Comprehensive Study Guide to the Shares Market and Equity Valuation

Comparison of Debt and Equity Instruments

Ownership Interest: * Debt: This does not represent an ownership interest in the company. Creditors are considered lenders, not owners. * Equity: Represents an ownership interest. Common stockholders have the right to vote on the board of directors and other corporate issues.
Voting Rights: * Debt: Creditors do not have voting rights. * Equity: Stockholders typically possess voting rights to influence corporate governance.
Tax Implications: * Debt: Interest paid on debt is considered a cost of doing business and is therefore tax-deductible for the corporation. * Equity: Dividends paid to shareholders are not considered a cost of doing business and are not tax-deductible.
Longevity and Maturity: * Debt: Debt instruments have a specific term (maturity) after which the capital must be repaid or rolled over into new debt. * Equity: Equity is infinitely lived; capital is effectively loaned to the company in perpetuity, as there is no specific date for repayment.
Return Risk: * Debt: Under normal circumstances, debt holders know their cash flows in advance (fixed interest and principal payments). * Equity: Equity holders receive a share of profits, the magnitude and timing of which are unknown in advance.
Credit Risk and Legal Recourse: * Debt: Creditors have legal recourse if interest or principal payments are missed, which can lead to bankruptcy or liquidation proceedings. * Equity: Dividends are not a legal liability of the firm. Stockholders have no legal recourse if no dividends are paid.
Definition of Shares: Shares are equity securities that serve as certificates of ownership in a company.

The Structure of the Shares Market

Primary Markets: * These are markets where companies issue new shares to the public for the first time to raise capital.
Secondary Markets: * These involve the buying and selling of outstanding shares among investors. * From an investor's perspective, secondary markets provide marketability and liquidity at a fair price for the securities they own. * In New Zealand, secondary equity market transactions primarily occur on the NZX (New Zealand Exchange).
Reading Share Market Listings: * Listings are found in financial media, such as the Business section of The New Zealand Herald or Yahoo Finance. * Standard information provided includes the Price, Volume (number of shares traded), and the total number of trades.

Concepts of Asset Valuation

Book Value: The price paid to acquire the asset (including betterments or improvements) less the accumulated depreciation over its useful life.
Market Value: The price of an asset as determined by participants in a competitive marketplace.
Intrinsic Value: A measurement of what an asset is "really" worth based on its underlying characteristics.

Primary Valuation Methods

Income-Based Valuation: * Relies on the concept of the present value ( $PV$ ) of expected future cash flows from the shares. * These cash flows are discounted at the decision-maker’s required rate of return, derived either from the Capital Asset Pricing Model (CAPM) or the investor's specific "true" required rate of return.
Asset-Based Valuation: * Relies on finding the value of the firm’s assets ( $V$ ) by calculating the present value of expected future cash flows from those assets, discounted at the cost of capital. * The value of equity ( $E$ ) is then obtained using the formula: $E = V - D$ , where $D$ represents Debt.
Market-Based Valuation: * Uses multiples or accounting ratios to estimate value. * This involve identifying publicly traded companies (comparables) engaged in similar business activities. * Analysts use the prices at which these comparables trade along with their accounting data (e.g., Price-earnings or P/E ratios) to estimate the target company's value. * Usually, an average multiple from several comparables is used, or a single multiple if one comparable is clearly superior.

Ordinary and Preference Shares

Shareholder Rights: Contracts generally define rights along three dimensions: voting rights, rights to income (dividends), and rights to the capital.
Ordinary Shares: * Owners are not guaranteed dividend payments. * Holders have the lowest priority claim on company assets in the event of insolvency. * Shareholders enjoy limited liability and typically possess voting rights.
Preference Shares: * Owners receive priority over ordinary shareholders for dividend payments and claims against assets during insolvency or liquidation. * Preference shares are legally equity, yet holders usually have no voting privileges. * Dividends are set in the preference share contract. * Failure to pay a preference dividend does not cause default, but it is a serious financial breach signaling financial distress. * All preference dividends must be paid before any ordinary dividends can be distributed. * Cumulative Preference Shares: Any unpaid dividends from the past must be paid in full before ordinary shareholders can receive any dividends.
The Debt vs. Equity Debate for Preference Shares: * Legally, they are equity and dividends are taxable like ordinary shares. * However, they share characteristics with debt (fixed payments, priority), leading some to argue they are a special type of bond.

