Session 5

Question 1

How do you calculate the present value (PV) of dividends?

Answer 1

Question 2

How do you determine the price per share

Answer 2

Question 3

What is the difference between a stock’s intrinsic value and its market price?

Answer 3

• Intrinsic Value: The fair value of a stock based on the present value (PV) of its expected future dividends, discounted at the investor’s required return.
• Market Price: The price at which the stock is currently trading in the market, which may differ from intrinsic value due to market inefficiencies or investor sentiment.
• If a stock’s market price is lower than its intrinsic value, investors can exploit this difference through arbitrage.

Question 4

How can an investor exploit an arbitrage opportunity when a stock is undervalued?

Answer 4

Question 5

How do you calculate the present value (PV) of arbitrage profit?

Answer 5

Question 6

How does a one-year investor value a stock?

Answer 6

A one-year investor values a stock based on its expected future cash flows, which include:

• Dividends (Div₁) received during the year.
• Sale price (P₁) of the stock at the end of the year.
• These future cash flows are discounted using the equity cost of capital (rₑ) to determine their present value.

The current stock price (P₀) should reflect this discounted value.

Question 7

What formula is used to determine the present value of a stock in one period?

Answer 7

Question 8

What happens if the stock price is different from its intrinsic value?

Answer 8

• If P₀ is lower than the intrinsic value, investors will buy the stock, driving up its price.
• If P₀ is higher than the intrinsic value, investors will sell, causing the stock price to fall.
• Market forces push the stock price toward its fair value, based on the discounted value of future dividends and sale price.

This ensures an efficient market where stocks trade close to their true worth.

Question 9

What is the formula for total return on a stock, also called the equity cost of capital?

Answer 9

Question 10

What are the two key components of total return on a stock investment?

Answer 10

Question 11

How does the market react if a stock’s return is too low or too high?

Answer 11

• If a stock’s return is too low, investors sell it, lowering its price until expected returns rise again.
• If a stock’s return is too high, more investors buy it, increasing the price until expected returns fall to equilibrium.
• Riskier stocks generally offer higher expected returns to compensate for increased uncertainty.

The total return of a stock should match the expected return of similar-risk investments.

Question 12

How do you determine the price of a stock when an investor holds it for multiple years?

Answer 12

Question 13

What is the Dividend Discount Model (DDM) and how does it apply to multi-year stock valuation?

Answer 13

The Dividend Discount Model (DDM) states that the price of a stock is the present value of all expected future dividends plus the expected selling price.

Question 14

What is the Constant Dividend Growth Model (Gordon Growth Model), and how is it used to value stocks?

Answer 14

• The Constant Dividend Growth Model (Gordon Growth Model) is a simplified version of the Dividend Discount Model (DDM) that assumes a firm’s dividends grow at a constant rate (g) forever.
• Not always realistic, as dividend growth can fluctuate due to economic conditions.

Question 15

How are dividends determined, and what trade-off does a company face between dividends and growth?

Answer 15

• A company can either pay out earnings as dividends to shareholders or reinvest them to grow the business.
• This creates a trade-off between paying dividends now vs. increasing future earnings.

How Can a Company Increase Dividends?

• Increase earnings (net income).
• Raise the dividend payout rate.

Question 16

How does a company’s retention rate affect its earnings growth?

Answer 16

Instead of paying all earnings as dividends, a company can retain some profits and reinvest them in the business.

Question 17

What determines a company’s earnings growth rate, and how is it calculated?

Answer 17

Question 18

How does retaining earnings instead of paying dividends impact stock price?

Answer 18

Retaining earnings can have two effects on stock price:

• Increasing growth rate (g) raises stock price.
• Reducing current dividend (Div₁) lowers stock price.

Question 19

When should a firm retain earnings versus paying dividends to maximize firm value?

Answer 19

The optimal policy depends on the profitability of the firm’s investments:

• If reinvestment generates high returns (positive NPV projects) → Retain more earnings to fund growth.
• If reinvestment yields low returns → Pay dividends, as shareholders can reinvest elsewhere for better returns.

