The Goodman Industries And Landry Incorporated Stock Prices

The Goodman Industries And Landry Incorporateds Stock Prices And Div

The Goodman Industries’ and Landry Incorporated’s stock prices and dividends, along with the market index, are provided for calculating various investment metrics. This includes the calculation of annual returns, standard deviations of returns, beta estimation through regression analysis, determination of required market returns, portfolio beta and returns, expected dividends, present value of future dividends, and the maximum purchase price based on future sale expectations. Additionally, the Black-Scholes model is used to determine the value of a call option given specific parameters.

Paper For Above instruction

Investing in stocks involves analyzing past performance to forecast future returns and assess risk. The data for Goodman Industries and Landry Incorporated, as well as the market index, provides a comprehensive basis for such analysis. This paper systematically calculates the essential metrics including annual returns, standard deviations, betas, required rates of return, dividend forecasts, present valuations, and option pricing models to inform investment decisions.

Calculation of Annual Returns

Annual returns are calculated by considering the change in stock price over the period, adding dividends received, and dividing the total by the initial stock price. For every year with available data, the capital gain/loss (ending price minus beginning price), plus dividends, provides the numerator, which is then divided by the beginning price. The formula applied is:

Return = (Ending Price - Beginning Price + Dividends) / Beginning Price

Applying the data from 2013 as an example:

Goodman Industries:

Beginning Price (2012): unknown (assuming provided data starts at 2013).

Ending Price (2013): $25.88

Dividend (2013): $1.73

Similarly, for Landry and the Market Index, the same method applies.

Once all yearly returns are calculated, average annual returns are obtained by summing these returns and dividing by the number of years analyzed. This provides a snapshot of the historical performance of each asset and the market.

Standard Deviations of Returns

The variability or volatility of stock returns is measured through their standard deviation. Using the sample standard deviation formula, differences between each year's return and the average return are squared, summed, and divided by n-1 (degrees of freedom), then rooted. This quantifies the risk associated with each stock and the market index.

Estimating Betas via Regression Analysis

Beta estimates gauge the sensitivity of a stock's returns relative to market movements. Using Excel’s SLOPE function, the regression of stock returns (dependent variable) on market returns (independent variable) yields beta, the slope coefficient. The resulting betas indicate whether stocks are more or less volatile than the market, consistent with observed data patterns.

Calculating the Market Required Rate of Return

The Capital Market Line (CML) or Security Market Line (SML) relates the risk-free rate, market premium, and expected return. Given a risk-free rate of 6.04% and a market risk premium of 5%, the required return on the market (equilibrium return) is calculated as:

Required Return = Risk-Free Rate + Market Risk Premium = 6.04% + 5% = 11.04%

Portfolio Beta and Return

A portfolio comprising 50% Goodman and 50% Landry stocks has a beta calculated as the weighted average of individual betas:

Portfolio Beta = (0.5 × Beta Goodman) + (0.5 × Beta Landry)

Similarly, the portfolio’s required return is derived using the CAPM:

Required Return = Risk-Free Rate + (Portfolio Beta × Market Risk Premium)

Dividends Forecasting

Forecasting dividends involves applying a compound growth rate to the most recent dividend. With D0 = $1.50 and an expected growth rate of 5%, the dividends over the next three years are:

  • D1 = D0 × (1 + g) = $1.50 × 1.05 = $1.575
  • D2 = D1 × 1.05 = $1.575 × 1.05 = $1.65375
  • D3 = D2 × 1.05 = $1.65375 × 1.05 = $1.73644

Valuation of Stock via Present Value of Dividends

Using a required return of 13%, the present value (PV) for each dividend is computed as:

PV = Dividend / (1 + Required Return)^t

Results for each year are summed to estimate the intrinsic value of the dividend stream, aiding in decision-making about stock valuation.

Maximum Purchase Price Based on Sale Expectation

Assuming the stock is sold after three years at the same price ($27.05), the maximum price willing to pay today is the present value of all dividends plus the discounted sale price, consistent with a discounted cash flow approach.

Black-Scholes Model for Call Option Pricing

Given parameters for the option (current stock price, strike price, time to expiration, risk-free rate, and variance), the Black-Scholes formula computes the fair price of the call option. The model involves calculating d1 and d2, then using the cumulative distribution function of the standard normal distribution to determine the option’s theoretical value.

The core formulas are:

d1 = [ln(S/K) + (r + 0.5 × σ²) × T] / (σ × √T)

d2 = d1 - σ × √T

Then, the call price is:

Call Price = S × N(d1) - K × e-rT × N(d2)

Conclusion

This comprehensive analysis combines historical return calculations, risk measurement, beta estimation, dividend valuation, and option pricing to provide a robust framework for investment decision-making. These methods together inform investors of potential returns, associated risks, fair valuations, and strategic entry points in the stock market.

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