ACC 371 Midterm Examination #2 Friday July 5, 2002 K. Vetzal Name: Student Number: Section Number: Duration: 2 hours Instructions: 1. Answer all questions in the space provided. 2. Show all of your calculations. 3. The examination has 11 pages (not including this cover page). Verify that your copy is complete. 4. Materials allowed: calculator. 5. Provide final answers relating to percentage rates to four decimal places (e.g. 6.48% or.0648). Provide final answers involving dollar amounts to two decimal places (e.g. $124.17). 6. To have your exam considered for re-grading, the exam must be written in ink. Mark Distribution 1. /25 2. /10 3. /20 4. /10 5. /20 6. /15 Total: /100
1 Question 1: 25 marks. Each of parts a)-e) is worth 5 marks. a) (5 marks) Barnett Company is investigating whether to buy a new machine to produce bubble gum wrappers. The firm has forecast that it will be able to sell a package of 50,000 wrappers for a price of $250. It is also expecting that unit variable cost (for each package of 50,000 wrappers) will be $170. The firm has a corporate tax rate of 40%. The machine will be depreciated for tax purposes using straight line depreciation in the amount of $70,000 per year. i) If the accounting break-even point for the machine is 5,400 packages, what are the fixed costs associated with the machine? ii) If the firm can sell 6,750 packages per year, what will be its net profit per year? b) (5 marks) You are given the following data for three stocks, X, Y, and Z: Stock X Stock Y Stock Z Share price, period 0 $19.25 $12.50 $27.00 Share price, period 1 $17.75 $15.00 $29.25 Number of shares outstanding, period 0 10 million 35 million 2.5 million Number of shares outstanding, period 1 10 million 35 million 2.5 million Calculate the rate of return from period 0 to period 1 for both a value-weighted and an (arithmetically averaged) equal-weighted index of these three stocks.
2 c) (5 marks) Stocks A and B have the following expected returns and standard deviations of returns: Stock A Stock B Expected return 14% 21% Standard deviation 15% 26% Doug has formed a portfolio with 30% of his money invested in A and 70% in B. i) What is the expected return of Doug s portfolio? ii) Without any further information, what can you say about the standard deviation of Doug s portfolio? (Hint: What is the lowest possible value of his portfolio standard deviation? What is the highest possible value?) d) (5 marks) Suppose that the standard deviation of the market portfolio s return is 25%. i) What is the standard deviation of a well-diversified portfolio with a β of 1.4? ii) What is the β of a well-diversified portfolio with a standard deviation of 18%? iii) What is the standard deviation of a well-diversified portfolio with a β of 0? iv) What can you say about the β of a poorly-diversified portfolio with a standard deviation of 25%?
3 e) (5 marks) Suppose that all stocks have a rate of return with a standard deviation of 40% and that the correlation between rates of returns for all pairs of stocks is 0.6. i) Consider forming an equally-weighted portfolio of 10 stocks. What is the standard deviation of this portfolio s return? ii) How many stocks would be required in an equally-weighted portfolio in order to have a portfolio standard deviation of 31%?
4 Question 2: 10 marks. a) (4 marks) Lakota Inc. is considering buying one of two machines. Machine A costs $100,000 initially and produces after tax net cash flows of $110,000 per year for two years, at which time has to be replaced. Machine B has an initial cost of $120,000. It produces after tax net cash flows of $115,000 per year for three years, at which time it must be replaced. Assume that the opportunity cost of capital is 10%. Which machine should be chosen? (Assume that the machines will be replaced as needed forever.) b) (6 marks) Suppose that the new machine (either A or B) will be used to replace an existing machine C which was purchased four years ago for $180,000. This machine will last at most for another three years, at which time it would have to be replaced. It will produce after tax net cash flows (excluding salvage value) of $75,000 after one year, $55,000 after two years, and $35,000 after three years. It can be salvaged today for $10,000, after one year for $8,000, after two years for $6,000, or after three years for $2,500. When should machine C be replaced?