A firm should retain more earnings only if it can achieve a high return on new investments; otherwise, paying dividends is a better strategy.

Question 20

Why can’t the constant dividend growth model be applied to all firms?

Answer 20

The constant dividend growth model assumes dividends grow at a fixed rate indefinitely.

However, this does not hold for many firms, especially young firms, because:

• They experience high initial earnings growth rates.
• They often reinvest all earnings instead of paying dividends.
• Their growth slows down over time, eventually leading to stable dividend payments.

When growth is not constant, the constant growth model cannot be applied directly.

Question 21

How do you value a stock when dividend growth is not constant?

Answer 21

A two-phase valuation approach is used:

Phase 1: High-Growth Period (Irregular Dividends)

• Forecast dividends for the years before growth stabilizes.
• Discount these dividends to their present value.

Phase 2: Constant Growth Period

• Apply the constant dividend growth model once dividends grow at a stable rate.
• Discount this future stock price back to today.

Question 22

What are the key limitations of the Dividend Discount Model (DDM)?

Answer 22

The Dividend Discount Model (DDM) has significant limitations:

1. High uncertainty in forecasting a firm’s dividend growth rate and future dividends.
2. Small changes in the assumed growth rate can lead to large variations in the estimated stock price.

This makes DDM less reliable for firms with unpredictable dividend policies.

Question 23

How does the Total Payout Model (TPM) differ from the Dividend Discount Model (DDM)?

Answer 23

Question 24

What is the Discounted Free Cash Flow (DCF) Model, and how does it determine a firm’s value?

Answer 24

The Discounted Free Cash Flow (DCF) Model determines a firm’s value by considering all investors (both equity and debt holders), using Free Cash Flow (FCF) instead of dividends or share repurchases.

Question 25

How is Free Cash Flow (FCF) calculated, and how does DCF estimate share price?

Answer 25

Question 26

How does the Discounted Free Cash Flow (DCF) Model estimate the total firm value?

Answer 26

Question 27

What is Terminal Value (TV) in the DCF Model, and how does DCF connect to capital budgeting?

Answer 27

Question 28

What is the Multiples Valuation Method, and what are its key approaches?

Answer 28

The Multiples Valuation Method is an alternative to DCF models, based on the Law of One Price: * The value of a firm should equal the present value of future expected cash flows. * Comparable firms with similar cash flows should have similar valuations. **Methods of Using Multiples:** 1.Comparable Company Approach: * Uses market values of publicly traded firms to estimate value. * Issue: Public firms are often much larger than private firms, leading to valuation mismatches. 2.Comparable Transactions Approach: * Uses M&A transaction data to derive valuation multiples. * Issue: Data is often limited, and valuations depend on market conditions & timing. This method is widely used but has some challenges, such as lack of theoretical foundation and the need for adjustments (discounts/premiums) for private firms.

Question 29

What are the challenges of the Multiples Valuation Method, and what multiples are commonly used?

Answer 29

**Challenges of Multiples Valuation:** * Lack of theoretical foundation (not favored in academia). * Requires adjustments for firm characteristics: Example: Private companies typically receive a 20–30% discount due to lower marketability. **Commonly Used Multiples:** Enterprise Value (EV) Multiples (used to value the firm): * EBITDA, EBIT, Sales, Number of customers, Units of output (e.g., clicks). Market Capitalization Multiples (used to value equity): * Earnings (Price/Earnings Ratio, P/E), Book Value of Equity. Multiples are often used due to their simplicity and ease of comparison, but they require adjustments for firm-specific differences.

Question 30

What is the Multiples Valuation Method, and what factors should be considered?

Answer 30

The Multiples Valuation Method estimates a company's value using comparable firms. ## Footnote Key Considerations: * Multiples are meaningful only if peer companies have similar ratios. * Averaging multiples works only if valuation estimates are close. * Private companies often require a discount compared to public firms due to lower liquidity and higher risk.

Question 31

What is the P/E ratio, and how is the Forward P/E ratio derived?

