Practice Problems
Prof. P.V. Viswanath

Optimal Capital Structure

Short Questions:

1. What is the difference between a warrant and an option?
   Ans: An option is a side bet between two parties, and does not involve the issuing corporation. When a warrant is exercised, on the other hand, the company issues new stock, because the writer of the warrant is the corporation.

2. Why would a firm want to issue floating rate debt?
   If the company has assets, whose cashflows are correlated with the interest rate, then floating rate debt would cause the net cashflows to be more stable. The company could also have an opinion on future interest rates, and it might believe that the current fixed rates are too high.

3. How would you come up with a synthetic rating for a firm that has debt that is not rated by a ratings firm like Moody's?

4. How would you estimate the beta for a firm that has just been established?

5. Which of these two companies would have higher asset betas, and why --

   1. Deere & Co. (DE) -- DE manufactures and distributes farm equipment, machines used in construction, earthmoving and forestry, and equipment for commercial and residential uses.

   2. AMN Healthcare Services is a temporary healthcare staffing company and a nationwide provider of travel nurse staffing services to hospitals and healthcare facilities throughout the United States.

   Ans: I think Deere and Co., would have a higher debt-to-equity ratio, because it has more tangible assets that could be used for securing debt. Agency costs of debt would be lower. The value of AMN is more from its strategies and its employees; these could be changed in a way to increase risk, which would be bad for bondholders.

   In terms of asset betas, I would look at other things. I would look at the ease with which new firms could compete against these two firms. Since new entrants would need to invest large amounts in the farm equipment manufacturing business, it might be able to maintain higher profit margins. This probably also means that its profits fluctuate more with demand. Along the same lines, it has a higher fixed cost component, probably because of the nature of its business. Manufacturing farm equipment must be capital intensive. Hence it has a higher operating margin. This, too, means that it would have a high asset beta

6. Name at least two different advantages of debt.

7. Name at least two different disadvantages of debt financing.

8. Give two examples of the indirect costs of bankruptcy.

9. Would a firm with high variance of operating cash flows tend to have high or low debt/equity ratios?  Why?

10. What is the difference between Chapter 7 and Chapter 11 bankruptcy?

11. How would you estimate the marginal tax rate of a firm?
    Ans: I could look at how its taxes paid change from year to year as income changes. The ratio of change in taxes paid to change in taxable income would give me an estimate of the marginal tax rate.

12. What does the Modigliani-Miller Theorem say?

13. If a firm wants to have greater flexibility in the future, should it use debt financing or equity financing today?

14. What sorts of firms would tend to have high indirect costs of bankruptcy?

15. What sorts of firms would tend to have high direct costs of bankruptcy?

16. Both the debt and the equity of a firm would be riskier, the higher its debt-equity ratio.  Since the cost of capital for the entire firm is a weighted average of the costs of debt and equity, it is clear that a firm with a higher leverage ratio will have a higher cost of capital than a firm with a lower leverage ratio.  Show why this statement is not necessarily true.  

Definitions:

1. Asset-backed borrowing

2. Bankruptcy

3. Best Efforts guarantee

4. Building the Book

5. Callable Debt

6. Contingent Value Rights

7. Conversion Premium

8. Convertible Preferred Stock

9. Direct and Indirect Costs of Bankruptcy

10. Ex-rights price

11. Floating Rate Bonds

12. Free cash flow

13. General Subscription

14. Hybrid security

15. Line of Credit

16. Marginal Tax Rate

17. Negative pledge clause

18. Offering Price

19. Original Issue Deep-Discount Bonds

20. Private Placement

21. Puttable Bonds

22. Red Herring

23. Rights Offering

24. Rights-on price

25. Seed-money Venture Capital vs. Start-up Venture Capital

26. Shelf Registration

27. Sinking Fund

28. Standby guarantee

29. Tombstone Advertisement

30. Tracking Stock

31. Underwriting guarantee

32. Venture Capital

33. Warrants

Problem 1. (solution) You are in a world where there are only two possible future outcomes--i.e., two states of the world--boom and depression. There are two companies, Dizengoff and Elysee. The following table shows the total payoffs from each company in each state of the world (e.g. if there is depression, Dizengoff pays $20 and Elysee pays $0).

