A buyer approaches the three owners of a private company. How much are the shares worth? There is no share price to look up. One adviser adds up the assets. Another multiplies profit by a price-earnings ratio borrowed from a listed rival. A third capitalises the dividend. They give three different numbers, and each is defensible.
The skill is to compute them all, explain the assumptions behind each and recommend a range for negotiation.
This topic covers why businesses are valued, the three families of method, asset-based valuation (book value, net realisable value and replacement cost), income-based valuation (price-earnings ratio, earnings yield, dividend yield and the enterprise value to EBITDA multiple), and their strengths and weaknesses. The previous topic covered international valuation standards. The next covers dividend valuation models. The May 2014 Pathfinder paper had a compulsory case study on valuing an unlisted company.
In 30 seconds
Valuations are needed for takeovers, flotations, private share sales, mergers and tax. Every method is an estimate. Asset-based: net asset value (book) is a minimum and ignores internal goodwill; net realisable (break-up) value is the floor, relevant for liquidation; replacement value still omits intangibles. Income-based: value = EPS × P/E; value = earnings ÷ earnings yield; value = dividend ÷ dividend yield (small holdings).
Use a lower P/E or higher yield for a private company. EV/EBITDA: apply a peer’s multiple to the target’s EBITDA to get enterprise value, then deduct debt for equity. Compare the results, state the assumptions and recommend a range. A company is never worth less than its break-up value.
Key terms in plain English
| Term | What it means |
|---|---|
| Net asset value | Assets less liabilities |
| Break-up value | What the assets would fetch if sold piece by piece |
| Price-earnings (P/E) ratio | Share price divided by earnings per share |
| Earnings yield | Earnings per share divided by share price |
| Dividend yield | Dividend per share divided by share price |
| EBITDA | Earnings before interest, tax, depreciation and amortisation |
| Enterprise value | The value of the business to all capital providers |
Syllabus check
This topic is in syllabus area B (business analysis). It covers:
- valuing shares and businesses using dividend yield, price-earnings ratio and asset-based methods;
- practical considerations in the valuation of shares.
CAMA 2020 and share valuation
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | Valuations should be reasoned and fair to the company and its shareholders |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should test the assumptions behind a valuation |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
A company’s articles may fix how shares are valued on a transfer or a buy-out; where they do, that rule applies.
Why value a business
Quoted companies already have a market price. A valuation is needed mainly for a takeover bid, because a bidder always offers more than the market price and needs to set a fair or maximum price. The value to a bidder depends on its plans for the target.
Unquoted companies are valued for a flotation (to set an issue price), for a private sale (the buyer sets a maximum and the seller a minimum), for a merger, or for the tax on an estate.
All methods rest on estimates and assumptions and give different results. You should use several, discuss the assumptions, compare the results and recommend a valuation as a basis for an offer. Price is finally agreed by negotiation. The families of method are asset-based, market-based (earnings or dividends) and cash-flow based.
Asset-based valuation
Net asset value (book value)
Uses book values from the statement of financial position: assets less liabilities. It is easy to compute but non-current assets may sit at historic cost, and internal goodwill and human capital are ignored. At best it is a minimum. A realistic offer must be “book value plus”. If an earnings- or cash-flow-based value comes out below book value, the bidder should worry. Adjust any assets that look wrongly valued, especially intangibles.
ICAN’s example (Company Z). Tangible non-current assets ₦250,000, intangibles ₦75,000, current assets ₦60,000. Bank loans ₦90,000 and current liabilities ₦20,000. Share capital ₦50,000 of ₦1 shares.
- Net assets.
385 − 90 − 20 = ₦275,000. - Per share.
275,000 ÷ 50,000 = ₦5.50. - Shareholders are unlikely to accept less, so an offer must exceed ₦5.50.
Net realisable value (break-up value)
Assets at their disposal values less liabilities: what shareholders would get if the company were liquidated. It is usually irrelevant for a going concern, and hard to estimate in a bid. But it is the floor: a company can never be worth less than its break-up value. It matters if assets are worth more sold than used.
