Mutually exclusive investments

SOLUTION AT My Australian Academy

Question 1
Consider the following mutually exclusive investments

T=0 1 2 3

Project X: -150 30 60 120Project Y: -150 110 30 60
a. Find IRRs for both projects.b. Find the cross over rate. Show the formula you need to use (in symbols) and with numbers plugged in.c. Draw a graph (NPV schedule), where you will show the NPV of each project as a function of its discount rate (i.e., NPV on the vertical axis and r on the horizontal axis). Both NPVs should be on the same graph.d. Please describe as fully as possible which project is the best and under which circumstances.
Question 2Lupace Corporation is planning to produce a grading machine for use in finance courses around the globe. Market research data indicate that the company will be able to sell 10,000 grading machines per year at $1,500 each for the next 6 years, after which the new model will have to be developed. The product will be produced in a section of an existing factory that is currently not in use. To produce grading machines, Lupace must invest in acquiring specialized equipment that costs $1,000,000. This equipment has an expected life of ten years. After six years, the equipment could be sold for $30,000. Lupace will depreciate the equipment over ten years using the straight-line method. In addition to the cost of the equipment, the company will incur annual incremental manufacturing costs of $370,000 for component parts, $500,000 for direct labor, and $200,000 of miscellaneous costs. Lupace has a tax rate of 20 percent, and the company’s required rate of return is 15 percent.a. Compute the Net Present Value of this project.b. Should Lupace make the investment required to produce these grading machines?
Question 3
The standard deviation of returns on ABC Corporation is 25% per year. The correlation coefficient between returns on ABC and the returns on the market portfolio is 0.65. The risk free rate is currently equal to 1% and the expected return on the market portfolio is 10%. The standard deviation of the market portfolio is 15%.a. Calculate ABC’s cost of equity using the capital asset pricing model (CAPM).b. Assuming a 21% tax rate, calculate ABC’s weighted average cost of capital. The ABC Corporation can borrow at 7%. The debt constitutes 40% of its assets.
Question 4
One year ago, your company purchased a 3D printer for $110,000. You have learned that a new, much better machine is available for $150,000. In will be depreciated on a straight-line basis and has no salvage value. You expect this new printer to produce $60,000 per year in revenue and cost $20,000 per year to operate for the next ten years. The current printer is expected to produce $40,000 per year in revenue and also costs $20,000 per year to operate. The current machine’s depreciation expense is $10,000 per year for the next 10 years, after which it will be discarded. It will have no salvage value. The market value of the current machine today is $50,000. Your company’s tax rate is 21% and the opportunity cost of capital is 10%. Should your company replace its year-old printer?
Question 5
You are considering investing in Microsoft stock. From Bloomberg, you download information on its beta coefficient, which is equal to 2. The risk free rate is currently 2% and the return on the S&P 500 index (which you use as a proxy for the market portfolio) is 15%. You estimate that Microsoft’s dividends are expected to grow at 5% per year.
a. What is the return on equity for Microsoft?b. If the standard deviation of returns on Microsoft is 40% per annum and the standard deviation of the S&P 500 is 20%, what is the correlation coefficient between returns on Microsoft and returns on S&P 500 index?c. What price should you pay for this stock, if it just paid $2 per share dividend?
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