Question regarding motives for taking the class, e.g., wealth generation versus acquiring job skills.
Distinction between valuation as a discipline and common misconceptions regarding its practice.
Possibility of distinguishing valuation as a science, art, or magic.
Valuation is framed as a craft, not wholly a science or an art, suggesting a structured but flexible approach.
The analogy of cooking is employed to illustrate that valuation is learned through practice and iteration.
The fundamental drivers of business value:
$$V = \frac{CF}{(1 +
r)^t}$$
where V is the value, CF is the cash flow, r is the discount rate, and t
is the time period.
The distinction between business value and market price, with a focus on how external factors can affect perception and valuation.
Value: Intrinsic measurement based on potential cash flows, risk, and growth.
Price: Market perception influenced by supply and demand, sentiment, and momentum.
Behavioral finance explains why prices deviate from value based on investor psychology.
The importance of integrating numbers and storytelling in valuation practices.
Use of real-world examples (e.g., Tesla, GameStop) to discuss valuation implications.
Encouragement to engage actively in the learning process through assignments and peer discussions.
Valuation is a critical skill in finance, and it often heavily influenced by biases and preconceptions. This set of notes summarizes key points covered in the course, focusing on concepts and equations relevant to valuation.
Market Sentiment: E.g., valuing companies like Nvidia amidst market excitement can create upward bias.
Hindsight Bias: Evaluating decisions with the benefit of hindsight can distort valuation approaches.
The Power of Suggestion: Influential market figures can sway personal valuation perspectives.
Incentives: The valuation can be skewed based on who is paying for the analysis (e.g., venture capitalists vs. appraisers).
When valuing one’s own business:
Expectation of upward bias (a higher value).
When valuing in a divorce context:
Expectation of downward bias (a lower value).
When valuing for tax:
Goal often leads to a desired lower value to reduce tax liability if you are the appraiser of the owner.
Sell-side Analysts are influenced by the need to maintain favorable relationships with companies they cover, often resulting in biased positive recommendations.
Buy-side Analysts work internally and may also face biases based on portfolio management goals.
The M&A process is typically characterized by:
Misaligned incentives between the acquiring and target companies, leading to biased valuations.
The search for synergistic value often used to justify inflated purchase prices.
Value of Asset = Present Value of Expected Cash Flows
Key
components include:
Cash flows
Discount rate
Life of the asset
Valuation is an objective search for truth. This is misleading since all valuations are affected by bias.
A good valuation guarantees the right answer. Instead, the critical factors include how wrong can the valuation be and what biases exist.
Bigger models yield better valuations. Complexity often obscures the essential inputs, leading to inaccuracies.
The three primary valuation approaches:
Intrinsic Valuation: Emphasizes cash flows and discounting.
Relative Valuation: Compares the subject to similar companies.
Option Pricing: Useful for assets with contingent cash flows.
Understanding biases and the nuances of valuation allows for better decision-making. It’s crucial to exercise self-awareness regarding biases, as well as consistency in the approach to evaluating companies.
Valuation is a crucial concept in finance and involves estimating the worth of a business or its assets. This class emphasizes two main approaches: intrinsic valuation and pricing.
Intrinsic valuation focuses on estimating the present value of expected cash flows generated by an asset. Key elements include:
Cash Flows: The cash inflows expected from the business or investment.
Discount Rate: The required return used to discount future cash flows to the present value.
The fundamental equation for intrinsic valuation is:
$$\text{Value of Asset} =
\sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}$$
where:
CFt = Cash flow at time t
r = Discount rate
n = Number of periods
Results tend to be sensitive to assumptions regarding cash flows and the discount rate.
Cash Flows to Equity (CFE): Cash flows available to equity holders after all expenses,
debts, and reinvestments have been accounted for.
Cash Flows to the Firm (CFF): Total cash flows before deducting debt payments. The valuation
of the entire business uses CFF, discounted at the Weighted Average Cost of Capital (WACC).
Weighted Average Cost of Capital (WACC)
WACC is calculated as a blend of the cost of equity and the cost of debt:
$$WACC = \left( \frac{E}{V} \cdot r_e \right) + \left( \frac{D}{V} \cdot r_d \cdot (1 -
T) \right)$$
where:
E = Market value of equity
D = Market value of debt
V = E + D (total market value of the firm)
re = Cost of equity
rd = Cost of debt
T = Corporate tax rate
Pricing is another method of valuation where the worth of an asset is determined based on what similar assets are selling for in the market.
Standardization of Price: For comparison, prices are often adjusted to per unit (e.g., price per share, price per square foot).
Finding Comparables: Identify similar companies and properties to assess value.
Common pitfalls in valuation include:
Misestimating future cash flows.
Using inappropriate discount rates.
Not adjusting for risk and market conditions.
The It Proposition states that if a factor does not affect expected cash flows or risk, it cannot affect value. Considerations highlighted include:
Control: The ability to run a company differently can increase its value.
Brand Name: Higher margins due to brand power will reflect in cash flows.
Synergy: Should reflect in the expected cash flows and not be viewed as an additional premium.
Valuation is both an art and a science, requiring both quantitative skills and qualitative judgments. Understanding cash flows, risk, and the market is critical to producing an accurate valuation.
This document serves as a comprehensive guide to understanding valuation principles, particularly focusing on Discounted Cash Flow (DCF) models, discount rates, and cash flows relevant for equity and firm valuation.
When valuing an enterprise, it is crucial to maintain consistency between cash flows and respective discount rates:
If cash flows are after debt payments and available to equity investors, use Cost of Equity as the discount rate.
If cash flows are to all claim holders (both equity and debt), use Cost of Capital.
This leads to two primary valuation methods:
Discount cash flows to the firm at the Cost of Capital to determine the firm’s total value.
Subtract outstanding debt from the firm value to derive equity value.
When transitioning from firm value to equity value, what type of debt should you subtract?
Do not subtract accounts payable, as these are non-interest-bearing liabilities.
Subtract the value of all interest-bearing debt, including long-term debt and lease commitments, to maintain consistency with the cost of capital.
You can approach equity valuation through two methods:
Discounting cash flows to equity at the Cost of Equity.
Discounting cash flows to the firm at the Cost of Capital and then subtracting the debt.
Ideally, both methods should yield the same equity value, maintaining consistency throughout the valuation process.
Given a set of cash flows and costs, let’s illustrate the valuation:
Cash flows to equity: 50M, 60M, 68M, 76.2M.
Cost of equity: re = 13.625%.
Market value of equity: E = 1.073 billion.
Market value of debt: D = 800 million.
The present value of cash flows to equity is calculated as follows:
$$PV =
\sum_{t=1}^{n} \frac{CF_t}{(1 + r_e)^t}$$
After calculations, suppose this gives a total equity
value of Ve = 1.73 billion. Alternatively, using
cash flows to the firm:
Cash flows to the firm = 90M
Then,
discounting at the Cost of Capital (assumed 9.94%):
$$PV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r_c)^t}$$
Calculating this gives total
firm value Vf = 1.87 billion, and adjusting for debt
yields equity value consistent with 1.73 billion.
When growing cash flows, ensure the growth rates reflect the cash flow type:
Equivalent growth rates in revenue, operating income, and earnings must be maintained.
Observe historical growth patterns as indicators for future projections.
For instance, note how growth rates may vary based on operational efficiency:
Growth rate = Reinvestment Rate × Return on Capital
The risk-free rate serves as the foundation of the discount rate:
Determine based on the time horizon and currency.
A common choice in the U.S. is the yield on a 10-year Treasury bond for long-term cash flows.
Utilizing the Capital Asset Pricing Model (CAPM):
re = rf + β × (E(Rm) − rf)
Where:
rf = Risk-free rate
β = Measure of systematic risk
E(Rm) = Expected market return
Risks in valuation can be categorized into:
Economic Risk: External factors beyond control (e.g., inflation, interest rates).
Estimation Risk: Uncertainties from data collection and analysis.
Micro and Macro Risk: Specific company risks versus market-wide risks.
When dealing with economic risk reflected in the discount rate, analysts must avoid double counting risks by ensuring that cash flows are based on expected values without further risk adjustment.
This document acts as a foundation for understanding the nuances in valuation processes, particularly emphasizing consistency across cash flows and discount rates, accurate growth rate projections, and the influence of risk. The methods and models discussed are essential for effective financial analysis and firm valuation.
In financial valuation, understanding the dynamics of risk-free rates and equity risk premiums is crucial, particularly in the context of valuing a company with diverse revenue streams.