Presumably, investors would hold portfolios of the two firm's shares to minimize the variability of their payoffs, all other things being the same. However, investors in this economy have other income in the two states of the world. Hence they would consider not simply the variability of the payoffs from holding the two shares described above, but rather, the variability of their total payoffs from all sources. (Recall the difference between considering an asset in isolation and as part of a portfolio.) Each investor's valuation of a dollar of income in a given state of the world would, thus, depend on his or her income from other sources in that state of the world, as well as on his or her willingness to take risks. (For example, an investor who already had income from other sources, say labor income, which gave him high payouts in the 'depression' state, and low payouts in the 'boom' state, would value more, a security that had a higher payout in the 'boom' state than in the 'depression' state.) The collective valuations of all investors in this economy would result in market prices for the shares of Dizengoff and Elysee. These market valuations for the two firms are given in the last column of the table above.

Answer the following questions, keeping in mind that short-selling of Dizengoff and Elysee shares is permitted. (Riskfree borrowing and lending is not permitted for questions a. through e.) You do not know the probabilities of occurrence of the two states. The solutions to the questions do not require assuming a particular value for the probabilities.:

1. Vitus has no income from other sources, and is infinitely risk-averse. What portfolio of the two firms' shares would he hold? (Assume for concreteness, that he has $15 of total wealth.)
2. Manuel has a consulting business, which provides him with income of $5 when the economy is doing well, but nothing when the economy is depressed. In addition to this, he also has $15 of total wealth. What portfolio of the two firms' shares would he hold if he were infinitely risk-averse?
3. If you were told that Maureen held the very same portfolio as Manuel in part b. above, but you knew that she had no other income, what would you conclude regarding her propensity to take risks?
4. If there were no other securities traded in the economy, what would be the return on the market portfolio in the two states?
5. Elysee and Dizengoff merge. Would Manuel, Vitus, and Maureen be as well off, after the merger, as before? Assume that there are no synergies due to the merger, and that the terms of the merger are decided upon using market prices, i.e. neither party to the merger has a bargaining advantage.
6. Answer question e. under the assumption that riskfree borrowing and lending is permitted.

Problem 2. Given the following information about Eastman Corporation, compute the expected rates of return on its debt, levered equity and assets as a function of its debt-equity ratio. Plot these rates of return as a function of Eastman's debt-equity ratio. Your graph should resemble the graph below, which has been created with the given information; however, your graph should extend the graph given below by showing expected rates of return for debt/equity ratios going upto 100. Do expected rates of return behave differently for higher values of the debt/equity ratio in this example? Why do you think this is so?

Confirm that Modigliani-Miller Proposition II (without taxes) holds.

Note: A state price is the market price of a security with a payoff of $1 in that state and zero otherwise.

Problem 3. The market value of a firm with $500,000 of debt is $1,700,000. EBIT are expected to be a perpetuity. The pretax interest rate on debt is 10 percent. The company is in the 34-percent tax bracket. If the company was 100-percent equity financed, the equity holders would require a 20-percent return.

A. Assume that the personal tax rate of the company's security holders is zero percent.

1. What would the value of the firm be if it was financed entirely with equity?
2. What is the net income to the stockholders of this levered firm?

B. Assume that the personal tax rate on equity income for the company's stockholders is 10%, while the personal tax rate on debt income for the company's bondholders is 25%.

1. What would the value of the firm be if it was financed entirely with equity?
2. What is the net income to the stockholders of this levered firm?

Problem 4. The Branch Company's debt holders are promised payments of $25. The expected earnings if the firm does well are $45, but only $20 if it does poorly. The probability of the firm performing poorly or well is 50%. If Branch's bonds are selling at a price of $20, and the interest rate on the bonds is 10%, estimate the reduction in the value of the firm today because of bankruptcy costs.

Problem 5. An entrepreneur has a patent on an invention that is likely to generate $100 million in one year with a probability of 20% and $40 million with a probability of 80%. He needs a capital outlay of $30 million. Since he is certain to make a minimum of $40 million, he should be able to borrow the $30 million at the risk- free rate of 10%.

Suppose, however, that the entrepreneur has another option: to invest in a hula hoop factory. If hula hoops come back into fashion, he will make a killing of $1500 million; if they don't, the best he can do is to recover costs. The probability of making a killing is 0.02.

1. Given this new information, show that a potential investor would no longer want to lend our entrepreneur the $30 million at the risk-free rate of interest. with no additional safeguards.
2. Assuming the investor is risk-neutral, what is the minimum rate of interest that he will charge the entrepreneur?
3. Is there any way that the entrepreneur can borrow the $30 million at the risk free rate of interest?

