When The Constant-Growth Model Is Inappropriate

When a Constant-Growth Estimate Is Not Trustworthy

The constant-growth dividend model is useful only when its central assumption is plausible: expected dividends can be represented as growing at one constant rate indefinitely. A calculation may produce a neat percentage even when that assumption is not credible. In that case, the arithmetic can be correct while the estimate is not useful.

This tutorial focuses on diagnosing that problem. The main warning signs are no meaningful dividend forecast, an unstable payout policy, a growth rate at or above the required return, and business conditions that are changing enough to make a single perpetual growth rate unrealistic. The distinction matters in practice: an unusable dividend-growth estimate is not, by itself, evidence that the equity has no value or that its cost of equity is zero.

Definition: The constant-growth dividend model assumes that dividends grow at the same rate $g$ forever. If $D_1$ is the dividend expected one period from now, $P_0$ is the current share price, and $k_e$ is the required return on equity, the model is $P_0 = D_1/(k_e-g)$, provided $k_e>g$. Rearranging gives the dividend-based estimate $k_e = D_1/P_0+g$.

The model is not a general rule that any dividend and any growth estimate can be combined. It needs a meaningful forecast of future dividends, a defensible long-run growth rate, and a required return greater than that growth rate. The growth assumption must describe the future stream relevant to the valuation, not just repeat a recent growth rate because it is easy to calculate.

Why the Model Requires Growth Below the Required Return

The formula follows from valuing an indefinitely growing stream of dividends. Assume the first dividend is $D_1$, each subsequent dividend grows at constant rate $g$, and the stream is discounted at a constant required return $k_e$. Also assume $k_e>g$, so the present values form a convergent geometric series.

P_0 = \frac{D_1}{1+k_e} + \frac{D_1(1+g)}{(1+k_e)^2} + \frac{D_1(1+g)^2}{(1+k_e)^3} +\cdots

The first term is the present value of the dividend at time 1. Each term after it is obtained by multiplying the previous term by the ratio $q=(1+g)/(1+k_e)$. When $k_e>g$, $q<1$, so the infinite geometric series converges. Its sum is:

P_0 = \frac{D_1}{1+k_e}\frac{1}{1-q} = \frac{D_1}{1+k_e} \frac{1}{1-\frac{1+g}{1+k_e}} = \frac{D_1}{k_e-g}

If $k_e=g$, the terms do not decline and the series has no finite sum. If $k_e<g$, the ratio exceeds one and the terms grow rather than approach zero; again, there is no finite value from this perpetual stream under the model. The condition $k_e>g$ is therefore part of the model, not a minor technical detail.

Four Conditions That Call for Caution

A good diagnosis asks whether the inputs describe the business and its expected distributions, rather than only whether the formula can be evaluated.

Warning sign	Why the constant-growth assumption is weak	Practical implication
No meaningful dividend forecast	The model values expected dividends, so a missing or unsupported $D_1$ cannot be repaired by inserting an arbitrary number.	Do not interpret a missing dividend-based estimate as a zero cost of equity.
Unstable payout	Recent dividend changes may reflect temporary earnings, a one-off distribution, or a changing payout policy rather than persistent growth.	A historical average growth rate may conceal rather than resolve the instability.
Growth at or above $k_e$	The present-value series does not converge when $g\geq k_e$.	Reject the model output; do not treat a negative or undefined result as an estimate.
Changing business conditions	A major transition can make near-term dividends and long-run dividends follow different patterns.	A single growth rate may misrepresent the dividend stream, even if the long-run rate seems reasonable.

Worked Examples: Diagnose Before Calculating

Worked Example: No Forecastable Dividend

A hypothetical technology firm has not paid a dividend and expects to retain earnings while it funds expansion. An analyst is asked to estimate its cost of equity. For an independent CAPM estimate, assume a risk-free rate of 3.2%, a market risk premium of 5.5%, and an estimated equity beta of 1.10. Treat these as the analyst’s stated inputs and assume the CAPM estimate is appropriate for this exercise.

Step 1: Test whether the dividend model has a usable input. The company has no current dividend and no supported forecast dividend for the next period. Thus the analyst cannot identify a defensible $D_1$ from the stated facts. The constant-growth formula $k_e=D_1/P_0+g$ is not available as a dividend-based estimate.

Step 2: Avoid the zero-dividend trap. Setting $D_1=0$ in the rearranged formula would produce $k_e=g$. But that result would be driven entirely by an unsupported growth input and would not estimate the required return from the absent dividend stream. A firm’s decision not to distribute cash now does not establish that its equity has no value or a zero required return.

