Econ 156
Gary Smith
Fall 2009
Midterm (75 minutes)
No calculators allowed; if calculations are needed, write the explicit equation(s), identifying the variables. Do not write “Y = aX; solve for X.” You can write “100 = 10X; solve for X.” If you want extra time, you can buy time at a price of 1 point a minute; for example, if your test is handed in 10 minutes after the scheduled finish time, 10 points will be subtracted from the test score.
1. On October 31, 2001, the U.S. Treasury surprised financial markets by announcing that it would no longer issue 30-year bonds to finance the government debt. A fixed-income strategist at Merrill Lynch argued that, “The Treasury is trying to shorten the maturity of their debt, which makes sense given the current climate of low yields.” (At the time, interest rates on 2-year Treasury notes were about 2.4 percentage points less than interest rates on 30-year Treasury bonds.) Explain why a switch from 30-year to 2-year securities might not reduce the Treasury’s interest expense.
2. The owner of a Washington, D.C. real estate firm says this equation basic to real estate:
Principal x Interest Rate per Period x Interest Periods (time) = Total Interest Paid
a. Explain why the total interest paid on a $100,000 conventional 30-year mortgage at 10 percent is not $100,000 x 10 percent/year x 30 years = $300,000.
b. Is the correct total interest larger or smaller than $300,000? Explain your reasoning.
3. Suppose that a firm has no debt and that all earnings are paid out as dividends. It has assets A that earn an annual rate of return ρ, and shareholder’s required rate of return is R. Which of these equations for the value of the firm is most consistent with Economic Value Added (EVA) analysis? Explain your reasoning.
a. V = (ρA - RA)/R
b. V = A + (ρA - RA)/R
c. V = A
d. V = sum of (ρA - RA)
4. During the 10-year period 1982–1992, three-fourths of the professionally managed bond mutual funds did worse than the Salomon Brothers Broad Investment Grade Bond Index. A managing director of PIMCO, one of the few funds that beat the index, said that regulatory and accounting rules compel many investors to buy one-year securities, making 1-year interest rates artificially low. Investors who are not subject to such constraints can do better buying a portfolio of 6-month and 2-year securities. Consider a 6-month Treasury zero with a 4 percent interest rate, a 1-year Treasury zero with a 3.5 percent interest rate, and a 2-year Treasury zero with a 4.0 percent interest rate. Instead of investing $1 million in the 1-year zero, how should an investor divide $1 million between the 6-month and 2-year zeros so that her portfolio of 6-month and 2-year zeros will have the same duration as a portfolio of 1-year zeros?
5. “During October [2008], Citadel had to crush a rumor that appeared on a blog about its leverage hitting a ratio as high as 13 to one. According to the firm, the ratio was actually four to one (that means for every $1 of assets under management, Citadel borrowed another $4).” [Marcia Vickers and Roddy Boyd, “Citadel Under Siege,” Fortune, December 22, 2008; p. 136.]
a. Explain how to calculate the leverage ratio if a firm borrows $4 for every $1 of equity.
b. Why did Citadel want to crush a rumor that its leverage was 13 to one?
6. Often, people who retire have the option of choosing: (a) a constant monthly income for as long as they live; or (b) a lump-sum payment equal to the present value of these monthly payments using the life expectancy of people their age. Pension-reform legislation passed in August 2006 allows companies to determine the value of the lump-sum payment by calculating the present value using a long-term corporate bond rate instead of a long-term Treasury bond rate, as had been done previously. Did this change increase or reduce the size of the lump-sum payment? Explain.
7. Explain why this advice is logical, but not very helpful:
It is obviously good sense to buy bonds when the Federal Reserve Banks start lowering interest rates. It is just as obviously bad sense to buy them at any time when, two or three or four months hence, the Fed is certain to start raising money rates and lowering the prices of outstanding bonds.
8. It was recently reported that a customer could rent a $1,000 television from Aaron’s for $108.33/month. After 24 months, the customer owns the television. [Suzanne Kapner, “Rent-to-Own Makes a Comeback,” Fortune, June 8, 2009.] What is the implicit annual percentage interest rate? (Just set up.)
9. CBA stock is selling for $80 a share. The company has $45 in assets per share and consistently earns a 20 percent return on its assets. This coming year, it is expected to earn an after-tax profit of $8 a share and to pay a dividend of $4 per share. Analyst 1 calculates the stockholders’ return as $4/$80 = 0.05 (5 percent). Analyst 2 calculates the stockholders’ return as $8/$80 = 0.10 (10 percent). Analyst 3 argues that the stockholders’ return must equal the firm’s profit rate, 20 percent. Explain and evaluate the logic behind each analyst’s calculation. If you had to come up with a rough estimate of the shareholders’ return using these data, what would your estimate be?
10. What is the value of q for the firm in Exercise 9? If CBA were to reduce its dividend by 10 cents a share and use these additional retained earnings to expand its operations, would you predict that this action will raise or lower the price of its stock? Explain your reasoning.