- Portfolio Returns (35 points: A, 5 points; B‒D, 10 points)
Sam has decided to invest in a stock portfolio that invests 60% in the U.S. market and 40% in a global fund that excludes the United States. The correlation between the U.S. fund and global fund is +40%. The following table provides the expected return and standard deviation for the two investments.
| Fund | Expected Return | Standard Deviation |
| U.S. fund | 8% | 20% |
| Global fund | 10% | 25% |
- What is the expected return of the portfolio? Show calculations.
- What is the standard deviation of the 60/40 U.S./global portfolio? Show calculations.
- In a graph similar to the following, plot the opportunity set of investments if you are able to invest in only the U.S. fund and global fund and you are not able to short sell either fund. Carefully label the following points: (1) U.S. fund, (2) global fund, and (3) portion of the opportunity set that represents the efficient set with these two funds.
- If an investor is risk averse and is choosing an investment in only the U.S. fund and global fund, what portfolio would she select from the graph depicted in (C)? Explain.
- Capital Budgeting (40 points: A, 30 points; B, 10 points)
You have been hired as a consultant for Zulu widgets to advise on a production project. Zulu would use land for the facility that it bought three years ago for $1 million. Based on a recent appraisal, the company believes it could sell the land for $800,000 on an after-tax basis. In three years, the land could be sold for $900,000 after taxes. The company has hired a marketing firm, at a cost of $125,000, to analyze the widget market. The market report concludes:
With the brand name recognition that Zulu brings to bear, we feel that the company will be able to sell 3,200 widgets each year for the next three years. We feel that a premium price of $780 can be charged for each widget. Because widgets are a fad, we believe that sales should be discontinued after three years.
Zulu estimates fixed costs for the project will be $425,000 per year, and variable costs are 15% of sales. The equipment necessary for production will cost $4.2 million and will be depreciated straight line to zero over three years. At the end of the project, the equipment can be scrapped for $400,000. Net working capital of $120,000 will be required immediately and recaptured at the end of Year 3. Zulu has a 40% tax rate.
- Projecting Cash Flows
Estimate the cash flows for the project using a table format similar to the following.
**NOTE: You do not need to calculate the NPV; just project cash flows.**
| Item | 0 | 1 | 2 | 3 |
- If you were using the internal rate of return (IRR) rule to evaluate Zulu’s project, how would you do so?
- Use your cash flows from (A) to set up the formula that could be used to find the IRR. (No need to calculate the IRR.)
- Describe the two shortcomings of the IRR rule that we discussed in class and whether they would be relevant in the case of Zulu’s cash flows.
- WACC (40 points: A, 15 points; B, 10 points; C‒E, 5 points)
You are given the following information for Magi Inc.:
- The market risk premium is 8%.
- The risk-free rate of return is 1%.
- The firm has 90 million shares outstanding.
- The price per share is $57.
- The beta of the firm’s stock is 1.10.
- The firm has 4 million bonds outstanding with a $1,000 par value.
- The bonds have 20 years to maturity.
- The bonds make semiannual payments.
- The bonds are selling for 125% of par value.
- The bonds have a coupon rate of 7% (annual percentage rate (APR), paid semiannually).
- The bonds have a yield-to-maturity of 5%.
- The effective tax rate is 20%; the marginal tax rate is 35%.
- What is Magi’s after-tax weighted average cost of capital?
- How precisely estimated is Magi’s after-tax weighted cost of capital? Explain.
- If you were not given an estimate of Magi’s beta, how would you estimate it?
- If you were not given the risk-free rate of return, how would you estimate it?
- If you were not given the market risk premium, how would you estimate it?
- Capital Structure (15 points: 5 points each)
Xtan Inc. has two major sources of financing—common stock and long-term debt. It currently has 1,000,000 shares of stock outstanding, which are trading at a price of $10 per share. Its debt carries a current market value of $5,000,000 and a yield-to-maturity of 7.5%. Currently, the debt has 20 years until maturity.
Given its current capital structure, Xtan has estimated that its cost of equity is 15%. Xtan faces a marginal tax rate of 40%.
The condensed current balance sheet (book value) for Xtan is provided below.
| Assets | Liability and Equity | ||
| Cash and short-term assets Inventory Receivables Property plant and equipment (net) | 1,000 200 300 6,900 | Accounts payable Long-term debt Shareholders equity | 400 4,000 4,000 |
| Total assets | 8,400 | Total liabilities and equity | 8,400 |
- Assuming Xtan has not retired any of its original debt issue and the issue was originally issued at par value, what has happened to the interest rate on its debt since it was originally issued? How do you know? What two factors might explain this change in interest rates?
- Based on Xtan’s current capital structure, what is its after-tax weighted average cost of capital?
- Assume that Xtan issues $2,500,000 of debt to retire equity. The firm has determined that it can comfortably afford the higher debt levels without any material effect on its competitiveness or financial condition. Calculate the change in the price of its stock (if any). What explains this change (or lack of change)?
- Short Answer (70 points: 10 points each)
- In class, we discussed how to value financial securities like stocks and bonds. Why does the valuation of stocks and bonds differ fundamentally from the valuation of gold? Explain.
- Two years ago, XYZ Corp. sold 10-year bonds at a par value of $1,000 with a 4% coupon rate. The bonds now have eight years to maturity and have a yield-to-maturity of 3%. Is the bond selling at a premium or discount? What are the two most likely factors explaining the change in the bond’s price?
- If you use the stock’s beta and the security market line to compute the discount rate for a project, what assumptions are you implicitly making?
- Today, the following announcement was made: “Early today the Justice Department reached a decision in the Universal Product Care (UPC) case. UPC has been found guilty of discriminatory practices in hiring. For the next five years, UPC must pay $2 million per year to a fund representing victims of UPC’s policies.” Assuming the market is efficient, should investors not buy UPC stock after the announcement because the litigation will cause an abnormally low rate of return? Explain.
- A firm has the opportunity to improve the safety of its products by spending $30 million. The firm estimates that doing so will save $20 million in product liability claims. If the firm’s objective is to maximize shareholder value, can you defend making the $30 million investment in the new safety initiative? Explain.
- In class, we discussed the potential gains from diversifying your stock portfolio by combining your home-country stock investments with international stock investments. Do the potential gains from international diversification depend on your home country (e.g., a U.S. investor versus a Taiwanese investor)? Explain.
- Despite its limitations, the CAPM provides sensible investment advice. In the CAPM framework, investments are fairly priced. What investments should an investor choose? How would you implement this advice in the real world?
