Dr. P.V. Viswanath

pviswanath@pace.edu

Exams

• Midterm
• Solutions to Midterm
• Final
• Solutions to Final

Midterm

Notes:

1. If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
2. If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
3. You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
4. You must explain all your answers.
5. Assume a tax rate of 40% where not provided.

1. (10 points each) Read the following article and answer the questions below:

a.       How could Miguet force creditors to make concessions?  Don’t creditors have an iron-clad contract whereby the company has to pay them a coupon and bond face value?
b.      We learnt in class how difficult it is for shareholders to control the Board of Directors of a company.  How did shareholders managed to vote out Eurotunnel’s Board, according to you?  Use the information in the article and any other information provided below. 

According to the Eurotunnel website, http://www.eurotunnel.com/ukcMain/ukcCompany/ukcInvestorRelations/ukcShareholderInfo/ukpShareholderAnalysis, as of Dec. 31, 2003, 6% of Eurotunnel’s shares are hold by banks, 29% are held by institutions and 65% are held by individuals.

According to the Eurotunnel website, there was 6.4billion euros of debt, as of 12/31/03.  Of this, 0.4b was senior debt, 4.5 was junior debt, 1.5 billion consisted of Participation Loan notes, while equity consisted of 1.1b euros.

The share price, as of  March 13, 2005 was 0.24 euros. 

Eurotunnel's Board Is Ousted by Shareholders
Jo Wrighton and Greg Keller. Wall Street Journal. (Eastern edition). New York, N.Y.: Apr 8, 2004. pg. A.6

PARIS -- Creditors of Eurotunnel, the struggling operator of the underwater "Chunnel" linking Britain and France, are bracing for tough negotiations with new management after the unprecedented ouster of the European company's two top executives and the rest of its board by a shareholders' revolt.

French politician and publisher Nicolas Miguet rallied shareholders around his own team of directors, promising to defend small investors and force creditors to make concessions in the restructuring of Eurotunnel's debt of GBP 6.4 billion ($11.8 billion), much of which is now held by hedge funds.

Mr. Miguet's campaign struck a chord with Eurotunnel's 1.1 million, mainly French, small investors whose shares have plummeted in value. At a shareholder meeting in Paris, 63% of investors voted to oust Chairman Charles Mackay, Chief Executive Officer Richard Shirrefs and the rest of the Eurotunnel board. They also voted for a new team of directors, including Jacques Maillot, former head of travel agency Nouvelles Frontieres, who is expected to become Eurotunnel's new chairman.

The move marked the first time shareholders tossed out the management of a listed company in France.

But while shareholders celebrated -- Eurotunnel shares rose 7% on the news in Paris -- creditors warned they won't give much ground to stockholders. The company has a market capitalization of GBP 1.4 billion, just one-fifth of debt outstanding.

While the new management has yet to detail its restructuring plans, bondholders think part of the rescue would involve swapping Eurotunnel debt for equity, a classic restructuring step. However, instead of wiping out shareholders, as would normally happen, they think the Eurotunnel rebels would like to save some equity for shareholders.

Whatever their stance, a new Eurotunnel management is under pressure to reach an agreement with creditors. The company will start to face a debt-repayment crisis at the end of next year, when it has to make all of its interest payments in cash, under the terms of the last debt- restructuring pact in 1997, said Markus Niemeier, research analyst at Barclays Capital in London.

2. (30 points) You wish to buy a car.  Unfortunately, you don’t have any ready cash.  On the other hand, you just recently invested $200,000 in a private equity fund.  The fund manager will not give you your money back right away, unfortunately.  However, according to your calculations, your investment in the fund should grow at the average rate of 15% a year for the next 5 years, at the end of which you can cash out.

Of course, you still want your car right now!  What to do?  Luckily for you, your friendly banker is willing to lend you some money using your investment as collateral.  Your banker believes that your investment has a beta of 1.5, the market risk premium is 6% and that the current five-year T-bond rate is 4.5%.  He is willing to lend you 80% of the estimated market value of your investment so that you can buy your car.  The APR on the loan is 18% and the money is to be repaid in monthly installments, starting 13 months from now.  If there are 48 payments in all, what is the size of each payment?