5 Question 3: 20 marks. Your firm is evaluating an investment project. The project would require purchasing some manufacturing equipment today for $1,500,000. The equipment is in CCA class 8 (20%). It is the only class 8 asset that your firm will ever have. You have forecast that it will have a salvage value after 10 years of $1,800,000 (nominal). The equipment will produce pre-tax operating revenues of $275,000 (real) after one year. This amount will grow by 3% per year in real terms during years 2 through 10. Pre-tax operating expenses are expected to be $120,000 (real) after one year. This amount will grow by 7% per year in nominal terms until the end of year 10. The project will require an investment in working capital of $150,000 today. Half of this amount (i.e. $75,000 (nominal)) will be recovered after 5 years, and the remaining $75,000 (nominal) will be recovered after 10 years. The nominal discount rate is 11%, the corporate tax rate is 36%, and the expected inflation rate is 2.5% per year. What is the NPV of this investment project? (Note that the next page of the exam has been left blank so that you may continue your calculations on it.)
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7 Question 4: 10 marks. a) (6 marks) Suppose that you own an abandoned gold mine. You can resume production again immediately by paying start up costs of $750,000. If you do so, the mine will produce 10,000 ounces of gold per year over the next 5 years. The price of gold is expected to remain constant (in real terms) at $300 per ounce during that time. The real opportunity cost of capital is 4%. Ignore any taxes. During the first year of operation, extraction costs are expected to be $250 per ounce, in real terms. At the end of the first year, there is a 60% chance that these costs will increase to $275 per ounce (in real terms), and there is a 40% chance that these costs will increase to $335 per ounce (in real terms). The extraction costs will remain constant at the new level (i.e. either $275 per ounce or $335 per ounce) until the end of year 5. Should you resume production? Assume that this decision is irreversible, i.e. if you decide to resume production, you are committed to operating the mine for the next 5 years. b) (4 marks) Assume instead that you can abandon the operation by paying a cost of shutting down the mine of $200,000 after the first year, once the new level of extraction costs is known. Should you resume production now? What is the value of your option to abandon production?
8 Question 5: 20 marks. Assume that the CAPM holds exactly throughout this question. You are given the following information about the three possible future states of the economy and the returns on stock X and the market portfolio M: Return on Return on Market State Probability Stock X Portfolio M 1.20-10% -5% 2.45 12% 9% 3.35 28% 18% a) (4 marks) Calculate the expected returns on stock X and the market portfolio M. b) (4 marks) Calculate the standard deviation of returns for the market portfolio M.
9 c) (5 marks) Calculate the β for stock X. d) (3 marks) Calculate the value of the risk free interest rate R f. e) (4 marks) Suppose there is another stock Z which has an expected return of 7%. If an investor constructs a portfolio by putting 25% of her money in the risk free asset, 25% in the market portfolio, 25% in stock X, and 25% in stock Z, what is the expected return and β of her portfolio?
10 Question 6: 15 marks. Each of parts a)-c) is worth 5 marks. Assess whether each of the following statements is true, false, or uncertain. Justify your answer. All marks are based on the quality of your argument supporting your answer. a) (5 marks) If firms can deduct depreciation for tax purposes on a straight line basis, then the break-even sales point calculated on the basis of accounting income will be lower than the breakeven sales point calculated on a present value basis. (You may assume that all relevant variables such as unit sales price, unit variable costs, fixed costs, etc. are constant throughout the life of the project.) b) (5 marks) If a stock lies below the security market line, it is undervalued.
11 c) (5 marks) Suppose that there are two risky portfolios, A and B, available with the following expected returns and standard deviations of returns: Expected Standard Portfolio Return Deviation A 10% 10% B 15% 20% Further suppose that investors are allowed to invest in only one of these two risky assets, along with a risk free asset (i.e. they can either combine A with the risk free asset or B with the risk free asset, but they cannot invest in both A and B.) In this situation, no matter what the risk free interest rate is, no rational risk-averse investor would invest in portfolio A because B offers higher expected return and its higher risk can be offset through investing in the risk free asset.