Practice Questions on Portfolio Theory and Capital Budgeting

Portfolio Theory

1: Portfolio Theory (10 Points)

You invest 60% of your financial assets in the Standard & Poor’s Depository Receipts (SPY) and 40% in the MSCI EAFE Index Fund (EFA). SPY has an expected return of 7% and a standard deviation of 16%. EFA has an expected return of 8% and a standard deviation of 18%. The correlation between the two investments is 80%. The risk-free rate is 2%.

a. Briefly explain the investment strategies of SPY and EFA. (2 Point)

b. What are the expected return, the standard deviation, and the Sharpe ratio of your portfolio? Show the mathematical equations that you use to derive these measures. (4 Points)

c. Which portfolio of SPY and EFA has the highest Sharpe ratio? (4 Points)

2: Capital Budgeting (15 Points)

Tito’s Handmade Vodka of Austin is considering expanding its production capacity by purchasing new distilling equipment. The firm has just completed a $10,000 feasibility study to analyze the decision to buy the equipment, resulting in the following estimates:

Capital Expenditures: The cost of the distilling equipment is $100,000 and needs to be paid immediately (i.e., year 0). The equipment will last for ten years. The firm expects to
recover a salvage value of $10,000 in year 10 (i.e., 10 years from now).

Marketing: Once the equipment is operating in year 1, the extra capacity is expected to generate $100,000 in additional sales in each of the subsequent ten years (i.e., year 1, year 2, …, year 10).

Operations: The disruption caused by the installation will decrease sales revenues by $20,000 in year 0. The costs of goods (COGS) sold are 60% of their sales revenues. The increased production will require additional inventory on hand of $20,000 to be added in year 0. You will continue to need the inventory of $20,000 until year 9 and it will be fully recovered in year 10 (i.e., the required inventory will be zero in year 10). The firm expects receivables to be 20% of revenues and payables to be 10% of the COGS.

Human Resources: The expansion will require additional sales and administrative costs of $10,000 per year from year 1 through year 10.

Accounting: The equipment will be depreciated equally every year over the 10-year life of the equipment. Thus, the book value after depreciation in year 10 will be zero. Tito’s marginal corporate tax rate is 20% and Tito expects to remain highly profitable in the foreseeable future.

a. Compute the NPV, the IRR, and the SIMPLE PAYBACK of the project. Use a discount rate of 12% (12 Points).

b. In the base case scenario, you assume annual additional sales between year 1 and year 10 to be equal to $100,000. At which annual additional sales does the project just break even (Hint: Use Solver in Excel)? (3 Points)

i. Base-Case Scenario

ii. Break-Even Sales