on equity (ROE) are unpredictable or inconsistent, undermining the model's foundational assumptions.

Answer 160

Key Takeaways -- The RI model is ideal for firms with limited or irregular dividends, negative cash flows, or when terminal value forecasts are uncertain. -- It is less suitable in cases of accounting inconsistencies or when key metrics like ROE and book value lack stability.

Question 161

Key Takeaways: - Residual Income Model (RI): Best for companies with unpredictable dividends or negative cash flows; relies on clean surplus accounting. - DDM: Suitable for dividend-paying firms with stable patterns; less applicable for growth firms or those not paying dividends. - FCF Model: Ideal for firms with stable cash flows; struggles when cash flows are highly volatile or negative. - Book Value Models: Work well for asset-heavy companies; limited by the reliability of book value and clean surplus assumptions. - Price Multiples: Effective for benchmarking against peers; less useful with negative or distorted values. - EV Multiples: Flexible for firms with leverage; sensitive to accounting adjustments and non-operating impacts.

Question 162

[Residual Income Valuation in Relation to Other Approaches] 1- Dividend Discount Model (DDM): -- The DDM calculates the present value of expected future dividends to determine stock value. -- Uses the cost of equity as the discount rate. -- Best for firms with stable and predictable dividend payments. 2- Free Cash Flow to Equity (FCFE): -- Measures the cash available to equity holders after all expenses, reinvestment, and debt repayment. -- Uses the cost of equity as the discount rate. -- Suitable for firms with positive and predictable free cash flows, even if they don't pay dividends. 3- Free Cash Flow to Firm (FCFF): -- Captures the cash flows available to all providers of capital (equity and debt). -- Uses the weighted average cost of capital (WACC) as the discount rate. -- Ideal for firms with significant leverage or complex capital structures. 4- Residual Income Model (RI): -- The RI model adjusts the book value of equity by adding the present value of expected future residual income. -- Residual income is recognized earlier than in other models, reducing the reliance on terminal value assumptions. -- Uses the cost of equity as the discount rate.

Answer 162

Key Takeaways -- All these models calculate intrinsic value as the present value of future returns, with specific applications based on company characteristics. -- The choice of model depends on dividend stability, cash flow predictability, and the firm’s capital structure. -- In theory, all models should yield consistent intrinsic values when used under equivalent assumptions.

Question 163

[Accounting Adjustments and Clean Surplus Violations in the Residual Income Model] 1- Required Accounting Adjustments for the Residual Income Model: -- Adjust the book value of common equity to account for off-balance sheet items. -- Adjust the reported net income to reflect comprehensive income. 2- Strength of the Residual Income Model: -- The model balances book value and future earnings under clean surplus accounting. -- Clean surplus accounting ensures that all changes in equity (except transactions with shareholders) flow through the income statement. 3- Challenges with Clean Surplus Accounting: -- IFRS and US GAAP often permit items to bypass the income statement, violating clean surplus accounting. -- For example: --- Capitalizing expenses increases book value while lowering future earnings through amortization. --- Aggressive past accounting may inflate book value and reduce future residual income. 4- Violations of the Clean Surplus Relationship: -- Violations occur when changes in stockholders’ equity bypass the income statement. -- Examples: --- Changes in the market values of certain investments. --- Foreign currency translation adjustments. -- Consequences: --- The book value may remain accurate, but net income may be misstated for residual income valuation. 5- Comprehensive Income in Residual Income Forecasts: -- Comprehensive income includes both net income and other equity changes. -- Residual income forecasts should be based on comprehensive income, not solely on net income, to address clean surplus violations.

Answer 163

Key Takeaways -- The accuracy of the residual income model depends on clean surplus accounting; violations can lead to valuation errors. -- Adjustments to book value and income are necessary to reflect comprehensive financial performance.

Question 164

[Adjustments for Valuation Accuracy] 1- Balance Sheet Adjustments for Fair Value: -- Off-balance sheet items, such as operating leases, deferred tax assets and liabilities, and intangible assets, must be adjusted to their fair value. -- Inventory and other assets or liabilities should also reflect fair values to provide an accurate assessment. 2- Intangible Assets: -- Intangible assets, though not always recognized in book value, can contribute significantly to a company’s value. -- Examples: --- Advertising can create valuable brands that only appear on balance sheets post-acquisition. --- Research and development (R&D) investments generate intangible assets, boosting ROE over time. -- M&A activities might cause the combined value of companies to differ from the sum of their book values due to intangible asset recognition. 3- Non-Recurring Items: -- Non-recurring items (e.g., extraordinary items, restructuring charges, and discontinued operations) must be excluded from earnings to forecast future profitability accurately. 4- Other Aggressive Accounting Practices: -- Practices like accelerating revenues, deferring expenses, or using cookie jar reserves may overstate earnings or assets, misleading valuation models. 5- International Considerations: -- Variations in accounting standards (e.g., IFRS vs. US GAAP) may hinder valuation comparability across countries. -- Clean surplus accounting and reliable earnings forecasts are essential for consistency. -- IFRS adoption is reducing discrepancies in international comparisons.

