Models for the valuation of shares

Financial Management (FM) · ACCA · 6 min read · Updated: Nov 2, 2026

Ever wondered how investors decide if a share price is a "bargain" or "too expensive"? In this chapter, we explore the tools used to put a price tag on a company. This is a crucial part of Section F: Business Valuations. Whether a company is looking to take over another business or someone is looking to sell their shares, we need a reliable way to calculate what those shares are worth.

Don't worry if the formulas look a bit intimidating at first. Think of valuation like buying a used car: you can look at the physical parts (Assets), how much money it saves you on the commute (Earnings), or the cash it puts back in your pocket (Dividends and Cash Flows). Let's dive in!

1. The Asset-Based Approach

This is the most straightforward method. It asks: "If we sold everything the company owns and paid off all its debts, what would be left for the shareholders?"

How to calculate it:
Value of equity = Total Assets - Total Liabilities

There are three ways to value those assets:
1. Net Book Value (NBV): Based on the statement of financial position. It’s easy to find but often outdated because historical cost does not reflect current market prices.
2. Net Replacement Cost: What would it cost to replace or buy these assets brand new today? This is useful for evaluating whether a competitor could easily start an equivalent business from scratch.
3. Net Realisable Value (NRV): What net amount could we realise if we sold the assets individually today? This represents a break-up or liquidation value, setting a minimum price floor for the company.

Quick Tip: Asset-based models are great for asset-rich "brick and mortar" businesses (like property investment firms) but poorly suited for service or technology companies because they fail to capture unrecognised intangible value such as brand reputation, patents, or human capital!

2. The Income-Based Approach

Most investors buy shares because they want a share of the profits. Income-based methods value a business on its sustainable earnings power.

A. The Price/Earnings (P/E) Ratio Method

The Price/Earnings (P/E) Ratio method is the most widely used technique to value a company based on its earnings.

The Logic: If a company earns \$1 per share, and similar companies sell for 10 times their earnings, then our share should be worth \$10.

The Formulas:
$ \text{Value per share} = \text{Earnings Per Share (EPS)} \times \text{P/E Ratio} $
$ \text{Total Equity Value} = \text{Total Earnings after Tax} \times \text{P/E Ratio} $

Important Note for Unlisted Companies: When valuing an unlisted company, we find a listed proxy company with similar operations and use its P/E ratio. Because unlisted shares lack marketability and liquidity, we discount the proxy P/E ratio (typically by 20% to 30%) to reflect the higher liquidity risk.

B. The Earnings Yield Method

The Earnings Yield (EY) is the inverse of the P/E ratio, showing profit as a percentage of share price:

$ \text{Earnings Yield} = \frac{\text{EPS}}{P_0} = \frac{1}{\text{P/E Ratio}} $

Valuation Formulas:
$ \text{Value per share} = \frac{\text{EPS}}{\text{Earnings Yield}} $
$ \text{Total Equity Value} = \frac{\text{Total Earnings after Tax}}{\text{Earnings Yield}} $

Example: If a company produces an EPS of \$0.50 and the appropriate earnings yield for the sector is 10% (0.10), the estimated share price is $ \frac{\$0.50}{0.10} = \$5.00 $.

Key Takeaway:

A high P/E ratio corresponds to a low earnings yield, reflecting high market confidence and strong future growth expectations.

3. Cash Flow-Based Models

Cash flow-based approaches look at the actual cash an investor or company expects to receive, discounted at the cost of capital.

A. The Dividend Valuation Model (DVM)

The DVM assumes that a share is worth the present value of all future dividends paid out.

No Growth (Constant Dividends):
$ P_0 = \frac{D}{r_e} $
Where $ D $ is the constant annual dividend and $ r_e $ is the cost of equity.

Constant Growth (Dividend Growth Model):
$ P_0 = \frac{D_0(1+g)}{(r_e - g)} = \frac{D_1}{(r_e - g)} $
Where:
• $ D_0 $: Dividend just paid or currently payable.
• $ D_1 $: Dividend expected in one year's time ($ D_1 = D_0(1+g) $).
• $ g $: Constant annual growth rate in dividends.
• $ r_e $: Shareholders' required rate of return (cost of equity).

Common Mistake Alert! Always check whether the dividend stated is $ D_0 $ (recently paid) or $ D_1 $ (next year's dividend). If it is $ D_0 $, you must compound it by $ (1+g) $ in the numerator.

B. The Discounted Cash Flow (DCF) Basis

Instead of relying on dividends or accounting profits, the Discounted Cash Flow (DCF) basis values a business based on its expected future operational cash flows.