Fundamental Share Valuation via Present Value

Cash Flow Sources: Share ownership produces cash flows through Dividends and Capital Gains (or losses).
General Intrinsic Value Principle: The intrinsic value of any asset is the present value of its expected future cash flows.
One-Period Model Example (Example 1): * Given: Expected dividend ( $D_1$ ) = $5.50; Expected stock price in one year ( $P_1$ ) = $120; Required return ( $R$ ) = 15%. * Calculation: $P_0=\frac{5.50}{1.15}+\frac{120}{1.15}=4.783+104.348=109.13$ .
Perpetuity Model: * Considers the share price as the present value of all expected future dividends ( $D_{\infty}$ ). * Formula: $P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+R)^t}$ . * 远-distant dividends have a small present value and contribute very little to the current price.

Dividend Growth Patterns and Models

Zero Growth Dividend Model

Assumption: Dividend payments remain constant over time ( $g = 0$ ), meaning $D_1 = D_2 = D_{\infty}$ .
Formula: $P_0 = \frac{D}{R}$ .
Example 2: Expected dividend = $0.50 per year; Required return = 10%. * P_0 = \frac{0.50}{0.1} = $5.00.
Example 3: Expected dividend = $0.50 per quarter; Required return = 10% per annum (quarterly compounding). * Quarterly rate = $\frac{0.1}{4}$ . * $P_0=\frac{0.50}{0.1 / 4}=20.00$ .

Constant Growth Dividend Model (Gordon Growth Model)

Applicability: Best for mature companies with stable growth history.
Assumption: Dividends grow at a constant average rate ( $g$ ) forever.
Formula: $P_0 = \frac{D_1}{R - g}$ .
Modified Formula for any time $t$ : $P_t = \frac{D_{t+1}}{R - g}$ .
Validity Constraint: Must satisfy g < R. If $g \ge R$ , the present value of dividends increases infinitely.
Estimating Growth ( $g$ ): * Can be linked to the GDP growth rate of the economy. * Sustainable Growth Rate ( $SGR$ ): $g = ROE \times \text{plowback ratio}$ . Note: Plowback ratio is the fraction of earnings retained by the firm.
Example 4: Recent dividend ( $D_0$ ) = $5.00; Growth rate ( $g$ ) = 10%; Required return ( $R$ ) = 15%. * $D_1=5.00\times(1+0.10)=5.50$ . * $P_0=\frac{5.50}{0.15 - 0.10}=110.00$ .
Example 5: Expected dividend next period ( $D_1$ ) = $4; Growth rate ( $g$ ) = 6%; Required return ( $R$ ) = 16%. * Current Price ( $P_0$ ): $P_0=\frac{4}{0.16 - 0.06}=40.00$ . * Expected Price in Year 4 ( $P_4$ ): First, find $D_5 = D_1 \times (1 + g)^4 = 4 \times (1.06)^4 = 5.0499$ . * Then, $P_4=\frac{D_5}{R - g}=\frac{5.0499}{0.16 - 0.06}=50.50$ .

