Stock Valuation: Models, Dividends, Growth, and Market Efficiency

Key Concepts and Models

1. Definition of Stock Valuation

Stock valuation is the process of determining the theoretical fair value of a company’s shares based on its fundamentals (earnings, dividends, growth) and market conditions. Unlike bonds (valued via fixed cash flows), stocks are valued using expected future cash flows (dividends or free cash flows) and a required rate of return (discount rate).

Why does this matter?

• Investors use valuation to decide whether a stock is overvalued (price > fair value) or undervalued (price < fair value).
• Companies use it to set initial public offering (IPO) prices or justify mergers/acquisitions.

2. Dividend Discount Model (DDM)

The simplest stock valuation model assumes a stock’s value equals the present value (PV) of all future dividends.

Types of DDM

flowchart TD
    A["Start"] --> B["Estimate next dividend \( D_1 \)"]
    B --> C["Determine required return \( r \)"]
    C --> D["Forecast growth rate \( g \)"]
    D --> E["Check \( g < r \)"]
    E -->|"Yes"| F["Apply \( P_0 = \frac{D_1}{r - g} \)"]
    E -->|"No"| G["Use multi-stage DDM"]
    F --> H["Compare \( P_0 \) to market price"]
    G --> H

Worked Example: Valuing a NEPSE Stock (Nepal Electricity Authority - NEA)

Assume:

• NEA pays a dividend of NPR 5 per share this year ($D_0=5$).
• Dividends grow at 4% annually ($g=4\%$).
• Investors require a 12% return ($r=12\%$).
• Current market price = NPR 80.

Step 1: Calculate $D_1$ (next year’s dividend). $$D_1=D_0\times (1+g)=5\times 1.04=\text{NPR }5.20$$

Step 2: Apply Gordon Growth Model. $$P_0=\frac{D_1}{r-g}=\frac{5.20}{0.12-0.04}=\frac{5.20}{0.08}=\text{NPR }65$$

Step 3: Compare to market price.

• Fair value (DDM) = NPR 65
• Market price = NPR 80
• Conclusion: NEA is overvalued by 23% (NPR 15). Investors should sell or avoid buying.

3. Free Cash Flow to Equity (FCFE) Model

For companies that do not pay dividends (e.g., growth firms like Daraz), valuation uses free cash flows available to equity shareholders.

Formula: $$P_0=\sum _{t=1}^{\infty }\frac{FCF{E}_t}{(1+r{)}^t}$$ Where:

• $FCF{E}_t=\text{Net Income}+\text{Depreciation}-\text{CapEx}-\text{ΔWorking Capital}+\text{New Debt}$
• $r$ = Cost of equity (from CAPM or dividend growth model).

Worked Example: Valuing a Nepali Retailer (Kathmandu Mart)

Assume:

• Net Income (Year 1) = NPR 20 million
• Depreciation = NPR 5 million
• Capital Expenditures (CapEx) = NPR 10 million
• ΔWorking Capital = NPR 2 million
• New Debt Issued = NPR 3 million
• Cost of Equity ($r$) = 15%
• Growth Rate ($g$) = 5% (stable)

Step 1: Calculate FCFE for Year 1. $$FCF{E}_1=20+5-10-2+3=\text{NPR }16\text{ million}$$

Step 2: Assume FCFE grows at 5% forever. Use Gordon Growth for terminal value. $$P_0=\frac{FCF{E}_1}{r-g}=\frac{16}{0.15-0.05}=\frac{16}{0.10}=\text{NPR }160\text{ million}$$

Step 3: If Kathmandu Mart has 1 million shares, the fair value per share is: $$\frac{160\text{ million}}{1\text{ million}}=\text{NPR }160\text{ per share}$$

4. Price-to-Earnings (P/E) Ratio

A relative valuation method comparing a stock’s price to its earnings per share (EPS).

Formula: $$P/E=\frac{\text{Market Price per Share}}{\text{Earnings per Share (EPS)}}$$

Types of P/E Ratios

Worked Example: Comparing NEPSE Stocks

Analysis:

• Ncell has a high PEG (5.33), suggesting it’s overpriced for its growth.
• Global IME (PEG = 2.5) is undervalued relative to its growth.

In the Real World

1. NEPSE (Nepal Stock Exchange)

   • IPO Valuation: When companies like NMB Bank or Ncell go public, underwriters use DCF (Discounted Cash Flow) and P/E multiples of comparable firms to set the IPO price.
   • Example: Before its IPO, NMB Bank was valued using a P/E ratio of ~20x (based on regional banks in India/Bangladesh).

