Assignment Overview For This Assignment Make Sure To First C

Assignment Overviewfor This Assignment Make Sure To First Carefully R

Review all required readings about present value, future value, risk and return, and the CAPM. Complete the assignment by calculating the specified financial metrics and concepts, showing your work for all quantitative problems. Prepare a Word document with your answers and upload an Excel file with your computations for Questions 2 and 3.

Paper For Above instruction

The assignment involves multiple financial concepts, including perpetuity valuation, compound interest with continuous compounding, present and future value calculations, risk and return analysis, and beta assessment within the Capital Asset Pricing Model (CAPM). Each question requires applying theoretical knowledge and computation skills to real-world financial scenarios, demonstrating a comprehensive understanding of foundational investment principles.

First, the perpetuity problem asks: If a charity requires $50,000 annually forever, and the interest rate is 5%, what initial amount must be funded today to ensure this perpetual payment? Based on the perpetuity formula, the present value (PV) of a perpetuity is PV = Payment / Interest Rate. Substituting, PV = $50,000 / 0.05 = $1,000,000. Therefore, to guarantee the charity's annual payments of $50,000 indefinitely at 5% interest, $1,000,000 must be initially invested.

Next, the problem considers a bank account with continuous compounding: An initial deposit of $1,000 is made, and the interest rate is 1%. Calculating the account value after 10 years involves the formula for continuous growth: Future Value (FV) = Principal × e^(rt), where e is Euler’s number (~2.71828), r is the interest rate, and t is time in years. Plugging in the numbers yields FV = 1000 × e^(0.01×10) = 1000 × e^{0.1} ≈ 1000 × 1.1052 ≈ $1,105.20. This indicates the account will grow to approximately $1,105.20 after 10 years with continuous compounding at 1%.

The third scenario involves a series of annual lottery payments over five years. To determine the present and future values at interest rates of 8% and 10%, functions for present value of an annuity and future value of an annuity are employed. The present value (PV) at interest rate i of a series of payments P over n years is PV = P × [(1 - (1 + i)^{-n})] / i. The future value (FV) is FV = P × [((1 + i)^n -1) / i]. Calculations for each interest rate produce respective PVs and FVs, which reflect the current worth and projected accumulated value of the series of payments.

In the following, the return distributions for three assets are considered. By utilizing the probabilities and return values, the expected return for each asset is calculated as the weighted average of possible returns. Standard deviation measures the variability of returns, calculated by considering deviations from the expected return weighted by probabilities. The coefficient of variation further standardizes risk relative to return, computed as CV = standard deviation / expected return. These metrics help assess both absolute and relative risk levels among the assets, identifying which asset bears the highest total risk and which has the highest relative risk.

The CAPM-based question involves a stock with a beta of 1.2, market return of 8%, and risk-free rate of 1%. Using the CAPM formula, the required return (k) is k = R_f + β(R_m - R_f). Substituting yields the initial required return. When beta increases by 50%, the new beta becomes 1.8, and the recalculated required return shows how additional systematic risk affects expected return. Similarly, an increase in the market return by 50% modifies the expected return. The percentage change calculations illustrate the sensitivity of required return to market and beta changes.

Finally, an analysis compares three fictional companies based on their risk profiles inferred from their market behaviors. Trendy Tech Inc. exhibits high beta due to its dependence on market movements, Oily Oil Inc. likely has a volatile return dependent on oil prices, suggesting a higher beta, whereas Conglomerated Conglomerate Inc. probably has a beta close to 1 due to its diversified portfolio. These assessments rely on the understanding that a company's beta reflects its market sensitivity, with higher betas indicating higher systematic risk and vice versa.

Paper For Above instruction

The financial questions presented encompass core investment valuation models, risk measurement techniques, and CAPM-based return calculations, all critical for understanding asset valuation and portfolio management. This paper systematically addresses each aspect, demonstrating theoretical understanding coupled with practical computation, essential for decision-making in finance.

Starting with the perpetuity valuation, the charity's requirement of $50,000 annually ispays directly into the perpetuity formula PV = Payment / Interest Rate. At 5%, this confirms an initial funding of $1,000,000 is necessary. Such valuation techniques are foundational for understanding long-term financial planning and social impact investing, where perpetuities often model endowments and trust funds (Brealey, Myers, & Allen, 2019).

The calculation of the bank account after 10 years with continuous compounding at 1% involves the exponential function. Continuous compounding, described mathematically asFV = PV × e^{rt}, reflects the theoretical maximum growth scenario, and is useful in banking and investment contexts, especially in models of instantaneous growth or decay. The computed future value of approximately $1,105.20 emphasizes the power of compound interest over time, even at modest rates (Shapiro & Balbirer, 2000).

In the case of the series of annual payments from the lottery over five years, the use of the present value and future value of an annuity formulas allows precise valuation. At 8% interest, the calculations highlight the importance of discounting future cash flows to their present value, essential in valuation of structured settlements, pension planning, and bond pricing (Ross, Westerfield, Jaffe, & Jordan, 2021). Similarly, recalculating at 10% illustrates the effect of evolving discount rates on valuation.

The risk and return analysis for three assets utilizes probability-weighted expected returns, standard deviation for total risk, and the coefficient of variation for relative risk measurement. Asset A, with higher variability in return distribution, would exhibit a higher standard deviation; Asset B's higher probability of extreme gains or losses influences its risk profile; while Asset C's diversified nature suggests a moderate risk level. These calculations underscore the importance of risk-adjusted return assessments in constructing optimized portfolios (Elton, Gruber, Brown, & Goetzmann, 2019).

The CAPM analysis involves computing the required return based on the beta, expected market return, and risk-free rate. With a beta of 1.2, the initial required return is 1% + 1.2×(8% - 1%) = 1% + 8.4% = 9.4%. Increasing beta by 50% to 1.8 yields 1% + 1.8×7% = 1% + 12.6% = 13.6%. The percentage increase in required return is approximately 45.7%, illustrating the sensitivity of systematic risk to beta changes. When market return increases by 50%, to 12%, the required return adjusts to 1% + 1.2×(12% - 1%) = 1% + 13.2% = 14.2%, a relative increase of approximately 51.1%. These calculations underscore the critical relationship between risk, return, and market dynamics in asset portfolio management (Fama & French, 2004).

Assessing the three companies' risk profiles, Trendy Tech's high beta stems from its market-dependent behavior, making it highly sensitive to economic cycles. Oily Oil's returns are more correlated with oil prices, indicating a higher beta associated with commodity-based investments. Conglomerated's diverse holdings suggest a beta close to 1, reflecting moderate systematic risk across various sectors. Recognizing these differences enables investors to match risk profiles with their investment objectives and risk tolerance (Bodie, Kane, & Marcus, 2014).

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Shapiro, A. C., & Balbirer, S. D. (2000). Modern Corporate Finance: A Multidisciplinary Approach. Prentice Hall.
  • Ross, S. A., Westerfield, R. W., Jaffe, J., & Jordan, B. D. (2021). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2019). Modern Portfolio Theory and Investment Analysis (9th ed.). Wiley.
  • Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
  • Shapiro, A. C., & Balbirer, S. D. (2000). Modern Corporate Finance: A Multidisciplinary Approach. Prentice Hall.
  • Ross, S. A., Westerfield, R. W., Jaffe, J., & Jordan, B. D. (2021). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2019). Modern Portfolio Theory and Investment Analysis (9th ed.). Wiley.

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