Cost of Equity: The Dividend Valuation Model

Every source of finance has a price, and the price of equity is the hardest to see. A bank charges a rate of interest that is written in the loan agreement. Shareholders do not send a bill: they are paid dividends that the directors choose, and gains that depend on the market.

Yet they are entitled to expect a return for the risk they take, and if the company cannot earn it they will sell their shares and the price will fall. The cost of equity is that required return, seen from the company’s side. This topic is the first of the group on the cost of capital.

It explains what the cost of equity is and why it is higher than the cost of debt, and then how to estimate it with the dividend valuation model: for constant dividends, with the cum-dividend adjustment, with constant growth (the dividend growth model), and with the growth estimated from past dividends or from the earnings retention model, with worked examples and the limits of the method. The next topic covers portfolio theory.

The dividend growth model was used to find the cost of equity in the weighted average cost of capital calculation in May Diet, 2026, Question 2(a) (7 marks). Read internal finance and dividend policy first.

What the cost of equity is

The cost of capital for investors is the return they require. For a company there is a cost of equity:

• the return required by ordinary shareholders, in the form of dividends and growth in the share price
• a cost for each item of debt (the yield required by the lender)
• a cost for preference shares

A company must earn at least these returns on its investments, or it cannot reward its investors. Theoretically the cost of capital for investors and for the company are the same. But they differ because interest is a tax-deductible expense for the company: the cost of debt is measured after tax, the cost of equity is not.

The cost of equity is always higher than the cost of debt, because equity is the riskier investment:

• interest is often fixed but earnings per share vary
• lenders have a legal right to interest and repayment, shareholders have no right to a dividend
• secured lenders can enforce their security
• in a liquidation lenders are paid before shareholders

Higher risk requires a higher expected return, and the tax relief on interest widens the gap.

The dividend valuation model

Shareholders’ return comes as dividends and share price growth, but share price growth reflects expectations of higher future dividends. So the value of a share is the present value of all its expected future dividends, discounted at the cost of equity.

The same model can be used either to find a price when the cost of equity is known, or, more often, to find the cost of equity when the price is known.

Constant dividends

If the dividend is expected to stay the same for ever, the share is a perpetuity: P₀ = d₁ ÷ K_e, so K_e = d₁ ÷ P₀, where d₁ is the dividend due in one year and P₀ is the price now, ex-dividend. For example a share priced at ₦48 (ex-dividend) paying ₦4.80 a year has a cost of equity of 4.80 ÷ 48 = 10%.

Cum-dividend prices. If a dividend is about to be paid and the share is still being traded with the right to it (cum dividend), the price includes that dividend, and must be reduced to the ex-dividend price. If the cum-dividend price is ₦52.80 and a dividend of ₦4.80 is due shortly, the ex-dividend price is 52.80 − 4.80 = ₦48 and the cost of equity is again 10%; using ₦52.80 would give 9.1%.

The dividend growth model

If dividends are expected to grow at a constant rate g a year for ever, the model is P₀ = d₁ ÷ (K_e − g) with d₁ = d₀(1 + g), so:

K_e = d₀(1 + g) ÷ P₀ + g

where d₀ is the dividend just paid. Example: a share is priced at ₦90 ex-dividend; the dividend just paid was ₦6.50 and growth is expected at 4% a year. Then d₁ = 6.50 × 1.04 = ₦6.76 and K_e = 6.76 ÷ 90 + 0.04 = 0.0751 + 0.04 = 11.5%. The two parts are the dividend yield (7.5%) and the growth (4%). The model needs K_e to be greater than g, and it assumes the first dividend is received in one year and then annually.

Estimating the growth rate

The growth rate that matters is the one investors expect. There are two ways to estimate it.

1. Extrapolating past dividends. Investors’ expectations are assumed to follow experience.
   Use the geometric mean of the growth: if dividends were ₦80, ₦88, ₦95, ₦104 and ₦112 over five years, there are four growth periods, so g = (112 ÷ 80)^1⁄4 − 1 = 1.4^0.25 − 1 = 8.8%.
   (A question that gives the dividend “five years ago” and the current dividend has five periods.)
2. The earnings retention (Gordon growth) model: growth comes from reinvesting retained profit, so g = r × b, where r is the return on the capital employed (profit after tax ÷ opening capital employed) and b the proportion of earnings retained.
   If profit after tax is ₦65m on opening capital employed of ₦500m, r = 13%
   with 60% retained, g = 0.13 × 0.60 = 7.8%.
   With no retained profit there is no new investment and no growth.

The retention model assumes that r and b are constant, that accounting profit measures the real return (inflation distorts it where assets are at historical cost), and that all new finance comes from retained profit.

Shortcomings of the model

• Assumptions: shares are valued for their dividends, which is not always so (some companies pay little or nothing and are valued for growth); dividends either stay constant or grow at a constant rate, but short-term variations affect the price; and historical growth or retention may not continue, so future market and economic conditions should be considered.
• Data: the share price changes daily and not always rationally; and the growth rate is uncertain. Growth in dividends should be linked to growth in earnings: dividends growing at 10% while earnings grow at 5% will run out of funds, and the reverse accumulates surplus cash.
• Result: the cost of equity from the model is an estimate, which can be compared with another estimate from the capital asset pricing model, covered later.

The ideas in more depth

Why the price is the present value of dividends

An investor who holds a share for ever receives only its dividends. One who sells it receives the price, which is what the next buyer will pay for the dividends after that. In both cases the value comes from the dividend stream. Rearranging the valuation gives the discount rate that makes the present value equal to the observed price: that rate is the return the market requires.

Why the growth rate matters so much

Because the formula divides by K_e − g, a small change in g moves the answer a lot when g is close to K_e. A growth rate of 4% against 5% changes the cost of equity by one point, but changes the share price implied for a given K_e by far more. Growth cannot exceed the growth of the economy for ever, which is a reason for caution with high estimates.

Sources and references

• No accounting standard governs the estimate of the cost of equity. The dividend valuation model and the retention model are on the formula sheet of the paper, so check which form is given.

These points are stated as at 5 November 2026.

Worked examples

1. Cost.
   4.80 ÷ 48 = 10%.

1. Next dividend.
   6.50 × 1.04 = ₦6.76.
2. Cost.
   6.76 ÷ 90 + 4% = 11.5%.

1. Return.
   65 ÷ 500 = 13%.
2. Growth.
   13% × 60% = 7.8%.

How to answer in the exam

• Check the price is ex-dividend and adjust a cum-dividend price.
• Find d₁ correctly: multiply the dividend just paid by (1 + g).
• Show how g was estimated and say what you assume about it.
• Comment on limits, and on whether the result is higher than the cost of debt.

Common mistakes in the exam

• Forgetting to deduct the dividend from a cum-dividend price.
• Using d₀ instead of d₁ in the growth model.
• Using the wrong number of periods for the geometric mean.
• Using closing capital employed for r in the retention model.
• Applying the model when growth exceeds the cost of equity.
• Treating the result as exact.

Quick revision

• Ke = d1 ÷ P0 (no growth)
  Ke = d0(1 + g) ÷ P0 + g (growth).
• Use the ex-dividend price.
• g from the geometric mean of past dividends, or g = r × b.
• Equity costs more than debt: more risk, no tax relief.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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