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.

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
– Leading 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.