Problem 6. (Fall 1999)

1.      (10 points) For ABM Industries, for the most recent period, compute the ratio of debt to total liabilities, the ratio of equity to total liabilities, and the ratio of preferred stock to total liabilities.  Use the following guidelines in your computation:

•  Ignore the value of current assets and liabilities

• Compute the value of debt as equal to the sum of Long Term Debt plus Other Long Term Liabilities

• Use the market value of equity as of July 30, 1999 as the value of equity

• Use the book value of preferred stock as the value of preferred stock. 

• Let the value of total liabilities be the sum of these three quantities. 

2.      (10 points) Estimate the before-tax cost of debt.

3.      (10 points) Estimate the marginal tax rate for the company and the after-tax cost of debt.

4.      (10 points) Estimate the cost of equity capital. 

5.      (10 points) Estimate the cost of preferred stock.

6.      (10 points) Compute the weighted average cost of capital, using your results from parts 1-5.

7.      (10 points) Suppose ABM paid off all of its debt with a new stock issue.  Compute  the new cost of capital of the firm.

8.      (15 points) Compute the resultant change in value of the firm. 

9.      (15 points) Why, do you think, did ABM increase its dividend (see Dec. 21, 1999 news item from Yahoo)?  Explain using the theories of dividend policy that we discussed in class (no more than one page of your exam booklet).

10.  (10 points) Bonus question: How does the fact that ABM’s debt is privately held affect its optimal debt-equity ratio? 

 Attachments:

A.     Business Summary
B.     Recent Market Related Information
C.     Balance  Sheets for 1995-1999
D.     Income Statements for 1995-1999
E.      Information Regarding ABM’s Long-Term Debt
F.      Recent History of Prime rates
G.     Recent History of LIBOR rates
H.     Regression results
I.        Dividend per share history
J.       Earnings per share history
K.    Summary of Recent News Items

 A.     Business Summary (From http://biz.yahoo.com) 

 ABM Industries Incorporated provides air conditioning, elevator, engineering, janitorial, lighting, parking and security services. Clients include thousands of commercial, industrial and institutional customers who outsource these services in hundreds of cities across North America. The Company's nine divisions operate in three functionally oriented segments: Janitorial, Public Service and Technical. The Company's Janitorial Divisions segment provides janitorial cleaning services as well as janitorial supplies and equipment to its customers. The Company's Public Service Divisions segment provides parking facility services, commercial security and investigative services, and "bundled" facility services to their customers. The Technical Divisions segment provides its customers with a wide range of elevator, engineering, HVAC (heating, ventilation and air conditioning), and lighting services through its four divisions. 

B.     Recent Market-related Information 

Closing price for ABM Stock as of July 30, 1999 was $27.8125 (http://chart.yahoo.com)
Closing price for ABM Stock as of December 21, 1999 was $20.6875 (http://chart.yahoo.com)
Average Annual Percentage Change of the S&P 500 from 1962 to 1999 was 8.75%.
The average dividend yield for the S&P 500 from 1962 to 1999 was about 4%.
The yield on the 3-mth Treasury bill was 5.514% on Dec. 22, 1999.
The yield on the 1-year Treasury bill was 5.926% on Dec. 22, 1999.
The yield on the 30 year Treasury bond was 6.451% on Dec. 22, 1999. 

C.     Balance Sheet (From Disclosure) 

Annual Assets (’000$)

Annual Liabilities (000$)                                                             

Note: 1. Series B 8% Senior Redeemable Cumulative Preferred Stock

D.    Income Statement  (000$) (From Disclosure):                                                                       

 E.     Information Regarding ABM’s Long-Term Debt

 From the section entitled “LONG-TERM DEBT AND CREDIT AGREEMENT,” in the Company’s 1998 Annual Report to Stockholders

During the third quarter of 1997, the Company replaced its $125 million syndicated line of credit expiring September 22, 1999 with a new $125 million syndicated line of credit expiring July 1, 2002. Effective November 1, 1997, the agreement was amended to increase the amount available to $150 million. The unsecured revolving credit facility provides, at the Company's option, interest at the prime rate or IBOR+0.35%. The facility calls for a commitment fee payable quarterly, in arrears, of 0.12% based on the average, daily, unused portion. For purposes of this calculation, irrevocable standby letters of credit issued in conjunction with the Company's self-insurance program plus cash borrowings are considered to be outstanding amounts.

