Equity Valuation - Detailed Notes

Understanding the concept of present value (PV) is crucial for effective equity valuation. PV allows investors to determine the current worth of future cash flows, which provides a foundational basis for investment decisions.
PV of Single Payment: This refers to the value today of a single future cash flow, taking into account the discounting factor due to the time value of money. This can be particularly useful in evaluating investments that promise a one-time return at a future date.
PV of Annuity: This is the sum of present values of multiple cash flows, usually in the form of periodic payments. Annuities are commonly found in financial products like bonds.
Core principle: Today's value is ultimately determined by the net present value (NPV) of all future cash flows, allowing for a holistic assessment of investments and their potential returns.

Discount Rate (k): This key component reflects the interest rates and risk premium associated with various investments. The discount rate can significantly impact the valuation, as higher perceived risk will increase the rate, thereby decreasing the present value.
Formula: r = RF + Risk Premium. Here, RF represents the risk-free rate, typically derived from government bonds, while the risk premium accounts for the expected additional returns required by investors for taking on riskier stocks.
Today's value of an equity investment is calculated using the NPV of expected future cash flows, which are derived from both anticipated dividends and the anticipated selling price of the stock in the future.

The market risk premium represents the additional return that investors earn from investing in riskier assets, such as stocks, compared to investing in risk-free assets, like treasury bonds. Understanding this concept is essential for assessing both individual stock performance and overall market trends.

Preferred shares are often treated as perpetuities due to their characteristic of providing constant dividends. This presents a distinct valuation framework compared to common shares, as their return is more predictable.
Price Calculation: The value of preferred shares is calculated using the formula P = D / r, where D is the annual dividend and r is the required rate of return for the investor.
- Example Calculation: For a preferred share with a Par Value of $100 and a Dividend Rate of 7%, the Annual Dividend would be calculated as $100 × 0.07 = $7.00. If the required return is 10%, the price would be calculated as P = $7.00 / 0.10 = $70.00.

In scenarios where the price of a preferred share is $57.25 and the annual dividend remains $7, the implied required return can be calculated using the formula r = D / P. This yields r = $7.00 / $57.25 = 12.22%, showcasing how changes in price directly affect required returns.

The cash flows associated with common stock are typically dependent on uncertain dividends. Thus, valuation methods need to account for these uncertainties effectively.
Intrinsic Value Calculation: This involves summing the present value of dividends for various periods and adding the present value of the expected selling price: P = D1 / (1 + k) + D2 / (1 + k)^2 + … + P / (1 + k)^n. Here, k represents the discount rate reflecting risk.
The intrinsic value of common shares ultimately hinges on several variables, including corporate profitability, prevailing interest rates, and the risk profile of the investment involved.

The Constant Growth Dividend Discount Model expands the DDM by assuming that dividends will grow at a constant rate (g) over time.
The new formula that connects stock price with profitability, interest rates, and risk is represented as P = D / (r - g).
- Changes that can significantly impact stock prices include an increase in dividends, an increase in the growth rate of dividends, or a decrease in the required return.

Example: ReeCorp's Stock Calculation can illustrate this model effectively:
- Current Dividend (D0) = $4.00, with an expected growth rate of 6%.
- To calculate the intrinsic price, first determine D1 = D0 × (1 + g) = $4 × 1.06 = $4.24.
- If the required return is established at 12%, the intrinsic price is calculated as Intrinsic Price = $4.24 / (0.12 - 0.06) = $70.66. This example demonstrates how factors like growth rates and required return affect valuations in real scenarios.

Formula: g = b × ROE, where b is the retention ratio (the proportion of earnings retained in the business) and ROE stands for return on equity (a measure of profitability).
DuPont Analysis: A thorough understanding of ROE can be achieved through DuPont Analysis, which decomposes ROE into three key components: ROE = (Net Income / Sales) × (Sales / Assets) × (Assets / Equity). This multi-faceted view aids in identifying the factors driving profitability.

Price-to-Earnings (P/E) Ratio: A crucial metric where EPS (Earnings Per Share) is calculated as Net Income divided by Shares Outstanding. The P/E ratio provides insights into how much investors are willing to pay per dollar of earnings, often indicating market sentiment.
Price-to-Book (P/B) Ratio: This ratio measures the market value relative to the book value of the equity, providing a perspective on how market valuations align with company fundamentals.

Types of DDM include:
- No-Growth Model: Computes value assuming zero growth in dividends.
- Constant Growth Model: Assumes dividends will grow at a steady rate indefinitely.
- Non-Constant Growth (Supernormal Growth): Accounts for variable growth rates over time, especially in the initial stages of a company’s life cycle before stabilizing into steady growth.

For investments where dividends grow at various rates, the multi-stage growth model is employed. This entails calculating the NPV of future cash flows, which includes dividends and the anticipated selling price, providing a comprehensive valuation approach based on differing growth phases.