Valuing shares: P/E, earnings yield, dividend yield and dividend growth models

Asset values say what a business owns. Market-based methods say what its profits and dividends are worth. They are the methods most Case Study valuations use, because they reflect earning power. This topic covers the price earnings method, the two yield methods and the dividend valuation models, ending with a worked multi-stage case from a past paper.

The price earnings method

The P/E ratio is the market price of a share divided by its annual earnings per share (EPS). A quoted company’s P/E comes straight from its price. For an unquoted company, use the P/E ratio of a similar quoted company. The value is then EPS × estimated P/E ratio. EPS might be last year’s, an average of recent years or a forecast.

The P/E ratio is chosen as one that seems suitable, often the average of similar quoted companies.

The range shows the method’s weaknesses. It depends on subjective choices of EPS and P/E. It is not scientific. And it uses accounting earnings, not the cash that an investor will receive. Even so it is widely used for valuing a private company seeking a listing and for takeover bids.

Its main strength is simplicity: it gives a quick benchmark for negotiation or for talks on a flotation price.

Earnings yield and dividend yield

Earnings yield. This is a variant of the P/E method with the same weaknesses. Earnings yield = EPS ÷ market price × 100, so price = EPS ÷ earnings yield. A private company should use a higher yield than similar quoted companies, to allow for its higher risk. For example, Debaco Nigeria Ltd earned ₦900,000. At a yield of 9% its equity is worth 900,000 ÷ 0.09 = ₦10,000,000. At 12% it is worth ₦7,500,000.

The gap shows how much the answer depends on an assumed yield.

Dividend yield. Dividend yield = dividend per share ÷ market price × 100, so price = dividend per share ÷ dividend yield. Again a private company would use a higher yield. This method suits small shareholdings, where the holder has little say in management and cares only about the income stream.

Dividend valuation models

The basic idea is that a share is worth the present value of all the dividends the shareholder expects to receive. It is more objective and cash-based than earnings methods. The expected dividends, in perpetuity, are discounted at the cost of equity (re).

The formulas assume that dividends are paid annually and that this year’s dividend has just been paid. The value changes with expected dividends, including g, and with the required return.

1. Value = 5 × 1.05 ÷ (0.15 − 0.05) = ₦52.50.
2. With no growth the value would be 5 ÷ 0.15 = ₦33.33.

1. It retains 60% and earns 10% on investment, so g = 0.6 × 0.10 = 6%.
2. With re at 8%, value = 2 × 1.06 ÷ (0.08 − 0.06) = ₦106.
3. Notice how sensitive this is: a small gap between re and g produces a large value.

Worked past case: multi-stage dividends, Mago Pharmaceuticals

In the November 2014 case the client believed a multi-stage dividend model was best. Profit after tax was ₦92.581 million on 100 million shares. The board planned to pay out 50% of profit, with dividends growing by 10% a year for five years and by 5% a year afterwards. The discount rate was 10%.

1. Dividend per share now.
   92.581 ÷ 100 × 50% = ₦0.4629.
2. Years 1 to 5. Dividends are 0.5092, 0.5601, 0.6161, 0.6777 and 0.7455. Because growth equals the 10% discount rate, each has a present value of about ₦0.4629, so the five add up to about ₦2.3145.
3. Value at the end of year 5.
   The year 6 dividend is 0.7455 × 1.05 = 0.7828.
   Value = 0.7828 ÷ (0.10 − 0.05) = ₦15.66.
4. Present value of that.
   15.66 × 0.6209 = ₦9.72.
5. Total.
   2.31 + 9.72 = about ₦12.04 a share.

Judgement. The result is about a third below the quoted price of ₦18. But the model assumes 10% growth for five years when profit had fallen by 43% in the latest year, and a lower growth rate would reduce the value further. The value is also very sensitive to the 5% long-term growth rate.

The client should be advised that the dividend model does not support paying the market price on its own, and that other methods and the reliability of the figures must be checked.

The November 2014 Pathfinder solution writes the dividend per share as 92,561,000 multiplied by 100,000,000 shares, uses profit of 92,561,000 where the accounts show 92,581,000, and writes the terminal formula as 0.1 minus 0.5. The correct workings divide profit by the number of shares, multiply by the 50% payout, and use 0.10 minus 0.05. Its answer of about ₦12 a share agrees with ours. The Pathfinder solution is slightly different from ours.

Choosing between the methods

The case and the purpose should decide which method leads.

Whatever you choose, present at least two methods, explain why they differ and give a range for the offer.

Common mistakes

• Choosing the P/E or yield without saying where it came from or why a private company needs an adjustment.
• Using the dividend just paid in the formula as if it were next year’s dividend.
• Using a growth rate equal to or above the cost of equity, which gives a meaningless value.
• Presenting a single value from one model with no comparison or sensitivity.
• Accepting a growth assumption that the trend of profits does not support.

Quick revision

• P/E value = EPS × P/E. Earnings yield price = EPS ÷ yield. Dividend yield price = DPS ÷ yield.
• Private company: adjust the P/E down or the yield up for risk.
• Constant dividend d1 ÷ re.
  Growth d0(1 + g) ÷ (re − g). g = b × r.
• Multi-stage: discount the early dividends, then a terminal value, then add.
• Test the inputs and compare methods.

Practice questions

These are original questions in the style of the Institute of Chartered Accountants of Nigeria exam. Try each one before you open the answer.

Model answer

The next topic covers accuracy, assumptions and professional scepticism in financial data analysis.

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