Stock Valuation

BA 323: Fundamentals of Finance

SDSU - Unit 3b: Stock Valuation
Presented by Isaac Green

What is a Stock?

  • Definition of Stock: Securities representing ownership in a company.
  • Investor Rights: Upon purchasing stock, investors receive two key rights:
    • Ownership Rights: Provides stake in the company’s assets and profits.
    • Control Rights: Includes voting rights to influence company policies.
  • Division of Rights: Companies have the flexibility to structure these rights as they see fit.

Types of Stock

  • Preferred Shares:
    • Pay fixed dividends.
    • Positioned higher in the capital structure than common stock.
    • Do not confer control rights to shareholders.
  • Common Shares:
    • Dividends are not guaranteed.
    • Positioned lowest in the capital structure, making them riskier than preferred shares.

How Stock is Traded

  • Auction Market:
    • Exchange and its employees facilitate the meeting of buyers and sellers.
    • Maintains a limit order book for transactions.
    • Traders can submit market orders as an alternative.
  • Dealer Market:
    • Transactions occur through securities dealers.
    • Dealers quote bid and ask prices to facilitate trading.

The Limit Order Book

  • Example of Limit Order Book:
    • A portion of the limit order book for Boeing on BATS BZX Exchange on November 20, 2017, at 09:51:03:
    • Bid Prices: 263.76 (1,100 shares), 263.73 (100 shares), 263.67 (100 shares), 263.61 (100 shares)
    • Ask Prices: 264.07 (200 shares), 264.12 (1 share), 264.13 (100 shares), 264.18 (200 shares)

Income from Stock Ownership

  • Ways to Receive Cash from Stocks:
    • Dividends: Periodic payments made to shareholders. These are not guaranteed for common stock and depend on the firm's profitability.
    • Selling Shares: Can sell stock either to other investors in the market or back to the company itself.

Value of Stock

  • Valuation Basis: The stock price equals the present value (PV) of expected cash flows.
    • Cash Income from Dividends: Represents direct returns as cash inflows.
    • Capital Gains: Realized from selling stock at a higher price than purchased.
  • Holding Period Implication: Stock has no maturity; an investor can hold it indefinitely, and returns vary based on the holding period.

One-period Example

  • Scenario: Considering purchase of Moore Oil, Inc. stock.
    • Expected $2 dividend in one year.
    • Anticipated selling price of $14.
    • Required return of 20% on risk investments.
  • Maximum Willingness to Pay: Needs calculation based on discounted expected cash flows; discount back cash flows at the required rate of return.

Solving the One-period Example

  • Cash Flows:
    • Dividend ($D_1$): $2 expected in one year.
    • The price upon selling ($P_1$): $14.
    • Total Cash Flow ($CF1$): $D1 + P_1 = 2 + 14 = $16.

Two-period Stock Price

  • Challenge: Knowing future stock price at time one is generally uncertain.
  • General Case: If future stock prices are known, current stock price can be established using:
    P<em>1=P</em>2+D11+RP<em>1 = \frac{P</em>2 + D_1}{1 + R}
  • Iterating Over Time: Stock price can constantly be decomposed into expected dividends and terminal price.

Pricing a Stock: General Case

  • Expected Future Dividends: The stock price reflects the present value of all expected future dividends.
  • Timing Independence: Stock price should remain stable regardless of individual investors’ selling plans.

Stock Price Formula

  • Key Issue: The need for expected future dividends to determine value.

Constant Dividends

  • Assumption: Dividends remain constant over time.
  • Implication: Can the stock be valued under these assumptions?
  • Example Calculation:
    • Expected annual dividends of $5; required rate of return = 10%.
    • Stock Price Calculation:
      P=Cr=50.1=50P = \frac{C}{r} = \frac{5}{0.1} = 50

Growth Stocks

  • Consideration: What if stocks do not pay dividends or are in rapid growth phases?
  • Scenario Analysis: Evaluating investments where funds are consumed rather than returned.

Dividend Growth

  • Future Dividend Expectations: Understanding future dividends with anticipated growth.
  • Example:
    • Current dividend = $5;
    • Expected growth = 4% for next year.
    • Future dividend sequence understanding.

Dividend Constant Growth

  • Formula Derivation:
    • The dividend in year t is given by:
      D<em>t=D</em>0imes(1+g)tD<em>t = D</em>0 imes (1 + g)^t
    • Present value of these dividends is expressed as a series:
      PV=D<em>0+D</em>0imes(1+g)(1+R)+D0imes(1+g)2(1+R)2+…PV = D<em>0 + \frac{D</em>0 imes (1 + g)}{(1 + R)} + \frac{D_0 imes (1 + g)^2}{(1 + R)^2} + …

Growing Perpetuity Formula

  • Key Equation: Formula to evaluate cash flows growing at a constant rate: P=C1R−gP = \frac{C_1}{R - g}
    • Where $C_1$ relates to cash flow received in one period.

Example: Stock with Constant Growth

  • Scenario: Stock pays a $7 dividend growing at 2% indefinitely; required return is 12%.
  • Price Calculation:
    • Apply growing perpetuity formula:
      P=7imes(1+0.02)0.12−0.02P = \frac{7 imes (1 + 0.02)}{0.12 - 0.02}

Returns and Capital Gains

  • Expected Capital Gain Definition: Percent change in the stock price annually.
  • Total Return Evaluation: Total return includes dividends and capital gains.
    • Components:
    • Dividend Yield: DP0\frac{D}{P_0}
    • Capital Gain Yield: P<em>1−P</em>0P0\frac{P<em>1 - P</em>0}{P_0}

Constant and Delayed Growth

  • Expected Price Calculations: Cases involving dividends expected to start after a delay.
  • Example of Delayed Dividend: Stock with no dividends for three years before beginning at $8, with growth thereafter.
    • Calculation of current stock price involves discounting back future expected values.

Additional Examples

  • Dividend Forecasting:
    • Example of expected dividends and growth in price based on anticipated returns.

Stock Prices and Earnings

  • Earnings Relation: Strong correlation between dividends and company profitability.
    • Firms not generating profits can't sustain dividends.
  • Investment Decision Framework:
    • Companies should reinvest only if it enhances overall investor value.

Example: Dividends and Earnings

  • Scenario Analysis: Firm expected to pay a $10 dividend with a 5% growth rate.
    • If earnings retained instead of paid out, how does reinvestment affect future dividends?
  • Calculation Breakdown:
    • Original Price with dividends.
    • Price with reinvestment effect analyzed through growth model evaluations.

Valuation by Comparables

  • Method Overview: Valuation by comparables involves analyzing similar firms within an industry.
    • Strategy: Use financial ratios like P/E to calculate target firm price.
    • Example Calculation: Industry average P/E ratio × Earnings per Share.

Comparables with No Earnings

  • Special Case Consideration: Young firms often have no dividends or earnings.
  • Alternative Ratios Usage: Use Price/Sales ratios instead of P/E ratios for early-stage businesses.