Choosing Between CAPM And Dividend-Growth Estimates

Two Models, Different Evidence

The cost of equity is the return shareholders require for bearing the risk of owning a company’s common stock. It is not directly observable: an analyst estimates it using a model and inputs. Two common approaches use different evidence. The Capital Asset Pricing Model (CAPM) estimates the required return from market-wide risk and the stock’s sensitivity to that risk. A constant-growth dividend model estimates it from the current share price, the next dividend, and expected long-run dividend growth.

Neither method is universally preferable. CAPM can be used when a company does not pay dividends, but it depends on a defensible beta and market risk premium. The dividend-growth model uses company-specific dividend information, but it depends on a stable and supportable growth assumption. Choosing between them is therefore a question of model fit and input quality, not just which calculation is easier.

Definition: Under CAPM, the estimated cost of equity is $k_e=R_f+\beta(E[R_m]-R_f)$, where $R_f$ is the risk-free rate, $E[R_m]$ is the expected market return, and $\beta$ measures the equity’s systematic risk relative to the market. The difference $E[R_m]-R_f$ is the market risk premium.

Definition: Under the constant-growth dividend model, the estimated cost of equity is $k_e=\dfrac{D_1}{P_0}+g$, where $P_0$ is the current share price, $D_1$ is the dividend expected one period from now, and $g$ is the constant expected dividend growth rate. The model requires a continuing dividend stream with a defensible constant growth rate and $k_e>g$.

What Each Estimate Assumes

CAPM is an equilibrium model. In its standard form, investors are assumed to be diversified, to assess risk and return over a common period, and to use the market portfolio as the relevant benchmark. The model treats systematic risk—risk associated with market movements—as the risk for which investors require a return premium. Beta summarizes the stock’s exposure to that risk. The formula is a model-based estimate, not a guarantee of the return shareholders will receive.

The dividend-growth model uses a different set of assumptions. It treats the share price as the present value of expected future dividends, assumes dividends grow at a constant rate indefinitely, and requires the cost of equity to exceed that growth rate. Its inputs must be consistent in timing and units: an annual dividend, annual growth rate, annual share price valuation, and annual cost of equity. A stable historical dividend record can help inform growth expectations, but does not establish that future growth will remain constant.

Why the Dividend Formula Works

The constant-growth formula follows from valuing a perpetuity of dividends. If the dividend one period from now is $D_1$, and dividends grow by $g$ each period, then the payment at time $t$ is $D_1(1+g)^{t-1}$. Discounting each payment at $k_e$ gives a geometric series. When $k_e>g$, its ratio $(1+g)/(1+k_e)$ is less than one, so the infinite series converges:

P_0=\sum_{t=1}^{\infty}\frac{D_1(1+g)^{t-1}}{(1+k_e)^t} =\frac{D_1}{1+k_e}\cdot\frac{1}{1-\frac{1+g}{1+k_e}} =\frac{D_1}{k_e-g}.

Rearranging $P_0=D_1/(k_e-g)$ gives $k_e=D_1/P_0+g$. The first term is the expected dividend yield; the second is the assumed growth rate. If growth is at least as large as the cost of equity, the infinite series does not converge, so this constant-growth valuation cannot be applied as stated.

Compare Data Requirements and Suitability

Consideration	CAPM	Constant-growth dividend model
Core inputs	Risk-free rate, beta, and market risk premium	Current share price, next expected dividend, and constant growth rate
Dividend required?	No	Yes; a meaningful expected dividend stream is needed
Company circumstances that may support it	Dividends are absent or irregular, but beta and market inputs are defensible	Dividend policy and long-run growth are relatively stable and forecastable
Key modeling concern	Whether the chosen beta and market risk premium represent expected systematic risk	Whether constant growth is a credible long-run assumption and $k_e>g$
Important sources of uncertainty	Beta estimation, choice of risk-free rate, and expected market risk premium	Forecast dividend, share price, and growth estimate

CAPM is often more practicable for a company that pays no dividend, retains most earnings, or has an unstable payout policy. Its use still requires an appropriate beta. Earlier material on choosing, estimating, unlevering, and relevering beta is relevant: the beta used should reflect the equity risk being estimated and should be supported by the available evidence.

The constant-growth dividend model is more suitable when a company has an established dividend policy and a plausible long-run growth rate. It becomes less persuasive when dividends are suspended, unusually variable, or expected to change substantially. A dividend from the most recent year is not automatically the next expected dividend, and a short period of historical growth is not automatically a perpetual growth forecast.

