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1. Using the data in the following table, calculate the return for investing in Boeing stock (BA) from January 2, 2008, to January 2, 2009, and also from January 3, 2011, to January 3, 2012. Historical Stock and Dividend Data for Boeing Date Price Dividend Date Price Dividend 1/2/2008 86.62 1/3/2011 66.40 2/6/2008 79.91 0.40 2/9/2011 72.63 0.42 5/7/2008 84.55 0.40 5/11/2011 79.08 0.42 8/6/2008 65.40 0.40 8/10/2011 57.41 0.42 11/5/2008 49.55 0.40 11/8/2011 66.65 0.42 1/2/2009 45.25 1/3/2012 74.22 2. Identify each of the following risks as most likely to be systematic risk or unsystematic risk, provide brief explanation of why the risk is likely systematic/unsystematic : a. The risk that your main production plant is shut down due to a tornado. b. The risk that the economy slows, decreasing demand for your firm’s products. c. The risk that your b est employees will be hired away. d. The risk that the new product you expect your R&D division to produce will not materialize. e. The risk that there may be a World War III in the coming year leading to shut down of global financial markets during the period of war f. The risk that the Federal Reserve announces immediate shut down of all the stimulus packages and bond buying programs (that is, there shall be no more financial market intervention by the Fed, and it will concentrate on just setting the short term interest rate s) 3 . Consider two assets: Core and More. Next year, 2021, there are 4 possible globally important scenarios a. World War III - Global economy already reeling from the pandemic comes to a grinding halt. Assume that there i s 20% chance that this may happen.b. Corona Over – In January, a potent and effective cure for Corona is discovered and the pandemic is over, with cities, countries, borders and trade slowly picking up again and life returns to normal by Spring. Assume that there is 40% chance that this may happen c. Same old – The pandemic continues till Summer; markets keep on performing as they have in 2020. Assume that there is 30% chance that this may happen d. All’s well – By Thanksgiving 2020, the pandemic is over, and life returns to normal by Christmas 2020. Assume that there is 10% chance that this may happen Use the return information below Scenario Core Return More Return WWIII - 20% 1% Corona Over 10% 15% Same Old 7.5% - 3% All’s Well 10% 20% Calculate the following:
a) Calculate the expected return of each asset b) Calculate the variance and volatility of each asset c) Calculate the covariance and correlation of returns between the assets 4 . C alculate the expected return and the volatility (standard deviation) of a portfolio consisting of Johnson & Johnson’s and Walgreens’ stocks using a wide range of portfolio weights in increments of 5% Plot the expected return as a function of the portfolio volatility.
Correlation is 0.22. Using your graph, identify the range of Johnson & Johnson’s portfolio weights that yield efficient combinations of the two stocks, rounded to the nearest percentage point5 . Arbor Systems and Gencore stocks both have a volatility of 40%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) + 1, (b) 0.50, (c) 0, (d) −0.50, and (e) −1.0. In which cases is the volatility lower than that of the original stocks? 6 . You are considering how to invest part of your retirement savings. You have decided to put $200,000 into three stocks: 50% of the money in Goldfinger (currently $25/share), 25% of the money in Moosehead (currently $80/share), and the remainder in Venture A ssociates (currently $2/share). If Goldfinger stock goes up to $30/share, Moosehead stock drops to $60/share, and Venture Associates stock rises to $3 per share, a. What is the new value of the portfolio?
b. What return did the portfolio earn?
c. If you do n’t buy or sell shares after the price change, what are your new portfolio weights?
7.
A hedge fund has created a portfolio using jus t two stocks. It has shorted $35,000,000 worth of Oracle stockand has purchased $85,000,000 of Intel stock. The correlation between Oracle’s and Intel’s returns is 0.65.
The expected returns and standard deviations of the two stocks are given in the table below, compute expected return and volatility of the portfolio. 8. Suppose you have $100,000 in cash, and you decide to borrow another $15,000 at a 4% interest rate to invest in the stock market. You invest the entire $115,000 in a portfolio J with a 15% expected return and a 25% volatility.
a. What is the expected return and volatility (standard deviation) of your investment?
b. What is your realized return if J goes up 25% over the year?
c. What return do you realize if J falls by 20% over the year?
9. Suppose Intel’s stock has an expected return of 26% and a volatility of 50%, while Coca - Cola’s has an expected return of 6% and volatility of 25%. If these two stocks were perfectly negatively correlated (i.e., their correlation coefficient is −1), a. Calculate the portfolio weights that remove all risk.
b. If there are no arbitrage opportunities, what is the risk - free rate of interest in this economy? In other wor ds, w hat is the expected return in p o rtfolio in part a. 10. Capital Budgeting Problem Vatsa Packaging is considering expanding its production capacity by purchasing a new machine, the MCC -750. The cost of the MCC -750 is $2.75 million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $50,000 feasibility study to analyze the decision to buy the MCC - 750, resulting in the following est imates: ■ Marketing: Once the MCC -750 is operating next year, the extra capacity is expected to generate $10 million per year in additional sales, which will continue for the 10 -year life of the machine. ■ Operations: The disruption caused by the install ation will decrease sales by $5 million this year. Once the machine is operating next year, the cost of goods for the products produced by the MCC -750 is expected to be 70% of their sale price. The increased production will require additional inventory on hand of $1 million to be added in year 0 and depleted in year 10. ■ Human Resources: The expansion will require additional sales and administrative personnel at a cost of $2 million per year. ■ Accounting: The MCC -750 will be depreciated via the straight -line method over the 10 -year life of the machine. The firm expects receivables from the new sales to be 15% of revenues and payables to be 10% of the cost of goods sold. Assume that cash requirements are 1.5 times the Accounts Receivable . Vatsa ’s m arginal corporate tax rate is 35 %. a. Determine the incremental earnings from the purchase of the MCC -750. b. Determine the free cash flow from the purchase of the MCC -750. c. If the appropriate cost of capital for the expansion is 1 2%, compute the NPV of the purchase. Extra Credit (2 Points) Extra credit shall be awarded only if all the three solutions to the subparts are logical, correct and supported by proper background work Using information from Question 10, answer the following additional questions to earn 2 points as extra credit a.
While the expected new sales will be $10 million per year from the expansion, estimates range from $8 million to $12 million. What is the NPV in the worst case? In the best case?
b. What is the break-even level of new sales from the expansion? What is the break-even level for the cost of goods sold? Hint - At break-even point NPV = 0 c. Vatsa could instead purchase the MCC-900, which offers even greater capacity. The cost of the MCC-900 is $4 million. The extra capacity would not be useful in the first two years of operation but would allow for additional sales in years 3–10. What level of additional sales (above the $10 million expected for the MCC-750) per year in those years would justify purchasing the larger machine?
