Are You Considering Two Possible Investments X And Y?

You Are Considering Two Possible Investments X And Y With Returns An

You are considering two possible investments (X and Y) with returns and related probabilities are as follows: Calculate the expected return, standard deviation, and coefficient of variation for each and determine which security will be preferred. Part 2 A company has beta = 1.8, the risk-free rate is 7%, and the market risk premium is 11%. What will be the required rate of return of the company? A company has required rate of return of 12%, the risk-free rate is 4%, and the market return is 11.5%. What will be the company's beta? A stock has a beta of 0.85, the risk-free rate is 5.50%, and the market risk premium is 4.0%. What is the stock's required rate of return? Part 3 Two projects with the following cash flows are being considered: Calculate the payback period, NPV, and IRR and determine which projects should be considered for mutually exclusive and for independent projects. The discount rate for both projects is 11.50%.

Paper For Above instruction

Investment decision-making plays a crucial role in financial management, involving the assessment of potential securities and projects to optimize returns while managing risk. The analysis of investments X and Y, the application of the Capital Asset Pricing Model (CAPM), and the evaluation of project cash flows through payback period, Net Present Value (NPV), and Internal Rate of Return (IRR) are fundamental tools used by investors and financial managers to inform their choices. This paper explores these concepts comprehensively, emphasizing their calculations, interpretations, and implications for selecting the most suitable investments and projects.

Analysis of Investments X and Y

The first part of the analysis involves calculating the expected return, standard deviation, and coefficient of variation for two investments, X and Y. These statistical measures help assess the attractiveness and risk profile of each security.

Suppose investment X has possible returns of 8% and 12%, with associated probabilities of 0.4 and 0.6, respectively. Investment Y has returns of 7% and 15%, with probabilities of 0.5 and 0.5. The expected return (ER) for each investment is calculated as:

ER = (Probability of outcome 1 Return in outcome 1) + (Probability of outcome 2 Return in outcome 2)

For Investment X: ER_X = (0.4 8%) + (0.6 12%) = 3.2% + 7.2% = 10.4%

For Investment Y: ER_Y = (0.5 7%) + (0.5 15%) = 3.5% + 7.5% = 11.0%

The standard deviation (σ) measures the dispersion of returns around the expected value and is calculated as the square root of the variance:

Variance = Σ [Probability * (Return - ER)^2]

Standard deviation = √Variance

Calculating for Investment X:

Variance_X = 0.4 (8% - 10.4%)^2 + 0.6 (12% - 10.4%)^2 = 0.4 (−2.4%)^2 + 0.6 (1.6%)^2 = 0.4 5.76 + 0.6 2.56 = 2.304 + 1.536 = 3.84

σ_X = √3.84 ≈ 1.96%

Similarly for Investment Y:

Variance_Y = 0.5 (7% - 11%)^2 + 0.5 (15% - 11%)^2 = 0.5 (−4%)^2 + 0.5 (4%)^2 = 0.5 16 + 0.5 16 = 8 + 8 = 16

σ_Y = √16 = 4%

The coefficient of variation (CV) is a normalized measure of risk per unit of return, calculated as:

CV = Standard deviation / Expected return

For Investment X: CV_X = 1.96% / 10.4% ≈ 0.189

For Investment Y: CV_Y = 4% / 11.0% ≈ 0.364

The investment with the lower CV, i.e., Investment X, is preferred due to its lower risk per unit of return.

Applying the Capital Asset Pricing Model (CAPM)

The second part involves calculating the required rate of return and beta for different companies and stocks using CAPM:

Required Rate of Return = Risk-Free Rate + (Beta * Market Risk Premium)

Given:

• Beta = 1.8, Risk-Free Rate = 7%, Market Risk Premium = 11%

Required Rate of Return = 7% + (1.8 * 11%) = 7% + 19.8% = 26.8%

This indicates the expected return demanded by investors for a company with a beta of 1.8, reflecting high volatility relative to the market.

For the second case:

• Required Rate of Return = 12%, Risk-Free Rate = 4%, Market Return = 11.5%

Rearranging the CAPM formula to find beta:

Beta = (Required Rate of Return - Risk-Free Rate) / Market Risk Premium

Market Risk Premium = Market Return − Risk-Free Rate = 11.5% - 4% = 7.5%

Beta = (12% - 4%) / 7.5% ≈ 8% / 7.5% ≈ 1.07

Lastly, for a stock with a beta of 0.85, the required rate of return is:

Required Rate = 5.50% + (0.85 * 4%) = 5.50% + 3.4% = 8.9%

This implies a relatively lower expected return in line with less market-related risk.

Financial Evaluation of Projects

The third part assesses two projects based on cash flows, calculating payback period, NPV, and IRR to determine their viability and appropriateness as mutually exclusive or independent investments.

Suppose Project A has initial investment of $100,000 with cash inflows of $30,000 annually over 5 years, and Project B has an initial investment of $100,000 with cash inflows of $20,000 in Year 1, $40,000 in Year 2, $30,000 in Year 3, and $50,000 in Year 4. The discount rate for both is 11.5%.

The payback period indicates how soon the initial investment is recovered. For Project A, the cumulative cash flow reaches $100,000 after approximately 3.33 years, calculated by dividing the remaining balance after 3 years ($10,000) by the cash inflow of Year 4. For Project B, cumulative cash flows accumulate over years, reaching the payback point in approximately 3 years when the cumulative cash inflows equal the initial investment.

NPV is calculated by discounting each cash flow to its present value and summing these amounts, subtracting the initial investment. Using the discount rate of 11.5%, the NPVs of both projects can be compared: Project A's NPV is positive, approximately $15,000, indicating profitability. Project B's NPV also is positive, roughly $10,500, suggesting acceptance.

IRR finds the discount rate that yields a zero NPV; calculations for both projects show IRRs exceeding the discount rate, affirming their desirability.

For mutually exclusive projects, the one with the higher NPV and IRR should be selected, assuming identical risk profiles. For independent projects, both can be undertaken if they meet the acceptance criteria.

In summary, these financial metrics guide decision-makers in selecting projects that maximize value and align with strategic goals, considering their cash flow timings, profitability, and risk.

Conclusion

This comprehensive analysis highlights the importance of statistical measures such as expected return, standard deviation, and coefficient of variation in evaluating securities. The application of CAPM aids in understanding required returns based on risk profiles, and the project evaluation metrics—payback period, NPV, and IRR—facilitate informed investment decisions. Effective integration of these tools enables investors and managers to optimize portfolio performance, balance risk and return, and ensure sound financial planning.

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