Step 3: Calculate the separate CAPM estimate. Under CAPM, $k_e=r_f+\beta_e(\text{market risk premium})$. Therefore:

k_e=3.2\%+1.10(5.5\%) =3.2\%+6.05\% =9.25\%

The CAPM-based estimate is 9.25%. It is an independent estimate based on the stated market inputs; it is not a dividend-model estimate. Check: the beta-scaled premium is 6.05%, and adding 3.2% gives 9.25%. The common mistake avoided is treating no dividend as a zero cost of equity.

Worked Example: A Historical Growth Rate Hides Payout Instability

A hypothetical insurer paid dividends per share of $1.00, $1.20, $0.95, and $1.331 in four successive years. Its current share price is $20.00. An analyst proposes using the compound annual growth rate across the three intervals as a perpetual growth assumption. Assess the calculation and its reliability.

Step 1: Calculate each annual change. From $1.00 to $1.20, growth is $(1.20/1.00)-1=20.00\%$. From $1.20 to $0.95, growth is $(0.95/1.20)-1=-20.8333\%$. From $0.95 to $1.331, growth is $(1.331/0.95)-1=40.1053\%$. These changes are large and move in different directions.

Step 2: Calculate the three-interval compound rate. The ending dividend is 1.331 times the starting dividend. Since $1.10^3=1.331$, the compound annual growth rate is exactly 10.00%:

g_{\text{historical}} = \left(\frac{1.331}{1.00}\right)^{1/3}-1 = 1.10-1 = 10.00\%

This rate summarizes the start and end values, but it does not remove the instability shown by the intervening dividend changes. If, solely to illustrate the model’s mechanical output, the analyst assumes 10.00% growth continues forever, then the next dividend is $D_4=1.331(1.10)=\$1.4641$. The implied cost of equity would be:

\frac{D_4}{P_0}+g = \frac{\$1.4641}{\$20.00}+10.00\% = 7.3205\%+10.00\% = 17.3205\%

The arithmetic is consistent, but the output depends on an unsupported claim: that the volatile three-year pattern justifies 10% perpetual dividend growth. The historical compound rate alone does not establish that claim. Check: the forecast dividend divided by the share price is 7.3205%; adding 10.00% gives 17.3205%. The common mistake avoided is treating a mathematically valid historical average as proof of stable future growth.

Worked Example: Growth Equals or Exceeds the Required Return

Suppose an analyst’s independent required-return estimate for a hypothetical utility is 9.0%. The proposed perpetual dividend growth rate is 10.0%, and the forecast next dividend is $1.10 per share. The current share price is $25.00. Determine whether the constant-growth model is usable with these inputs.

Step 1: Check the model condition. Here $g=10.0\%$ and $k_e=9.0\%$, so $g>k_e$. The required condition $k_e>g$ fails before any valuation is accepted.

Step 2: Show the invalid result if the inputs are forced into the price formula.

P_0 = \frac{\$1.10}{0.09-0.10} = \frac{\$1.10}{-0.01} = -\$110.00

A negative share value is not a meaningful estimate here; it signals that the formula’s convergence condition has been violated. At equality, the denominator would be zero and the formula would be undefined.

Step 3: Compare with the return implied by the stated market price. If the analyst instead inserts the proposed growth rate and the observed price into the rearranged expression, the mechanical result is:

\frac{\$1.10}{\$25.00}+10.0\% = 4.4\%+10.0\% = 14.4\%

This 14.4% differs from the independent 9.0% estimate, so the inputs do not jointly support a consistent constant-growth estimate. Check: $1.10/25=0.044$, or 4.4%; adding 10.0% gives 14.4%. The correction is to reject the dividend-model result under these assumptions, not to report the negative price or silently change the required return.

Worked Example: Business Conditions Are Changing

A hypothetical manufacturer is changing its product mix after closing an older business line. Its expected dividends per share are $1.00 next year, $1.50 in the following year, and $1.80 in the third year. Management expects that after the transition the dividend may grow at a stable 4% rate. The current share price is $36.00. Explain why a constant-growth estimate is not supported by these facts.

Step 1: Calculate the changes during the transition. Growth from the first forecast dividend to the second is $(1.50/1.00)-1=50\%$. Growth from the second to the third is $(1.80/1.50)-1=20\%$. Neither rate equals the proposed 4% long-run rate.

