Link dividends, retention and mature growth

Learning goals

• Calculate stock value using the next dividend.
• Explain why 4% applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 90 minutes, excluding further revision.

Shared case and decision context

StableCo just paid dividend 2.00. Long-run growth is 4% and equity required return 10%. ROE is 12% with a sustainable retention ratio one-third under the constant-policy assumption. The analyst proposes 11% perpetual growth without changing the discount rate.

Economic or professional mechanism

The Gordon model discounts next period’s dividend, not the dividend just paid. Sustainable growth b*ROE links retention and profitability under stable leverage and no new external equity assumptions; it is not a universal growth guarantee. Multistage models allow an exceptional phase to fade toward a defensible mature growth rate.

Apply, challenge and communicate

Next dividend is 2.08 and estimated value 34.6667. An 11% perpetual rate with a 10% required return violates this formula’s finite-value condition. Higher retention creates value only when reinvestment economics justify it; sensitivity to the small ke−g gap should be disclosed.

Choose the equity cash-flow proxy

Dividends work well when payout tracks sustainable capacity; FCFE can help when payout differs materially from capacity and financing is forecastable; residual income can help where book value and accounting earnings are meaningful. None is universally best. Reconcile the selected proxy with reinvestment, leverage and accounting quality. A firm paying no dividend can still have positive equity value.

Discount both interim dividends and sale proceeds

For a finite holding horizon, equity value equals discounted expected dividends plus discounted expected sale price. One dividend2 and expected sale price50 in one year at10% imply52/1.10=47.2727. The sale price itself must be justified and may embed later dividends. Do not add an undiscounted terminal price to present-value dividends or count the same final dividend twice.

Value a fixed perpetual preferred dividend

A noncallable perpetual preferred share paying a fixed dividendD has valueD/required return under the perpetuity assumptions. Dividend5 and required return8% imply62.5. Preferred priority, cumulative features, credit risk and tax treatment matter. A callable or convertible preferred requires additional analysis; do not apply the plain perpetuity unchanged when the issuer can redeem at a capped price.

Infer growth from price with the right dividend

With next dividendD1 known, the Gordon relation implies g=ke−D1/P0. IfD1=2,P0=40,ke=9%,g=4%. When the input is the just-paidD0 instead, solveP0=D0(1+g)/(ke−g); using the first shortcut would be inconsistent. The inferred growth is conditional on the required return and the model, not a verified company forecast.

Separate no-growth value and growth opportunities

A simple PVGO decomposition writesP0=E1/ke+PVGO whenE1 and the no-growth policy are defined consistently. If price50,earnings4 andke10%,no-growth value40 andPVGO10. Growth can destroy value when retained earnings earn below the required return. A high growth rate is therefore not automatically a high PVGO; reinvestment profitability is decisive.

Derive a justified P/E

Under Gordon assumptions leadingP/E=(1−b)/(ke−g),whereb is retention andg=bROE under the sustainable-growth assumptions. A60% payout,ke10% andg4% give leadingP/E10. TrailingP/E additionally reflects the next-period earnings growth relation whenE0 is used. Low risk, profitable growth and payout interact; increasing retention is not universally beneficial ifROE is too low.

Solve the required return from price

In a constant-growth dividend modelke=D1/P0+g. With next dividend2,price40 andgrowth3%,impliedke8%. A multistage model usually requires numerical solving for the rate that equates projected dividends and terminal value to price. The solution inherits all cash-flow assumptions and does not establish the investor will realize that return. Test whether forecasts and the terminal condition are economically plausible.

Compare price with a conditional estimate

If a defensible DDM estimates value35 while market price30,the stock appears undervalued relative to that model. The margin is5,or16.67%of price,not a guaranteed return. Investigate what assumptions differ from market expectations and what could reveal them. A tiny apparent discount inside a wide valuation range may not justify an investment after costs and uncertainty.

Model growth phases economically

A growth phase can feature high reinvestment and expanding market share; transition brings competitive pressure and slowing growth; maturity can support more stable margins and payout. These are modeling descriptions, not fixed calendar stages every issuer must follow. Link each phase to reinvestment needs,ROE and payout so a rapid growth forecast does not coexist with implausibly negligible capital requirements.

Choose abrupt or gradual growth transition

A two-stage DDM assumes a distinct high-growth phase followed by stable growth. The H-model approximates a linear decline from a high rate to a stable rate over a specified transition,while a three-stage model can explicitly separate high growth,transition and maturity. Choose the path from business economics,not solely ease of calculation. A growth fade should have compatible payout and reinvestment changes.

Carry a two-stage terminal value back to today

If a share pays2 inyear1and3 inyear2,then grows at4%forever withke10%,terminal value atyear2is3.12/.06=52. Present value is2/1.1+(3+52)/1.1²=47.2727. The final explicit dividend and the first terminal dividend occur at different dates. For more phases repeat the dated cash-flow schedule rather than averaging growth rates.

Audit the dividend spreadsheet

A dividend model should label periods,dates,earnings,retention,dividends andterminal assumptions explicitly. Use separate inputs andformulas,check cash-flow timing,and test a stable-growth case against a closed-form result. Sensitivity tables forkeandg often reveal more uncertainty than the headline value. Avoid circular growth or payout formulas that silently force the desired price.

Formula and assumptions

V0=D0*(1+g)/(ke−g); sustainable g=b*ROE

Case analysis with explicit assumptions

1. StableCo just paid dividend 2.00. Long-run growth is 4% and equity required return 10%. ROE is 12% with a sustainable retention ratio one-third under the constant-policy assumption. The analyst proposes 11% perpetual growth without changing the discount rate.
2. Method: V0=D0*(1+g)/(ke−g); sustainable g=b*ROE
3. Case result: 34.67. Next dividend is 2.08 and estimated value 34.6667. An 11% perpetual rate with a 10% required return violates this formula’s finite-value condition. Higher retention creates value only when reinvestment economics justify it; sensitivity to the small ke−g gap should be disclosed.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• Already a present value in every case is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov