Chapter 7 Notes: Equity Markets and Share Valuation (Key Concepts and Formulas)

Shareholders’ Equity and the Capital Structure

• Shareholders’ equity = Assets − Liabilities. $ext{Equity} = ext{Assets} - ext{Liabilities}$
• Firms with debt (liabilities) typically give creditors (e.g., bondholders) the first claim to a firm’s cash flows.
• Equity holders (shareholders) are entitled to the residual value after creditors are paid: the so‑called “shareholders’ equity.”
• In this course we learn about features of shares (Chapter 7) and bonds (Chapter 6).

Features of Shares: Ordinary vs Preference

• Ordinary shares (common stock): no priority in dividends or liquidation; ordinary shareholders are residual claimants.
• Preference shares: generally do not carry voting rights; dividends must be paid before ordinary shareholders; can be cumulative; not a liability of the firm and can be deferred indefinitely.
• Dividend imputation (NZ and Australia): shareholders receive a tax rebate for tax already paid by the firm to avoid double taxation.

Features of Ordinary Shares (continued)

• Ordinary shares (publicly listed): voting rights on the board and other issues; typically the Board is elected at an AGM by ordinary shareholders.
• Straight voting: one share, one vote; owner of 10,000 shares has 10,000 votes.
• Proxy voting: shareholders can appoint someone else to vote on their behalf; proxy fights occur when a minority seeks enough proxy votes to influence outcomes.
• Australia/New Zealand note: a single class of ordinary shares with one vote per share.

Rights and Voting

• Proxy vote: authority granted to someone else to vote the shareholder’s shares; common in large public corporations.
• Proxy fights: when minority owners attempt to secure enough proxy votes to win a vote (e.g., seats on the board).

Rights Issue (Rights Offering)

• Sale of new shares to existing shareholders; existing shareholders receive rights to buy additional shares at a discount to the market price and within a timeframe.
• Rights give existing shareholders the opportunity to maintain their proportional ownership; allows the company to raise funds while protecting current holdings.

Dividend Characteristics and Tax Implications

• Dividends are not a liability until declared by the Board of Directors.
• A firm cannot default on an undeclared dividend; non-payment of an undeclared dividend does not trigger liquidation.
• Dividends are not a business expense for the firm.
• Dividends received by individual shareholders are typically treated as ordinary income for tax purposes.
• Dividend imputation systems (NZ/Australia) provide rebates to avoid double taxation.

The Share Markets: Structure and Participants

• Primary market vs Secondary market:
  • Primary: new issues; shares are issued to raise funds.
  • Secondary: trading of existing shares among investors.
• Dealers vs Brokers:
  • Dealer: buys/sells from inventory; maintains an inventory; profit from bid–ask spread; ready to trade at bid/ask.
  • Broker: brings buyers and sellers together; does not hold risk for own account.
• NZX operations: main exchange in NZ; aims to attract order flow; orders include limit and market orders; trading on computer networks; NZX is an auction market.
• Orders:
  • Limit order: buy/sell at a specified price or better (e.g., buy at $4.50 when market is $4.80; limit sell at $5).
  • Market order: execute at the best available price immediately.

NZX Trading and Market Mechanics

• Trading conducted on computer networks; brokers match buyers and sellers; brokers charge fees for their services; brokers do not bear risk.

Ordinary Share Valuation: Return on Shares

• A share provides cash in two ways: (i) Dividends (if paid) and (ii) Sale of the share.
• The price of a share is the present value of these expected cash flows.

General Valuation Framework

• Present value of expected future cash flows (dividends and sale price):
  $P<em>0 \,=\, \sum</em>{t=1}^{\infty} \frac{D_t}{(1+R)^t}$
• Dividend growth models (DGM): use predicted future cash flows (dividends) and any anticipated price at the end of a holding period.
• Cases:
  • Zero growth: constant dividend forever.
  • Constant growth: dividends grow at a constant rate g forever.
  • Non-constant growth: initial non-constant growth, then stabilizes to g.
• Valuation using multiples (for shares that do not pay dividends): PE ratios and EPS.
• Required return implications of the DGM: decomposition of R into dividend yield and capital gains yield.

Dividend with Zero Growth (General Case)

• If the firm pays a constant dividend D forever, the share is a perpetuity.
• Price formula: $P_0 = \frac{D}{R}$
• Note: If dividends are quarterly, the discount rate must be the corresponding quarterly rate.

Example 1: Zero Growth (Annual Dividend)

• Paradise Beachwear pays a dividend of $10 per share every year indefinitely.
• Required return R = 20% = 0.20.
• Price: $P_0 = \frac{D}{R} = \frac{10}{0.20} = 50.$

Example 2: Constant Dividends (Semi-Annual)

• A share pays a dividend of $0.50 every half-year forever.
• Required return is 10% with semi-annual compounding.
• Semi-annual discount rate: $r = \frac{0.10}{2} = 0.05$
• Price: $P_0 = \frac{D}{r} = \frac{0.50}{0.05} = 10.$
• Note: use a semi-annual rate when dividends are paid semi-annually.

