Cost of Equity: CAPM and Dividend Growth

Why This Topic Matters for the CTP Exam

The cost of equity is one of the most heavily tested calculations in the Capital Structure and Long-Term Capital section of the AFP Certified Treasury Professional (CTP) exam. It is the return that common shareholders require for bearing the risk of owning the firm, and it is a critical input into the Weighted Average Cost of Capital (WACC). Treasury professionals rely on the cost of equity to set hurdle rates for capital budgeting, evaluate whether to raise new capital through debt or equity, assess share repurchase and dividend policy, and judge whether the firm is creating or destroying shareholder value.

Unlike the cost of debt, which is observable from coupon rates, yields, and loan agreements, the cost of equity is not stated in any contract. It must be estimated. The CTP body of knowledge focuses on two estimation approaches: the Capital Asset Pricing Model (CAPM) and the Dividend Growth Model (DGM), also called the Gordon Growth Model or Dividend Discount Model. Expect to see both conceptual questions (which model is appropriate, what the inputs mean) and numerical questions requiring you to compute a cost of equity from given data.

What Is the Cost of Equity?

The cost of equity (often written as R_e, K_e, or r_s) is the minimum rate of return that a company must earn on the equity-financed portion of its investments to keep shareholders satisfied. From the investor's perspective it is the required return; from the firm's perspective it is a cost. Key characteristics to remember:

• Equity is riskier than debt because shareholders are paid last, so the cost of equity is almost always higher than the after-tax cost of debt.
• Dividends are paid from after-tax earnings, so there is no tax adjustment to the cost of equity (unlike debt, where interest is tax-deductible).
• The cost of retained earnings is the same as the cost of existing equity because retained earnings represent an opportunity cost to shareholders who could otherwise have received the cash as dividends.
• The cost of newly issued common stock is higher than the cost of retained earnings because of flotation costs (investment banking fees, legal and registration expenses, underpricing).

Method 1: The Capital Asset Pricing Model (CAPM)

CAPM estimates the cost of equity based on the principle that investors must be compensated for the time value of money and for systematic (non-diversifiable) risk.

Formula:
R_e = R_f + β × (R_m − R_f)

Where:
• R_f = Risk-free rate, typically the yield on U.S. Treasury securities (T-bills for short horizons, long-term Treasury bonds for long-horizon projects).
• β (Beta) = A measure of the stock's systematic risk relative to the overall market. A beta of 1.0 means the stock moves with the market; a beta greater than 1.0 means greater volatility and risk than the market; a beta below 1.0 means less. The market itself has a beta of 1.0 and a risk-free asset has a beta of 0.
• R_m = Expected return on the overall market (for example, the S&P 500).
• (R_m − R_f) = The market risk premium (also called the equity risk premium), which is the additional return investors require for holding the market portfolio rather than the risk-free asset.
• β × (R_m − R_f) = The stock-specific risk premium.

Worked Example (CAPM):
The risk-free rate is 4%, the expected market return is 10%, and the company's beta is 1.3.
R_e = 4% + 1.3 × (10% − 4%) = 4% + 1.3 × 6% = 4% + 7.8% = 11.8%

Alternate Example (Market Risk Premium Given Directly):
The risk-free rate is 3.5%, the market risk premium is 5.5%, and beta is 0.9.
R_e = 3.5% + 0.9 × 5.5% = 3.5% + 4.95% = 8.45%
Notice that when the question already gives the market risk premium, you do NOT subtract the risk-free rate again.

Strengths of CAPM:
• Explicitly incorporates risk through beta.
• Can be applied to any publicly traded company, including those that pay no dividends.
• Widely used in practice and grounded in financial theory.

Weaknesses of CAPM:
• Beta is estimated from historical data and may not reflect future risk.
• The market risk premium is an estimate and varies by source and time period.
• Assumes investors hold diversified portfolios and that only systematic risk matters.
• Difficult to apply to private companies without a traded beta (a proxy or industry beta must be used).

Method 2: The Dividend Growth Model (Gordon Growth Model)

The Dividend Growth Model derives the cost of equity from the current stock price and the stream of dividends investors expect to receive. It rests on the idea that a stock's price equals the present value of all future dividends, assuming dividends grow at a constant rate forever.

Starting from the valuation formula P₀ = D₁ / (R_e − g), rearrange to solve for the cost of equity:

Formula:
R_e = (D₁ / P₀) + g

Where:
• D₁ = The dividend expected to be paid one year from now (next period's dividend).
• P₀ = The current market price of the stock.
• g = The constant expected growth rate of dividends.
• D₁ / P₀ = The expected dividend yield.

Critical Relationship: If the question gives you the dividend just paid (D₀), you must grow it one period forward:
D₁ = D₀ × (1 + g)

Worked Example (DGM with D₁ given):
A stock sells for $50. The company expects to pay a dividend of $2.50 next year, and dividends are expected to grow 5% annually.
R_e = ($2.50 / $50) + 5% = 5% + 5% = 10%

Worked Example (DGM with D₀ given):
A stock sells for $40. The company just paid a dividend of $2.00, and dividends are expected to grow 6% per year.
D₁ = $2.00 × 1.06 = $2.12
R_e = ($2.12 / $40) + 6% = 5.3% + 6% = 11.3%
Using $2.00 instead of $2.12 would give 11.0%, a common wrong answer that will almost certainly appear as a distractor.

Estimating the Growth Rate (g):
The exam may require you to estimate g rather than giving it directly. Two common approaches:
• Historical growth: the compound annual growth rate of past dividends.
• Sustainable (internal) growth: g = Retention Ratio × Return on Equity (ROE), where Retention Ratio = 1 − Dividend Payout Ratio. For example, if ROE is 15% and the firm pays out 40% of earnings, g = 0.60 × 15% = 9%.