A risk-free rate is the return on an investment with zero risk of financial loss, typically derived from government bonds.
When valuing a multinational company like Nestlé, which draws revenue from various countries and currencies, it’s important to align the risk-free rate to the currency of the cash flows being evaluated. Given the revenue distribution:
10% in Switzerland
30% in the EU
40% in the US
20% in India
The question arises: Which risk-free rate to use for valuation?
Avoid Simple Averages: A simple average of different risk-free rates, especially from different currencies, lacks meaning.
Weighted Averages: While this might seem like a necessary alternative, without a consistent base (i.e., using the same currency), it doesn’t provide rational insight.
Select Based on Cash Flow Currency: The risk-free rate must match the currency in which cash flows are estimated. If analyzing cash flows in Swiss Francs, use the Swiss risk-free rate.
In regions where government bonds come with default risks (e.g., emerging markets), it is essential to remove the default spread to evaluate the true risk-free rate.
Compare to Dollar or Euro Denominated Bonds: If available, compare the yield of the local bond with that of US or German bonds to derive the default spread.
Sovereign Credit Default Swap (CDS) Market: Use CDS rates to estimate default spreads based on insurance costs against default.
Country Ratings: For countries without dollar or euro bonds, look up the sovereign rating and estimate the corresponding default spread using historical data for other countries with similar ratings.
The equity risk premium is defined as the excess return that investing in the stock market provides over a risk-free rate. It reflects the additional risk investors assume by investing in equities.
There are several methods to estimate the ERP:
Historical Approach: Calculate the historical average returns of equity over a long period compared to risk-free rates.
Given a hypothetical scenario:
$$\begin{aligned}
\text{Return of Stocks} &= 26\% \\
\text{Return of T-bonds} &= 3.88\% \\
\text{ERP}_{\text{last year}} &= 26\% - 3.88\% = 22.12\%\end{aligned}$$
This single-year ERP can be misleading due to its noise and should not be isolated without context.
Standard error measures the accuracy of the historical mean and reflects uncertainty in the calculated ERP. It
can be determined as follows:
$$\begin{aligned}
\text{Standard Error} &= \frac{\sigma}{\sqrt{n}} \end{aligned}$$
where σ is the standard deviation of returns and n is the number of observations.
Organize and maintain consistency in the currency of analysis.
Use appropriate risk-free rates based on cash flow currencies.
Understand implications of historical data on expected future premiums.
Consider inflation and economic conditions when assessing risk-free rates.
Focus on Cash Flow Projections: Valuation must align with projections of cash flow and associated risks.
Regional Adjustments: For multinational corporations, regional risks and respective equity risk premiums must be factored in, aligning with operational geography.
The discussion foregrounds the need for valuing companies and understanding equity risk premiums (ERPs). Students are encouraged to choose a company for valuations, emphasizing timely decision-making since the course has progressed through several sessions.
Traditional methods for estimating equity risk premiums rely heavily on historical data. Key points include:
Historical ERPs often use the risk premium data from the past 50 to 100 years.
Problems associated with historical data include:
Backward-Looking Nature: Reflects the past rather than projecting future expectations.
Noisy Data: Historical risk premiums can vary significantly, posing reliability issues (measured by standard error).
Market-Specific Challenges: In emerging markets where historical data may be insufficient or unavailable (e.g., Vietnam).
An implicit method can be used to derive the ERP by examining investors’ behaviors and their willingness to pay for equities:
If an individual pays $50 for a perpetuity of $1 annually, the implied expected return can be reflected in
the payment amount. For example, an investment guaranteeing $1/year in perpetuity at a risk-free rate of 4% implies:
$$\text{Expected Return} =
\frac{\text{Cash Flow}}{\text{Price Paid}} = \frac{1}{50} = 2\%$$
Risk aversion directly influences equity risk premiums; generally, older investors may demand higher risk premiums due to increased responsibilities or life experiences.
Gender differences in risk aversion may yield varying ERPs, although individual circumstances play a significant role.
The approach to estimating country risk can be streamlined using a measure called Lambda (Λ):
Λ indicates exposure to country-specific risk; based on company operations and revenues.
Λ > 1: Indicates higher exposure to risk compared to average companies in the market.
Λ < 1: Represents lower exposure.
Example Usage: Comparing Embraer (lower exposure) versus another company with significant local reliance.
To calculate implied equity risk premiums, follow these steps:
Derive cash flows based on recent historical data.
Project future cash flows while factoring in growth expectations.
Solve for discount rates that equate the present value of expected cash flows to the current market price of
an equity index.
$$\text{Discount Rate} = r_{\text{internal}} \quad
\text{where} \quad \frac{CF}{(1+r)^t} = P$$
For example, using data from early 2020:
S&P 500 was priced at 3231.
Projected cash flows with a growth rate of 4%.
Estimated discount rate yielded 7.12% at that time, with an implied ERP
calculated as:
Implied
ERP = E[R] − Rf = 7.12% − 1.92% = 5.2%
The systematic understanding and calculation of equity risk premiums play a vital role in company valuation. Using implied approaches over historical data can yield more relevant and actionable insights. This evolving nature of risk can allow for strategic investment decisions in alignment with current market conditions.
Beta measures the risk associated with a security relative to the market as a whole. The formula for beta is:
$$\beta = \frac{\text{Covariance}(R_i,
R_m)}{\text{Variance}(R_m)}$$
Where:
Ri = returns on the stock
Rm = returns on the market
Investors are diversified.
Beta comes from stock prices, which can be volatile.
Some investors, including notable figures like Warren Buffett, are skeptical about relying on past stock prices for estimating beta. The main arguments against beta include:
Prices may not reflect intrinsic value.
Market fluctuations can lead to noise in beta estimates.
If you are uncomfortable with beta, consider the following alternatives:
Instead of adjusting discount rates for risk, one could use a fixed rate across all companies, such as 10%. However, this could lead to misvaluing risky and safe companies.
Transform standard deviations of earnings or cash flows instead of using price measures to estimate risk.
If we assume investors are not diversified, it becomes necessary to consider all forms of risk, not just market risk.
Consider using "total beta," which captures both market risk and total risk when assessing business valuation.
Hamada’s equation helps adjust beta for financial leverage:
$$\beta_L = \beta_U \left(1 + \frac{D}{E}(1 - T)\right)$$
Where:
βL = levered beta
βU = unlevered beta
D = debt
E = equity
T = tax rate
This equation shows that as a company increases its debt relative to equity, its beta (and thus cost of equity) also increases, given that debt is a fixed cost.
The cost of equity can be estimated through the CAPM formula:
Cost of
Equity = rf + β(rm − rf)
Where:
rf = risk-free rate
rm = expected market return
The cost of debt is determined based on the interest rates at which companies can borrow long-term debt. The formula is:
Cost of Debt = rt + Default Spread
Where:
rt = risk-free rate
To adjust for taxes, we compute the after-tax cost:
After-Tax Cost of
Debt = rd(1 − T)
Where T is the tax rate.
In summary, beta is crucial for understanding the relationship between risk and return. While traditional methods to estimate beta exist, alternative approaches and updates in this area can lead to better assessments in the context of financial management.
When valuing a company, using the most updated information is crucial:
Financial statements are updated quarterly but may take weeks after the end of a quarter to become available.
Consider various methods for updating figures: If 2023 financials are not available:
Using trailing twelve-month (LTM) data can be effective, comprising the most recent four quarters.
Alternatively, you may use estimates for the most recent quarter along with past data, though this carries risks.
Understanding the differences between operating expenditures (OPEX) and capital expenditures (CAPEX):
OPEX: Expenses that directly affect the current year’s earnings (e.g., salaries, materials).
CAPEX: Investments that provide benefits over several years (e.g., factories).
OPEX affects the income statement immediately.
CAPEX shows as an asset on the balance sheet and is depreciated over time.
The cost of debt measures the long-term borrowing rate and is described by the equation:
Cost of Debt = Risk-Free Rate + Default Spread
- To determine the risk-free
rate, the long-term Treasury bond rate is typically used. - The default spread is usually estimated from the
company’s credit rating.
Subsidized debt presents a unique challenge:
Companies like green energy firms may borrow at rates below market rates, creating potential complications in valuation.
WACC combines the cost of equity and cost of debt, weighted by their respective proportions:
$$\text{WACC} = \left(\frac{E}{V} \cdot r_e\right) + \left(\frac{D}{V} \cdot r_d \cdot (1 -
T))\right)$$
where:
E: Market value of equity
D: Market value of debt
V = E + D: Total market value of the firm
re: Cost of equity
rd: Cost of debt
T: Corporate tax rate
Free Cash Flow (FCF) to Equity: Cash available to equityholders after all expenses, reinvestments, and debt payments.
Free Cash Flow to the Firm: Cash available to all capital providers (both equity and debt holders).
FCFFirm = Operating Income − Taxes − Net CAPEX − Change in Working
Capital
FCFEquity = Net Income − Debt Repayment + New Debt
It’s vital to correct accounting inconsistencies:
Convert operating leases to debt using their present value.
Treat R&D as capital expenditures to reflect long-term benefits.
When valuing companies, always ensure:
Use the most accurate and up-to-date financial numbers available.
Adjust for accounting discrepancies with operating leases and R&D expenses.
Be aware of the company’s capitalization and assess how it impacts the cost of capital.
Understanding cash flows, capital expenditures (capex), research and development (R&D), and tax impacts is essential for accurate company valuation.
When valuing money-losing companies, normalizing earnings can be a challenge.
Key conditions for normalizing earnings:
The company has previously been profitable.
The causes for loss are temporary.
No fundamental change in business conditions has occurred (e.g., new competitors).
Earnings averaging must not distort historical data due to significant growth or downsizing.
Let’s examine the formula for FCFE:
FCFE = Net Income + Depreciation − Capex − Change in Working
Capital
If a company projects negative FCFE for several years, consider the reasons:
High operating expenses or losses.
Significant capital expenditures for growth.
High debt payments without positive cash flow to service the debt.
Companies may capitalize R&D expenses, treating them as assets rather than expenses.
Rationale: Long-term benefits of R&D should not be fully reflected in a single year’s expenses.
If R&D expenses are X over a period, they can be amortized as follows:
$$\text{Amortization Expense} = \frac{X}{n} \quad \text{ (where \(n\) is the
useful life)}$$
Example for amortization of X over n years:
Year 1: Write-off $\frac{X}{n}$
Year 2: Write-off $\frac{X}{n}$
Year n: Last portion of amortization.
When accounting for investments like R&D:
Capitalizing R&D increases operating income and the balance sheet value.
Restate financials accordingly to reflect true investment in the future.
Different firms are valued based on their business model:
Service-oriented (e.g., Uber): Focus on customer acquisition costs.
Product-oriented (e.g., Coca-Cola): Focus on branding and advertising.
This document provides detailed notes on critical finance concepts related to cash flows, growth rates, valuations, and the importance of accurate financial forecasting. It emphasizes understanding company potential through free cash flow analysis and company growth projections.
Free Cash Flow to the Firm (FCFF) is calculated as follows:
FCFF = After-tax Operating
Income − Reinvestment
Start with after-tax operating income (effective tax rate).
Subtract reinvestment, which includes:
Capital expenditures (CAPEX)
Capitalized R&D (if applicable)
Changes in working capital
Free Cash Flow to Equity (FCFE) is defined as:
FCFE = FCFF − Net
Debt Payments
where net debt payments include debt issuances minus repayments.
The difference between FCFF and FCFE is crucial, as FCFE considers cash flows available after meeting all obligations to debt holders.
Estimating growth rates involves multiple metrics, primarily focused on revenue, operating income, net income, and earnings per share (EPS).
Historical Growth Rate
Analyst Estimates: Often optimistic and may not accurately reflect future potential.
Sustainable Growth Rate: Calculated based on reinvestment rates and returns on capital.
If a company reinvests a percentage of its income:
Growth Rate = Reinvestment Rate × Return on Equity
When assessing growth, one must account for scaling effects—larger companies typically grow at slower rates due to their size.
Analysts often overestimate growth based on recent performance without considering market saturation or competition.
Historical growth may not accurately predict future growth, especially for businesses moving from small to large scales.
The DCF model is essential for understanding the value of a company based on its expected future cash flows.
DDM calculations can sometimes confuse due to the distinction between dividends and available free cash. It is crucial to focus on cash available rather than just dividends paid.
While analysts provide valuable insights, their forecasts are often only marginally better than using historical
data.
Problems include:
Reliance on historical performance
Bias towards management (optimistic forecast tendencies)
Lack of rigorous scrutiny in growth estimation
Sustainable growth is achieved through balance between reinvestment and return on investment:
Sustainable Growth = Retention Ratio × Return on Equity
Understanding cash flows and growth rates is vital for financial analysis and valuation. Analysts must consider various perspectives, including historical data and sustainable growth potential, rather than solely relying on stylized projections based on recent performance.
Reinvestment:
The growth a company can achieve depends on how much it reinvests back into the business (retention ratio) and how effective those reinvestments are (return on equity).
Retention Ratio: The portion of earnings retained in the business after dividends.
Return on Equity (ROE): Measures how effectively management is using a company’s assets to create profits.
Sustainable Growth Rate = Retention Ratio × Return on Equity
Expected Growth in Operating Income = Reinvestment Rate × Return on Invested
Capital
Valuation based on Growth - Growth and Value:
High growth does not always equate to high value. It’s crucial to assess the underlying earnings and returns relative to the cost of capital.
Companies that grow at a rate lower than their cost of capital can destroy value.
Future evaluations will consider growth rates, margins, and reinvestment rates to provide more accurate valuations of companies.
Understanding how to determine realistic growth assumptions based on market sizes, competition, and reinvestment efficiencies is critical for successful financial modeling.
The terminal value is a critical component in discounted cash flow (DCF) valuation, as it represents the present
value of all future cash flows beyond a certain projection period, typically extending for an infinite timeline.
The formula for terminal value can be expressed using two common methodologies:
1. Gordon Growth Model (Perpetuity Growth Model):
$$\text{Terminal Value} =
\frac{CF_1}{r - g}$$
Where: - CF1
= Cash flow in the first year after the projection period - r =
Discount rate (Cost of Capital) - g = Growth rate in
perpetuity
2. Exit Multiple Approach:
This approach involves applying a market multiple (e.g. EBITDA multiple) to an estimate of the company’s financial metric at the end of the projection period, typically year 5 or year 10.
Liquidation Value: Suitable for companies expected to be liquidated in the foreseeable
future. It is commonly applied in cases of owner-dependent businesses.
Stable Growth Models: Applicable for growing companies. However, caution must be exercised
regarding the selection of growth rates, which should realistically reflect long-term growth expectations
relative to economic growth.
Growing Annuity: Used when companies are expected to last only for a defined period (e.g., a natural resource company).
The Exit Multiple Approach should be avoided in intrinsic valuations, as it tends to conflate pricing with intrinsic valuation methodologies. Many bankers rely on this method leading to inflated valuations based on market sentiment rather than intrinsic value.
Underestimating the need for reinvestment: Higher growth rates often necessitate increased reinvestment. Failure to account for reinvestment can result in overestimated terminal values.
Understanding growth is vital when estimating terminal value:
Reinvestment Needs: Higher growth requires higher reinvestment rates. The reinvestment required can be calculated using the following relationship:
$$\text{Reinvestment Rate} = \frac{g}{ROIC}$$
Where:
g = Growth Rate
ROIC = Return on Invested Capital
Effect of Growth Rates: Increasing growth rates elevate terminal values only if the company can sustain growth above the cost of capital. Therefore, return on capital is a crucial factor in determining the viability of growth assumptions.
Revenue Growth is often assessed through market size analysis, competition, and historical performance.
Margins reflect the profitability of a business. Operating margins can be projected by analyzing gross margins, SG&A, and determining how economies of scale affect overall profitability.
Perceptions of unfair advantages created by diversity initiatives can impact workplace dynamics, leading to perceived favoritism or reverse discrimination, particularly among different ethnic groups, such as Asian communities.
The necessity of inclusive practices across the workforce is essential for fostering a fair workplace environment that benefits all demographics and encourages talent maximization without bias.
Companies should employ a comprehensive strategy toward DEI by:
Educating employees on bias and inclusion.
Collaborating across all levels of the organization to foster a safe and diverse environment.
Holding teams accountable for maintaining inclusive practices.
Active listening is vital for leaders. Encouraging open dialogue and understanding diverse perspectives allows for improved teamwork and social connections within organizations.
Develop an intrinsic valuation model accounting for terminal value accurately and understand the implications of growth, reinvestment rates, and the need for diverse and inclusive workplaces to maximize potential and tackle biases effectively. Continuous self-reflection and open communication can drive meaningful change in both business valuations and societal structures.
