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Using a dividend discount model, what is the value of a stock that pays an annual dividend of $5 that is not expected to grow and the discount rate is 10%? What will be the value of the stock if the dividend is expected to grow 5% per year?

Explain whether each of the following is systematic or unsystematic risk using references to the required background readings: a. There is a large recession. b. It is discovered that a company lied about its earnings and it is not nearly as profitable as they claimed. c. The CEO of a successful company gets arrested for some serious crimes, and the company has trouble finding a good replacement.

Use the CAPM to calculate the following: a. The expected return of a stock with a beta of 2, and risk-free rate of 1%, and a market return of 7%. b. The beta if the expected return of the stock is 8%, the risk-free rate is 2%, and the market rate of return is 6%.

Do you think the following companies would have a high, low, or average beta? Explain your answer using references from the background readings and your knowledge of CAPM and beta: a. The ACME Umbrella company’s stock goes up a lot when it rains, but goes down when it is sunny. Nothing else but the weather seems to impact ACME’s stock price. b. Vultures, Inc., specializes in buying assets of bankrupt companies at a discount. Vultures’ stock price seems to go up whenever other companies are doing poorly and going bankrupt, but goes down when other companies are doing well and they have few bankrupt companies to prey on. c. Unoriginal, Inc., can never decide what products they want to focus on so they make many different products in several different industries. They also invest much of their profits into 100 or so other companies that are listed on the stock exchange.

Suppose the Tweedledee Company has an average return of 18%, and the Tweedledum Company has an average return of 10%. They both have a standard deviation of return of 10%, but Tweedledee has a beta of 2 and Tweedledum has a beta of 1. The risk-free rate is 1%. What are the Treynor and Sharpe Ratios of these two companies? What do these ratios tell you about the relative risk and return of these two companies?

Sample Paper For Above instruction

Introduction

Financial analysis and valuation are critical components in investment decision-making, enabling investors to assess the intrinsic value of stocks, evaluate risks, and make informed choices. This paper explores key financial concepts, including the dividend discount model (DDM), risk classification, the Capital Asset Pricing Model (CAPM), beta analysis, and performance ratios such as Treynor and Sharpe ratios. Through a detailed examination of computational and conceptual questions, the paper aims to elucidate the application of these frameworks within the financial context.

Dividend Discount Model (Questions 1)

The dividend discount model (DDM) is a valuation method used to estimate the intrinsic value of a stock based on its expected future dividends discounted to the present value. When dividends are not expected to grow, the valuation simplifies to the perpetuity formula. Specifically, the stock's value (P) is calculated as the dividend (D) divided by the discount rate (r):

P = D / r

Given the parameters: D = $5, r = 10% (or 0.10), the value of the stock (V) as a non-growing dividend is:

V = $5 / 0.10 = $50

When dividends are expected to grow at a constant rate (g), the Gordon Growth Model applies:

V = D1 / (r - g), where D1 is the dividend next year:

D1 = D × (1 + g) = $5 × 1.05 = $5.25

Substituting the known values:

V = $5.25 / (0.10 - 0.05) = $5.25 / 0.05 = $105

Thus, the stock's value increases significantly with growth expectations, illustrating the impact of dividends' growth rate on valuation.

Risk Classification (Question 2)

Risk can be categorized into systematic and unsystematic types. Systematic risk, also known as market risk, affects all securities due to macroeconomic factors, whereas unsystematic risk pertains to individual companies or industries and can be mitigated through diversification.

a. A large recession is an example of systematic risk since it influences the entire economy and the overall stock market (Graham & Smart, 2012). It cannot be eliminated through diversification.

b. Discovering that a company lied about earnings is an unsystematic risk specific to that company’s integrity and financial health (Ross, Westerfield & Jordan, 2007). It can be mitigated by diversifying across multiple stocks.

c. The arrest of a CEO impacts only that particular company, representing an unsystematic risk that could be minimized through diversification.

