Lesson 7 of 9
Dividend discount and residual income
One model discounts dividends. The other starts from book value and adds only the earnings above what shareholders require. Both can return the same answer.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A dividend discount model values equity as the present value of the dividends a share is expected to pay.
- A residual income model starts from book value and adds only the present value of earnings above a charge for using that book value.
- On the same inputs the two return the same number, because a dividend not paid out stays in the book value that residual income already counts.
Both models answer the same question from different starting points. One discounts what a shareholder actually receives. The other starts from what a shareholder already owns and adds only the earnings above what that ownership is charged for.
The same company, two starting points, one answer
- Dividend discount model$40
- Residual income model$40
The dividend model
Value (Gordon growth) equals Next year's dividend divided by Required return − growth.
Example$2.00 ÷ (0.09 − 0.04) = $40
Williams set out the underlying idea in The Theory of Investment Value in 1938: a share is worth the present value of what it distributes to its owner, nothing more. Gordon's growth model gives that idea one tractable form for a dividend expected to grow at a constant rate forever: divide next year's dividend by the required return minus the growth rate.
The residual income model
With the example's inputs: 20 + (0.05 × 20) ÷ 0.05 = 20 + 20 = 40.
Penman's textbook builds valuation on this form: start from book value, which is already on the balance sheet, and add the present value of residual income, the earnings above a charge for the book value the shareholders have tied up. Ohlson gave this structure its formal treatment, linking a firm's value to its book value and its expected abnormal earnings rather than to its dividends directly.
Why they agree
Whatever earnings a company does not pay out as a dividend stay in the business and raise its book value instead. A dividend model counts that retained amount when it is eventually paid out later; a residual income model counts it immediately, because it is already sitting in the book value the model starts from. Fed consistent inputs, the two present values agree, and the choice between them is a choice of which anchor is more reliable for a given company.
Why residual income is anchored on something known
A dividend forecast for a company that pays nothing out, or that pays irregularly, is close to a guess. Book value, by contrast, is on the balance sheet today, filed and auditable. Residual income starts from that known number and forecasts only the smaller, more bounded quantity: earnings above a charge on capital already employed. That is why the model suits banks and other companies whose dividend policy tells you little and whose book value is the more stable anchor.
Check yourself
A company retains all of its earnings and pays no dividend. Which model can still be applied without first forecasting a payout?
- The dividend discount model, since dividends are zero
- The residual income model, anchored on book value
- Neither model can be used
Show the answer
Answer: B.
Residual income starts from book value, which exists whether or not a dividend is paid. A dividend model needs a dividend forecast, which a company paying nothing does not provide.A company's return on equity exactly equals its required return. What does residual income add to book value?
- A large positive amount
- Nothing: residual income is zero
- A negative amount
Show the answer
Answer: B.
Residual income is (return on equity minus required return) times book value. When the two returns are equal, that term is zero, and the model's value is book value alone.Why do the dividend discount model and the residual income model return the same value on consistent inputs?
- Because required return and growth cancel out identically in both formulas
- Earnings retained instead of paid out raise book value, which residual income already counts
- Because both models ignore growth
Show the answer
Answer: B.
A dividend not paid stays inside the company and shows up later as a higher book value and higher future earnings. Residual income counts that value immediately through book value; the dividend model counts it later when it is finally paid.Sources
- Williams, The Theory of Investment Value, 1938, on value as the present value of what a business distributes to its owner.
- Penman, Financial Statement Analysis and Security Valuation, on reformulated statements and residual earnings.
- Gordon, "Dividends, Earnings, and Stock Prices", Review of Economics and Statistics, 1959, on the constant-growth dividend model.
- Ohlson, "Earnings, Book Values, and Dividends in Equity Valuation", Contemporary Accounting Research, 1995, on linking value to book value and abnormal earnings.
What this leaves out
- The worked example uses round invented inputs, chosen so the two models can be checked against each other by hand.
- The constant-growth form of each model breaks down when growth is expected to exceed the required return, or to change over time; a multi-stage version is then needed.
- The two models agree only when every change in book value, other than dividends and share issues, passes through earnings. Items booked straight to equity, and buybacks at prices away from book, break the tie.
- A dividend model is only as good as the payout forecast, and a residual income model only as good as the return on equity forecast: neither escapes needing an estimate of the future.
- Nothing here is advice about any security.