Valuation is a crucial process in finance that helps determine the worth of a company or a specific asset. The insights presented here are based on practical approaches to valuation, emphasizing the importance of using accurate data and methodologies.
While researching for valuation, maintain a focus on the specific inputs you feel uncertain about. Organizing information into folders based on categories (growth, profitability, reinvestment) may streamline the process.
For companies with a large cash balance, such as Google, one must assess whether this cash is efficiently utilized. The equity analyst’s claim that cash is a bad investment because it earns only 5% while Google’s return is 30% may miss important contexts.
Let C represent the cash balance, Rc represent the company’s return on capital, and Rm represent the market return on cash equivalents:
$$\text{Net Present Value (NPV)} = C - \frac{C \cdot R_m}{R_c}.$$
Cash can be a neutral investment depending on the situations; it is crucial to understand its context within the
company.
Cross holdings refer to a situation where a company owns equity stakes in other companies (subsidiaries).
When a company owns more than 50% of another, consolidation is needed as per accounting rules, affecting both revenue and expenditure reporting.
For minority stakes (between 20%-50%):
Include a proportional share of net income.
Adjust the balance sheet for retained earnings.
For significant minority stakes (less than 20%):
Report dividends received as income.
When conducting Discounted Cash Flow (DCF) analysis, remember:
1. Free Cash Flow to the Firm (FCFF):
FCFF = Operating
Income × (1 − Tax Rate) + D - Change in Working Capital − Capital Expenditure.
2. Discount Rate: The discount rate can be the weighted average cost of capital (WACC) for firm
valuations, expressed as:
$$\text{WACC} = \frac{E}{V} \cdot R_e + \frac{D}{V}
\cdot R_d \cdot (1 - T),$$
where:
E = market value of equity,
D = market value of debt,
V = E + D,
Re = cost of equity,
Rd = cost of debt,
T = tax rate.
While assets are typically included in valuations, avoid double-counting. For instance, if a headquarters is already factored into cash flows, don’t add its market value to the valuation.
Evaluate whether goodwill represents actual value. If management decisions lead to underperformance, adjust expectations accordingly.
Consider overfunded pension plans; they can be adjusted to reflect surplus assets that benefit shareholders:
Overfunding = Total plan assets − Total pension obligations.
This document serves as a guideline for understanding key valuation theories and practices. Engage actively with your provided financial data and apply these principles judiciously in your valuation assignments.
This document provides a summary of the key concepts covered in discussions regarding corporate valuation, the role of corporations in societal issues, and the complexities associated with market and stakeholder influences.
DCF is a financial model used to determine the value of an investment based on its expected future cash flows.
The formula for DCF is:
$$PV = \sum \frac{CF_t}{(1 + r)^t}$$
where:
PV = Present Value
CFt = Cash Flow at time t
r = Discount Rate
t = Time period
Consider the company’s DCF-derived value, for example, if the DCF gives $100 million, and the debt has a market value of $80 million:
Equity Value = DCF Value − Market Value of Debt
Hence, the equity value would be:
Equity Value = 100 million − 80 million = 20 million
When performing DCF analysis, one should subtract the market value of debt from the company’s overall value to determine equity.
Important Note: The market value of debt can be less than its book value due to distress risk:
If a company is in distress, the market perceives the odds of repayment as lower which diminishes the market value of its debt.
Companies with complex structures or opaque accounting practices complicate valuation.
Investors must differentiate between simple and multi-business structures.
A scoring system can be developed to judge complexity, where complexities stem from:
Geographic diversification with non-standard areas.
Multiple unrelated business lines.
Understanding the impact of equity-based compensation on valuation:
Stock options granted need to be valued using an option pricing model.
Restricted Stock Units (RSUs) and their impact on shareholder value need to be included in the total share count.
The notion has evolved from shareholder-focused strategies towards considering broader societal impacts.
Companies are increasingly expected to take stances on social justice, climate issues, and employee rights.
Public platforms amplify stakeholder voices leading to increased scrutiny on corporate practices.
Corporate statements that lack alignment with actual practices can lead to accusations of hypocrisy.
Companies should develop clear engagement policies that outline when and how to speak on social issues while considering:
The alignment of values with tactical responses and actions.
Engagement with diverse stakeholders to gather a variety of perspectives.
Identify which issues are core to business operations and understand lodging and political contexts.
An evaluation of the potential reputational and market risks associated with either engaging or remaining silent on social issues.
It is crucial to manage discrepancies between internal company culture and external stakeholder expectations.
Regular employee feedback mechanisms can facilitate improved alignment between values and practices.
Understanding the balance between corporate accountability and societal expectations is vital for contemporary leaders. The effectiveness of corporate strategies within the context of stakeholder capitalism will likely depend on companies’ ability to address societal needs while managing their core business objectives harmoniously.
Valuation is not just a technical activity involving spreadsheets and numbers; it inherently contains storytelling elements that provide context and understanding of the numbers involved. This document aims to consolidate the key concepts discussed in the lecture, focusing on valuation practices, compounded annual growth rates, margins, reinvestment, and the significance of narrative in financial analysis.
Every valuation tells a story, even spreadsheets implicitly narrate a context.
A valuation with high numbers needs a corresponding narrative that rationalizes these figures.
Consider a valuation with the following estimates:
Compounded Annual Growth Rate (CAGR): 50% over the next 10 years.
Operating Margin: 20% (twice the industry average).
Reinvestment: Low given growth assumptions.
Cost of Capital: 7%, below the market average.
Company Size: Likely a small company that can sustain high growth due to a smaller base.
Market Dynamics: The market is probably growing, enabling capture of market share.
Competitive Advantages: High growth and margins with limited reinvestment suggest a strong competitive position.
Business Model: Low capital intensity (related to the idea of high margins with little reinvestment) is important.
Product Type: Product/service is likely non-discretionary, which allows for more stable demand.
Example: A valuation with assumptions that do not realistically connect.
Fairness opinions serve as a ’fig leaf’ in M&A transactions to defend against lawsuits.
A DCF (Discounted Cash Flow) analysis may become impossible if it assumes unrealistically high terminal growth rates without justifications.
These can happen but must be backed by strong narratives.
For instance:
High growth without reinvestment might make sense under certain conditions, such as a pharmaceutical company capitalizing on past R&D.
High growth, high margins, low reinvestment, and low risk often don’t match up unless special stories justify them.
When conducting a valuation, consider:
Revenue Growth: High, average, low, or negative.
Reinvestment Requirements: High, average, low, or negative.
Cost of Capital: Above, at, or below the median for similar firms.
Develop the narrative first, then define the metrics.
Estimate revenues based on realistic market shares and growth rates aligned with industry norms.
Evaluate reinvestment needs and ensure they match growth expectations.
Set a cost of capital that reflects the risk profile associated with the company.
Market Size: Estimated total market of $100 billion growing at 6%.
Market Share: Assigned a 10% share leading to revenues of $3.6 billion in Year 10.
Operating Margins: Estimated at 40% due to a low intermediary role.
Reinvestment: Low due to the business model of not owning cars.
$$\text{Value} = \sum \frac{\text{Cash Flow}}{(1 + r)^t}$$
where
r is the cost of capital and t
is time.
Always subject valuations to feedback, especially from those with differing views. Understand the rationales behind their feedback.
Maintain an openness to change your valuation based on new information (e.g., earnings reports, regulatory news).
Valuations are an iterative process integrating numbers with narratives. Understanding the implications of growth rates, reinvestment, and margins within a storytelling framework leads to more effective and realistic valuations.
Valuing companies is a vital skill in finance, involving an understanding of not just numerical values but also the storytelling aspect behind these valuations. This document summarizes key concepts and methodologies discussed in a class setting.
To establish a company’s value, particularly using the Discounted Cash Flow (DCF) method, several core inputs must be considered:
Revenue Growth Rate (g): The rate at which the company’s sales are expected to grow.
Target Operating Margin (OM): The expected profit margin from operations.
Sales to Capital Ratio (S/C): The efficiency of the company in generating sales from capital invested.
Cost of Capital (r): The expected return required by investors; accounts for the risk of the investment.
To compute value per share using DCF, the general formula is:
$$\text{Value per Share} = \frac{PV(FCF)}{N}$$
Where:
PV(FCF) = Present Value of Free Cash Flows.
N = Number of Shares Outstanding.
Employees sometimes find their computed intrinsic value below the market price. Common explanations include:
Market Mispricing: Your analysis may be correct, pointing to overpricing in the market.
Self-Doubt: New analysts may feel their inputs (e.g., growth rates) have inflated expectations that differ from market sentiment.
