Dividend valuation models

A share pays a dividend. What is the share worth? If dividends were all that an investor ever received, the share would be worth the present value of every dividend still to come. That simple idea, discounting the dividend stream at the shareholder’s required return, gives a family of valuation models.

They show why a share’s price rises when dividends are expected to grow or when the required return falls.

This topic covers the dividend valuation model with constant dividends, cum-dividend and ex-dividend prices, the model with constant growth, finding the growth rate implied by a price, delayed growth (two-stage models), Gordon’s growth model (g = br), using the model for minority holdings and takeovers, and the assumptions behind it. Cost of equity from the same models is in the cost of capital topic.

The previous topic covered asset and income-based valuation. The next covers the valuation of debt and preference shares. The May 2014 Pathfinder paper tested the model in its multiple-choice section.

Key terms in plain English

Syllabus check

This topic is in syllabus area B (business analysis). It covers:

• valuing shares with the dividend valuation model;
• practical considerations in the valuation of shares.

CAMA 2020 and dividends

The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.

The dividend rules of CAMA 2020 matter because the model assumes dividends will be paid: a company may pay dividends only out of distributable profits, and only after the directors recommend and the shareholders declare them. See the topic on dividend policy.

Constant dividends

If a constant dividend is paid every year, starting one year from now, the share is a perpetuity: MV = d ÷ k_e. The usual exam assumption is that the current year’s dividend has just been paid and the next is due in a year. If the current dividend is yet to be paid, the formula gives the ex-dividend price; add the dividend for the cum-dividend value.

1. (a) Value = 48 ÷ 0.12 = ₦400.
2. (b) If the dividend is ₦54: 54 ÷ 0.12 = ₦450.
3. (c) If the cost of equity is 12.5%: 48 ÷ 0.125 = ₦384.

So value rises with expected dividends and falls with the required return.

Constant growth

If dividends grow at a constant rate g: MV (ex-div) = d₀(1 + g) ÷ (k_e − g). It requires k_e to exceed g. With ₦48 just paid, growth of 4% and k_e 12%, value = 48 × 1.04 ÷ 0.08 = ₦624. If growth falls to 3%, value = 48 × 1.03 ÷ 0.09 = ₦549.

Implied growth and revised expectations

Given the price and next year’s dividend, solve for g. ICAN’s example: price ₦400, k_e 12%, next dividend ₦20. 400 = 20 ÷ (0.12 − g), so g = 7%. New information then cuts next year’s dividend by 10% to ₦18 and growth to 4%: value = 18 ÷ (0.12 − 0.04) = ₦225.

Delayed growth (two-stage)

Value the later dividends at the date growth begins, then discount them back. ICAN’s example: ₦63 has just been paid, stays constant for two more years, then grows 3% from year 3. Cost of equity 10%. Value at the end of year 2 = 63 × 1.03 ÷ (0.10 − 0.03) = ₦927. PV = 63 × 0.909 + 63 × 0.826 + 927 × 0.826 = 57 + 52 + 766 = ₦875.

Gordon’s growth model

Growth can come from retained profit: g = b × r, where b is the proportion of earnings retained and r the return on new investment. ICAN’s example: EPS ₦50, 60% retained, so the dividend is ₦20 and r is 10%, with k_e 8%. g = 0.6 × 10% = 6%. Value = 20 × 1.06 ÷ (0.08 − 0.06) = ₦1,060. The model assumes b and r stay constant and all growth comes from retained profit.

Using the model for stakes and takeovers

The model suits a non-controlling interest, where the holder’s return is the dividend stream. For a private company, add a premium to the cost of equity. ICAN’s example: Target paid ₦250,000 and the peer return is 12%, plus 2% for being small and unquoted, so k_e = 14%. No growth gives 250,000 ÷ 0.14 = ₦1,785,714. Growth of 4% gives 250,000 × 1.04 ÷ 0.10 = ₦2,600,000. Growth of 3% for three years and 2% afterwards gives about ₦2,181,000.

1. Pinky.
   g = 0.15 × 0.2 = 3%
   value = 650,000 × 0.8 × 1.03 ÷ (0.21 − 0.03) = ₦2,975,556.
   Perky: g = 12%
   value = 240,000 × 0.2 × 1.12 ÷ 0.12 = ₦448,000.
2. Combined.
   g = 0.17 × 0.35 = about 6%
   next year’s earnings = 650,000 × 1.03 + 240,000 × 1.12 + 85,000 = ₦1,023,300
   dividend = 65% = ₦665,145
   value = 665,145 ÷ (0.20 − 0.06) = ₦4,751,036.
3. Gain = 4,751,036 − 2,975,556 = ₦1,775,480, the most Pinky should pay.

Assumptions and weaknesses

• Investors are rational and have uniform expectations, and dividends alone drive value (yet shares that pay nothing still have value).
• The latest dividend is representative of the trend; if it is a rogue figure, adjust it.
• The estimates of future dividends and the cost of equity are reasonable, but both are hard to estimate with confidence.
• Dividends have no growth or constant growth, and if g = br, b and r are constant.
• Earnings must grow enough to support the dividend growth, and the cost of equity must exceed g.
• Other influences on the share price are ignored.

The rules in more depth

Why the growth formula uses d₀ × (1 + g)

The first dividend to be valued arrives in a year. It is the one just paid, grown by one year.

Why k_e must exceed g

If growth were at least as high as the discount rate, the sum of the discounted dividends would never settle, giving an infinite or negative value.

Why the price is so sensitive

The denominator is the difference between two small numbers. A small change in either k_e or g moves the value a great deal.

Why two stages

A single growth rate does not fit a company that will grow differently for a while, so the value is built in two parts.

Effect on analysis

State the assumptions, compute the value, test it with a sensible change in growth or required return and say what drives the answer.

Worked examples

1. Ex-dividend value.
   30 ÷ 0.10 = ₦300.
2. The imminent dividend adds ₦30.
3. Cum-dividend value = ₦330.

1. d₁ = 20 × 1.05 = ₦21.
2. Value = 21 ÷ (0.13 − 0.05) = 21 ÷ 0.08.
3. Value = ₦262.50.

1. d₁ ÷ MV = 15 ÷ 250 = 6%.
2. g = 14% − 6%.
3. g = 8%.

1. Dividend = ₦20. g = 0.5 × 12% = 6%.
2. Value = 20 × 1.06 ÷ (0.11 − 0.06) = 21.2 ÷ 0.05.
3. Value = ₦424.

How to score full marks

• Write the right formula for the dividend pattern.
• Check whether the price is cum or ex dividend.
• Use d₀ or d₁ correctly.
• For two stages, value at the date growth starts, then discount.
• Test sensitivity to growth and required return.
• State the assumptions.

Common mistakes in the exam

• Forgetting to grow d₀ by (1 + g).
• Using a cum-dividend price in a cost of equity calculation.
• Discounting the terminal value for the wrong number of years.
• Using g above k_e.
• Applying the model to a controlling stake without adjustment.
• Confusing the retention ratio with the payout ratio.

Quick revision

• Constant: MV = d ÷ k_e. Growth: MV = d₀(1 + g) ÷ (k_e − g).
• Ex-dividend value; add the imminent dividend for cum-dividend.
• Implied g = k_e − d₁ ÷ MV.
• Two stages: value at the switch date, then discount.
• Gordon: g = b × r.
• CAMA 2020: ss. 305, 308, 377(1), 378, 385.

Practice questions

These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.

Recall check: multiple choice

Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.

Written questions

Model answers

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