Dividend Valuation of Shares

A share is a claim on a company’s future dividends. That is all a shareholder who holds for ever will ever receive, and what a buyer pays for the share is simply the present value of those dividends. This idea, the dividend valuation model, is the foundation of the cost of equity, which the earlier topic used in reverse (from the price to the required return).

Here it is used forwards: given a required return and a forecast of dividends, what is the share worth? It is the proper method for valuing a small, non-controlling holding in a company, where the holder has no say in the business and the dividend is the only return.

Whether the dividend is constant, grows steadily, or grows quickly for a few years and then slowly, the method is the same: discount the dividends at the cost of equity, and a formula gives the sum of an infinite stream.

This topic explains the model with constant dividends, constant growth, two stages of growth and growth estimated from retained earnings, the cost of equity to use for an unquoted company, how the model links to the price/earnings ratio, and its limits, with worked examples. The next topic covers valuation by discounting the cash flows of a whole business.

The syllabus asks for the estimate of the value of a business using the dividend valuation model. Read income-based valuation with price/earnings ratios, yields and enterprise value multiples first.

Constant dividends and constant growth

If the dividend per share is expected to stay the same for ever, the shares are a perpetuity: V = D ÷ K_e. A share paying ₦4.80 a year when the required return is 12% is worth 4.80 ÷ 0.12 = ₦40. (This is the cost-of-equity formula of the earlier topic turned round.) If dividends grow at a constant rate g, then with D₀ the dividend just paid and D₁ = D₀(1 + g) the next:

V = D₀(1 + g) ÷ (K_e − g)

A share whose latest dividend was ₦5 and is expected to grow at 6% a year, with a required return of 14%, is worth 5 × 1.06 ÷ (0.14 − 0.06) = 5.30 ÷ 0.08 = ₦66.25. The formula requires K_e to exceed g; and it assumes the first dividend is paid in a year. If a dividend is about to be paid, the price is cum-dividend; the value of the share ex-dividend excludes it.

The cost of equity for an unquoted company

The required return should reflect the company’s risk. A small unquoted company is riskier and less liquid than a quoted one in the same industry, so a risk premium is added: with a return of 11% on similar quoted shares and a premium of 3%, the cost of equity is 14%. Where possible the capital asset pricing model, with a beta adjusted for the company’s risk, may be used instead.

Valuing a holding: three growth patterns

A target company paid a total dividend of ₦300,000 this year, and the required return is 14%.

1. No growth:
   V = 300,000 ÷ 0.14 = ₦2,142,857.
2. Constant growth of 5%:
   V = 300,000 × 1.05 ÷ (0.14 − 0.05) = 315,000 ÷ 0.09 = ₦3,500,000.
3. Two-stage growth: growth of 4% for three years and 2% for ever after.

For the two-stage case, take the first three years’ dividends separately and discount each at 14% (figures in ₦000):

From year 4 the dividends grow at 2% for ever. At the end of year 3 their value is D₃ × 1.02 ÷ (0.14 − 0.02) = 337.5 × 1.02 ÷ 0.12 = 2,868.8, and discounted three years: 2,868.8 × 0.675 = 1,936.1. The total value is 751.1 + 1,936.1 = ₦2,687,000. Faster growth in the early years raises the value above the no-growth figure but well below the 5% constant-growth figure, because 5% is assumed to last for ever.

Growth from retained earnings

If the growth rate is not given, it can be estimated from the earnings retention model: g = retention ratio × return on retained funds (the return on the capital employed). A company earns ₦100m and pays out 40% (₦40m) in dividends, retaining 60%; it earns 15% on new investment, so g = 0.6 × 0.15 = 9%. The next dividend is 40 × 1.09 = ₦43.6m, and at a required return of 14% the value of the equity is 43.6 ÷ (0.14 − 0.09) = ₦872m.

The model assumes that the retention and the return stay constant and that all new investment is financed from retained profit. A small change in the assumptions changes the value greatly: at g = 10% the value would be 44 ÷ 0.04 = ₦1,100m.

The link to the price/earnings ratio

Dividing the growth model by earnings per share gives P/E = payout ratio × (1 + g) ÷ (K_e − g). Thus a high P/E reflects high growth, a high payout or a low required return. This shows why the P/E method of the last topic must use comparables with similar growth and risk.

When to use it, and its limits

• Suitable for minority shareholdings, where the holder cannot influence dividends. It is not the right method to value control, since a controlling owner can change the dividend policy and use the company’s cash flows directly (the next topic).
• Sensitive: the value depends enormously on g and K_e, particularly when g is close to K_e; both are estimates.
• Dividend policy: the model fails for companies that pay no dividend or an erratic one, although the dividends that they could pay may be estimated.
• Constant growth for ever is unrealistic; two-stage models are more reasonable.
• Estimating K_e for an unquoted company is subjective.
• Consistency: the growth of dividends must be consistent with the growth of earnings and with what the company retains and invests.

The ideas in more depth

Why the formula divides by K_e − g

A dividend that grows at g and is discounted at K_e forms a geometric series whose sum is D₁ ÷ (K_e − g). The gap between the two rates is the net rate at which the present value of each successive dividend declines.

As g approaches K_e, the denominator approaches zero and the value becomes extremely large and then meaningless, which is why g must be well below K_e and, for ever, no higher than the growth of the economy.

Why dividends, and not earnings, give the value of a minority stake

A minority holder cannot force the company to pay out its earnings; what it receives is the dividend. Retained earnings help the holder only through the dividends they will eventually generate (the growth).

For a controlling owner the position is different: the owner can take the cash flows out in other ways, so the value of control is based on all the cash flows (the next topic), not on dividends alone.

Sources and references

• No accounting standard governs the dividend valuation model. Dividends in Nigeria are paid from distributable profits (the Companies and Allied Matters Act 2020, sections 426 to 428) and are subject to withholding tax at 10%, which affects the net return to shareholders and the required return before tax.

These points are stated as at 5 November 2026.

Worked examples

1. Value.
   4.80 ÷ 0.12 = ₦40.

1. Next dividend.
   5 × 1.06 = ₦5.30.
2. Value.
   5.30 ÷ 0.08 = ₦66.25.

1. Growth.
   0.6 × 15% = 9%.

How to answer in the exam

• State the cost of equity used and any premium for an unquoted company.
• Match the formula to the growth pattern: constant, constant growth or two-stage.
• Use D₀(1 + g) in the growth model and discount stage-one dividends separately.
• Comment that the method values minority holdings and is sensitive to g and K_e.

Common mistakes in the exam

• Using D₀ instead of D₁ in the growth formula.
• Applying the constant-growth formula when g exceeds K_e.
• Forgetting to discount the stage-two value back to today.
• Using the quoted company’s return for an unquoted company without a premium.
• Using the model to value control of a company.
• Using a cum-dividend price as the ex-dividend value.

Quick revision

• V = D ÷ K_e; V = D₀(1 + g) ÷ (K_e − g).
• Two-stage: discount stage one; value stage two as a perpetuity and discount back.
• g = retention × return on retained funds.
• Minority holdings only; very sensitive to g and K_e.

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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