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1- The parents of a newborn girl decide to place $10,000 in a bank today with the aim of forming a fund to finance her education.
a) If the interest rate earned on the deposit were 6% per year, compounded every 30 days, how much money will the girl have when she is 12 years old and starts high school? Assume a year of 365 days.
b) How much will she have in 17 years, when she starts college?
2- A company has financial surpluses for 60 days and you must determine the best of the following investment alternatives.
a) Fixed term of 40 days, with TNA interest of 10% with capitalization every 40 days.
b) For the first 30 days TNA interest of 10% with capitalization every 30 days. for the remaining 30, an effective rate of 2% for 45-day operations.
c) Purchase of public titles at $65 with 1% of purchase expenses. See estimated sale in 60 days at $70 with 0.5% cough expense.
1- Suppose that the risk-free rate is 5% and the expected return of the market portfolio is 15%. If a common stock has a Beta of 0.60, what is its expected return according to the CAPM? If another common stock has an expected return of 15%, what must its beta be?
2-The risk-free interest rate is 5% and the expected return of the market portfolio is 12%. Assuming that the CAPM hypotheses are met:
a) What is the market risk premium?
b) What is the required return on an investment with a Beta of 1.5?
c) If a stock has a Beta=1 and offers an expected return of 10%, is it overvalued?
d) Draw a graph showing how the expected return varies with Beta.
3- An American Treasury bond offers a yield of 5%. A common stock has a Beta of 0.70 and an expected return of 12%.
a) What is the expected return of a portfolio made up of equal investments in these two assets?
b) If a portfolio made up of these two assets has an expected return of 15%, what is its Beta?
c) If a portfolio made up of these two assets has a Beta of 1.20, what are the weighting factors? How is the weight factor for the risk-free asset interpreted?
8- The Caracol company is contemplating the possibility of issuing shares to finance an expansion project. Caracol’s financial analysts have determined that the project has the same risk as the market portfolio, since it has an expected return of 15% and the risk-free rate is 5%. The yield of the project is estimated at 20%. The project will go ahead unless:
a) The Beta of the company is greater than 1.5.
b) The Beta of the company is less than 1.5.
c) Whatever the Beta of the company, because what matters is the Beta of the project
In this essay, we will explore and provide solutions to various financial and investment-related problems presented in the homework assignment.
a) To calculate the future value of the deposit compounded every 30 days, we can use the formula for compound interest:
��=�×(1+��)��
Where:
Plugging in these values, we get:
��=10000×(1+0.0612)12×12≈$18,347.75
Therefore, the girl will have approximately $18,347.75 when she starts high school.
b) Similarly, for 17 years, we have:
��=10000×(1+0.0612)12×17≈$31,058.76
Thus, she will have approximately $31,058.76 when she starts college.
Among the given investment alternatives:
a) The effective annual rate for this option would be ���=(1+0.11)1−1=0.1 or 10%.
b) The effective annual rate for the combination of these two periods would be:
���=(1+0.11)1×(1+0.021)1−1=0.126 or 12.6%.
c) The profit from this option would be 70−65−0.01×65=4.35.
Where:
Plugging in these values, we get �(�)=0.05+0.60×(0.15−0.05)=0.11 or 11%.
�=�(�)−���(��)−��=0.15−0.050.15−0.05=1
a) The expected return of a portfolio with equal investments in the two assets can be calculated as the weighted average of their expected returns:
�(��)=�1�(�1)+�2�(�2)
Where �1 and �2 are the weighting factors for the investments.
b) To calculate the Beta of a portfolio, use the following formula:
��=�1�1+�2�2
c) To find the weighting factors when the portfolio has a Beta of 1.20:
1.20=�1×0.70+�2×�2
The weight factor for the risk-free asset is interpreted as the proportion of the portfolio’s total investment allocated to a risk-free investment.
Given the expected return of the market portfolio is 15%, and the risk-free rate is 5%, the project’s expected return is 20%, exceeding the market’s expected return. This suggests that the project has an attractive potential.
a) The decision whether the project goes ahead or not is determined by the project’s Beta. If the Beta of the company is greater than 1.5, it indicates higher risk compared to the market, and the project may not proceed. Conversely, if the Beta is less than 1.5, the project is relatively less risky and might proceed. However, the Beta of the project itself matters most in this scenario, as the project’s riskiness aligns with the market’s.
In conclusion, these problems cover various aspects of financial and investment analysis, including time-value of money, compounding interest, CAPM, portfolio analysis, and project evaluation. By applying these concepts, we can make informed decisions regarding investment opportunities and risk management.
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