Double Counting Diluents: Be cautious about valuations incorporating estimates of future capital raising that could be embedded in cash flow projections.
Consider the stable growth dividend discount model’s application to utilities:
Mature, stable dividend-paying company.
Growth rates should be aligned to overall economic growth.
Cost of equity (r): Risk-free rate plus equity risk premium should be close to average market figures.
For ConEd, expected dividend next year (D1) is calculated as:
D1 = D0 × (1 + g)
Where:
D0 = Last year’s dividend,
g = Growth rate (e.g., g = 2.1%).
$$\text{Intrinsic Value per Share} = \frac{D_1}{r - g}$$
An intrinsic valuation exercise around significant market events illustrates how market conditions can drastically affect valuations.
The price of risk increases (equity risk premium surges).
Cash flows must adapt to economic downturns, thus factoring into valuations.
An aggregate value assessment for indices can be done through;
Expected cash flow estimates from dividends and buybacks.
Calculating expected earnings growth based on analyst projections.
External market sentiment influences valuations.
Analyst expectations can often be optimistic or biased.
The challenges in valuing young companies stem from:
Lack of historical data.
Uncertainty in future growth trajectories and cash flows.
Small revenues paired with large operational losses challenged traditional valuation approaches.
Estimation of future growth and operating margins needed to reflect realistic potential.
To attain reasonable values, apply:
$$\text{Valuation} = \frac{\text{Future Cash Flows}}{(1 + r)^t}$$
Where: - r = cost of capital, - t = time periods.
Valuation is both an art and science. It requires thorough analysis of inputs, awareness of market psychology, and an understanding of financial mechanics to create an accurate picture of a company’s worth.
This document contains detailed notes about valuing high-growth companies like Amazon based on discussions from the previous quiz and various valuation techniques. The key concepts discussed include discount cash flows (DCF), regression, revenue growth, operating margins, and the significance of risk in valuation.
Key Insight: Time is an ally when correcting valuation disparities; predictions take time to
manifest.
Example: In early 2000, Amazon’s stock price was significantly higher than its intrinsic valuation of $35 per
share. Despite being overvalued, selling short was discouraged due to time constraints.
Young companies pose unique valuation challenges due to rapid changes and inherent uncertainty.
Avoid reliance on regression betas for young companies.
Case Study: Amazon’s regression beta in January 2000 was 2.23 with a standard error of 0.50.
Calculation of Range:
True Beta Range = Beta Mean ± 2 × Standard
Error
This gives a beta range for Amazon of [1.2, 3.2].
Use adjacent sectors for beta estimates:
For the first five years, Amazon’s beta was derived from only online retailers due to its growth stage. year five, the evaluation transitioned towards all retailers with a composite beta of approximately 1.60.
Assumption of a compounded annual growth rate (CAGR) of 42% based on visualizing success within the industry. Approach to determine growth: Utilize an end-goal approach to backtrack growth figures.
Starting Operating Margin: -36.71%
Target Operating Margin: 10% (75th percentile of successful retailers).
Mechanism to achieve transition:
$$\text{Interpolated Margin}_{n} = \frac{\text{Target Margin} - \text{Current
Margin}}{N}$$
Where N represents the number of years to
reach the target margin.
Importance of projecting long enough to see a business transition, with common growth limits of 3-5 years often referenced for high-growth companies.
Introduce a sales-to-capital ratio to bridge growth expectations with required reinvestment levels.
Failure Rate: Data indicates a high failure rate for startups, particularly in tech sectors.
Visual representation of company survival rates from startups over 10 years shows substantial positive selection bias after the initial years.
Company valuations can shift dramatically with market conditions and perceptions, as illustrated by Amazon’s valuation fluctuations between 2000 and 2001.
Emphasis that valuation changes are not solely based on internal metrics but often reflect broader economic and market trends.
Valuation of high-growth companies such as Amazon requires adaptive thinking. The valuation process should include rigorous assessments of both qualitative and quantitative factors while remaining agile to market changes. Key factors include growth projections, risk assessment, realistic margin expectations, and thorough analyses of corporate governance and management.
These notes summarize key concepts in intrinsic valuation, particularly focusing on the challenges of valuing banks, the importance of regulatory capital, and considerations when valuing distressed companies.
When assessing company valuations:
Key metrics include Revenue Growth, Margins, and Reinvestment rates.
Expect straightforward feedback; deep insights are often subjective.
Remember: you know more about your company than anyone else.
Valuing banks is particularly challenging due to:
Regulatory Capital Requirements: Banks must meet a minimum regulatory capital ratio, typically defined in terms of equity.
Historical Context:
Past self-regulation efforts by banks before regulatory requirements were established (e.g., post-Great Depression changes).
Regulatory Capital Ratio: If the minimum requirement is 15%, banks may maintain a ratio above this threshold for various strategic reasons.
$$\text{Regulatory Capital Ratio} = \frac{\text{Regulatory
Capital}}{\text{Risk-Weighted Assets}} \geq 15\%$$
Allows for evaluation of banks’ balance sheet strength to ensure protecting depositors.
Banks can vary in their capital strategies (conservative vs. aggressive capitalization).
When changing debt ratios:
Replacing equity with cheaper debt generally lowers cost of capital.
However, increased debt also raises the risk, leading to an increase in the cost of equity due to higher beta.
Cost of
Equity = rf + β × (E[Rm] − rf)
where:
rf = risk-free rate
E[Rm] = expected market return
β = measure of systematic risk
Cost of debt may also increase as the firm’s financial risk escalates:
Cost of
Debt = rf + spread
Valuing distressed companies poses unique challenges:
Declining revenues and shrinking margins impact cash flows negatively.
Future growth rates may need to be negative, signaling company liquidation rather than growth.
Determining realistic reinvestment needs versus cash flows.
Understanding management’s ability to adapt to distress conditions.
Discussed valuation reflects:
Historical ranges of revenue and margins.
Strategic moves (store closures, cost reduction).
Estimation based on future forecasts vs. liquidation value considerations.
Final share value calculated based on expected cash flows discounted.
When valuing a company, understand the relationship between:
The likelihood of growth vs. probability of failure.
Adjusting valuation metrics according to potential risks (distress, management issues).
Assessing a company under various scenarios can help establish more realistic valuations:
Expected Value = P(Success) × Value if Successful + P(Failure) × Value if
Failed
Key approaches discussed:
Discounted Cash Flows (DCF)
Dividend Discount Model (for banks)
For banks, the focus is on equity and regulatory capital requirements rather than traditional free cash flows.
The free cash flows to equity must consider the investment in regulatory capital.
Considered cash flows expected based on the profitability turnaround strategy and adjusted for regulatory capital
needs:
$$\text{Value per Share} = \frac{\text{Projected Cash Flows}}{(1 +
k)^t}$$
where:
k = cost of equity
t = time period
Understanding the nuances of intrinsic valuation is critical, especially in unique sectors like banking or in challenging scenarios like distressed company valuations. Focus on financial metrics, be mindful of regulatory impacts, and approach valuations with an understanding of inherent risks.
This lecture discusses the mindset differences between intrinsic valuation and pricing in equity analysis. The emphasis shifts when valuing companies based on cash flows (CF), growth rates (g), and risk factors (r).
Intrinsic valuation relies on detailed assumptions about cash flows, growth, and risks using discounted cash flow (DCF) models. Analysts explicitly estimate cash flows based on business fundamentals.
In pricing, the focus is on market multiples like Price-to-Earnings (P/E), Enterprise Value (EV) to EBIT (Earnings Before Interest and Taxes), and Price-to-Sales (P/S) ratios.
The mindset shift indicates data and statistics drive pricing decisions, while finance and core principles drive intrinsic valuations.
When using multiples such as P/E ratios, analysts are still making assumptions about future cash flows, growth,
and risks. For instance:
$$P/E = \frac{\text{Price per Share}}{\text{Earnings per
Share}}$$
If a company like NVIDIA trades at 100× earnings, the
market implicitly assumes significant growth in cash flows.
Consider the distribution of P/E ratios among publicly traded companies. Given that P/E ratios can’t be less than zero, they tend to form a right-skewed distribution:
The lowest P/E ratio is 0 (when earnings are negative), while the upper end theoretically can reach infinity.
This skewness affects valuation strategies and indicates that analysts must be cautious when interpreting pricing.
When encountering a stock trading at a low P/E ratio compared to its peers, consider asking:
What is the growth rate of the company?
How risky is the company?