Answer 164

Key Takeaways -- Accurate valuations require adjustments for fair value, particularly for off-balance sheet items and intangible assets. -- Analysts should be vigilant about non-recurring items and aggressive accounting practices to avoid distorted valuations. -- Harmonization of international standards (e.g., IFRS) facilitates global comparability of valuation models.

Question 165

[Adjustments and Accounting Practices for Residual Income Model] 1- Dependence on Accounting Data -- The residual income model relies heavily on accounting data, which requires certain adjustments to ensure accuracy. 2- Necessary Adjustments for Residual Income Model -- Adjustments to the book value of equity for off-balance sheet items. -- Adjustments to reported net income to derive comprehensive income. 3- Balancing Book Value and Future Earnings -- Book value and future earnings tend to balance each other in the residual income model. --- Aggressive accounting practices (e.g., capitalizing expenses rather than expensing them) can lead to: ---- Overstated current earnings and book value. ---- Understated future earnings due to higher future depreciation expenses. --- Conservative accounting practices may result in: ---- Lower book value. ---- Higher future earnings. -- Ultimately, the present value of differences in both components offsets each other. 4- Violations of Clean Surplus Accounting -- Clean surplus accounting requires that all changes in equity, except for transactions with shareholders, flow through the income statement. -- Examples of violations under IFRS and US GAAP include: --- Bypassing the income statement for items like currency translation adjustments and changes in market value of investments.

Answer 165

Key Takeaways -- Proper adjustments to book value and net income are crucial for accurate residual income valuation. -- Clean surplus violations can distort the model, necessitating additional adjustments to maintain consistency. -- The balancing effect between book value and future earnings ensures that differences in accounting practices do not significantly alter intrinsic valuation.

Question 166

Treatment of Non-Recurring Items in Residual Income Valuation 1- Overview of Non-Recurring Items -- Non-recurring items, such as restructuring charges, are one-time expenses that do not reflect the ongoing earning potential of a firm. -- When using residual income models or other valuation methods, including these items in future earnings forecasts can distort the results. 2- Correct Treatment -- The appropriate action is to exclude non-recurring items, such as the restructuring charge, from the estimate of net income. --- This ensures the valuation reflects normalized earnings, which are representative of the firm’s ongoing performance. -- Adjustment process: --- Add back the restructuring charge to net income. --- This upward adjustment avoids understating future earnings and residual income, which could lead to an undervaluation of the firm.

Answer 166

Key Takeaways -- Excluding non-recurring charges like restructuring expenses is essential for accurate forecasts in residual income valuation. -- Valuations should focus on recurring items to capture a firm's sustainable earnings potential.

Question 167

Multistage Residual Income Model for Intrinsic Value Estimation 1- Overview of the Formula -- The intrinsic value per share is calculated using the multistage residual income model: --- Formula: "V0 = B0 + ∑ [(Et - rBt-1) ÷ (1 + r)^t] + [(ET - rBT-1) ÷ (1 + ω)(1 + r)^(T-1)]" --- Where: --- B0: Beginning book value per share. --- Et: Earnings per share in year t. --- r: Cost of equity. --- Bt-1: Book value at the end of the previous period. --- ω: Persistence factor for residual income. --- T: Last year before terminal value calculation. 2- Steps for the Calculation -- 1- Calculate residual income per share for each year: --- ROE = Earnings ÷ Book Value. --- Growth rate = ROE × Retention rate. --- Retention rate = 1 - (Dividends ÷ Earnings). --- Equity charge per share = Book Value × Cost of Equity. --- Residual income per share = EPS - Equity charge per share. -- 2- Project book value for subsequent years: --- Formula: "Book value = Book value_(t-1) + Earnings_(t-1) - Dividends_(t-1)". -- 3- Calculate terminal value: --- Formula: "PV(Terminal Value) = [(ET - rBT-1) ÷ (1 + ω)] ÷ [(1 + r)^(T-1)]". -- 4- Discount residual incomes and terminal value to present value: --- Sum all discounted residual incomes and the present value of terminal value. 3- Calculation Results -- Year-by-year residual income (RI): --- 2022 RI = 2.52. --- 2023 RI = 2.31. --- 2024 RI = 1.98. --- Terminal value (2025): PV = 3.0203. -- Intrinsic value (V0): --- "V0 = 7.60 + (2.52 ÷ 1.10) + (2.31 ÷ 1.10^2) + (1.98 ÷ 1.10^3) + 3.0203 = R16.31".

Answer 167

Key Takeaways -- Multistage residual income models effectively account for fading residual income over time. -- Persistence factors (ω) capture the expected decay in residual income contributions beyond a certain period. -- Accurate book value, earnings projections, and cost of equity are critical for reliable valuations.

