Problem Set (50 marks)

[This problem set contributes 25% to your overall mark in this course.]

[You should answer all the questions.]

Question 1 – Investment Evaluation (15 marks)

Rust Industrial Systems Company is trying to decide between two different projects.

a. Project A requires an initial investment of $320,000 in equipment, has a four-year life, and generates earnings before interest & tax (EBIT) of $110,000 per year.

b. Project B costs an initial investment of $450,000 in equipment, has a six-year life, and generates earnings before interest & tax (EBIT) of $100,000 per year

Equipment in both projects are to be depreciated straight-line to zero over their lives and will have zero salvage value. Both projects will require additional investment in working capital of $25,000, which will be recovered at the end of the project (year 4 for Project A and year 6 for Project B). The interest expense will be $10,000 per year.

If the tax rate is 21 percent and the discount rate is 8 percent, which project should the firm choose?

Question 2- Investment Evaluation (15 marks)

A company is evaluating whether to replace its existing production machine with a newer, more efficient model. The new machine costs $1.2 million and will be depreciated straight-line to zero over its six-year life. It is expected to be worth about $150,000 at the end of six years.

The old machine is being depreciated at a rate of $150,000 per year with current book value of $450,000 (fully depreciated in three years). The old machine can be sold now for $300,000, but in two years, it will likely have a resale value of $100,000. The new machine is expected to reduce annual operating costs by $250,000. The company’s tax rate is 25%, and the discount rate is 10%. If the company does not replace the machine now, it will have to replace it in two years. Should the company replace it now or wait? (Hint: This is a choice between “investing” in keeping the old machine or investing in the new one. Note that the two options have unequal lives.)

Question 3 (10 marks)

The following table outlines the information for 3 risky assets. Assume the correlation between the returns on assets A and B is 0.6, the correlation between the returns on assets A and C is 0.2 and the correlation between the returns on assets B and C is -0.8. The risk-free rate is 2%

a. If you are considering an equally weighted portfolio of B and C, calculate the portfolio’s expected rate of return and standard deviation of rates of return. (4 marks)

b. If you are considering an equally weighted portfolio of A, B and C, calculate the portfolio’s expected rate of return and standard deviation of rates of return. (4 marks)

c. The investor must develop a complete portfolio by combining the risk-free asset with one of the risky assets. Which risky asset will be preferred? (2 marks)

Question 4 (10 marks)

The following table outlines the information for 2 risky assets. Assume the correlation between the returns on assets A and B is perfect negative (i.e. coefficient ρ = -1).

a. Determine the proportions of a portfolio to be made up of A and B such that this portfolio is risk free. (3 marks)

b. How should we allocate capital between Asset A and Asset B in order to construct a portfolio with a standard deviation of return equal to 4%? (7 marks)

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