CAPM Calculations (Question 3)

The CAPM formula predicts the expected return of a stock based on its beta:

Expected Return (E(R)) = Risk-free rate (Rf) + Beta (β) × (Market Return (Rm) - Rf)

a. For a stock with β=2, Rf=1%, Rm=7%:

E(R) = 0.01 + 2 × (0.07 - 0.01) = 0.01 + 2 × 0.06 = 0.01 + 0.12 = 0.13 or 13%

b. To find beta when E(R)=8%, Rf=2%, Rm=6%:

8% = 2% + β × (6% - 2%)

0.08 = 0.02 + β × 0.04

β = (0.08 - 0.02) / 0.04 = 0.06 / 0.04 = 1.5

Beta indicates the sensitivity of the stock to market movements, with higher values reflecting greater volatility relative to the market.

Beta Analysis (Question 4)

The estimation of a company's beta depends on how its stock performance correlates with overall market movements.

a. The weather-dependent stock of ACME Umbrella Company, rising when it rains and falling when sunny, likely has a high beta because its returns are highly sensitive to a specific macro factor (weather), which can be viewed as an external systematic factor (Graulich, 2013).

b. Vultures Inc., which benefits from bankruptcies during economic downturns, shows an inverse relationship with the overall economy. Its beta may be negative or low positive, reflecting an atypical or contrarian response that could be considered a form of negative beta (Bennet, 2014).

c. Unoriginal Inc., with a diversified product portfolio and investments in numerous companies across industries, likely has a beta near the market average (approximately 1), indicating average sensitivity to market movements (Madura, 2013).

Performance Ratios (Question 5)

The Treynor and Sharpe ratios evaluate risk-adjusted returns, providing insights into the performance relative to risk undertaken.

Treynor Ratio = (Return - Risk-Free Rate) / Beta

Sharpe Ratio = (Return - Risk-Free Rate) / Standard Deviation

For Tweedledee:

Treynor = (0.18 - 0.01) / 2 = 0.17 / 2 = 0.085

Sharpe = (0.18 - 0.01) / 0.10 = 0.17 / 0.10 = 1.7

For Tweedledum:

Treynor = (0.10 - 0.01) / 1 = 0.09 / 1 = 0.09

Sharpe = (0.10 - 0.01) / 0.10 = 0.09 / 0.10 = 0.9

Interpretation

The higher Treynor ratio of Tweedledum indicates better reward per unit of market risk, whereas the higher Sharpe ratio of Tweedledee suggests superior overall risk-adjusted performance considering total volatility. Investors may prefer Tweedledum for its efficient market risk compensation and Tweedledee for its better total risk-adjusted return.

Conclusion

Understanding and applying financial models such as the dividend discount model, CAPM, and performance ratios are vital for informed investment decisions. These tools assist in valuing stocks, assessing risk types, and evaluating risk-adjusted returns, enabling investors to diversify effectively and optimize their portfolios. Accurate computation and conceptual clarity in these areas are essential for sound financial analysis and strategic planning.

References

• Bennet, T. (2014). Understanding volatility - What is beta? Kilik & Co.
• Graulich, V. (2013). CAPM: Capital asset pricing model. I Hate Math.
• Madura, J. (2013). Chapter 11: Stock valuation and risk. Financial Markets and Institutions. Cengage Learning.
• Ross, S., Westerfield, R., & Jordan, B. (2007). Chapter 11: Risk and return. Essentials of Corporate Finance. McGraw Hill.
• Graham, J., & Smart, S. (2012). Chapter 6: The trade-off between risk and return. Introduction to Corporate Finance. Cengage Learning.
• Smith, T. (n.d.). Cost of equity: CAPM. Finance for Non-Financial Managers. Coursera.
• Workman, T. (2013). Constant growth dividend discount model - How to value stocks. Subjectmoney.
• Side, T. (2014). Stock Valuation Using the Gordon Growth Model. Investopedia.
• Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives.
• Sharpe, W. F. (1966). Mutual Fund Performance. Journal of Business.