Welcome to Share Valuation!
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). 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 business = Total Assets - Total Liabilities
There are three ways to value those assets:
1. Net Book Value (NBV): Based on the balance sheet. It’s easy to find but often outdated because it doesn't reflect current market prices.
2. Replacement Cost: What would it cost to buy these assets brand new today? This is useful for seeing if a competitor could easily start a similar business.
3. Net Realisable Value (NRV): What could we get if we had a "garage sale" of the assets today? This is usually the minimum value of a company.
Quick Tip: Asset-based models are great for "brick and mortar" companies (like property firms) but terrible for service companies (like software developers) because they don't value "brainpower" or brand names!
2. The Income-Based Approach (P/E Ratio)
Most investors buy shares because they want a share of the profits. The Price/Earnings (P/E) Ratio method is the most popular way to value a business based on its earnings power.
The Logic: If a company earns \$1 per share, and similar companies are selling for 10 times their earnings, then our share should be worth \$10.
The Formula:
\( \text{Value per share} = \text{Earnings Per Share (EPS)} \times \text{P/E Ratio} \)
\( \text{Total Value of Company} = \text{Total Profits} \times \text{P/E Ratio} \)
Analogy: Imagine a lemonade stand that makes \$100 profit a year. If you think it's fair to pay "5 years' worth of profit" to buy it, the P/E ratio is 5, and the price is \$500.
Important Note: When valuing an unlisted company (a private one), we usually find a similar listed company (a public one) and use their P/E ratio. However, because private shares are harder to sell, we usually reduce (discount) that P/E ratio by about 20% to 30% to be safe.
Key Takeaway:
The P/E ratio reflects the market’s confidence. A high P/E means investors expect high future growth!
3. The Dividend Valuation Model (DVM)
The DVM assumes that a share is worth the present value of all the future dividends it will pay out. After all, dividends are the actual cash that reaches the investor's pocket.
A. No Growth (The "Steady Eddy" Model)
If the dividend is expected to stay exactly the same forever:
\( P_0 = \frac{D}{r_e} \)
Where:
\( P_0 \) = Current share price
\( D \) = The constant dividend
\( r_e \) = The shareholders' required rate of return (cost of equity)
B. Constant Growth (The Dividend Growth Model)
In the real world, companies usually try to grow their dividends each year. This is the formula you will use most often in your exam:
\( P_0 = \frac{D_0(1+g)}{(r_e - g)} \)
Alternative version: \( P_0 = \frac{D_1}{(r_e - g)} \)
Definitions:
• \( D_0 \): The dividend just paid (or about to be paid).
• \( D_1 \): The dividend expected in one year's time (\( D_1 = D_0 \times (1+g) \)).
• \( g \): The constant annual growth rate of dividends.
• \( r_e \): The cost of equity.
Common Mistake Alert! Always check if the question gives you the dividend now (\( D_0 \)) or the dividend in one year (\( D_1 \)). If it's "just paid," you must multiply it by \( (1+g) \) before putting it into the formula!
4. How to Calculate Growth (g)
If the exam doesn't give you "g," you have two ways to find it:
Method 1: Historical Growth
Look at what happened in the past. If the dividend was \$10 four years ago and is \$14.64 today:
\( g = \sqrt[n]{\frac{\text{Latest Dividend}}{\text{Earliest Dividend}}} - 1 \)
In this case: \( g = \sqrt[4]{\frac{14.64}{10}} - 1 = 0.10 \text{ or } 10\% \).
(Note: \( n \) is the number of years of growth, which is usually the number of dividends minus one).
Method 2: Gordon's Growth Model (RB Model)
This looks at how much profit the company keeps to reinvest.
Formula: \( g = r \times b \)
• \( r \): The return the company earns on its new investments.
• \( b \): The retention ratio (the % of profits kept in the business). If a company pays out 40% of profits as dividends, they retain 60%. So, \( b = 0.60 \).
Did you know?
The "b" in \( g = rb \) stands for "plow-back" ratio—literally plowing profits back into the company like a farmer plowing seeds back into the soil!
5. Cum-Div vs. Ex-Div Prices
This is a small but vital detail that can trip you up. When a share is sold, does the buyer get the upcoming dividend?
• Cum-Div (With Dividend): The buyer gets the next dividend. The price is "inflated" by the dividend amount.
• Ex-Div (Without Dividend): The seller keeps the dividend. This is the true market price we use in our formulas.
The Rule: If you are given a Cum-Div price, subtract the dividend to get the Ex-Div price before doing any calculations.
\( \text{Ex-Div Price} = \text{Cum-Div Price} - \text{Upcoming Dividend} \)
6. Summary & Quick Review
When you face a valuation question, follow these steps:
1. Identify the goal: Are you valuing assets, earnings, or dividends?
2. Check the timing: Is the dividend \( D_0 \) (today) or \( D_1 \) (next year)?
3. Check the price: Is it Cum-div or Ex-div?
4. Find 'g': Use the historical method or \( g=rb \) if growth isn't given.
5. Apply the formula: Plug your numbers into the DVM or P/E model carefully.
Don't worry if this seems tricky at first! Share valuation is a mix of art and science. Practice the Dividend Growth Model formulas until they become second nature, and you'll be well on your way to passing Section F!