Question 168

Residual Income Calculation Example 1- Formula for Residual Income (RI): -- Residual income measures the excess income after accounting for the equity cost. -- Formula: "RI_t = E_t - r × B_(t-1)" --- E_t: Earnings in the current period. --- r: Required return on equity. --- B_(t-1): Book value of equity at the beginning of the period. 2- Steps to Calculate RI: -- 1- Determine the required return on equity (r) using CAPM: --- Formula: "r = Risk-free rate + (Beta × Equity Risk Premium)". --- Substituting values: "r = 2.3% + (1.20 × 5.2%) = 8.54%". -- 2- Calculate the book value of equity at the start of 20X8 (B_20X7): --- Formula: "B_(t) = B_(t-1) + Earnings_(t-1) - Dividends_(t-1)". --- Given: --- Initial book value at the start of 20X7 = $10.17. --- Earnings for 20X7 = $3.27. --- Dividends for 20X7 = 65% of earnings = 0.65 × $3.27 = $2.13. --- Book value for the start of 20X8: "B_20X7 = $10.17 + $3.27 - $2.13 = $11.31". -- 3- Compute Residual Income for 20X8: --- Formula: "RI_20X8 = E_20X8 - (r × B_20X7)". --- Earnings for 20X8 = $3.94. --- Required return component: "r × B_20X7 = 8.54% × $11.31 = $0.966". --- Residual income: "RI_20X8 = $3.94 - $0.966 = $2.97".

Answer 168

Key Takeaways -- Residual income is a critical measure of value added to equity beyond its cost. -- Accurate calculation requires understanding book value changes due to earnings and dividends. -- In this example, the RI for 20X8 is $2.97

Question 169

Justified Price-to-Book Ratio Calculation Example 1- Formula for Justified Price-to-Book (P/B) Ratio: -- The justified P/B ratio is derived using the residual income model. -- Formula: "P/B = (ROE - g) / (r - g)" --- ROE: Return on equity. --- g: Sustainable growth rate. --- r: Required return on equity. 2- Steps to Calculate the P/B Ratio: -- 1- Determine the sustainable growth rate (g): --- Formula: "g = b × ROE", where b is the retention rate. --- Retention rate (b): "b = 1 - Dividend payout ratio". --- Dividend payout ratio = 65%, so: --- "b = 1 - 0.65 = 0.35". --- Sustainable growth rate: "g = 0.35 × 15% = 5.25%". -- 2- Substitute into the P/B formula: --- Given: ROE = 15%, r = 8.54%, g = 5.25%. --- Calculation: "P/B = (15% - 5.25%) / (8.54% - 5.25%)". --- "P/B = 9.75% / 3.29%". --- "P/B = 2.96".

Answer 169

Key Takeaways -- The justified P/B ratio reflects the relationship between the return on equity, sustainable growth rate, and required return on equity. -- A higher ROE relative to r increases the P/B ratio, while a higher g reduces it. -- In this example, the justified P/B ratio is calculated to be 2.96.

Question 170

Intrinsic Value Calculation Example 1- Formula for Intrinsic Value Using the Residual Income Model: -- Formula: "V0 = B0 + [(ROE - r) / (r - g)] × B0". --- V0: Intrinsic value per share. --- B0: Beginning book value per share. --- ROE: Accounting return on equity. --- r: Required return on equity. --- g: Sustainable growth rate. 2- Calculating the Inputs: -- 1- Calculate Book Value per Share (B0): --- Formula: "B0 = BVt-1 + Et - Dt". --- BVt-1 = $10.17 (previous book value per share). --- Et = $3.27 (earnings per share). --- Dt = $2.13 (dividend per share). --- Calculation: "B0 = $10.17 + $3.27 - $2.13 = $11.31". -- 2- Determine the Required Return (r): --- Formula: "r = rf + (β × ERP)". --- rf = 2.3% (risk-free rate). --- β = 1.20 (beta). --- ERP = 5.2% (equity market risk premium). --- Calculation: "r = 2.3% + (1.20 × 5.2%) = 8.54%". -- 3- Calculate the Growth Rate (g): --- Formula: "g = b × ROE". --- b = 1 - Dividend Payout Ratio = 1 - 0.65 = 0.35. --- ROE = 15%. --- Calculation: "g = 0.35 × 15% = 5.25%". 3- Substitute into the Formula for Intrinsic Value: -- Step 1: "ROE - r = 15% - 8.54% = 6.46%". -- Step 2: "r - g = 8.54% - 5.25% = 3.29%". -- Step 3: "[(ROE - r) / (r - g)] × B0 = (6.46% / 3.29%) × $11.31 = $22.21". -- Step 4: "V0 = B0 + [(ROE - r) / (r - g)] × B0". --- "V0 = $11.31 + $22.21 = $33.52".

Answer 170

Key Takeaways -- The intrinsic value of the equity is calculated as $33.52 per share. -- The share price of $29.83 is below the intrinsic value, indicating the stock is undervalued. -- This valuation demonstrates the importance of the residual income model in assessing equity values beyond earnings-based approaches.

Question 171

Impact of Dividend Payout on Intrinsic Value Calculation 1- Formula for Intrinsic Value Using the Residual Income Model: -- Formula: "V0 = B0 + [(ROE - r) / (r - g)] × B0". --- V0: Intrinsic value per share. --- B0: Beginning book value per share. --- ROE: Accounting return on equity. --- r: Required return on equity. --- g: Sustainable growth rate. 2- Analysis of Scenarios: -- 1- Retention Rate Effect on Growth (g): --- The growth rate (g) is calculated as "g = Retention Rate × ROE". --- A higher retention rate results in a higher growth rate since more earnings are reinvested instead of being distributed as dividends. -- 2- Book Value per Share (B0): --- B0 reflects retained earnings. When dividends are reduced, a greater portion of earnings is retained, leading to a higher book value. --- As B0 increases, it contributes more to the intrinsic value calculation through the residual income formula. -- 3- Comparison Between Scenarios: --- In Scenario 3, the dividend payout is reduced to 60% for 20X7, compared to 65% in Scenario 2. --- This results in a higher retention rate and a larger book value per share at the end of 20X7. 3- Conclusion: -- Since B0 is higher in Scenario 3 and directly affects the intrinsic value formula, the intrinsic value of the stock in Scenario 3 is higher than in Scenario 2. -- The retention of additional earnings in Scenario 3 enhances the firm’s equity base, reinforcing its future income-generating capacity.

