In-Depth Notes on Share Valuation and Financial Assets

Overview of Shares

• Ordinary Shares: Represents ownership in a firm with rights to dividends and voting. Not guaranteed dividends; varies with company profitability and management decisions.

• Preference Shares: Ownership interest with priority in dividends and liquidation but no voting rights.

Valuation of Shares

1. Valuation Principle: The value equals the present value of expected future cash flows.

   • Important for determining share prices based on future cash generated by the investment.

2. Dividends and Share Value:

   • Value of a share, $P<em>0$, can be calculated as: $P</em>0 = rac{D<em>1}{1 + r</em>E} + rac{D<em>2}{(1 + r</em>E)^2} + …$

   • Where $D<em>n$ are future dividends and $r</em>E$ is the required return.

The Dividend-Discount Model

1. Basic Concepts:

   • Shares are valued based on the present value of future dividends. Unlike bonds, there are no promised payments.

   • Calculation involves estimating the timing and amount of future cash flows:

   • Steps for valuing shares:

     • Estimate future cash flows (dividends).

     • Assess risk and determine required rate of return (equity cost of capital, $r_E$).

     • Discount cash flows to present value.

2. Example Calculations:

   • For a share with a one-year holding period with a $1.75 dividend and a sell price of $50:
     $P_0 = 1.75 + rac{50}{1.15} = 45$

   • For multiple years with consistent dividends, sum the discounted cash flows:
     $P<em>0 = rac{D</em>1}{1+r<em>E} + rac{D</em>2}{(1+r<em>E)^2} + … + rac{P</em>n}{(1+r_E)^n}$

3. Constant Growth Model:

   • When dividends grow at a constant rate:
     $P<em>0 = rac{Div</em>1}{r_E - g}$

   • Where $g$ is the growth rate of dividends.

Estimating Future Dividends

• To estimate dividends for companies expecting constant growth:

  • Forecast dividend for next year, $Div<em>1 = Div</em>0 (1 + g)$.

• Required Conditions:

  • Conditions for valid constant growth model:

    • $g$ must be less than $r_E$ to avoid negative share values.

Limitations of the Dividend-Discount Model

1. Uncertainty:

   • Future dividends are inherently uncertain and can fluctuate an estimated share price significantly depending on growth rate assumptions.

   • Investors need to consider non-dividend paying shares and their valuation through other models (i.e., discounted free cash flow).

2. Investment Decisions:

   • Firms can influence share value through decisions about dividend payouts versus reinvesting profits, impacting both dividends and growth rates.

   • Key factors affecting firm's growth include earnings retention and returns on new investments.

Conclusion

• Share Price Determinants:

  • Ultimately, the price of a share reflects future dividend expectations, growth opportunities, and risks. Investors should weigh expected dividends against the required return when determining share value.