Are all growth rates equal? What about return on equity and necessary reinvestments?
Companies like pharmaceuticals (e.g., Novo Nordisk), technology (e.g., Apple), and entertainment (e.g., Disney) embody substantial intangible assets:
The challenge in valuing these companies arises from accounting practices that do not capitalize R&D expenditures, affecting earnings and capital return ratios.
To adjust financials, consider capitalizing R&D expenses, thus transforming operating expenses into capitalized assets, allowing for a more accurate financial assessment.
The adjusted operating income can be calculated as:
Adjusted Operating
Income = Operating Income + R&D Expense − Amortization of Capitalized R&D
A practical approach mitigating uncertainty in valuation is the Monte Carlo Simulation, which enables analysts to incorporate variability in their forecasts:
Instead of choosing a single value (point estimate) for growth or other metrics, define a range or distribution for each variable.
Perform numerous simulations varying these inputs to generate a distribution of possible outcomes:
V = f(Growth Rate, Marginal Sales, Cost of
Capital)
The end output is a probability distribution of possible values for the asset being analyzed that can better inform investment decisions.
Throughout the course, the discussion emphasized the need to balance intrinsic valuations with pricing strategies. Although intrinsic valuation focuses on the fundamental worth of an asset, it’s essential to ensure assessments align with market sentiment and trends:
Price volatility and irrational market behaviors necessitate the use of pricing methods alongside intrinsic assessments.
In practice, a combination of both valuation methods provides a stronger investment thesis.
Pricing is fundamentally about identifying mismatches in value. As an investor, seek:
Low Price-to-Earnings (PE) ratios
High growth potential
Low risk profiles
High return on equity
Commonly calculated revenue metrics include:
Price-to-Sales (P/S) ratio
Price-to-Revenue ratio
When comparing retailers, we must consider business models:
Discount retailers generally trade at lower revenue multiples due to their volume-driven low-margin operations while luxury brands, which have high margins, can command higher multiples.
Multiples should meet definitional tests ensuring they correlate properly with company performance and metrics. For example, when evaluating stocks based on PE ratios, ensure that:
Positive earnings are present.
Comparisons are made among similar companies.
A higher growth rate leads to higher PE ratios.
As risk increases, the PE ratio typically declines.
Multiple regression can help evaluate the relationship among variables affecting company valuations:
Dependent variable: PE Ratio
Independent variables: Interest rates, GDP growth rates, country risk
Understanding the statistical distribution of PE ratios can provide insight into whether a stock is undervalued or overvalued:
The distribution is often skewed with a peak on the left and a long tail on the right.
The median PE is more informative than the mean, as it is less influenced by outliers.
The PEG ratio, calculated as:
$$\text{PEG} = \frac{\text{PE Ratio}}{\text{Growth
Rate}}$$
is intended to evaluate a stock’s valuation relative to its growth prospects. However, two
main biases need consideration:
Risk adjustment: Higher risk should correlate with lower PEG.
Growth assumption: Growth does not always lead to a proportional increase in PE.
Important book value multiples:
Price-to-Book (P/B) Ratio: $\text{P/B} = \frac{\text{Market Value of Equity}}{\text{Book Value of Equity}}$
Enterprise Value-to-Invested Capital (EV/Invested Capital)
Key determinants include:
Return on equity (ROE)
Payout ratio
Cost of equity
For EV/EBITDA, significant factors are:
Tax rate: Higher taxes lead to lower EV/EBITDA ratios.
Growth rate: Higher expected growth results in higher multiples.
When evaluating companies, it is critical to ask the right questions, consider the underlying fundamentals, and control for economic risks and growth predictions. Use multiple valuation methods to gain a comprehensive view of a company’s worth.
In the field of finance, valuation and pricing of stocks is crucial. This document summarizes insights on various pricing metrics, including PEG (Price/Earnings to Growth) ratios, Enterprise Value (EV) ratios, and their implications when comparing similar firms.
The PEG ratio is defined as:
$$\text{PEG} = \frac{P}{g}$$
where
P is the price per share and g
is the growth rate. It is important to remember that if we assume P
grows proportionately with g, we might fall into the trap of avoiding
high PEG ratio stocks, which could affect our investment decisions.
Enterprise Value is calculated using the formula:
EV = Market
Cap + Debt − Cash
The EV-to-EBITDA ratio is often used to assess whether a company is over or
undervalued:
$$\text{EV/EBITDA} = \frac{\text{EV}}{\text{EBITDA}}$$
When evaluating a company with minority holdings, the impact on EV/EBITDA should be considered. Having minority holdings may inflate the numerator while leaving the denominator unchanged, making a company appear more expensive than it is.
Revenue multiples serve as a crucial valuation tool because they are less likely to be impacted by negative earnings. The two common ways to calculate revenue multiples are:
Market Cap divided by Revenues
EV divided by Revenues:
$$\text{EV/Sales} = \frac{\text{EV}}{\text{Revenue}}$$
The EV/Sales ratio is influenced by:
Reinvestment Rates: Higher reinvestment rates typically lead to lower multiples of revenue.
Cost of Capital: Riskier companies tend to have lower EV/Sales ratios.
Growth Rates: Companies with higher growth prospects generally command higher sales ratios.
Operating Margins: High margin companies tend to have higher EV/Sales ratios.
A strong brand can enhance pricing power, leading to:
Higher Margins ⇒ Higher
EV/Sales Ratios
Example: Coca-Cola’s brand name allows it to charge premium prices compared to
generic alternatives.
To assess the value of a brand name:
Determine the intrinsic value based on cash flows and growth (e.g., Coca-Cola estimated at $80 billion).
Consider brand power in pricing, potentially adding premiums based on market assessments.
Identifying a comparable group can be challenging. Analysts must consider:
Cash flow similarities
Growth rates
Risk profiles
Sectors considered (this often involves bias).
Multiple regression analysis provides a framework to predict P/E ratios based on growth and risks, allowing for better comparability across firms.
A regression setup could be:
P/E = β0 + β1Growth + β2Payout + β3Risk + ϵ
The intercept indicates the baseline P/E when other factors are controlled.
Coefficients provide insights on how much the P/E changes with unit changes in each variable.
Pricing dynamics can change over time, impacted by market conditions, economic events, etc.
This occurs when independent variables in regressing analysis are correlated, leading to unreliable coefficient estimates.
Understanding the various metrics and approaches for pricing a stock is essential for making informed investment decisions. Continuous analysis and adjustment of models will lead to better forecasts and valuations.
Valuation and pricing are critical aspects of finance, encompassing methods to determine the worth of companies and their assets. This document provides a structured overview of key concepts, equations, and methodologies relevant to these subjects.
Intrinsic valuation involves determining the value based on the fundamentals of a company, typically using the
Discounted Cash Flow (DCF) model:
$$V_0 = \sum_{t=1}^{N}
\frac{FCF_t}{(1+r)^t}$$
Where:
V0 = Present value of the company
FCFt = Free cash flow at time t
r = Discount rate
N = Number of periods
Asset-based valuation focuses on valuing individual assets and summing them up. This method is commonly used in
liquidation scenarios and is heavily tied to financial statements, particularly the balance sheet. The basic
approach is:
$$V = \sum_{i=1}^{m} V_{asset_i}$$
Where:
V = Total asset value
m = Total number of distinct assets
Vasseti = Value of the individual asset
When pricing a company, considerations should be made regarding growth rates, operating margins, and capital reinvestment, which can vary across different sectors and companies.
Considerations for pricing might include:
Revenue growth
Margins and cost efficiency
Reinvestment needs
Economic conditions and market timing
This approach allows analysts to value individual business units separately before summing them for total value:
$$V_{total} = \sum_{j=1}^{n} V_{business_j}$$
Where:
Vtotal = Total company value
n = Number of business segments
This method acknowledges that different units may have different growth rates and risk profiles.
In conducting pricing through regression analysis, understanding statistics like T-Statistics is critical:
$$T = \frac{\hat{\beta}}{SE(\hat{\beta})}$$
Where:
β̂ = Estimated coefficient
SE(β̂) = Standard error of the estimated coefficient
The T-statistic is used to determine the significance of predictors in the regression model.
Multicollinearity occurs when independent variables in a regression model are correlated, leading to difficulties in estimating the regression coefficients reliably.
