Stock Valuation Models

Stock valuation is a cornerstone of investment analysis. The CFP exam tests your ability to calculate intrinsic value using dividend discount models and interpret relative valuation metrics like P/E and PEG ratios. These concepts are heavily tested and require both formula application and conceptual understanding.

The Dividend Discount Model (DDM)

The Dividend Discount Model values a stock as the present value of all expected future dividend payments. The fundamental premise is that a stock's value derives from the cash flows (dividends) it generates for shareholders.

General DDM Formula:

Stock Value = Sum of [D(t) / (1 + r)^t]

Where:

• D(t) = Expected dividend in period t
• r = Required rate of return (discount rate)
• The sum extends to infinity for a stock held indefinitely

This general formula is impractical for calculation, so we use simplified versions based on dividend growth assumptions.

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The Gordon Growth Model (Constant Growth DDM)

The Gordon Growth Model (also called the Constant Growth DDM) assumes dividends grow at a constant rate forever. This simplifying assumption allows for a closed-form solution.

Gordon Growth Model Formula (on CFP Exam Formula Sheet):

V = D1 / (r - g)

Where:

• V = Intrinsic value of the stock
• D1 = Expected dividend next period (D0 x (1 + g))
• r = Required rate of return
• g = Constant dividend growth rate
• Critical Requirement: r must be greater than g

Calculating D1 from D0:

D1 = D0 x (1 + g)

Where D0 is the most recent dividend already paid.

CFP Exam Tip: Pay careful attention to whether a problem gives you D0 (just paid) or D1 (expected next period). Using the wrong dividend is a common error.

Worked Example 1: Basic Gordon Growth Model

XYZ Corporation just paid a dividend of $2.00 per share. Dividends are expected to grow at 5% annually. If the required return is 12%, what is the stock's intrinsic value?

Step 1: Calculate D1

• D1 = $2.00 x (1.05) = $2.10

Step 2: Apply Gordon Growth Model

• V = $2.10 / (0.12 - 0.05) = $2.10 / 0.07 = $30.00

Worked Example 2: Finding Growth Rate from Historical Data

Five years ago, a company paid a dividend of $1.36. The current annual dividend is $2.00. Calculate the compound growth rate and the stock's intrinsic value if the required return is 12%.

Step 1: Calculate historical growth rate using TVM

• PV = -$1.36, FV = $2.00, N = 5, Solve for I/Y
• Growth rate (g) = 8.01% (approximately 8%)

Step 2: Calculate D1

• D1 = $2.00 x (1.08) = $2.16

Step 3: Calculate intrinsic value

• V = $2.16 / (0.12 - 0.08) = $2.16 / 0.04 = $54.00

Key Relationships in the DDM

CFP Exam Tip: These inverse and direct relationships are frequently tested. Remember: Higher required returns mean lower values (investors discount future cash flows more heavily).

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Expected Rate of Return

By rearranging the Gordon Growth Model, we can solve for the expected return if we know the market price:

Expected Return Formula (on CFP Exam Formula Sheet):

r = (D1 / P) + g

Where:

• D1/P = Dividend yield
• g = Expected growth rate

Worked Example:

A stock trades at $45.00, just paid a dividend of $3.25, and has a 6% growth rate. An investor requires an 11% return. Should they buy the stock?

Step 1: Calculate expected return

• D1 = $3.25 x 1.06 = $3.445
• r = ($3.445 / $45.00) + 0.06 = 0.0766 + 0.06 = 13.66%

Step 2: Compare to required return

• Expected return (13.66%) > Required return (11%)
• Conclusion: The stock offers a higher return than required, so it is undervalued and attractive to buy.

Step 3: Calculate intrinsic value for confirmation

• V = $3.445 / (0.11 - 0.06) = $3.445 / 0.05 = $68.90
• Intrinsic value ($68.90) > Market price ($45.00)
• Confirms the stock is undervalued

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Multi-Stage Dividend Discount Models

For companies with non-constant growth, we use multi-stage models that assume high growth initially, transitioning to stable growth.

Two-Stage DDM Approach:

1. Calculate the present value of dividends during the high-growth phase
2. Calculate the terminal value at the start of stable growth using Gordon Growth Model
3. Discount the terminal value back to today
4. Sum all present values

Worked Example: Two-Stage DDM

A company will pay the following dividends:

• Year 1: $2.00
• Year 2: $2.50
• Year 3: $3.00
• After Year 3: Dividends grow at 8% forever

Required return is 10%. What is the intrinsic value?

Step 1: PV of dividends in Years 1-3

• PV of Year 1: $2.00 / 1.10 = $1.818
• PV of Year 2: $2.50 / 1.10^2 = $2.066
• PV of Year 3: $3.00 / 1.10^3 = $2.254

Step 2: Calculate terminal value at end of Year 3

• D4 = $3.00 x 1.08 = $3.24
• Terminal Value = $3.24 / (0.10 - 0.08) = $3.24 / 0.02 = $162.00

Step 3: PV of terminal value

• PV of Terminal Value = $162.00 / 1.10^3 = $121.72

Step 4: Sum all present values

• Total Value = $1.818 + $2.066 + $2.254 + $121.72 = $127.85

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When Does the DDM Work (and When Doesn't It)?

Limitations of the DDM:

1. Requires dividend payments: Companies that don't pay dividends can't be valued with DDM
2. Constant growth assumption: Real dividend growth varies over time
3. Sensitivity to inputs: Small changes in r or g dramatically affect value
4. Requires r > g: If growth equals or exceeds required return, the model produces meaningless results

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Relative Valuation: P/E Ratio

The Price-to-Earnings (P/E) Ratio compares a stock's price to its earnings per share, indicating how much investors pay for each dollar of earnings.

P/E Ratio Formula:

P/E Ratio = Stock Price / Earnings Per Share (EPS)

Or, rearranged to find price:

Stock Price = EPS x P/E Multiple

Types of P/E Ratios:

Interpreting P/E Ratios:

Worked Example:

Ice Cream Corp has earnings per share of $3.00 and trades at $40 per share. What is the P/E ratio?

P/E = $40.00 / $3.00 = 13.3x

This means investors pay $13.30 for every $1 of earnings.

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PEG Ratio: Growth-Adjusted Valuation

The PEG Ratio adjusts the P/E ratio for expected earnings growth, helping compare stocks with different growth rates.

PEG Ratio Formula:

PEG Ratio = P/E Ratio / Earnings Growth Rate (%)

Note: Growth rate is expressed as a whole number (e.g., 15 for 15% growth, not 0.15)

Interpreting PEG Ratios:

Worked Example:

Two technology stocks:

• Stock A: P/E of 30, expected growth of 25%
• Stock B: P/E of 20, expected growth of 10%

Which is more attractive based on PEG?

• Stock A PEG = 30 / 25 = 1.2
• Stock B PEG = 20 / 10 = 2.0

Conclusion: Stock A has the lower PEG ratio, suggesting it offers better value relative to its growth prospects, despite having the higher P/E ratio.

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Dividend Payout Ratio and Retention Rate

The Dividend Payout Ratio shows what percentage of earnings is distributed as dividends.

Dividend Payout Ratio Formula:

Dividend Payout Ratio = Dividends Per Share / Earnings Per Share

Retention Rate (Plowback Ratio):

Retention Rate = 1 - Dividend Payout Ratio

Sustainable Growth Rate:

g = ROE x Retention Rate

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Intrinsic Value vs. Market Price

The goal of valuation is to compare intrinsic value (what a stock is worth) to market price (what it costs).

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Stock Valuation Summary Table