ICAN’s example: assets at disposal value ₦20m, liabilities ₦4m, 200,000 shares, so (20 − 4) ÷ 200,000 = ₦80 a share.
Replacement value
Net assets at the cost of acquiring them on the open market. More accurate than book value, but still excludes intangibles and is hard to identify asset by asset. All asset-based methods can be criticised because a business is worth the returns it will generate, not the cost of its assets, unless the assets will be sold.
Income-based valuation
The P/E ratio method
Value = EPS × estimated P/E ratio. EPS may be last year’s, an average or a forecast. The P/E is usually the average of similar quoted companies. ICAN’s example: EPS ₦15 last year, ₦18 forecast; peers range from 10.0 to 15.6 with an average of 12.5. Forecast EPS × average = 18 × 12.5 = ₦225. Using the lowest peer P/E reduced by 10% to allow for the lack of a quotation (P/E 9), 18 × 9 = ₦162, and 15 × 9 = ₦135.
Weaknesses: the EPS and the ratio are subjective; it uses accounting profit, not cash. Advantage: simplicity, and it is a useful benchmark for flotations and bids.
Earnings yield
Value = earnings ÷ earnings yield (earnings yield = EPS ÷ price). A variation of the P/E method with the same criticisms. For a private company use a higher yield to reflect risk. Kickstart earned ₦450,000; at 9% the value is ₦5.0m; at 10% it is ₦4.5m.
Dividend yield
Value = dividend ÷ dividend yield. It suits small shareholdings where the holder cares only about the income and has little say in running the company. For a private company, use a higher yield than peers.
The EV/EBITDA multiple
Enterprise value (EV) = market value of equity + preference shares + debt + minority interest − cash. EV/EBITDA = EV ÷ EBITDA. It strips out depreciation and amortisation and ignores capital structure, so companies can be compared. ICAN’s example: Kemi Plc has equity of 1.75 × 27.3m = ₦47.8m and bonds of ₦20m book trading at 125, worth ₦25m, so EV = ₦72.8m. EBITDA is 10 + 2.2 = 12.2 (2020) and 12.6 + 2.2 = 14.8 (2021), so the multiples are 6.0x and 4.9x.
Aka Ltd’s EBITDA is 8.7 + 0.5 + 0.3 = 9.5 and 10.1. EV = 6.0 × 9.5 = ₦57.0m or 4.9 × 10.1 = ₦49.5m. Deduct Aka’s debt (₦16.25m at 80 = ₦13m) to get equity of ₦36.5m to ₦44m. A 25% discount for non-marketability gives ₦27.4m to ₦33m.
Advantages: unaffected by capital structure; takes net debt into account; ignores differences in capital spending, tax planning and depreciation policy; widely used by investors. Disadvantages: it is simplistic; ignoring capital spending and tax may mislead; it is static; and multiples differ for many reasons (capital intensity, growth, competitive position and sustainability of cash flows). A low multiple does not prove a bargain.
The rules in more depth
Why a private company gets a lower value
Its shares are hard to sell and its information is less reliable, so investors accept a lower P/E or require a higher yield.
Why book value is a floor, not a price
Sellers expect to be paid for the earning power of the business as well as its assets.
Why use adjusted earnings
Past profits may contain one-offs, owners’ pay that differs from market pay, or errors. A buyer values the profit it can expect to keep.
Why several methods are used
Each shows a different angle. The spread between them shows how uncertain the value is.
Effect on analysis
List the values, rank them, explain what drives the differences and recommend a bid range.
Worked examples
Example 1: the May 2014 case. Wazobia Ltd’s three years of profit are adjusted for an inventory error, directors’ remuneration set at a realistic charge and depreciation at replacement cost. The adjusted profits are ₦3,725k, ₦3,875k and ₦4,550k. The average P/E of two peers (5.4 and 6.6) is 6.
- Average earnings.
(3,725 + 3,875 + 4,550) ÷ 3 = ₦4,050k. - P/E value.