Adjusting for Flotation Costs (New Common Stock):
When a firm issues new shares, it receives less than the market price because of flotation costs (F), usually expressed as a percentage of the issue price.
R_e(new) = D₁ / [P₀ × (1 − F)] + g

Worked Example (Flotation Costs):
Stock price $40, D₁ = $2.12, g = 6%, flotation costs 5%.
Net proceeds = $40 × (1 − 0.05) = $38
R_e(new) = ($2.12 / $38) + 6% = 5.58% + 6% = 11.58%
Compare this with the 11.3% cost of retained earnings. New equity is always more expensive than retained earnings.

Strengths of the Dividend Growth Model:
• Simple and intuitive; uses readily observable price and dividend data.
• Directly ties the cost of equity to what the company actually pays shareholders.

Weaknesses of the Dividend Growth Model:
• Only works for companies that pay dividends with a reasonably stable, predictable growth pattern.
• Extremely sensitive to the estimate of g; a small change in g produces a large change in R_e.
• Mathematically requires that g be less than R_e; if growth exceeds the required return, the model breaks down.
• Does not explicitly account for risk (risk is only implicitly embedded in the market price).

Comparing the Two Models

In practice, analysts frequently compute the cost of equity using both approaches and then average them or use a judgmental range. The CTP exam may ask which model is appropriate given a fact pattern:
• Company pays no dividends or has erratic dividends → use CAPM.
• Company has a stable, growing dividend and the question gives price, dividend, and growth → use DGM.
• Question gives beta, risk-free rate, and market return or market risk premium → use CAPM.
• Question asks about the impact of systematic risk or market volatility → think CAPM and beta.
• Question asks about flotation costs → think DGM adjusted for net proceeds.

Related Concept: Cost of Preferred Stock
Though not a cost of common equity, it is frequently tested alongside it. Preferred stock pays a fixed dividend with no growth, so:
R_p = D_p / P_p (or D_p / net proceeds if flotation costs apply).
Like common equity, preferred dividends are not tax-deductible, so no tax adjustment is made.

How the Cost of Equity Feeds into WACC

WACC = (E/V) × R_e + (P/V) × R_p + (D/V) × R_d × (1 − T)

Where E, P, and D are the market values of common equity, preferred stock, and debt; V is their total; and T is the marginal tax rate. The cost of equity is typically the largest single component, and because equity usually carries the highest cost, errors in estimating R_e have an outsized effect on WACC. Treasury uses WACC as the discount rate for NPV analysis and as the benchmark for Economic Value Added (EVA) and other value-creation measures.

Exam Tips: Answering Questions on Cost of Equity: CAPM and Dividend Growth

1. Identify the model from the data given. Scan the question for keywords. Beta, risk-free rate, market return, or market risk premium signal CAPM. Stock price, dividend, and growth rate signal the Dividend Growth Model. If both data sets are provided, read the question stem carefully to see which approach is requested, or whether you are asked to average them.

2. Watch the market return versus market risk premium trap. If the question says the expected market return is 10% and the risk-free rate is 4%, the premium is 6%. If the question says the market risk premium is 6%, use 6% directly. Subtracting the risk-free rate from an already-stated premium is the single most common CAPM error.

3. Watch the D₀ versus D₁ trap. Phrases like just paid, most recent dividend, current dividend, or last year's dividend indicate D₀, which must be multiplied by (1 + g). Phrases like expected to pay next year, next dividend, or D₁ can be used directly.

4. Never apply a tax adjustment to equity. Only the cost of debt is multiplied by (1 − T). If an answer choice shows the cost of equity reduced by taxes, eliminate it.

5. Handle flotation costs on the price, not the dividend. Reduce the price by the flotation percentage to get net proceeds, then divide the dividend by net proceeds. Flotation costs raise the cost of new equity above the cost of retained earnings.

6. Keep decimals and percentages consistent. Convert everything to decimals (0.05) or everything to percentages (5%) before computing. Mixing them produces nonsensical answers that often match a distractor.

7. Perform a sanity check. The cost of equity should exceed the after-tax cost of debt and the risk-free rate. A higher beta should produce a higher cost of equity. A higher growth rate or higher dividend yield should produce a higher DGM result. If your answer violates these relationships, recheck your arithmetic.

8. Know the conceptual interpretations. Be prepared for questions like: What does a beta of 1.5 mean? (The stock is 50% more volatile than the market and requires a higher return.) Why does CAPM work for non-dividend payers? (It relies on market risk, not dividends.) Why is DGM sensitive to g? (g appears both in the numerator through D₁ and as a direct addition.) Why is new equity more expensive than retained earnings? (Flotation costs.)

9. Remember the sustainable growth formula. If the question gives ROE and payout ratio instead of g, compute g = (1 − payout) × ROE before plugging into the DGM.

10. Connect to the bigger picture. Many CTP questions embed the cost of equity inside a WACC calculation. Compute the component costs first, write them down, apply the market-value weights, and remember that only debt receives the tax shield.

Quick Reference Summary

• CAPM: R_e = R_f + β(R_m − R_f)
• Dividend Growth: R_e = D₁/P₀ + g, where D₁ = D₀(1 + g)
• New equity with flotation: R_e = D₁/[P₀(1 − F)] + g
• Sustainable growth: g = Retention Ratio × ROE
• Preferred stock: R_p = D_p/P_p
• No tax adjustment for equity or preferred; tax adjustment applies only to debt.
• Cost of retained earnings = cost of existing equity; cost of new equity is higher.

Master these formulas, memorize the traps, and practice reading question stems for the key signal words, and you will handle cost of equity questions on the CTP exam with confidence.