Mixed (Supernormal) Growth Model

Applicability: For successful companies experiencing high initial growth before leveling off.
Valuation Process: * Step 1: Forecast all individual dividends during the supernormal growth period (from period 1 to $t$ ). * Step 2: Calculate the terminal value ( $P_t$ ) at the point growth stabilizes using either the zero-growth or constant-growth model for dividends after time $t$ . * Step 3: Calculate the present value of all forecasted dividends and the present value of $P_t$ ; sum them to find $P_0$ .
Master Formula: $P_0=\sum_{i=1}^{t}\frac{D_i}{(1+R)^i}+\frac{P_t}{(1+R)^t}$ .
Example 6: Last dividend ( $D_0$ ) = $1; Growth year 1 = 20%; Growth year 2 = 15%; Growth thereafter = 5% indefinitely; Required return ( $R$ ) = 20%. 1. $D_1=1.00\times1.20=1.20$ . 2. $D_2=1.20\times1.15=1.38$ . 3. $D_3=1.38\times1.05=1.449$ . 4. Terminal Value at $t=2$ : $P_2=\frac{D_3}{R - g}=\frac{1.449}{0.20 - 0.05}=9.66$ . 5. $P_0=\frac{1.20}{1.20}+\frac{1.38 + 9.66}{(1.20)^2}=1.00+7.6667=8.67$ .

Valuation of Preference Shares

Maturity Factors: Valuation depends on whether the share has an effective maturity (sinking fund/call option) or no maturity.
No Maturity: Treated as a perpetuity with constant dividends. * Formula: $P_0 = \frac{D}{R}$ . * Example 7: Par value = $50; Dividend rate = 8.25%; Required return = 9.5%. *5 $D=50\times0.0825=4.125$ . * $P_0=\frac{4.125}{0.095}=43.42$ . * Example 8: Price ( $P_0$ ) = $40; Dividend ( $D$ ) = $4.125. * Expected Return ( $R$ ): $R = \frac{4.125}{40} = 0.1031 \text{ or } 10.31\%$ .
Fixed Maturity: Valued similarly to a bond. * $P_0 = PV(\text{Dividends}) + PV(\text{Par value})$ . * General formula for $m$ payments per year (usually $m=2$ for semi-annual): * $P_0 = \sum_{i=1}^{mn} \frac{D / m}{(1 + R / m)^i} + \frac{Par}{(1 + R / m)^{mn}}$ .

Market Equilibrium and Efficiency

Market Equilibrium: Occurs when market prices reflect the intrinsic value of shares. The required return ( $R_{required}$ ) equals the expected return ( $R_{expected}$ ).
Deriving Returns: * Required Return ( $r_E$ ): Typically calculated via the Capital Asset Pricing Model (CAPM): $r_E = r_f + (r_M - r_f) \times \beta$ . * Expected Return: Inferred from market prices: $R = \text{Dividend Yield} + \text{Capital Gain Yield}$ . * Investment return formula: $R = \frac{D_1}{P} + g$ .
Example 9: Current Price ( $P_0$ ) = $80; Annual Dividend ( $D_1$ ) = $5; Expected Return = 14%. * Find Price in one year ( $P_1$ ): * $0.14 = \frac{5 + P_1 - 80}{80}$ . * $0.14 \times 80 = P_1 - 75$ . * $11.2 + 75 = P_1$ . *0 $P_1=86.20$ $P_1=86.20$
Comprehensive Example (Example 10): * Parameters: $\beta = 1.2$ , $r_f = 7\%$ , $r_M = 12\%$ , D_0 = $2.00, $g = 6\%$ . * Step 1: Required Rate of Return: * $r_E = 0.07 + (0.12 - 0.07) \times 1.2 = 0.13 \text{ or } 13\%$ . * Step 2: Market Value Today ( $P_0$ ): *2 $D_1=2.00\times1.06=2.12$ . * $P_0=\frac{2.12}{0.13 - 0.06}=30.29$ . * Step 3: Market Value in One Year ( $P_1$ ): *7 $D_2=2.12\times1.06=2.247$ 47. * P_1 = \frac{2.247}{0.13 - 0.06} = $32.10. * Step 4: Yield Analysis: * Dividend Yield: \frac{D_1}{P_0} = \frac{2.12}{30.29} = 7.0\%. * Capital Gains Yield: \frac{P_1 - P_0}{P_0} = \frac{32.10 - 30.29}{30.29} = 6.0\%. * Total Return: 7\% + 6\% = 13\%$$.