6 × 4,050 = ₦24.3m. - Break-up value.
15,000 + 5,400 + 8,000 + 4,825 + 650 − 4,150 = ₦29.725m.
Dividend yield (average 10%) on ₦2.25m of dividends gives ₦22.5m.
Example 2: P/E with a private discount. Maintainable earnings are ₦160m. The peer P/E is 10. A 20% discount applies.
- P/E used.
10 × 0.8 = 8. - Value = 160 × 8.
- Value = ₦1,280m.
Example 3: dividend yield. A shareholder with a small stake receives ₦60m of dividends in total. Peers yield 5%, and a private premium of 1% is added.
- Yield used = 6%.
- Value = 60 ÷ 0.06.
- Value = ₦1,000m.
Example 4: EV/EBITDA. A peer trades at 6 times EBITDA. The target has EBITDA of ₦250m and market value of debt of ₦300m.
- EV = 6 × 250 = ₦1,500m.
- Equity = 1,500 − 300 = ₦1,200m.
- A discount for non-marketability would reduce it further.
How to score full marks
- Adjust earnings before applying a ratio.
- Use a peer ratio and adjust it for being private.
- Show each valuation on its own line.
- Rank the values and explain the differences.
- State the limits of each method.
- Recommend a range and the minimum.
Common mistakes in the exam
- Applying a quoted P/E without any private company discount.
- Using raw profit without adjusting for one-offs.
- Presenting net asset value as the likely price.
- Forgetting to deduct debt from an enterprise value.
- Using a dividend yield valuation for a controlling stake.
- Giving numbers with no comment.
Quick revision
- Asset-based: book (minimum), net realisable (floor), replacement.
- P/E: value = EPS × P/E; yields: value = earnings or dividend ÷ yield.
- Private: lower P/E, higher yield.
- EV/EBITDA: EV less debt = equity.
- Several methods, compare, recommend a range.
- 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.
Question 1. Net asset value from the balance sheet is usually seen as a:
- Minimum value
- Maximum value
- Fair price
- Tax value
Show the answer
A. It omits internal goodwill.
Question 2. A company can never be worth less than its:
- Break-up value
- Book value only
- P/E value
- Dividend yield value
Show the answer
A. Net realisable value is the floor.
Question 3. Value by the P/E method is:
- EPS × P/E
- EPS ÷ P/E
- Dividend × P/E
- Assets ÷ P/E
Show the answer
A. Using a suitable ratio.
Question 4. For a private company, compared with a quoted peer, use a:
- Lower P/E
- Higher P/E
- The same P/E
- No P/E
Show the answer
A. To allow for risk and illiquidity.
Question 5. Earnings yield valuation equals:
- Earnings ÷ earnings yield
- Earnings × earnings yield
- Dividends ÷ price
- Assets ÷ yield
Show the answer
A. A variation of P/E.
Question 6. Dividend yield valuation suits:
- Small shareholdings
- Controlling stakes
- Liquidation
- Debt
Show the answer
A. The holder wants income.
Question 7. Enterprise value equals:
- Equity + debt − cash
- Equity only
- Debt only
- Assets
Show the answer
A. Plus preference shares and minorities.
Question 8. To get equity value from EV, deduct:
- Debt (net of cash)
- Tax
- Dividends
- Goodwill
Show the answer
A. EV belongs to all capital providers.
Question 9. A weakness of EV/EBITDA is that it:
- Ignores capital expenditure and tax
- Needs a dividend
- Uses debt only
- Is exact
Show the answer
A. And is static.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain three asset-based valuation methods. (6 marks) (b) State why an asset-based valuation is often a minimum. (4 marks)
Question 12 (20 marks). Zuma Ltd, a private company, has 2m shares. Profit after tax is ₦150m after a one-off cost of ₦30m (after tax). Book net assets are ₦600m. Dividends are ₦60m. A quoted peer has a P/E of 10 and a dividend yield of 5%. Zuma’s EBITDA is ₦250m, its debt has a market value of ₦300m and the peer EV/EBITDA is 6.
