KN

Lecture 20: Stocks (Part 2)

Estimating Dividends in the Dividend-Discount Model

Constant Dividend Growth Model

  • Definition: A method to value a stock by treating its dividends as a constant growth perpetuity.

  • Key Assumptions:

    • Dividends will grow at a constant rate, g, indefinitely.

    • The firm's value is determined by next year's dividend divided by the cost of capital adjusted for growth.

  • Formula: [ P0 = \frac{D1}{r_E - g} ] Where:

    • ( P_0 ): Current price of the stock

    • ( D_1 ): Next year's dividend

    • ( r_E ): Equity cost of capital

    • ( g ): Growth rate of dividends

Example: Valuing Hydro One

  • Information:

    • Expected dividend ( D_1 ): $2.30 per share

    • Equity cost of capital ( r_E ): 7%

    • Growth rate ( g ): 2%

  • Calculation:
    [ P_0 = \frac{2.30}{0.07 - 0.02} = 46.00 ]

  • Interpretation:

    • Investors are willing to pay 20 times the current dividend ($2.30) for Hydro One's stock, valuing it based on the dividends it will provide.

Dividends Versus Investment and Growth

  • Dividend Determination:

    • Dividends can be determined through earnings per share (EPS) and dividend payout rate:
      [ \text{Dividends} = EPS \times \text{Dividend Payout Rate} ]

Increasing Dividends

  • A firm can increase dividends by:

    • Increasing earnings

    • Raising the dividend payout rate

    • Reducing the number of shares outstanding

  • Investment Effect:

    • Changes in earnings can stem from new investments funded through retained earnings.

Investment Growth Formula

  • New Investment:
    [ \text{New Investment} = \text{Earnings} \times \text{Retention Rate} ]

  • Earnings Growth Rate:
    [ ext{Earnings Growth Rate} = \text{Retention Rate} \times \text{Return on New Investment} ]

Example: Canadian Tire's Dividends

  • Scenario:

    • EPS is $6

    • Initially pays all earnings as dividends, leading to stock price of $60.

    • Plans to cut payout to 75%, focusing on growth with expected ROI of 12%.

  • New Dividend Calculation:

    • New dividend = 75% of $6 = $4.50.

  • Growth Rate Calculation:
    [ g = 25\% \times 12\% = 3\% ]

  • New Share Price:
    [ P_0 = \frac{4.50}{0.10 - 0.03} = 64.29 ]

  • Outcome: Share price rises from $60 to $64.29, indicating value creation through investment.

Consideration of Unprofitable Growth

  • Scenario: If Canadian Tire's investment returns drop to 8%, new growth rate becomes 2% with a similar dividend cut to $4.50.

  • New Share Price:
    [ P_0 = \frac{4.50}{0.10 - 0.02} = 56.25 ]

  • Evaluate: Cutting dividends to invest in projects with lower returns reduces shareholder value, conflicting with value creation rationale.