Answer 171

Key Takeaways -- A higher retention rate contributes to a greater intrinsic value due to its effect on both growth rate and book value. -- The relationship between dividend payouts and intrinsic value is crucial in evaluating equity under the residual income model.

Question 172

5.6 Private Company Valuation

Answer 172

-- Contrast important public and private company features for valuation purposes. -- Describe uses of private business valuation and explain key areas of focus for financial analysts. -- Explain cash flow estimation issues related to private companies and adjustments required to estimate normalized earnings. -- Explain factors that require adjustment when estimating the discount rate for private companies. -- Compare models used to estimate the required rate of return to private company equity (for example, the CAPM, the expanded CAPM, and the build-up approach). -- Explain and evaluate the effects on private company valuations of discounts and premiums based on control and marketability. -- Explain the income, market, and asset-based approaches to private company valuation and factors relevant to the selection of each approach. -- Calculate the value of a private company using income-based methods. -- Calculate the value of a private company using market-based methods and describe the advantages and disadvantages of each method.

Question 173

[Uses of Private Company Valuation] 1- Transaction-Related Uses -- Venture Capital Financing (Early Stage) --- Early-stage companies receive minority or majority investments tied to achieving milestones. --- Valuation methods are informal, based on negotiations between founders and investors. -- Private Equity Financing (Growth or Buyout Stage) --- Valuations help in leveraged acquisitions to unlock value through restructuring operations. --- Private equity investors aim for higher exits with growing firms. -- Debt Financing --- Assesses the company's ability to generate sufficient cash flows for repaying current or prospective debt obligations. -- Initial Public Offering (IPO) --- Used to value firms going public, often referencing similar public companies. --- Applicable for spin-offs, capital-intensive early-stage firms, or firms returning public post-restructuring. -- Acquisitions and Divestitures --- Valuations support buying or selling mature firms, specific business units, or entire entities. -- Bankruptcy --- Determines whether to restructure capital or liquidate assets. Asset-based methods are common in these scenarios. -- Share-Based Payment (Compensation) --- Used to value stock grants or restricted shares for accounting and tax purposes.

Question 174

[Uses of Private Company Valuation (Compliance- and Litigation-Related)] 1- Compliance-Related Uses -- Financial Reporting --- Valuations are required for accounting standards, such as goodwill impairment testing. -- Tax Reporting --- Used to determine tax obligations for private companies and individual shareholders. --- Relevant for equity transfers as gifts or part of a deceased individual’s estate. 2- Litigation-Related Uses -- Corporate Disputes --- Applied in legal matters like contractual disputes, product liability claims, or financial damages. -- Shareholder Disputes --- Minority shareholders may challenge majority decisions affecting the company’s valuation or operations.

Answer 174

Key Considerations -- Each purpose requires specific expertise, such as compliance knowledge for financial reporting or legal experience for dispute resolution. -- Discrepancies in valuation may arise depending on the objective (e.g., tax valuation vs. acquisition valuation).

Question 175

[Private Company Areas of Focus] 1- Intrinsic Enterprise Value Calculation -- Formula: "Enterprise Value = ∑_(i=1)^n [FCFF_i ÷ (1 + WACC)^i] + [Terminal Value ÷ (1 + WACC)^n]" 2- Earnings Normalization -- Free Cash Flow to the Firm (FCFF) formula: "FCFF = EBITDA(1 - t) + Depreciation(t) - ΔLT Assets - ΔWorking Capital" -- Reported earnings and cash flows must be adjusted for accurate private company valuation projections. 3- Discount Rate/Rate of Return Adjustments -- The CAPM-based WACC for public companies may not suit private companies due to the absence of market-observed prices. 4- Valuation Discount or Premium -- Adjustments for FCFF numerator and denominator account for illiquidity and the degree of control granted by buyer positions.

Question 176

[Private Company Financial Statements and Adjustments 1- Differences in Financial Statements: Public vs. Private Companies -- Public companies typically provide detailed, audited financial statements, whereas private companies may disclose less information. -- Private company financial reporting is often influenced by factors such as the owner's personal expenses being conflated with business expenses or above-market compensation arrangements. 2- Types of Private Company Financial Statements -- Compiled financial statements: Basic reports prepared without independent auditor assurance. -- Reviewed financial statements: Include an auditor's opinion letter but lack the rigor of audited financials. 3- Challenges with Private Company Financial Statements -- Compiled and reviewed financial statements are subject to less scrutiny than public company audited reports. -- These reports may not accurately reflect the company's operational performance post-acquisition. 4- Need for Adjustments -- Analysts must normalize earnings and cash flows to reflect a more accurate operational picture of the private company. -- Adjustments may include separating personal expenses from business expenses or standardizing compensation levels.

