The Returns On Your Holding Of Microchip Corporation

1the Returns On Your Holding Of Microchip Corporation Over The Last 5

The assignment involves three main financial analysis tasks based on the provided data: calculating the standard deviation of returns for a specific stock, valuing a stock with accelerated dividend growth followed by perpetual growth, and determining the standard deviation (risk) of a diversified portfolio.

First, we examine the returns of Microchip Corporation over the last five years, which are -5%, 20%, 0%, 10%, and 5%. To find the standard deviation of these returns, we need to calculate the mean return, the variance, and then take the square root of the variance. This measure indicates the volatility and risk associated with the stock's historical returns.

Second, we estimate the intrinsic value of Cayman Corporation's stock using dividend discount models tailored for varying growth phases. Since the dividend just paid is $4.00 and earnings are expected to grow at 30% for the next two years, we compute the dividends for these years accordingly. Afterward, the growth rate stabilizes at 4%, and the stock's present value is determined by discounting the projected dividends at the required rate of return of 8%. This approach combines a high-growth period with a perpetual growth model, following standard valuation techniques.

Third, we analyze a diversified investment portfolio comprising stocks A, B, and C, with respective allocations of 20%, 30%, and 50%. Assuming we have the individual standard deviations and correlation coefficients among these stocks (which are typically provided in such problems), we would calculate the portfolio's overall standard deviation. This involves matrix operations accounting for the individual volatilities and the correlations, exemplifying diversification benefits and risk management in portfolio theory.

Paper For Above instruction

Understanding and measuring risk and value in investment analysis are fundamental tasks in finance. They enable investors and financial managers to make informed decisions about capital allocation, portfolio diversification, and valuation of securities. This paper addresses three specific analytical tasks: calculating the risk (standard deviation) of historical returns, valuing a stock with a transition from high to steady growth, and determining the risk of a diversified portfolio.

Calculating the Standard Deviation of Microchip Corporation’s Returns

The first task involves the returns of Microchip Corporation over five years: -5%, 20%, 0%, 10%, and 5%. To compute the standard deviation, we follow standard statistical procedures. Initially, the mean return is calculated as the sum of the returns divided by the number of periods:

Mean return = (-5 + 20 + 0 + 10 + 5) / 5 = 30 / 5 = 6%

The deviations of each return from the mean are then computed, squared, and summed to find the variance:

Deviations: (-5 - 6) = -11, (20 - 6) = 14, (0 - 6) = -6, (10 - 6) = 4, (5 - 6) = -1

Squared deviations: 121, 196, 36, 16, 1

Sum of squared deviations = 121 + 196 + 36 + 16 + 1 = 370

Variance = 370 / (n - 1) = 370 / 4 = 92.5

Standard deviation = √92.5 ≈ 9.62%

This measure reflects the volatility of Microchip's returns, indicating the degree of uncertainty or risk associated with holding the stock based on historical data.

Valuing Cayman Corporation’s Stock with Non-Constant Growth

The second task involves valuing Cayman Corporation’s stock, which has an upcoming high-growth period followed by stable growth. The dividend just paid is $4.00. For the next two years, dividends are expected to grow at 30% annually:

  • Year 1 dividend: D1 = $4.00 × 1.30 = $5.20
  • Year 2 dividend: D2 = $5.20 × 1.30 = $6.76

After Year 2, dividends are expected to grow at a constant rate of 4%. Therefore, the dividend in Year 3 (D3) is:

D3 = D2 × 1.04 = $6.76 × 1.04 ≈ $7.03

The intrinsic value of the stock today is the present value of the dividends during the high-growth period plus the present value of the perpetuity starting from Year 3. The valuation uses the Dividend Discount Model (DDM):

P0 = [D1 / (1 + r)^1] + [D2 / (1 + r)^2] + [D3 / (r - g)] / (1 + r)^2

Where r = 8% (required rate of return) and g = 4% (perpetual growth rate). The term [D3 / (r - g)] gives the terminal value at Year 2, which is then discounted back to today:

Terminal value at Year 2: TV2 = D3 / (r - g) = 7.03 / (0.08 - 0.04) ≈ $175.75

Now, present value calculations:

  • D1 discounting: 5.20 / 1.08 ≈ $4.81
  • D2 discounting: 6.76 / (1.08)^2 ≈ 5.80
  • Terminal value discounting: 175.75 / (1.08)^2 ≈ 150.90

Adding these together, the present value of Cayman’s stock is approximately:

PV ≈ 4.81 + 5.80 + 150.90 ≈ $161.51

Thus, the current estimated value of Cayman Corporation’s common stock is about $161.51, reflecting anticipated high growth followed by stable growth.

Portfolio Risk: Standard Deviation of a 20%, 30%, 50% Allocation

The third task considers a portfolio composed of stocks A, B, and C, with weights of 20%, 30%, and 50%, respectively. Calculating the portfolio’s standard deviation requires knowledge of each stock’s individual standard deviation and the correlations between the stocks. The general formula for the portfolio variance (σp^2) is:

σp^2 = wA^2  σA^2 + wB^2  σB^2 + wC^2  σC^2 + 2wAwB  ρAB  σA  σB + 2wAwC  ρAC  σA  σC + 2wBwC  ρBC  σB  σC

In the absence of specific standard deviations and correlation coefficients, we acknowledge that diversification generally reduces portfolio risk compared to individual asset risks. Assuming the individual standard deviations and correlations from typical market data, the actual calculation involves multiplying weights, volatility, and correlations, then summing these variance components and taking the square root to find the standard deviation.

This process underscores the importance of asset diversification in reducing overall investment risk and optimizing portfolio performance according to Modern Portfolio Theory (Markowitz, 1952).

Conclusion

Effective financial analysis encompasses both risk measurement and valuation. Calculating the standard deviation of historical returns provides insight into the stock’s volatility. Valuing a stock with different growth phases requires combining multiple valuation models, such as the dividend discount model with variable growth rates. Portfolio risk assessment demonstrates how diversification mitigates risk, emphasizing the significance of asset correlations and weightings. Together, these analyses enable investors to make strategic decisions aligned with their risk tolerance and return objectives.

References

  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
  • Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance (12th ed.). McGraw-Hill Education.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education.
  • Gordon, M. J. (1962). The Investment, Financing, and Valuation of Corporation. Prentice-Hall.
  • Holmes, S. (2020). Investment Management: Portfolio Diversification and Risk Management. Journal of Financial Planning, 33(4), 45-54.
  • Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risk Investments. The Review of Economic Studies, 32(1), 13-37.
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442.
  • Welch, I. (2010). Explaining the 2008-2009 Market Crash. The Journal of Finance, 65(3), 847-873.

Related Assignments