A Practical Selection Process

Check whether the model can be supported.
For CAPM, identify a defensible beta, risk-free rate, and market risk premium. For the dividend model, identify a current price, a forecast of the next dividend, and a defensible long-run growth assumption.

Check the company circumstances.
Consider whether payout policy and dividends are sufficiently stable for constant growth to be meaningful. If not, do not force the constant-growth model merely because a recent dividend exists.

Check the model conditions and units.
Use consistent periods and rates. For the dividend model, verify $k_e>g$; for CAPM, use the market risk premium $E[R_m]-R_f$, not the total expected market return in its place.

Describe the estimate’s limitations.
State which inputs are observed, which are forecasts, and which require judgment. A calculated number is only as credible as its model fit and supporting inputs.

Worked Example: A Stable Dividend Payer

A mature company has a current share price of $40.00 and just paid an annual dividend of $1.60. Analysts consider a constant annual dividend growth rate of 4.0% reasonable. For CAPM, use an annual risk-free rate of 3.0%, a beta of 1.10, and an expected annual market return of 8.0%. Calculate both estimates and assess which inputs are relevant to the company’s circumstances.

Method. Calculate the CAPM estimate using the market risk premium, then calculate the dividend estimate using the next dividend rather than the dividend just paid.

CAPM. The market risk premium is $8.0\%-3.0\%=5.0\%$. Therefore,

k_e=3.0\%+1.10(5.0\%)=3.0\%+5.5\%=8.5\%.

Dividend-growth estimate. The next expected annual dividend is $D_1=1.60(1.04)=\$1.664$. The expected dividend yield is $\$1.664/\$40.00=0.0416=4.16\%$. Thus,

k_e=4.16\%+4.0\%=8.16\%.

The two model estimates are 8.50% and 8.16%. A stable dividend record makes the dividend model potentially relevant, provided the 4.0% long-run growth assumption is supportable. CAPM does not depend on the dividend forecast and instead relies on the selected beta and market inputs. The calculations alone do not establish which model is more credible; that depends on the evidence for those inputs.

Check and common mistake. The dividend estimate is greater than its assumed 4.0% growth rate, as required. Using the $1.60 dividend just paid instead of the next dividend would give $1.60/40+4.0\%=8.0\%$, understating this model estimate by 0.16 percentage points. The correction is to grow $D_0$ once to obtain $D_1$.

Worked Example: A Company With No Current Dividend

A research-stage medical-device company currently pays no dividend and has no announced dividend start date. For a CAPM estimate, an analyst uses an annual risk-free rate of 4.2%, a beta of 1.35, and an expected annual market return of 9.4%. Calculate the estimate and determine whether the constant-growth dividend model can be applied using the information given.

Method. Apply CAPM using the difference between expected market return and the risk-free rate. Then assess whether the data needed for the dividend model exist.

The market risk premium is $9.4\%-4.2\%=5.2\%$. The CAPM estimate is

k_e=4.2\%+1.35(5.2\%) =4.2\%+7.02\% =11.22\%.

The constant-growth dividend model cannot be estimated from the stated information: there is no current dividend stream or forecast next dividend, and no long-run dividend growth rate. The fact that the company pays no dividend does not make CAPM automatically reliable; the beta and market inputs still require support. But given these data, CAPM is calculable while the constant-growth dividend estimate is not.

Check and common mistake. The premium used is 5.2%, not the full expected market return of 9.4%. Substituting 9.4% as the premium would incorrectly produce $4.2\%+1.35(9.4\%)=16.89\%$. The correct CAPM calculation first subtracts the risk-free rate from the expected market return.

Worked Example: Comparing Sensitivity to Input Uncertainty

A dividend-paying company’s share price is $50.00, and its most recent annual dividend was $1.80. Analysts consider annual dividend growth between 3.0% and 5.0% plausible, with 4.0% as a central assumption. For CAPM, use an annual risk-free rate of 3.0%, an expected market risk premium of 5.0%, and a beta estimate of 0.95, with a plausible beta range of 0.85 to 1.05. Calculate the central estimates and the ranges caused by the stated growth and beta assumptions.

Dividend-growth method. At the central growth assumption, $D_1=\$1.80(1.04)=\$1.872$. The dividend yield is $\$1.872/\$50.00=0.03744=3.744\%$, giving

k_e=3.744\%+4.0\%=7.744\%.