Answer 176

Key Takeaways -- Valuing private companies often requires additional adjustments to financial statements to ensure accuracy. -- Analysts rely on normalization techniques to present a clearer picture of private company performance.]

Question 177

[Earnings Normalization for Private Companies 1- Overview of Normalization Challenges -- Comparing private company earnings to public companies is complex due to non-recurring, non-economic items, and recurring anomalies. -- Adjustments ensure financial statements reflect the company's true operational performance. 2- Common Normalization Issues -- Revenue adjustments: Revenues may be inflated or understated due to related-party transactions involving entities owned by the founder or family members. -- COGS adjustments: Cost of goods sold may include non-market compensation packages or other irregular costs. -- Interest expense: Loans to shareholders or related-party terms may skew reported interest expenses. -- Depreciation: Founders’ personal asset use (e.g., real estate, airplanes) can lead to overstated depreciation expenses. -- Taxable income: Income adjustments may arise due to different tax treatments, especially if the company becomes public. -- Dividend adjustments: Dividend payments may need to be normalized to reflect expected levels under new ownership. 3- Real Estate Considerations -- Real estate holdings are often analyzed separately, as their revenues and expenses are excluded from core financial statements. -- These assets are treated differently due to varying risk levels and growth expectations compared to company operations.

Answer 177

Key Takeaways -- Normalization ensures private company financials are comparable to public companies by adjusting for non-economic items and anomalies. -- Separate treatment of real estate ensures accuracy in reflecting operational performance.]

Question 178

[Cash Flow Estimation Issues for Private Companies 1- Overview of Cash Flow Challenges -- Estimating cash flows for private companies involves unique challenges compared to public companies due to ownership structures, uncertainty, and potential biases. 2- Key Estimation Factors -- Ownership Impact on FCFE: Estimates of free cash flow to equity (FCFE) depend on whether the investor is acquiring a majority or minority stake. -- Uncertainty: Private companies face greater uncertainty in projections due to factors such as product development, acquisitions, and regulatory changes. --- These events often have larger impacts on private companies and require scenario-based or probability-weighted forecasting methods. -- Management Bias: Managers have deeper insights into the business than external analysts, but their forecasts can be biased: --- Results may be biased high for goodwill impairment testing. --- Results may be biased low for considerations such as stock option grants.

Answer 178

Key Takeaways -- Cash flow estimation for private companies requires adjustments to account for ownership intent, uncertainty, and potential management biases. -- Probability-weighted scenarios can improve the accuracy of cash flow projections under varying conditions.]

Question 179

[Factors Affecting Private Company Discount Rates] 1- Size Premiums -- Analysts often add size premiums to discount rates for private companies due to their smaller size. -- Caution is needed to avoid applying premiums based on data from the smallest publicly traded companies (e.g., microcaps), which may reflect financial distress and not equivalency with small private firms. 2- Availability and Cost of Debt -- Private companies typically have less access to debt compared to public companies, leading to higher borrowing costs. -- Increased reliance on equity financing raises the weighted average cost of capital (WACC). -- Smaller private companies face higher operating and financing risks. 3- Acquisition Context -- The cost of capital for valuing a target should align with the target’s capital structure and cash flow riskiness. -- Using the acquirer’s lower cost of capital artificially inflates valuations, transferring additional value to the target’s shareholders. 4- Adjustments for Projection Risk -- A premium should be added to the discount rate to account for private companies’ limited data and greater uncertainty. -- Challenges such as less experienced management and incomplete information can lead to overly optimistic or pessimistic projections.

Answer 179

Key Takeaways -- Discount rates for private companies are influenced by size premiums, higher debt costs, and projection uncertainties. -- Proper adjustments are essential to avoid mispricing during valuations.

Question 180

[Required Rate of Return Models] 1- Standard CAPM Formula -- Formula: re = rf + β(rm - rf) -- Variables: --- rf: Risk-free rate. --- β: Beta, indicating sensitivity to market equity risk. --- rm: Expected equity market return. --- (rm - rf): Equity risk premium (ERP). 2- Expanded CAPM for Private Companies -- Adjustments: Adds premiums for small-cap stocks and company-specific risks. -- Formula: re = rf + β(rm - rf) + Small-cap stock premium + Company-specific stock premium. -- Purpose: Suitable for small private companies that are not public or plan not to go public. 3- Build-Up Method -- Assumption: Beta is set to 1. -- Formula: re = rf + (rm - rf) + Small-cap stock premium + Company-specific stock premium ± Industry premium/discount. -- Applications: Adds industry-specific premiums or discounts, reflecting risk adjustments not captured by beta.

Answer 180

Key Takeaways -- CAPM serves as the baseline for estimating equity cost but is insufficient for private companies with unique risks. -- Expanded CAPM and the build-up method provide more flexibility for valuing small, private entities or those with industry-specific risk factors.