Constant Growth: Dividend Discount Model (DGM)

• Dividends grow at a constant rate g forever; D1 = D0(1+g).
• Price: $P<em>0 = \frac{D</em>1}{R - g}$ with R > g.
• This implies the total return R equals dividend yield plus growth: $R = \frac{D<em>1}{P</em>0} + g$
• Conditions: dividends grow forever, price grows forever, dividend yield constant, capital gains yield constant (equal to g), and R > g.

Example 1: Outback Ltd (DGM)

• D0 just paid = $0.50; growth g = 2% (0.02); required return R = 15% (0.15).
• D1 = D0(1+g) = 0.50 × 1.02 = 0.51.
• Price: $P<em>0 = \frac{D</em>1}{R - g} = \frac{0.51}{0.15 - 0.02} = \frac{0.51}{0.13} \approx 3.92.$

Example 3 (Gordon Growth / Growth with D1, g, R)

• D1 = $4 next period; g = 6% (0.06); R = 16% (0.16).
• Current price: $P<em>0 = \frac{D</em>1}{R - g} = \frac{4}{0.16 - 0.06} = 40.$
• From the same setup, P4 can be computed to illustrate growth: P4 = (D5)/(R − g) where D5 = D1(1+g)^4 = 4(1.06)^4 ≈ 5.0499; thus P4 ≈ 5.0499 / 0.10 ≈ 50.50.
• Check: P4 ≈ P0(1+g)^4 ≈ 40(1.06)^4 ≈ 50.50.
• Implied return from price change over 4 years: (P4/P0)^(1/4) − 1 = 6% (consistent with g).

Non-Constant Growth (Supernormal Growth)

• Dividends do not grow at a constant rate initially; growth eventually settles to a constant g.
• General approach:
  • Compute early dividends: D1, D2, D3, …
  • Once growth becomes constant, compute the terminal price at end of the transition period: Pk = \frac{D{k+1}}{R - g}
  • Present value: $P<em>0 = \sum</em>{t=1}^{k} \frac{D<em>t}{(1+R)^t} + \frac{P</em>k}{(1+R)^k}$
• Non-constant growth example:
  • Last dividend D0 = $1.00; D1 = $1.20; D2 = $1.38; D3 = $1.449; long-run g = 5% (0.05) after year 2; R = 20% (0.20).
  • Terminal price at year 2: $P<em>2 = \frac{D</em>3}{R - g} = \frac{1.449}{0.20 - 0.05} = 9.66.$
  • Present value: $P<em>0 = \frac{D</em>1}{(1+R)^1} + \frac{D<em>2}{(1+R)^2} + \frac{D</em>3 + P_2}{(1+R)^2}$
  • Numeric result: $P_0 = \frac{1.20}{1.20} + \frac{1.38 + 9.66}{(1.20)^2} = 1.00 + \frac{11.04}{1.44} ≈ 8.67.$
• Takeaway: non-constant growth requires separating early sums and the terminal value when growth stabilizes.

Valuation Using Multiples: PE Ratio Method

• For shares that do not pay dividends, price can be estimated via price–earnings (PE) multiples:
  $P_0 = ext{PE} imes ext{EPS}$
• Sources for benchmark PE: industry average/median or a company’s own historical values.
• Example: Inactivision Limited has EPS over the four most recent quarters of $2; industry PE ratio is 20; price: $P_0 = 20 \times 2 = 40.$

Implications of the Dividend Growth Model (DGM)

• Decompose the required return: $R = \text{Dividend yield} + g$ where dividend yield ≡ D1 / P0 and g is the growth rate.
• Dividend yield can be computed from current price and next period dividend: $ext{DY} = \frac{D<em>1}{P</em>0}$.
• The model emphasizes two components of return: income from dividends and appreciation due to growth in dividends (capital gains).

Practical Example: Finding the Required Return from the DGM

• Example: A firm’s shares sell for $10.50; they just paid a dividend of $1 and dividends are expected to grow at 5% per year.
• D1 = D0(1+g) = 1 × 1.05 = 1.05;
• Required return: $R = \frac{D<em>1}{P</em>0} + g = \frac{1.05}{10.50} + 0.05 = 0.10 + 0.05 = 0.15 = 15\%.$
• Dividend yield: $\text{DY} = \frac{1.05}{10.50} = 0.10 = 10\%.$
• Capital gains yield: $g = 5\%.$

Summary of Share Valuation Concepts

• Price equals the present value of all expected future cash flows (dividends and eventual sale price).
• Four valuation paths discussed:
  • Zero growth (perpetual constant dividend): $P_0 = \frac{D}{R}$.
  • Constant growth (Gordon/DGM): $P<em>0 = \frac{D</em>1}{R - g}$.
  • Non-constant growth (supernormal): early irregular growth, then constant; PV incorporates early dividends plus terminal value.
  • Valuation by multiples (PE): $P_0 = ext{PE} \times \text{EPS}$ when dividends are not paid.
• The required return decomposes into dividend yield and growth: $R = \text{DY} + g = \frac{D<em>1}{P</em>0} + g.$