Step 2: Identify the mismatch. The first three forecast dividends describe a business in transition; the 4% figure describes a possible later stable period. Applying one growth rate to the entire dividend stream would ignore this distinction. The fact that 4% may be a plausible long-run rate does not make it a suitable description of the near-term forecast.

Step 3: Show what a mechanical constant-growth calculation would imply. If an analyst incorrectly treats the next dividend of $1.00 as the start of a 4%-growing stream forever, the rearranged model gives:

k_e = \frac{\$1.00}{\$36.00}+4\% = 2.7778\%+4\% = 6.7778\%

That percentage is the output of the imposed constant-growth assumption, not a supported estimate given the different forecast growth rates. A valuation approach that can represent a transition separately from a stable period is needed before using dividends to estimate the return. Check: $1/36=0.027777\ldots$, or 2.7778% to four decimals; adding 4% gives 6.7778%. The common mistake avoided is assuming that a reasonable long-run rate makes the whole forecast constant-growth.

A Practical Diagnostic Sequence

Before reporting a constant-growth cost of equity, check the model inputs in order. This keeps the calculation from giving false precision to assumptions that do not fit the business.

Confirm a usable dividend forecast.
Identify a supported next-period dividend $D_1$. If distributions are absent or cannot be forecast credibly, the dividend-growth estimate is unavailable; do not substitute zero automatically.

Assess payout stability.
Review whether changes reflect persistent growth or changes in earnings, payout policy, or one-time decisions. A historical average is a summary, not evidence that the same rate will continue.

Check the convergence condition.
Verify $k_e>g$. If $g\geq k_e$, the perpetual present-value series does not converge and the formula cannot produce a valid finite value.

Test business conditions against the assumption.
Ask whether the firm is in a transition that makes near-term and long-run dividends materially different. If so, one perpetual growth rate may not represent the expected stream.

Report the limitation clearly.
Distinguish a valid estimate from a mechanical calculation. If the dividend model is unsupported, state why and use an appropriate independent basis, such as a CAPM estimate when its inputs are suitable.

Common Exam Trap

A frequent error is to calculate $D_1/P_0+g$ first and check the assumptions afterward. For example, if $D_1=\$1.10$, $P_0=\$25.00$, and $g=10\%$, the arithmetic gives 14.4%. That result does not validate the model. If the required return being tested is 9%, then $g$ exceeds $k_e$, so the underlying constant-growth present-value series does not converge. The correction is to test whether the assumptions hold before interpreting the output.

Another error is to call a dividend-based estimate “zero” merely because the company currently pays no dividend. The formula needs a supported expected dividend stream. Its absence means this particular method cannot provide the estimate; it does not settle the equity’s value or required return.

Key takeaway: The constant-growth model is defensible only when a meaningful dividend forecast and a credible perpetual growth assumption exist, business conditions support stable growth, and $k_e>g$. A calculated percentage outside those conditions is a warning about the assumptions, not a reliable cost-of-equity estimate.

Check Your Understanding

For each situation, decide whether the constant-growth dividend estimate is supported and perform the requested calculation where possible.

A hypothetical firm has no dividend forecast because it plans to retain all cash for an uncertain period. An analyst sets $D_1=0$ and reports a zero cost of equity. What is the correct diagnosis? (Answer: The dividend-growth estimate is unavailable; the missing dividend does not imply a zero cost of equity.)
A company’s dividend rises from $2.00 to $2.20 and then falls to $1.76 over two years. Calculate the two annual growth rates and explain whether one historical rate is clearly stable. (Answer: 10.00% and -20.00%; the changes are not evidence of stable growth.)
A proposed model uses $D_1=\$0.90$, $P_0=\$30.00$, and perpetual growth $g=8\%$. Calculate the mechanical implied return, then state what must be checked before accepting it. (Answer: $0.90/30+8\%=11.00\%$; confirm that the growth assumption is credible and that the required return exceeds 8%.)
An independent estimate gives $k_e=7\%$, while the proposed perpetual growth rate is 7%. What happens to the constant-growth price formula, and why? (Answer: It is undefined because $k_e-g=0$; the present-value series does not converge.)
A company forecasts dividends of $1.20, $1.44, and $1.50 over the next three years while operations are being reorganized; after that, management expects 3% long-run growth. Is a single 3% growth rate suitable for all forecast periods? (Answer: No. The early dividend changes are 20.00% and approximately 4.17%, so the transition forecasts do not follow a constant 3% rate.)

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