As of October 31, 1998, the total outstanding amount under this facility was $101 million comprised of $30 million in loans and $71 million in standby letters of credit. The interest rate at October 31, 1998 on loans outstanding under this agreement ranged from 5.54% to 6.16%. The Company is required, under this agreement to maintain financial ratios and places certain limitations on dividend payments. The Company is prohibited from paying cash dividends exceeding 50% of its net income for any fiscal year.

In February 1996, the Company entered into a loan agreement with a major U.S. bank which provides a seven-year term loan of $5 million. This loan bears interest at a fixed rate of 6.78% with annual payments of principal, in varying amounts, and interest due February 15, 1997 through February 15, 2003. The long-term debt of $34,585,000 matures in the years ending October 31 as follows: $865,000 in 1999; $859,000 in 2000; $895,000 in 2001, $30,907,000 in 2002, $981,000 in 2003,and $78,000 in subsequent years.

(Note: Interbank Offered Rate IBOR is the rate of interest at which banks lend to other prime banks.  This is essentially the same as LIBOR or London Interbank Offered Rate)

 Long-term debt at October 31, 1998 is summarized as follows:

 F.      Recent Prime Rate History 

(The prime rate is defined by The Wall Street Journal as "The base rate on corporate loans posted by at least 75% of the nation's 30 largest banks.) (data obtained from HSH Associates: http://www.hsh.com):

 G.    History of Recent 6-month maturity average LIBOR rates
 (data obtained from HSH Associates: http://www.hsh.com) (LIBOR is an abbreviation for "London Interbank Offered Rate," and is the interest rate offered by a      specific group of London banks for U.S. dollar deposits of a stated maturity. LIBOR is used as a base index for setting rates of some adjustable rate financial instruments.)

 H.    Regression Results for ABM Stock Returns

 A regression of the monthly return on ABM on the monthly percentage change in the S&P500 for the 59 months, Jan. 1995 to November 1999 yielded the following regression equation:

R_ABM = 0.000429 + 0.7543 R_SP500
R² of the regression: 0.1449
T-statistic for the slope coefficient of the regression: 3.108228 

I.       Dividend per share history (from http://chart.yahoo.com): 

 J.      Earnings per share history
(from Disclosure, except for the year ending Oct. 1999, which is from http://biz.yahoo.com)

 K.    Summary of Recent News Items pertaining to ABM
from http://biz.yahoo.com/n/a/abm.html on Dec. 21, 8:00 p.m. (all times are Eastern)
 

Tuesday December 21, 1999

·        ABM Industries Inc raises dividend - Reuters Securities - 1:54 pm

·        ABM Industries Increases Quarterly Dividend by 11% - Business Wire - 1:47 pm

ABM Industries Increases Quarterly Dividend by 11%
(http://biz.yahoo.com/bw/991221/ca_abm_ind_1.html)
Tuesday December 21, 1:47 pm Eastern Time
Company Press Release 

SAN FRANCISCO--(BUSINESS WIRE)--Dec. 21, 1999--The Board of Directors of ABM Industries Incorporated (NYSE:ABM - news) today declared an all-time high quarterly cash dividend of 15.5 cents per common share for payment on February 3, 2000, to stockholders of record on January 14, 2000. 

This will be ABM's 135th consecutive quarterly cash dividend, and is 11% greater than the 14 cents per share that were paid in each of the four previous quarters. 

Just last week, ABM reported over $1.6 billion in annual revenues (up 9%) and diluted net income per share of $1.65 (up 15%) for the fiscal year that ended on October 31, 1999.

