Assignment 2: The Capital Asset Pricing Model You Are Consid

Assignment 2 The Capital Asset Pricing Modelyou Are Considering A

Assignment 2: The Capital Asset Pricing Model You are considering an investment in Concordia Utilities and have some questions regarding the income generating abilities of the company. Concordia Utilities has 4 plants in five states and they all operate as separate entities. All five plants are financed by Concordia and have no holdings of their own, but operate as if they were separate companies. You have gathered some information about the company's plants as follows: Table-1: Plant Beta Coefficient % of Concordia's Income South Town 0.% North Town 0.% East Town 1.% West Town 1.% You have also gathered some information about the market and found that the risk-free rate of interest is 3% and that the company adds a market risk premium of 4% to all investments. The possible market returns and their probabilities are found in Table-2: Table-2: Probability Return 0.15 8% 0.2 9% 0.5 10% 0.1 11% Questions: What is the Beta coefficient for Concordia? Explain your answers. What is Concordia's required rate of return on any new investments? Explain your answers. What is the equation for the Security Market Line (SML)? Show the equation and graph the equation on a graph. Explain what the SML is telling you, and the implications for the firm. Suppose Concordia has the opportunity to purchase an additional plant. The cost of the new plant will be $200 million and have a beta coefficient of 1.60. If the new plant is expected to return 12%, should Concordia make the investment? Explain your answers and justify your calculations. Present your analysis of the assigned problems in Excel format. Enter non-numerical responses in the same worksheet using textboxes.

Paper For Above instruction

This paper analyzes the investment decision-making process for Concordia Utilities using the Capital Asset Pricing Model (CAPM). It involves calculating the company's beta coefficient, determining the required rate of return for new investments, understanding the security market line, and assessing an opportunity to acquire a new plant based on risk and expected return. The objective is to apply financial theories to real-world investment decisions, bringing clarity to risk evaluation and return expectations within the context of corporate finance principles.

Calculation of the Beta Coefficient for Concordia

The beta coefficient (β) measures the sensitivity of an asset’s returns relative to the market. Since Concordia operates through separate plants with differing risk profiles, and its overall beta is the weighted average of each plant’s beta, we must identify the beta for each plant. From the data, two plants (East Town and West Town) have a beta of 1.0, indicating they are equally risky as the market. The other two plants (South Town and North Town) have a beta of 0, implying they are risk-free or have no systematic risk component.

The overall beta for Concordia is calculated as:

    β_concordia = (w_East β_East) + (w_West β_West) + (w_South β_South) + (w_North β_North)

Assuming the income contributions of each plant are proportional to their revenue share, and given the percentages, summing these contributions yields an aggregate beta. Notably, South Town and North Town have zero beta, so they do not influence the systematic risk. The weighted average simplifies assuming equal income contributions, leading to an aggregate beta around 0.5, reflecting the combined risk profile of all plants.

Calculating the Required Rate of Return

The CAPM provides the expected return for any asset based on risk-free rate (Rf), market risk premium (MRP), and beta:

    Re = Rf + β * (MRP)

Using Rf = 3% and MRP = 4%, and assuming the weighted average beta of 0.5, the required rate of return (Re) is:

    Re = 3% + 0.5 * 4% = 3% + 2% = 5%

This indicates that any new investment should ideally offer an expected return of at least 5% to be acceptable, given its risk.

The Security Market Line (SML): Equation and Graph

The SML depicts the relationship between expected return and beta across all assets, illustrated by the equation:

    Expected Return = Rf + β * (Market Risk Premium)

Plugging in the numbers:

    Expected Return = 3% + β * 4%

Graphically, this is a straight line starting at the risk-free rate (3%) with a slope equal to the market risk premium (4%).

The SML serves as a benchmark for evaluating whether an asset offers a fair return for its risk; assets lying above the line are undervalued, while those below are overvalued. For firms, understanding where their projects or assets sit relative to the SML guides investment decisions and capital allocation to optimize shareholder value.

Investment Decision for the New Plant

The proposed new plant costs $200 million, has a beta of 1.60, and is expected to yield a 12% return. To assess whether this investment is viable, we calculate its required rate of return using CAPM:

    Re_new = 3% + 1.60 * 4% = 3% + 6.4% = 9.4%

Since the expected return of 12% exceeds the required return of 9.4%, the project provides a positive risk-adjusted excess return, making it an attractive investment. Therefore, Concordia should consider proceeding with the purchase, as it is expected to generate value by surpassing the minimum required return dictated by the asset’s systematic risk.

In conclusion, applying the CAPM framework helps quantify the risk and return profiles of company assets and new projects, enabling informed investment decisions that align with the company's strategic risk appetite and shareholder wealth maximization goals. The analytical process underscores the importance of systematic risk assessment, the utility of the SML, and the critical evaluation of project returns relative to risk-adjusted benchmarks.

References

• Fama, E.F., & French, K.R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
• Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3), 425-442.
• Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13-37.
• Ross, S.A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341-360.
• Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th Edition). McGraw-Hill Education.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd Edition). Wiley.
• Copeland, T., Weston, J., & Shastri, K. (2005). Financial Theory and Corporate Policy (4th Edition). Pearson.
• Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. The American Economic Review, 48(3), 261-297.
• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th Edition). Cengage Learning.
• Hull, J. C. (2018). Options, Futures, and Other Derivatives (10th Edition). Pearson.