Question 181

[Private Company Valuation Adjustments and Investor Types] 1- Types of Buyers -- Strategic Buyers: --- Larger competitors integrating operations for synergies (e.g., cost savings, increased revenues). --- Willing to pay a higher price reflecting a synergistic control premium. -- Financial Buyers: --- Focused on fundamentals, seeking majority ownership. --- Lack expertise/resources for synergies but may target synergistic buyers for potential sale. 2- Discounts in Valuation -- Discount for Lack of Control (DLOC): --- Applied when a minority ownership position lacks significant influence over decisions. -- Discount for Lack of Marketability (DLOM): --- Reflects restrictions on share liquidity (e.g., timing of liquidity events like IPOs). --- Valuation may align with an equivalent public company if DLOM is absent.

Answer 181

Key Takeaways -- Strategic buyers often pay more due to synergy potential, while financial buyers prioritize fundamentals. -- DLOC and DLOM reflect control and liquidity limitations, affecting valuation significantly.

Question 182

[Lack of Control and Marketability Discounts] 1- Lack of Control Discounts (DLOC): -- Reflects a valuation reduction for a minority owner's lack of authority to: --- Appoint or influence directors, executives, or key managers. --- Adjust returns through above-market compensation. --- Determine timing of shareholder distributions. -- Formula for DLOC: --- "DLOC = 1 - (1 ÷ (1 + Control premium))" 2- Lack of Marketability Discounts (DLOM): -- Represents a reduction in valuation due to limited liquidity compared to publicly traded shares. -- Factors influencing DLOM: --- Restriction periods on share sales. --- Uncertainty about sale price and future liquidity events. --- Volatility of underlying assets, which can be approximated through put option premiums.

Answer 182

Key Takeaways -- DLOC adjusts for the absence of control, while DLOM addresses limited liquidity. -- Combined discounts often apply to non-controlling interests using multiplicative rather than additive methods.

Question 183

[Combined Discounts Example] 1- Given: -- Lack of control discount (DLOC) = 10% -- Lack of marketability discount (DLOM) = 20% 2- Formula for Total Discount: -- "Total discount = 1 - [(1 - DLOC) × (1 - DLOM)]" 3- Calculation: -- Substituting the values: --- "Total discount = 1 - [(1 - 0.1) × (1 - 0.2)]" --- "Total discount = 1 - (0.9 × 0.8)" --- "Total discount = 1 - 0.72" --- "Total discount = 0.28 or 28%"

Answer 183

Key Takeaways -- The multiplicative approach ensures accurate combined discounts. -- Total discounts reflect compounded effects of DLOC and DLOM.

Question 184

[Valuation Discounts and Premiums for Private Companies] 1- Strategic Control: -- Represents the highest valuation due to synergies achieved by integrating the target company's resources with existing operations. -- Includes synergistic control premium. 2- Financial Control: -- Provides a control premium but lacks strategic synergies. -- Valuation is lower than strategic control. 3- Comparable Public Company Valuation: -- Based on public market benchmarks without adjustments for control or lack of marketability. -- Serves as a midpoint reference for private company valuations. 4- Non-Controlling Minority Interest: -- Reflects a discount for lack of control (DLOC). -- Represents a valuation lower than comparable public company valuation due to the inability to influence key decisions. 5- Non-Controlling, Non-Marketable Minority Interest: -- Reflects both DLOC and a discount for lack of marketability (DLOM). -- Represents the lowest valuation, as it includes restrictions on control and liquidity.

Answer 184

Key Takeaways -- Valuations decline from strategic control (highest) to non-controlling, non-marketable minority interest (lowest). -- DLOC and DLOM represent significant reductions in value for minority and illiquid positions.

Question 185

[Private Company Valuation Approaches] 1- Major Approaches to Private Company Valuation: -- Income Approach: Estimates intrinsic value by discounting expected future earnings or cash flows to the present value. -- Market Approach: Uses relative valuation based on price or enterprise value multiples. -- Asset-Based Approach: Calculates value as the total assets minus liabilities. 2- Income-Based Approach: Free Cash Flow Valuation Method -- Formula Name: Intrinsic Value Formula. -- Formula: "Intrinsicvalue = T∑_i=1 [ FCFF_i ÷ (1 + WACC)^i ] + [ TerminalValue ÷ (1 + WACC)^n ]" -- Where: --- FCFF_i: Free cash flow to the firm in period i. --- WACC: Weighted average cost of capital. --- TerminalValue: Future value of the firm beyond the forecast horizon. --- n: Forecast period. -- Key Features: --- Uses discount rate (WACC) to reflect the risk of expected cash flows. --- Terminal value estimation relies on growth rate assumptions or pricing multiples. --- The method is comparable to public company valuation, tailored for private firms.

Answer 185

Key Takeaways -- Free cash flow valuation incorporates cash flow projections for both lenders and shareholders. -- The choice between income, market, or asset-based methods depends on the company's stage, operations, and size.