How it works:
1. Forecast the business's future operating cash flows (revenues minus operating costs and capital investment requirements) over an explicit planning horizon.
2. Add a terminal value representing cash flows beyond the planning horizon.
3. Discount all future cash flows back to present value using the company's Weighted Average Cost of Capital (WACC) to determine the total value of the firm (Enterprise Value).
4. Deduct the current market value of debt to obtain the market value of equity:
$ \text{Market Value of Equity} = \text{PV of Future Cash Flows} - \text{Market Value of Debt} $

Advantages & Limitations: DCF directly accounts for the time value of money and focuses on cash generation rather than accounting conventions. However, it relies heavily on long-term cash flow forecasts and accurate estimation of the discount rate.

4. How to Calculate Dividend Growth (g)

If the growth rate $ g $ is not given directly, the syllabus specifies two techniques:

Method 1: Historical Growth

Extrapolate past dividend history:
$ g = \sqrt[n]{\frac{\text{Latest Dividend}}{\text{Earliest Dividend}}} - 1 $
Where $ n $ is the number of years of growth (number of dividend intervals). If the dividend was \$10.00 four years ago and is \$14.64 today:
$ g = \sqrt[4]{\frac{14.64}{10.00}} - 1 = 0.10 \text{ or } 10\% $.

Method 2: Gordon's Growth Approximation

Gordon's growth model links growth to profit reinvestment:
Formula: $ g = b \times r_e $
Where:
• $ b $: The earnings retention rate (fraction of earnings not distributed as dividends: $ b = 1 - \text{dividend payout ratio} $).
• $ r_e $: The return earned on equity/reinvested funds.

5. Cum-Div vs. Ex-Div Prices

When shares trade near a dividend payment date, the quote is either cum-dividend or ex-dividend:

• Cum-Div (With Dividend): The buyer receives the impending dividend. The market price includes the value of that dividend.
• Ex-Div (Without Dividend): The seller retains the right to the dividend. This is the clean, ongoing market price used in valuation models.

The Rule: If given a cum-div share price, deduct the dividend to arrive at the ex-div price before using it in formulas:
$ \text{Ex-Div Price} = \text{Cum-Div Price} - \text{Upcoming Dividend} $

6. Summary & Quick Review

When tackling valuation questions in Section F:
1. Identify the model category: Asset-based (NBV, replacement cost, NRV), Income-based (P/E ratio, earnings yield), or Cash flow-based (DVM, DCF basis).
2. Adjust unlisted multiples: Apply an appropriate marketability discount to listed proxy P/E ratios.
3. Check dividend timing: Identify clearly whether the dividend is $ D_0 $ or $ D_1 $.
4. Ensure clean prices: Convert cum-div quotes to ex-div before evaluating cost of equity or share value.
5. Derive growth accurately: Use historical compounding or Gordon's growth approximation ($ g = b \times r_e $) where required.

References

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the fundamental logic of the asset-based valuation approach and how is equity value calculated under it?

The asset-based approach calculates the net amount remaining for shareholders if all assets were liquidated and all liabilities paid off: $ \text{Value of equity} = \text{Total Assets} - \text{Total Liabilities} $.

How is equity valued using the Price/Earnings (P/E) ratio method, and how should proxy P/E multiples be adjusted for unlisted firms?

$ \text{Value per share} = \text{EPS} \times \text{P/E Ratio} $ (or $ \text{Total Equity Value} = \text{Total Earnings after Tax} \times \text{P/E Ratio} $), with the proxy P/E discounted by 20% to 30% for unlisted firms.

What is the Earnings Yield (EY) and how is it used to determine share value?

Earnings Yield is the inverse of the P/E ratio ($ \text{EY} = \frac{\text{EPS}}{P_0} = \frac{1}{\text{P/E}} $), and value per share is calculated as $ \text{Value per share} = \frac{\text{EPS}}{\text{Earnings Yield}} $.

What are the formulas for valuing a share under the Dividend Valuation Model (DVM) with and without dividend growth?

Without growth: $ P_0 = \frac{D}{r_e} $; with constant growth: $ P_0 = \frac{D_0(1+g)}{(r_e - g)} = \frac{D_1}{(r_e - g)} $.

How is the market value of equity derived under the Discounted Cash Flow (DCF) basis?

Forecast future operating cash flows, discount them using WACC to find total firm value, and subtract the market value of debt: $ \text{Market Value of Equity} = \text{PV of Future Cash Flows} - \text{Market Value of Debt} $.

How is historical dividend growth calculated when estimating the annual dividend growth rate ($ g $)?

$ g = \sqrt[n]{\frac{\text{Latest Dividend}}{\text{Earliest Dividend}}} - 1 $, where $ n $ is the number of dividend growth intervals.

How is the dividend growth rate ($ g $) calculated using Gordon's growth approximation model?

$ g = b \times r_e $, where $ b $ is the retention rate ($ 1 - \text{payout ratio} $) and $ r_e $ is the return on equity/reinvested funds.

What is the difference between cum-dividend and ex-dividend share prices, and how are they adjusted?

Cum-div includes the right to the upcoming dividend, whereas ex-div excludes it; $ \text{Ex-Div Price} = \text{Cum-Div Price} - \text{Upcoming Dividend} $.

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