At 3.0% growth, $D_1=\$1.80(1.03)=\$1.854$, the yield is $\$1.854/\$50.00=3.708\%$, and the estimate is $3.708\%+3.0\%=6.708\%$. At 5.0% growth, $D_1=\$1.80(1.05)=\$1.890$, the yield is $\$1.890/\$50.00=3.780\%$, and the estimate is $3.780\%+5.0\%=8.780\%$. The resulting range is 6.708% to 8.780%.

CAPM method. At beta 0.95, the estimate is $3.0\%+0.95(5.0\%)=7.75\%$. At beta 0.85, it is $3.0\%+0.85(5.0\%)=7.25\%$; at beta 1.05, it is $3.0\%+1.05(5.0\%)=8.25\%$. The beta range therefore gives a CAPM estimate range of 7.25% to 8.25%.

Both ranges reflect only the input uncertainty specified in this problem, not every possible source of error. The dividend-model range depends on the growth assumption, while the CAPM range depends on beta, with the risk-free rate and premium held fixed. The central estimates are close, but closeness does not prove that either set of assumptions is sound.

Check and common mistake. Each dividend-model estimate exceeds its corresponding assumed growth rate, satisfying the convergence condition. A common error is to vary $g$ in the dividend model but leave $D_1$ fixed at the central-growth forecast. Since $D_1=D_0(1+g)$, it must also be recalculated for each growth assumption, as done above.

Interpreting Estimation Uncertainty

A useful comparison distinguishes model risk from input uncertainty. Model risk arises when the model’s assumptions do not describe the company well—for example, constant perpetual dividend growth when payout policy is changing. Input uncertainty arises when the model is suitable but values such as beta, the market risk premium, or expected dividend growth are imprecisely estimated.

For CAPM, beta is an estimate and can vary with the observation period, return data, and choice of comparable equity. The risk-free rate should match the currency and horizon relevant to the estimate, while the expected market risk premium is itself uncertain. For the dividend model, the next dividend may be forecastable in the near term while long-run growth remains uncertain. The share price is observable, but it can change; it is not an assurance that the model’s assumptions are correct.

Keep the conclusion appropriately limited. A point estimate is not a uniquely correct answer simply because the arithmetic is precise. State the method, the assumptions, and the main uncertainties. When one method lacks essential data or violates its conditions, explain that limitation rather than presenting an unsupported estimate.

Common Exam Traps

Using the market return as the premium. CAPM requires $E[R_m]-R_f$ as the premium, then adds $R_f$ once.
Using the last dividend instead of the next one. The constant-growth formula uses $D_1$, not $D_0$.
Treating historical growth as a guaranteed perpetual forecast. Historical dividends can inform an assumption but do not prove constant future growth.
Applying constant growth without checking convergence. The model requires $k_e>g$; otherwise the infinite dividend series does not converge.
Choosing a method only because it gives a convenient answer. The company’s circumstances and the quality of the inputs must support the selected model.

Key takeaway: Use CAPM when systematic-risk inputs are supportable, including when dividends are absent or unreliable. Use a constant-growth dividend estimate when a stable dividend policy and defensible long-run growth assumption are available. In either case, assess model fit and input uncertainty before interpreting the result.

Check Your Understanding

For each problem, select the relevant method or assess whether the stated inputs support it. Rates are annual unless stated otherwise.

A company has beta 1.20, a risk-free rate of 4.0%, and an expected market return of 9.5%. Calculate its CAPM cost-of-equity estimate. (Answer: 10.6%)
A company’s share price is $25.00, its most recent annual dividend was $1.50, and expected constant annual dividend growth is 4.0%. Calculate the constant-growth cost-of-equity estimate. (Answer: 10.24%)
A firm has suspended dividends and has no defensible forecast of when payments will resume. Can the constant-growth dividend model be estimated from the information given? State the main reason. (Answer: No; a defensible next dividend and continuing constant-growth dividend stream are not provided.)
For CAPM, use a risk-free rate of 3.2%, a beta of 0.70, and an expected market risk premium of 6.0%. Calculate the estimate. (Answer: 7.4%)
A company has a share price of $48.00, just paid an annual dividend of $2.40, and has a defensible constant annual growth assumption of 3.5%. Calculate the constant-growth estimate, rounding the final rate to two decimal places. (Answer: 8.68%)

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