Question 186

[Capitalized Cash Flow Method] 1- Overview: -- The capitalized cash flow method (CCM) estimates a firm's value by dividing projected free cash flow (FCFF) by a capitalization rate. -- This approach assumes a constant growth rate, g, for FCFF and capitalizes it at the weighted average cost of capital (WACC). 2- Formulas: -- Formula Name: Enterprise Value Formula (using FCFF). -- Formula: "Enterprisevalue_k = FCFF_(k+1) ÷ (WACC - g)" -- Formula Name: Reinvestment Rate (RIR). -- Formula: "RIR = g ÷ WACC" -- Enterprise Value Formula (using EBIT and RIR): --- Formula: "Enterprisevalue_k = [EBIT_(k+1)(1 - t)(1 - RIR)] ÷ (WACC - g)" --- Where: ---- EBIT_(k+1): Earnings before interest and taxes for period (k+1). ---- t: Tax rate. ---- RIR: Proportion of net income reinvested in working capital and fixed assets. ---- WACC: Weighted average cost of capital. ---- g: Assumed growth rate. -- Formula Name: Equity Value Formula. -- Formula: "Equityvalue_k = FCFE_(k+1) ÷ (re - g)" -- Where: --- FCFE_(k+1): Free cash flow to equity for period (k+1). --- re: Required return on equity. 3- Key Points: -- Enterprise value includes the combined market values of debt and equity. -- RIR measures the reinvestment portion of net income based on growth and WACC. -- Analysts may estimate market-based values of debt or use face value as a proxy if operations are stable. -- Valuations are sensitive to small changes in inputs, especially the expected growth rate, g.

Answer 186

Key Takeaways -- CCM assumes a constant growth rate in FCFF or FCFE. -- Valuation results depend on accurate inputs for growth, WACC, tax rates, and reinvestment proportions. -- Intrinsic equity value is derived by adjusting enterprise value for debt or directly capitalizing FCFE.

Question 187

[Excess Earnings Method (EEM)] 1- Overview: -- The EEM estimates the value of a company's intangible assets by capitalizing future earnings exceeding required returns on working capital and fixed assets. -- It is primarily used to value intangible assets and is most applicable for very small businesses or when market approaches are unfeasible. 2- Steps for Calculating Firm Value: Step 1: Calculate required returns on working capital and fixed assets. -- Formulas: --- "Required return on working capital = Working capital × r_WC" --- "Required return on fixed assets = Fixed assets × r_FA" -- Explanation: --- r_WC: Required return on working capital, which is lower due to its liquidity. --- r_FA: Required return on fixed assets, which is higher due to their illiquidity. Step 2: Calculate residual income. -- Formula: --- "Residual income = Normalized income - (Working capital × r_WC) - (Fixed assets × r_FA)" -- Explanation: Residual income is the income available after accounting for required returns on tangible assets. Step 3: Capitalize residual income to find intangible asset value. -- Formula: --- "Value of intangibles = (Residual income × (1 + g)) ÷ (r_RI - g)" -- Explanation: --- r_RI: Required return on residual income, higher than r_FA and r_WC due to the risk and illiquidity of intangible assets. --- g: Constant growth rate of residual income. Step 4: Calculate the firm's total enterprise value. -- Formula: --- "Total enterprise value = Valueofintangibles + Fair value of working capital + Fair value of fixed assets" -- Explanation: The firm's enterprise value is the sum of intangible and tangible assets. 3- Key Notes: -- The EEM relies on assumptions about required returns and growth rates, making it subjective and challenging for larger companies. -- Residual income aligns with financial reporting standards for intangible asset valuation.

Answer 187

Key Takeaways -- EEM is ideal for valuing intangible assets in small firms or unique cases. -- Required returns are higher for intangible assets due to their risk and illiquidity. -- Total enterprise value includes all tangible and intangible assets at their fair market values.

Question 188

[Income-Based Approaches: Excess Earnings Method] 1- Overview of the Excess Earnings Method (EEM): -- The EEM evaluates intangible assets by calculating excess earnings above required returns for working capital and fixed assets. -- It is a supplementary valuation tool and provides additional data points for estimating the value range. 2- Key Challenges and Subjectivity: -- The method requires estimates for: --- Working capital returns. --- Fixed asset returns. --- Intangible asset returns. -- Analysts acknowledge that these estimates are highly subjective. 3- Usefulness and Limitations: -- EEM-derived valuations are not considered precise but can inform a broader valuation range. -- Best suited for providing a secondary perspective in determining a firm's value.

Answer 188

Key Takeaways -- The excess earnings method complements other approaches by focusing on intangible asset valuation. -- Valuation precision depends heavily on subjective inputs, making it a less definitive method. -- It provides another data point to refine the estimated valuation range.

Question 189

[Market-Based Approaches to Valuing Private Companies] 1- Overview of the Market-Based Approach: -- This approach values private companies by comparing them to public companies or acquired firms using metrics like enterprise value (EV) or market price per share. -- EV-based metrics are favored for their ability to analyze firm-wide value and their stability compared to equity values. 2- Key Valuation Techniques: -- 1- Guideline Public Company Method: --- Uses multiples from public company trading activities, adjusted for the private company's risk and growth prospects. -- 2- Guideline Transactions Method: --- Applies pricing multiples from past acquisitions of public or private companies. -- 3- Prior Transaction Method: --- Utilizes actual past transactions involving the subject private company. 3- Advantages and Challenges: -- Market-based methods are preferred due to their reliance on real market data and transactions. -- Challenges include difficulties in finding directly comparable transactions for private companies due to unique company-specific factors.