2. Google (Alphabet Inc.)

   • FCFE Model: Google reinvests most earnings, so analysts use FCFE to value its stock. In 2023, Google’s P/E ratio (~25x) was justified by its high growth in cloud computing (Google Cloud).
   • Dividend Growth: Though Google pays a small dividend (~0.5%), its stock price growth (driven by innovation) is the primary driver of returns.

3. Khalti (Fintech App)

   • Growth Valuation: Khalti was valued at $100M+ in 2021 using multi-stage DDM, assuming:
     • High growth in digital payments (30% YoY).
     • Transition to stable cash flows post-IPO.
   • Comparison: Similar to PayPal’s early valuation, which relied on user growth and transaction volumes.

4. NTC (Nepal Telecom)

   • Dividend Valuation: NTC pays dividends (~10% of net profit). Investors use Gordon Growth Model to value its stock, assuming:
     • Dividends grow with telecom revenue growth (~8% annually).
     • Required return = 14% (higher due to regulatory risks).

Comparing Valuation Methods

Dividend Policy and Stock Valuation

A company’s dividend policy (how much to pay vs. reinvest) affects stock price.

Types of Dividend Policies

pie
    title Dividend Policy Impact on Stock Price
    "High Dividends (Stable)" : 30
    "Low Dividends (Growth)" : 40
    "No Dividends (Reinvest)" : 30

Market Efficiency and Stock Valuation

The Efficient Market Hypothesis (EMH) states that stock prices reflect all available information. There are three forms:

Real-World Test: NEPSE’s Efficiency

• Weak-Form: Studies show NEPSE stock returns are not predictable from past prices (supports weak-form EMH).
• Semi-Strong: Fundamental analysis works—e.g., stocks like Global IME (undervalued by P/E) outperform after earnings beats.
• Strong-Form: Insider trading scandals (e.g., 2018 NEPSE IPO leaks) prove markets are not perfectly efficient.

Exam Tip

What Examiners Want to See

1. Correct Formula Application

   • Always show step-by-step calculations (e.g., DDM, FCFE).
   • Label all variables ($D_1,r,g$) clearly.

2. Real-World Context

   • Nepal examples: Use NEPSE stocks (Ncell, NMB Bank, Global IME) or Nepali firms (Kathmandu Mart, Khalti).
   • Global examples: Google (FCFE), PayPal (growth valuation).

3. Comparisons and Critiques

   • Compare DDM vs. P/E for the same stock.
   • Discuss limitations (e.g., DDM fails for non-dividend stocks).

4. Diagrams and Tables

   • Draw a DDM flowchart or FCFE calculation table.
   • Use P/E comparison tables (like the NEPSE example above).

5. Common Pitfalls to Avoid

   • Assuming $g>r$ (leads to infinite value—wrong).
   • Ignoring taxes (dividends are taxed in Nepal at 10%).
   • Using trailing P/E without justification (forward P/E is better for growth stocks).

Sample Exam Question & Answer Structure

Question: *"Using the Gordon Growth Model, value the stock of Nepal Bank given:

• Last dividend ($D_0$) = NPR 10
• Growth rate ($g$) = 6%
• Required return ($r$) = 14% Assume the market price is NPR 150. Is the stock overvalued or undervalued?"*

Model Answer:

1. Calculate $D_1$: $$D_1=D_0\times (1+g)=10\times 1.06=\text{NPR }10.60$$

2. Apply Gordon Growth Model: $$P_0=\frac{D_1}{r-g}=\frac{10.60}{0.14-0.06}=\frac{10.60}{0.08}=\text{NPR }132.50$$

3. Compare to Market Price:

   • Fair Value = NPR 132.50
   • Market Price = NPR 150
   • Conclusion: The stock is overvalued by 13.2% (NPR 17.50).

4. Real-World Link: *"Nepal Bank’s high P/E (~25x) suggests investors are paying a premium, possibly due to brand trust rather than fundamentals. A better comparison would be NMB Bank (P/E ~20x)."*

Final Checklist Before Submission

✅ Formulas: Did I use the correct DDM/FCFE/P&E formula? ✅ Numbers: Did I plug in values correctly (e.g., $g<r$)? ✅ Real-World Tie: Did I link to a Nepali or global company? ✅ Visuals: Did I include a flowchart, table, or comparison? ✅ Critique: Did I discuss limitations or alternatives?