The cost of capital reflects the return expected by investors and can be calculated using a weighted average of
equity and debt costs, typically referred to as:
$$WACC = \frac{E}{V} r_e +
\frac{D}{V} r_d (1 - T)$$
Where:
WACC = Weighted average cost of capital
E = Market value of equity
D = Market value of debt
V = Total market value of the company (E + D)
re = Cost of equity
rd = Cost of debt
T = Tax rate
Valuing private companies presents unique difficulties, such as the lack of public market data, illiquidity issues, and dependability on individual owner performance. Key issues include:
Limited financial history and transparency
Difficulty in estimating appropriate betas for risk analysis
Potentially significant personal compensation and expenses that distort financial statements.
Understanding the distinctions between pricing and valuation, as well as the importance of context in assessments is essential. Analysts should be prepared to use various methodologies and statistical tools to arrive at comprehensive and actionable valuations.
Private company valuation involves distinct challenges compared to public company valuation. Two key aspects affecting valuation are the cost of equity and liquidity.
The cost of equity for private companies is typically higher due to a lack of diversification among investors. Private company investors bear all risks and demand a higher rate of return.
Liquidity concerns arise, as it is challenging to sell private company shares. A liquidity discount is often applied; standard practice suggests a flat discount of 25%.
Liquidity discounts can vary based on several criteria:
Profitable companies typically have lower liquidity discounts than unprofitable companies since they generate cash flow.
Different types of buyers will exhibit varying willingness to pay based on their financial constraints. Long-term buyers may be willing to pay more than cash-constrained buyers.
Liquidity discounts increase during economic downturns when investors prioritize cash over assets.
Discounts should reflect the variability due to all factors discussed: profitability, buyer type, and overall economic conditions.
To estimate the cost of equity, typically a beta factor used in the Capital Asset Pricing Model (CAPM) is heightened to incorporate total risk:
Cost of
Equity = Rf + β ⋅ (Rm − Rf)
Where:
Rf = Risk-free rate
Rm = Expected market return
For private companies, the process is adjusted as follows:
1. Total Beta Calculation:
$$\text{Total Beta} =
\frac{\text{Market Beta}}{\text{Correlation}}$$
This is derived from publicly traded companies within the same industry.
2. Debt to Equity Ratio:
Leverage observed from comparable public companies influences the cost of equity. However, for private businesses,
reliance on market-derived debt ratios is essential.
The valuation of private companies is complex but can be simplified into a systematic approach involving:
Adjusting Financial Statements: Clean up income statements by capitalizing operating leases and correcting for key person risks.
Adjusted Operating Income → 370, 000 (Example)
Estimating Growth Rates:
Stable growth rates reflecting inflation or industry trends are employed.
Reinvestment Rates:
Evaluate returns on capital and company life to understand necessary reinvestments and growth
sustenance.
Discounting Cash Flows: Use an appropriate discount rate that considers the adjusted financials and projected inflows.
Instead of uniformly applying a flat 25% discount, suggest a model that varies:
Discount = f(Profitability, Buyer Type, Economic State)
Restricted stock studies and IPO studies offer insights into observed liquidity discounts. Evidence suggests that substantial variations exist based on health and revenue of companies sampled.
In transactions where a private company is sold to a public entity: The considerations of cost of capital drastically change:
Market beta applies without additional total beta calculations, and the liquidity discount is negligible.
Utilizing two contrasting valuations:
Private Buyer Valuation: e.g. $44,000
Public Buyer Valuation: e.g. $1.48 million
When transitioning from a private company to an IPO:
Companies have to register and prepare a prospectus detailing plans post-offering.
Key decisions involve utilization of proceeds (cash reserves or debt repayment).
Account for complexities arising from convertible preferred shares and stock options.
Initial Public Offerings often witness a phenomenon where the offering price is lower than market demand:
Market Price Increase on Offering Day = Underpricing Rate
Private company valuation is intricate due to unique risks and the factors influencing discounts. Understanding liquidity, profitability, and buyer types are essential. As companies transition to public offerings, valuation methods must evolve to reflect market dynamics and investor behavior.
An option is a financial derivative that represents a contract giving the holder the right (but not the obligation) to buy or sell an asset at a predetermined price before a specific termination date. Options are categorized mainly into two types:
Call Option: Right to buy an asset at a specified strike price K.
Put Option: Right to sell an asset at a specified strike price K.
Right vs. Obligation: Options give you the right but not the obligation to execute the trade.
Underlying Asset: Options derive their value from an underlying asset, such as stocks or commodities.
Contingent Payoff: The payoff depends on the asset price at expiration.
The payoff diagrams for call and put options are crucial for understanding their value:
Call Option Payoff:
$$\text{Payoff} = \max(S_T - K, 0) \tag{where } S_T
\text{ is the stock price at expiration}$$
Put Option Payoff:
Payoff = max (K − ST, 0)
A real option is a choice made available to a business regarding investment opportunities in capital projects. The nature of real options is similar to financial options but is applied to physical assets or investments.
Option to Delay: The right to wait before making an investment.
Option to Expand: The right to increase the scale of an investment.
Option to Abandon: The right to cease a project if circumstances render it unviable.
Real options provide value beyond discounted cash flows (DCF) by allowing managers to make strategic decisions as new information becomes available.
To value options, we can apply various pricing models. The two most recognized models are the Binomial Model and the Black-Scholes Model.
The binomial model approximates the price of options by constructing a decision tree representing different paths the underlying asset price can take:
At each node, you evaluate the potential payoffs based on future stock prices.
Work backward to determine the present value by discounting payoffs.
For example, if S0 is the current stock price:
If ST = S0 × (1 + u) (up
state) and ST = S0 × (1 − d) (down
state)
Here, u and d are the up and down factors, respectively.
The Black-Scholes model provides a formula for pricing European call and put options. The formula is given by:
C = S0N(d1) − Ke − rTN(d2)
Where:
$$\begin{aligned}
d_1 & = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \\
d_2 & = d_1 - \sigma\sqrt{T} \\
N(d) & \text{ is the cumulative distribution function of the standard normal distribution} \\
S_0 & \text{ is the current stock price} \\
K & \text{ is the strike price} \\
r & \text{ is the risk-free interest rate} \\
T & \text{ is the time to expiration} \\
\sigma & \text{ is the volatility of the stock}\end{aligned}$$
The following variables influence the value of options:
Current Stock Price S0: Higher stock prices increase call options value and decrease put options value.
Strike Price K: Increasing strike price decreases call options value and increases put options value.
Time until Expiration T: Longer times to expiration increase the value of both call and put options.
Volatility σ: Greater volatility increases the value of both call and put options.
Interest Rate r: Higher interest rates increase the value of call options and decrease the value of put options.
Understanding options and real options is crucial for finance professionals. These tools help to analyze investment scenarios, make strategic decisions, and ultimately optimize the value of both financial and physical assets.
This lecture covers the concept of real options and their evaluation in the context of capital budgeting. The focus will be on three primary options:
Option to Delay
Option to Expand
Option to Abandon
The current financial landscape often leads to projects with misleading net present values (NPV).
Many promising technologies are considered nonviable today but could hold future potential.
A clear understanding of real options can influence decision-making in investments.
To assess a project with a negative NPV (e.g., an AI technology costing \$2 billion but expected to return \$1.5 billion):
NPV = PV of Cash Flows − Initial Investment
Where:
PV of Cash Flows = 1.5 billion
Initial Investment = 2 billion
Result: NPV = 1.5 − 2 = − 0.5 billion
Holding exclusive rights to a technology involves a significant future market potential.
Willingness to pay for nonviable technology relies on the potential for positive change in the market scenario.
Real options assess flexibility in investment opportunities. The main types include:
This option allows an investor to postpone a project with a negative NPV to observe future developments.
Payoff Diagram:
The underlying asset is the project (equivalent to stock price).
Strike price is the investment needed to start the project.
When the initial project is linked to potential expansions, it may justify pursuing a project with a negative NPV
based on future prospects.
Example: An investment in a hotel project that has the option to expand further based on market outcomes.
This option allows you to exit a project if it performs poorly, limiting losses.
Example: Airbus allowing a partner to walk away from a joint venture with a guaranteed minimum return.
Underlying Asset Value (S): Current value of future cash flows.
Strike Price (K): Initial investment cost or development cost.
Volatility (σ): Measure of uncertainty around cash flows.
Time to Expiration (T): Remaining time for the option before expiration.
Risk-Free Rate (r): The rate used to discount future cash flows.