Answer 31

The Price-Earnings (P/E) Ratio measures a company's valuation relative to its earnings, helping investors compare firms of different sizes and capital structures. ## Footnote Firms with high growth & strong cash flows can sustain high payout rates, leading to higher P/E multiples.

Question 32

What are Enterprise Value (EV) Multiples, and how do they differ from P/E ratios?

Answer 32

Enterprise Value (EV) Multiples compare a firm's total value (equity + debt) to its operational performance, making them useful for cross-company comparisons. ## Footnote * Higher multiples occur in firms with high growth rates and low capital requirements (where FCF is high relative to EBITDA). * Unlike P/E ratios, EV multiples adjust for leverage, making them better for comparing firms with different capital structures.

Question 33

What are the key advantages of using multiples-based valuation?

Answer 33

Question 34

What are the key disadvantages of using multiples-based valuation?

Answer 34

Question 35

How can multiples-based valuation be misused, and what should analysts be cautious about?

Answer 35

**Potential Misuse of Multiples:** 1.Easily Misused & Manipulated: * Bias can occur in selecting comparable firms, making adjustments, or choosing which multiple to use. 2.Active Role in Valuation: * Be critical of valuation results based on multiples. * Understand the underlying assumptions and choices made in the comparison process. Key takeaway: While useful, multiples should be applied carefully with proper adjustments to avoid misleading valuations.

Question 36

What are the data issues in multiples-based valuation, and how can they be mitigated?

Answer 36

**Key Data Issues in Multiples Valuation:** * Negative earnings make the P/E ratio meaningless, leading to exclusion from calculations. * This creates a selection bias, as only profitable firms remain in the sample. * The average P/E ratio is artificially lowered since money-losing firms are removed. **Solutions to Mitigate Bias:** 1.Adjust P/E Ratio Upwards * Compensates for missing firms due to exclusion. 2.Aggregate Data Instead of Selecting Firms * Compute the total market value of equity (sum of all firms). * Compute the total net income (or loss) (sum of all firms). * Then, calculate the P/E ratio using aggregated values to include unprofitable firms. 3.Use Alternative Multiples That Work for All Firms: * EV/EBITDA (Enterprise Value / EBITDA) * EV/Sales (Enterprise Value / Sales) * P/B (Price-to-Book Ratio) * These alternative multiples solve the negative earnings issue, making valuation more accurate and widely applicable.

Question 37

What is the Capital Asset Pricing Model (CAPM), and how is it used to estimate the cost of equity?

Answer 37

Estimating the cost of equity, which is the return that investors require to invest in a company. will require two steps: * Measure the investment’s systematic risk * Determine the risk premium required to compensate for that amount of systematic risk ## Footnote The Capital Asset Pricing Model (CAPM) is the most widely used method to estimate the cost of equity.

Question 38

What is systematic risk, how is it measured, and what does beta (β) indicate?

Answer 38

Question 39

What is the Market Risk Premium, and how is it calculated? What is the risk-free rate?

Answer 39

The market risk premium represents how much extra return investors expect for investing in the market portfolio instead of a risk-free asset. ## Footnote Risk-Free Rate (𝑟𝑓) is the return on an investment that carries zero risk of default. Typically represented by government bond yields, such as: * U.S. Treasury Bonds (T-bonds) * German Bunds (for Eurozone) * UK Gilts (for the UK) * Japanese Government Bonds (JGBs) These bonds are considered risk-free because governments are unlikely to default on their debt.

Question 40

What is the Expected Return Formula, and how does CAPM use it?

Answer 40

Question 41

What are the key assumptions of CAPM, and what does it say about efficient capital markets?

Answer 41

**CAPM Assumptions:** * The cost of capital of any investment depends on its beta. * The cost of capital depends only on systematic risk, and systematic risk can be measured precisely using beta with the market portfolio. **Efficient Capital Markets:** * In an efficient market, the cost of capital depends only on systematic risk and not on unsystematic risk. * This is why CAPM ignores firm-specific risk, assuming investors can diversify it away. Key takeaway: CAPM assumes that markets price assets efficiently based on systematic risk, measured by beta.