Finance 4000 Midterm 1 Sample Test Solutions
Suggested Solutions to Sample Midterm #1
Fi 4000—Fall 2014
Problem 1 (20 points)
Part A
Suppose Mike wants to prepare an amount of money today to support his son’s college education. He expects his son to enter a college in 16 years with annual tuition and expenses of $25,000 for 4 years. His first college tuition and expenses will due in exactly 16 years from now. Mike decides to put all the money that is required for his son’s college education today at a bank account earning rate of return of 8 percent per year, compounded annually. How much money must Mike set aside today? (10 points)
We can calculate the present value of the tuition payments as a discounted annuity:
Note that we discount the annuity by 15 periods since the first payment is in year 16.
Part B
Suppose that, instead of preparing a lump sum today, Mike will deposit a fixed amount of money every year for the next 12 years in the same bank account. The first deposit will start at the end of this year. How much amount must he deposit per year? (10 points)
Look for an annuity that will be equal to $26,103.01 in present value. Let S be the unknown amount of fixed annual savings.
Problem 2 (30 points)
Consider the following two stocks.
Stock BBT has an expected return of 19% and a standard deviation of 23%. Stock DIS has an expected return of 13% and standard deviation of 17%.The correlation coefficient between the returns of the two stocks is 0.3. The risk free rate of return is 8%.
An investor constructs an optimal risky portfolio with the two stocks BBT and DIS.
Let the optimal portfolio weights of DIS and BBT in the risky portfolio be 40% and 60%, respectively.
The investor decides to construct a complete portfolio with the optimal risky portfolio and risk free asset and decides to allocate 35% of the total investment in risk free asset and 65% of the total investment in the risky portfolio.
A. Compute the expected
Fi 4000—Fall 2014
Problem 1 (20 points)
Part A
Suppose Mike wants to prepare an amount of money today to support his son’s college education. He expects his son to enter a college in 16 years with annual tuition and expenses of $25,000 for 4 years. His first college tuition and expenses will due in exactly 16 years from now. Mike decides to put all the money that is required for his son’s college education today at a bank account earning rate of return of 8 percent per year, compounded annually. How much money must Mike set aside today? (10 points)
We can calculate the present value of the tuition payments as a discounted annuity:
Note that we discount the annuity by 15 periods since the first payment is in year 16.
Part B
Suppose that, instead of preparing a lump sum today, Mike will deposit a fixed amount of money every year for the next 12 years in the same bank account. The first deposit will start at the end of this year. How much amount must he deposit per year? (10 points)
Look for an annuity that will be equal to $26,103.01 in present value. Let S be the unknown amount of fixed annual savings.
Problem 2 (30 points)
Consider the following two stocks.
Stock BBT has an expected return of 19% and a standard deviation of 23%. Stock DIS has an expected return of 13% and standard deviation of 17%.The correlation coefficient between the returns of the two stocks is 0.3. The risk free rate of return is 8%.
An investor constructs an optimal risky portfolio with the two stocks BBT and DIS.
Let the optimal portfolio weights of DIS and BBT in the risky portfolio be 40% and 60%, respectively.
The investor decides to construct a complete portfolio with the optimal risky portfolio and risk free asset and decides to allocate 35% of the total investment in risk free asset and 65% of the total investment in the risky portfolio.
A. Compute the expected