The Capital Asset Pricing Model
The Capital Asset Pricing Model
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 and Income Percentages
| Plant | Beta Coefficient | % of Concordia's Income |
|---|---|---|
| South Town | 0.85 | 55% |
| North Town | 0.90 | 20% |
| East Town | 1.25 | 15% |
| West Town | 1.60 | 10% |
You also gathered 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 as follows:
| Return | Probability |
|---|---|
| 8% | 0.15 |
| 9% | 0.20 |
| 10% | 0.50 |
| 11% | 0.10 |
| 12% | 0.05 |
Questions:
1. What is the Beta coefficient for Concordia? Explain your answer.
2. What is Concordia's required rate of return on any new investments? Explain your answer.
3. What is the equation for the Security Market Line (SML)? Show the equation and graph the equation. Explain what the SML is telling you, and the implications for the firm.
4. 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 answer and justify your calculations.
Paper For Above instruction
The Capital Asset Pricing Model (CAPM) offers a framework for understanding the relationship between risk and return in investment analysis. In this scenario, Concordia Utilities operates multiple plants, each with distinct risk profiles, which collectively influence the company's overall risk and potential return. Calculating the company's aggregate beta coefficient enables investors and managers to assess its systematic risk and determine the required return on investments.
Calculating the Beta Coefficient for Concordia
The beta coefficient for Concordia can be computed as a weighted average of the individual betas of its plants, weighted by each plant's contribution to total income. Using the provided data:
- South Town: 0.85, 55%
- North Town: 0.90, 20%
- East Town: 1.25, 15%
- West Town: 1.60, 10%
The overall beta (βconcordia) is calculated as:
βconcordia = (0.85 × 0.55) + (0.90 × 0.20) + (1.25 × 0.15) + (1.60 × 0.10) = 0.4675 + 0.18 + 0.1875 + 0.16 = 0.995
The combined beta coefficient is approximately 0.995, indicating that Concordia's overall systematic risk is very close to that of the market. This confirms the company's moderate risk profile, with a beta close to 1, which implies that its returns tend to move in tandem with market movements.
Required Rate of Return Based on CAPM
The required rate of return (rrequired) per CAPM is calculated as:
rrequired = risk-free rate + beta × market risk premium
Given a risk-free rate of 3% and a market risk premium of 4%, the calculation becomes:
rrequired = 3% + 0.995 × 4% = 3% + 3.98% ≈ 6.98%
This means that any new investment with a beta similar to Concordia's should yield at least 6.98% to satisfy investor risk-return expectations.
The Security Market Line (SML)
The SML represents the relationship between expected return and beta for efficient portfolios or individual assets, as described by the CAPM. Its equation is:
Expected Return = Risk-Free Rate + Beta × Market Risk Premium
Substituting the known values, the SML equation becomes:
Expected Return = 3% + Beta × 4%
Graphically, this line slopes upward, illustrating that assets with higher betas should offer higher expected returns to compensate for greater risk. The SML serves as a benchmark for evaluating whether an asset offers a fair risk-adjusted return. Assets plotting above the SML are undervalued, indicating good investment opportunities, while those below are overvalued.
For Concordia, with an aggregate beta of approximately 0.995, its expected returns should align closely with the SML, just under 7%. This alignment suggests the company is fairly valued given its systematic risk profile.
Evaluation of the New Plant Investment
The opportunity involves purchasing a new plant costing $200 million, with a beta of 1.60 and an expected return of 12%. To determine if this investment is justified, compare its expected return to the required return derived from CAPM:
rrequired = 3% + 1.60 × 4% = 3% + 6.4% = 9.4%
Since the expected return of the new plant (12%) exceeds the required return (9.4%), this indicates that the investment offers a higher return than what is required for its risk level, making it a favorable opportunity. Therefore, Concordia should proceed with the purchase, as it adds value to the firm's portfolio.
However, a comprehensive decision should also consider qualitative factors like strategic fit, regulatory environment, and operational risks. Nonetheless, based on quantitative analysis, the investment appears sound.
Conclusion
The analysis reveals that Concordia's overall systematic risk, as measured by its beta coefficient, is approximately 0.995, positioning it near the market risk level. The required rate of return, based on CAPM, is about 6.98%. The Security Market Line provides a visual and analytical benchmark for assessing new investments, with Concordia's risk profile aligning closely with expected market returns. The evaluation of the prospective new plant shows that, given its higher expected return relative to its required return, the investment would likely increase shareholder value. These insights are essential for informed strategic decision-making and optimizing the company's portfolio of assets.
References
- Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
- Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25–46.
- Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley Finance.
- Ross, S. A., Westerfield, R., & Jaffe, J. (2021). Corporate Finance (12th ed.). McGraw-Hill Education.
- Sharpe, W. F., & Alexander, G. J. (1990). Investments (4th ed.). Prentice Hall.
- 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.
- Scholes, M., & Williams, J. (1977). Estimating Betas from Weekly Data. Journal of Financial Economics, 5(3), 3–20.
- Statman, M. (2014). What Investors Really Want: Find, Keep, and Profit from the Investments You Need. McGraw-Hill Education.
- Lewellen, W. (1968). Portfolio Theory and Capital Market Equilibrium: The Development of the Securities Market Line. The Journal of Business, 41(2), 167–198.
- Ciochettino, D., & Lo, K. (2018). Strategic Capital Budgeting and Market Risk. Journal of Financial Management, 49(4), 125–148.