The Black-Scholes formula is used for calculating the theoretical value of options. Key variables are needed for
input:
$$\begin{aligned}
d_1 &= \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma \sqrt{T}} \\
d_2 &= d_1 - \sigma \sqrt{T} \\
N(d) &= \text{Cumulative distribution function of d}\end{aligned}$$
Biogen projects the present value of cash flows for a new drug at \$3.42 billion, with development costs of \$2.875 billion. If S ≥ K, it is viable; otherwise, it is not.
NPV = PV − Initial Investment = 3.42 × 109 − 2.875 × 109
If the anticipated cash flows are uncertain, the downside of waiting to invest is the loss of exclusive rights, represented as d1 and d2 in the Black-Scholes model.
Valuation of undeveloped reserves representing an option to exploit based on oil price fluctuations.
Present value calculations incorporate uncertainty in future prices and cost of waiting.
Real options provide a framework to assess flexible investment strategies, allowing businesses to capitalize on potentially profitable opportunities while managing risks. The concepts discussed today form foundational tools for corporate finance and investment decision-making.
Companies value financial flexibility to preserve debt capacity for unexpected investment opportunities.
Maintaining excess debt capacity can reduce the cost of capital, yielding:
$$\text{Cost of Capital} = \frac{\text{Debt}}{\text{Total Capital}}$$
A projected investment (once-in-a-lifetime project) has an associated net present value (NPV) contributing to the payoff of maintaining that flexibility.
Inputs to Value Financial Flexibility:
Reinvestment needs (s) as a percentage of firm value.
Variability in reinvestment needs (variance).
Internal cash flow generation without using excess debt capacity.
An example is illustrated with Disney’s optimal debt ratio, calculated as follows:
$$\text{Optimal Debt Ratio} = \frac{40\% \text{ (debt)}}{60\% \text{
(equity)}}$$
Companies that are more capital-constrained (e.g., in emerging markets) tend to value financial flexibility more than those in developed markets.
Businesses facing unpredictable reinvestment needs (e.g., technology firms) appreciate financial flexibility significantly.
Financial flexibility is less valuable in firms with expected returns near their cost of capital (low return environment).
Equity represents a residual claim on assets, meaning shareholders receive residual cash flow after debt obligations are met.
Equity also has limited liability; shareholders cannot lose more than their investment.
As a call option, equity allows shareholders to benefit from increases in firm value.
If a firm’s assets are valued at 100millionwithadebtobligationof80
million, the equity value (E) can be calculated as:
E = S − K
where S is the asset value and K is
the debt face value.
Target company shareholders typically see a rise in stock price post-announcement, while acquiring company stock prices often decline.
Studies show that approximately:
83% of acquisitions do not create anticipated synergies.
Acquiring firms pay too high premiums for target firms.
Risk Transference: Misjudging risk associated with acquiring a target.
Overestimation of Control Premium: The perceived value of control may not translate into actual value.
Misvaluation of Synergies: Over-reliance on synergy estimates without rigorous analysis.
Misplaced pricing strategies: Blindly applying averages from past acquisitions.
Failure to appropriately adjust cost of capital: Using inappropriate discount rates.
Reactivity: Decision to acquire based on impulse rather than thorough analysis.
Lack of accountability: Consequences for poor acquisitions are inconsistent.
Control premium varies significantly; the history of the acquisition process suggests excessive control premiums on average.
Operating synergies focus on cost reduction and increased returns, while financial synergies often tie to lower costs of capital and risk sharing.
Synergies must be quantifiable and arise from the combination of entities able to achieve efficiencies that standalone operations could not.
Value enhancement focuses on increasing a company’s intrinsic value rather than merely affecting its market price. Understanding the difference between intrinsic value and market price is crucial for financial decision-making.
Intrinsic Value: The actual worth of a company based on fundamentals, such as cash flow, risk, and growth prospects.
Market Price: The price at which a company’s shares trade in the stock market, which can be influenced by external factors not related to intrinsic value.
Value vs. Pricing: Value remains constant while pricing can fluctuate due to market sentiment.
When considering factors that can change a company’s value, the following aspects should be understood:
A stock split increases the number of shares but does not affect the company’s fundamental value. It may enhance liquidity and potentially affect market price.
Implication: Although stock splits can make shares more attractive to investors, they do not change the underlying value of the company.
Goodwill reflects the amount paid over the book value of an asset in an acquisition. Impairment occurs when the value of goodwill is deemed excessive.
Non-Cash Expense: Impairment is a non-cash expense and does not directly affect cash flows.
Tax Deductibility: Impairment of goodwill is not tax-deductible, which can complicate its impact on financial statements.
Changing depreciation methods can make earnings appear higher without affecting cash flows.
Straight-Line vs. Accelerated Depreciation: Accelerated depreciation results in higher expenses earlier in an asset’s life.
Earnings Manipulation: Companies may switch methods to manage reported earnings.
Tracking stocks are issued against a particular segment of a company’s business. They do not create value by themselves but can affect market perception.
Value Transfer: The issuance of tracking stocks is typically just for marketing rather than creating real value.
Selling off segments of a business can influence overall company valuation.
Selling Valuation: The price at which a company sells a business segment matters; selling a good business for less than its worth diminishes overall value.
Share buybacks involve a company purchasing its own shares, commonly perceived as a way to return value to shareholders.
A CFO mistakenly compared the NPV of buybacks to investment projects, which is not correct. Buybacks do not create new value but rather transfer value amongst shareholders.
Value Transfer: Buybacks shift wealth from selling shareholders to remaining shareholders and should not be seen as value creation.
Most acquisitions fail to create value due to overpayment and mismanagement.
Operating Synergies: Potential for cost savings or growth opportunities post-merger.
Financial Synergies: Improved borrowing capacity as a combined entity.
Realistic Valuation: Always evaluate modern methods and relevant risks during a merger.
Avoiding Bidding Wars: Acquiring companies should avoid bidding wars as they often result in excessive premiums.
Focus on efficiency and cost-cutting.
Management of working capital and reducing tax expenses legally.
Analyze whether to reinvest profits based on whether the company is earning above its cost of capital.
Strategies for growth must be cautious and informed.
Stabilize barriers to entry (brand name, legal protections).
Optimize debt-equity mix and consider different financial strategies to reduce risk.
Understanding these concepts helps in making informed financial decisions that can ultimately enhance the value of a company. This requires a balance between strategic vision, market analysis, and careful management of internal processes.
There are three main methods for valuing an asset:
Intrinsic Valuation: This method involves estimating the intrinsic value of an asset through various techniques.
Pricing Comparables: This approach involves comparing similar companies’ pricing to derive a fair value.
Option Pricing Models: This method assesses the value of financial options, factoring in the potential for liquidation.
The discounted cash flow (DCF) model answers four essential questions:
1. What are the base earnings and cash flows from existing assets? 2. What is the value of the company’s future growth? This can be positive, zero, or negative and is influenced by:
Revenue growth rate
Reinvestment rate (reflects efficiency in delivering growth)
3. How risky is your company? The cost of capital reflects the operating risk. Higher operating risk results in a higher cost of capital and vice versa. 4. When will the company reach maturity? Maturity points allow for a terminal value to be estimated.
The DCF incorporates the following inputs:
Revenue Growth: Captures the growth potential of the business.
Operating Margin: Reflects the company’s profitability.
Reinvestment Rate: Measures how efficiently a company reinvests its earnings.
The formula for Free Cash Flow (FCF) to the firm may be stated as:
FCF = Operating Income − Reinvestment
As you conduct an intrinsic valuation, consider the relationship within the valuation triangle:
High growth usually indicates high reinvestment and might correspond with a higher cost of capital.
Low growth typically correlates with low reinvestment and lower risk.
During the evaluation process:
Keep track of growth, reinvestment, and risk to ensure they align logically.
Avoid discrepancies in the intrinsic valuation story.
Students selected various companies to analyze, including names such as NVIDIA, Celsius, AMC, and others. Each valuation is unique based on inputs submitted and market sentiment.
Based on median DCF valuations:
More overvalued stocks (150) than undervalued stocks (86) were identified.
The average stock was assessed to be overvalued by approximately 14.2%.
The process of pricing companies also includes using earnings multiples linked back to DCF elements. Variances exist due to different assumptions and frameworks used in real-life evaluations.
Intrinsic valuation necessitates understanding your time horizon and market beliefs.
Remember that valuation is both an art and a science, and your unique approach will evolve through practice.
Always maintain an option to abandon if circumstances suggest a need for reevaluation.
Valuation techniques must be understood thoroughly, with intrinsic valuation focusing on the fundamentals: cash flows, growth, and risk. Questions around corporate governance, market conditions, and management efficiency play a crucial role in the valuation process.