 Monday December 13, 1999

·        ABM Industries Q4 results - Reuters Securities - 3:12 pm

·        ABM Industries Reports $1.6 Billion in Annual Revenues and a 15% Increase in Net Income Per Share - Business Wire - 2:55 pm

 Friday December 10, 1999

·        ABM Industries On the Grow from Alaska to Florida - Business Wire - 6:01 am

 Tuesday November 30, 1999

·        Amtech Elevator Services Awarded General Motors Contract - Business Wire - 9:08 am (Note: Amtech Elevator Service is a wholly-owned subsidiary of ABM Industries)

 Thursday November 18, 1999

·        ABM Janitorial Services Scores At STAPLES Center - Business Wire - 6:03 am (Note: ABM Janitorial Services is a wholly-owned subsidiary of ABM Industries)

 Tuesday November 2, 1999

·        Promotions in the Officer Corps of ABM Industries Incorporated - Business Wire - 2:09 pm

 Monday October 18, 1999

·        Henrik Slipsager to Succeed Jack Egan as president of American Building Maintenance - Business Wire - 5:14 pm (Note: American Building Maintenance Company is a wholly-owned subsidiary of ABM Industries)

 Friday October 8, 1999

·        Ampco System Parking Receives Sioux City Parking Contract - Business Wire - 12:15 pm (Note: Ampco System Parking is a wholly owned subsidiary of ABM Industries)

 Friday September 24, 1999

·        ABM Engineering Receives ISO 9002 Certification - Business Wire - 12:04 pm (Note: ABM Engineering Services is a wholly-owned subsidiary of ABM Industries)

 Wednesday September 22, 1999

·        ABM Industries Incorporated Announces Stock Repurchase Program - Business Wire - 6:08 pm

Problem 7 (Spring 1999):  Using the information provided below on Columbia/HCA, answer the following questions below.

 I.

1. Compute the cost of equity for Columbia. (10 points)

2. Compute the after-tax cost of debt. (10 points)

3. Compute Columbia’s debt-equity ratio as the ratio of Long Term Debt to Common Shareholders Equity (Including Minority Interest).  (5 points)

4. What percentage of Columbia’s return is explained by market movements? (5 points)

5. Compute the covariance of returns between Columbia and the NYSE (5 points).

6. Compute the weighted average cost of capital using your answer in part c) above.  (5 points)

7. Estimate the growth rate of Columbia’s earnings. (10 points)

8. Suppose Columbia wishes to swap $3 billion of debt for equity.  Assume that the swap will reduce Columbia’s cost of debt by 1%.  Compute the new weighted average cost of capital.  Estimate the impact of this capital structure change on the market value of the entire firm. (10 points)

 II. Can you explain the company’s debt-equity ratio.  Would you recommend any changes?  Why or why not?  Use no more than one page for your answer.  (20 points)

 III. Can you explain the firm’s dividend policy? Would you recommend any changes?  Why or why not? Use no more than one page for your answer. (20 points)

1. Financial Statement Information from Disclosure.

2. Financial Information from the Wall Street Journal’s website.

3. General Information from the Wall Street Journal’s website.

4. General Information from Columbia’s website.

5. Bond Information

6. Regression of Columbia stock returns on the NYSE Composite Index returns

 A. Financial Statement Information from Disclosure.

 Balance Sheet as of 12/31/97

 
INCOME STATEMENT (000'S) 

 B. Financial Information from the Wall Street Journal’s website. 

 C. General Information from the Wall Street Journal’s website.

COL, together with its subsidiaries, operates hospitals and related health care entities. As of 12/98, COL operated 281 hospitals and 102 outpatient surgery centers. (From http://interactive.wsj.com/)

 D. General Information from Columbia’s website.

Columbia/HCA owns and operates over 300 hospitals and other healthcare facilities with approximately 60,000 licensed beds in 36 states, England and Switzerland. We are dedicated to providing healthcare services that meet each community's local healthcare needs, integrating various services to deliver patient care with maximum efficiency. (From http://www.columbia-hca.com/)

 E. Bond Information

The yield on the 30-year T-bond as of 5/7/99 was 5.81%, while the yield on the one-year T-bill as of 5/7/99 was 4.78% (http://www.bloomberg.com/markets/C13.html)

According to Standard and Poor’s Rating Service, Columbia’s unsecured bonds are rated B+.  Historically, bonds with this rating yield about 3% over the T-bond rate, according to Table 18.9 in Damodaran’s book, Corporate Finance: Theory and Practice.

 F. Regression Information

A regression of the monthly Columbia stock return on the NYSE Composite return for the period June 1994 to April 1999 yields the following results:

R_Columbia = -0.0156 + 1.1744 R_NYSE
R² = 0.21
Using the same data, the volatility of Columbia stock and the NYSE Composite was estimated as follows:
The standard deviation of R_Columbia = 9.74% per month
The standard deviation of R_NYSE = 3.8% per month

Problem 8: 

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