Answer 189

Key Takeaways -- Market-based approaches leverage external comparisons to provide realistic valuation estimates. -- The availability and comparability of relevant market data are critical to the accuracy of this approach.

Question 190

[Guideline Public Company Method] 1- Overview of the Guideline Public Company Method: -- This method values private companies by identifying comparable public companies, selecting pricing multiples, and adjusting them for differences in risk and growth prospects. -- It incorporates weighted averages of different peer groups for industries where a private company operates in multiple sectors. 2- Key Calculation Adjustments: -- 1- Unlevered Beta Calculation: --- Formula: "β_unlevered = β_levered / [1 + (1 - t) × (Debt ÷ Equity)]". --- Variables: ---- β_unlevered: Beta adjusted for the absence of leverage. ---- β_levered: Beta reflecting the impact of debt and equity. ---- t: Tax rate. ---- Debt ÷ Equity: Debt-to-equity ratio. -- 2- Levered Beta Calculation for Private Company: --- Formula: "β_levered = β_unlevered × [1 + (1 - t) × (Debt* ÷ Equity*)]". --- Variables: ---- β_levered: Adjusted beta for the private company's leverage. ---- β_unlevered: Unlevered beta of the comparable public company. ---- t: Private company tax rate. ---- Debt* ÷ Equity*: Private company's debt-to-equity ratio. 3- Additional Considerations: -- 1- Control Premium Adjustments: --- Public company prices often exclude control premiums as they reflect minority share prices. --- Adjustments are necessary for valuing private companies where a majority ownership position is involved. -- 2- Type of Buyer: --- Strategic buyers typically pay a higher control premium than financial buyers due to expected synergies. -- 3- Industry Dynamics: --- Peer prices may already reflect partial control premiums if acquisitions are anticipated within the industry. -- 4- Forms of Consideration: --- Acquisitions using stock-based payments can distort control premium indications if overvalued shares are used.

Answer 190

Key Takeaways -- The guideline public company method is useful for leveraging the valuation metrics of publicly traded peers. -- Adjustments for differences in leverage, taxation, and control premiums ensure a more accurate valuation for private companies. -- Careful selection of comparable public companies and accurate adjustments are critical for the method's reliability.

Question 191

[Guideline Transactions Method and Prior Transaction Method] 1- Overview of Guideline Transactions Method: -- The guideline transactions method (GTM) is similar to the guideline public company method (GPCM), but it uses pricing multiples from acquisitions of comparable companies rather than quoted market prices. -- Transaction data is typically sourced from public regulatory filings, although such data is subject to higher uncertainty compared to market price data. -- Transaction multiples are particularly relevant when valuing private companies for acquisition purposes. 2- Key Factors to Consider in GTM: -- 1- Regulatory Documentation: Rely on transaction details from public sources like regulatory filings to ensure transparency. -- 2- Uncertainty in Data: Recognize the limitations of private transaction data, as it may not reflect broader market trends. 3- Overview of Prior Transaction Method: -- The prior transaction method derives the value of a private company based on historical transactions involving its equity. -- It is particularly useful for valuing minority equity positions but is less reliable when transaction records are infrequent or dated. 4- Key Factors to Consider in Prior Transaction Method: -- 1- Synergies: Transaction prices in strategic acquisitions may not be comparable to financial transactions due to differences in expected synergies. -- 2- Contingent Consideration: Transaction prices may include potential future payments dependent on certain conditions. -- 3- Non-Cash Consideration: Acquisitions financed largely with stock can reduce comparability to all-cash transactions. -- 4- Relevance of Transaction Data: The relevance of older transaction data may diminish due to market and economic changes. -- 5- Timing Differences: Valuation multiples created for specific transactions may lose accuracy over time due to changes in valuation conditions.

Answer 191

Key Takeaways -- GTM uses acquisition multiples to value private companies, requiring adjustments for uncertainty and comparability. -- The prior transaction method is most relevant for minority equity valuations but is limited by the availability and relevance of historical data. -- Both methods rely heavily on accurate adjustments for synergies, contingent payments, and transaction timing to provide reliable valuations.

Question 192

Appropriateness of Valuation Methods: FCFE vs. FCFF 1- Difference Between FCFE and FCFF Approaches -- Free Cash Flow to Equity (FCFE) reflects cash available to equity holders after all obligations, including debt servicing, have been met. -- Free Cash Flow to the Firm (FCFF) reflects cash generated by the business available to all capital providers (both debt and equity holders). 2- Sensitivity to Leverage Changes -- FCFE is directly impacted by changes in leverage, as adjustments to debt levels influence cash flows available to equity holders. -- FCFF is less sensitive to leverage changes because it considers the firm's cash flows before interest payments, with WACC used to account for capital structure. 3- Rationale for FCFF Appropriateness -- If significant changes to the capital structure are expected, the FCFF approach is more appropriate because it avoids direct sensitivity to leverage. -- In this situation, WACC, which accounts for the target capital structure, is a stable discount rate for valuation under FCFF.

Answer 192

Key Takeaways -- When a firm anticipates a major shift in leverage, FCFF is preferred over FCFE as it mitigates the influence of leverage on valuation. -- The FCFF approach allows for a clearer representation of the firm’s intrinsic value under an expected new capital structure.