Apply a 20% discount to the P/E for private status. (a) Calculate net asset value per share. (2 marks) (b) Value Zuma by the P/E method, in total and per share. (4 marks) (c) Value it by dividend yield. (3 marks) (d) Value its equity by EV/EBITDA. (4 marks) (e) Compare the results and recommend a range. (4 marks) (f) State three reasons why a private company may need a valuation. (3 marks)
Question 13 (10 marks). (a) State three advantages and three disadvantages of the EV/EBITDA multiple. (6 marks) (b) Explain why the P/E method is simple but weak. (4 marks)
Model answers
Show the model answer to Question 11
(a) Methods (6 marks). Net asset value uses book values of assets less liabilities. (2) Net realisable value uses disposal values and is the break-up value, relevant if assets are worth more sold than used. (2) Replacement value uses the cost of acquiring the assets on the open market. (2)
(b) Minimum (4 marks). Book values may be historic costs. (1) Internal goodwill and human capital are not in the statement of financial position. (1.5) Shareholders expect to be paid for the earning power of the business, so offers need to exceed book value. (1.5)
Show the model answer to Question 12
(a) NAV (2 marks). 600m ÷ 2m = ₦300 per share. (2)
(b) P/E (4 marks).
- Maintainable earnings.
150 + 30 = ₦180m. (1) - P/E used.
10 × 0.8 = 8. (1) - Value = 180 × 8 = ₦1,440m, or ₦720 per share. (2)
(c) Dividend yield (3 marks).
- 60 ÷ 0.05 = ₦1,200m, or ₦600 per share.
- A higher yield for a private firm would lower it. (3)
(d) EV/EBITDA (4 marks).
- EV = 6 × 250 = ₦1,500m. (2)
- Equity = 1,500 − 300 = ₦1,200m, or ₦600 per share. (2)
(e) Comparison (4 marks). Values per share are ₦300 (assets, the minimum), ₦600 (dividend yield and EV/EBITDA) and ₦720 (P/E). (2) Recommend a range of about ₦600 to ₦720 per share, well above the net asset floor, with the lower end for negotiation and the earnings-based values supported by the one-off adjustment. (2)
(f) Reasons (3 marks). A flotation, a private sale, a merger or the tax on an estate. Any three. (1 each)
Show the model answer to Question 13
(a) EV/EBITDA (6 marks). Advantages: unaffected by capital structure; takes net debt into account; ignores depreciation, capital spending and tax differences; widely used. Disadvantages: simplistic; ignores capital spending and tax; static; hard to compare. Any three of each. (1 each)
(b) P/E (4 marks). Simple because it needs only earnings and a ratio. (1.5) Weak because the earnings figure and ratio are subjective and it uses accounting profit, not cash. (2.5)
Pathfinder on Net assets, P/E, earnings yield, dividend yield and EV/EBITDA
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
The 15-mark compulsory question asked for the value of Wazobia Limited by three methods and two limitations of each. The model answer adjusts three years of profit (inventory error, directors’ pay at ₦1,875k and depreciation at ₦3,000k), averages them to ₦4,050k and applies an average peer P/E of 6 for ₦24.3m. Break-up value is ₦29.725m. Dividend yield at an average 10% on ₦2.25m gives ₦22.5m. The examiners said performance was poor because candidates did not understand the valuation methods. Read the sections on asset-based and income-based valuation.
Revise first: Income-based valuation
Adeoye Plc (quoted) has a P/E ratio of 20. Moonshine Limited, which is not quoted and is similar in all respects, has after-tax earnings per share of ₦1.50. The value of a Moonshine share is 20 × ₦1.50 = ₦30.00 (option D). Read the section on the P/E ratio method.
Revise first: Income-based valuation
Case questions ask for net assets and break-up value. See the section on asset-based valuation.
Revise first: Asset-based valuation
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: May 2014 question 1 (case study) and multiple-choice 15.
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