A stock with a beta of 0.5 is
1. exactly half as volatile as the market portfolio
2. less than half as volatile as the market portfolio
3. more than half as volatile as the market portfolio

2. Why would low-beta stocks outperform the market during market declines?
3. Are the betas in the list of ten below historical betas, or are they prospective betas?
4. What is the implicit definition of the market portfolio in the estimation of these betas?
5. Pick any stock from the list of ten below and explain, based on its industry membership, why it has a high beta.
6. Many economists believe that the economy is in a recovery phase and predict that the stock market will do much better than T-bills over the next year. Assuming the truth of this forecast, explain which of the ten stocks below you would buy.

SmartMoney Stock Screen / High-Beta Stocks
Jack Hough. Wall Street Journal. (Eastern edition). New York, N.Y.: Jan 13, 2005. pg. D.2

DON'T LET A HIGH BETA dissuade you from buying an otherwise promising growth stock.

Beta is a measure of volatility. It's based on a statistical comparison of the fluctuations of a given company's share price versus the fluctuations of an index -- usually the Standard & Poor's 500- stock index -- over a certain time period. A stock with a beta of 0.5, for example, is said to be only half as volatile as the S&P 500; a stock with a beta of 2.0 is doubly so. A stock with a negative beta zags when the S&P 500 zigs.

Bearish and safety-first investors usually look for low-beta stocks -- those with betas of, say, 0.5 and lower -- because these have shown a tendency to outperform the S&P 500 during broad market declines. But low-beta stocks also tend to underperform during surges. So bullish or aggressive investors might wish to search specifically for high betas.

The 10 stocks on the list below have betas of 2.0 or higher; that is, they've shown at least twice the volatility of the S&P 500 over the past three years. All have posted share-price gains of at least 12% over the past 26 weeks (again, about double that of the S&P 500), and have had their current-year and next-year earnings consensuses boosted within the past four weeks. All have topped earnings expectations, on average, in their past four quarterly reports, and have debt/capital ratios of 0.4 or lower. Finally, all are projected to boost their earnings by at least 12% annually over the next five years.

To get an idea of how expensive each stock is relative to its growth prospects, give its price/earnings-to-growth, or PEG, ratio a look. The measure is calculated by dividing a company's price/earnings multiple by its projected long-term earnings growth rate. Stocks with PEGs near or below 1.0, in particular, are considered possible bargains.

As always, please research thoroughly any stocks on our list before buying them.

When Volatility Is a Good Thing

These 10 stocks carry high betas as a result of their rapid price gains.

4. Philip Morris is examining the costs of equity and capital it uses to decide on investments in its two primary businesses – food and tobacco.  It has collected the following information on each business:

·           The average beta of publicly traded stocks in the tobacco business is 1.10 and the average debt/equity ratio of such firms is 20%.

·           The average beta of publicly traded firms in the food business is 0.809, and the average debt/equity ratio of such firms is 40%.

Philip Morris has a beta of 0.95 and a debt ratio of 25%; the pre-tax cost of debt is 8%.  The treasury bond rate is 7% and the corporate tax rate is 40%.  The market risk premium is estimated to be 5%.

a.       (10 points) Estimate the cost of capital for the tobacco business; also estimate the cost of capital for the food business.

b.       (10 points) Estimate the cost of capital for Philip Morris, as a firm

c.      (10 points) Having looked at your estimates of the cost of capital for the tobacco and food divisions at Philip Morris, the financial managers have come back with a question.  Where, they want to know, does the substantial risk posed by tobacco lawsuits show up in the costs of capital that you have estimated?  Respond.

Solutions to Midterm

1. a. Creditors do have a contract whereby the company has to pay them a coupon and bond face value. However, there are often provisions in bankruptcy law, whereby a company may be allowed to suspend payments to its creditors if doing so is necessary for the company to maintain itself as a going concern. The key word, here, is suspend. Once a company enters into bankruptcy there is a procedure in place, whereby the company has to be reorganized or liquidated. In principle, the creditors are not supposed to lose out at all; and the purpose of the suspension of payments is only supposed to prevent an unwarranted scramble for repayment on the part of creditors that might force an otherwise healthy company into bankruptcy -- this would be akin to a trading halt on an exchange, in a company's stock, if the price starts dropping precipitously because of investor panic.

However, where the bankruptcy law gives existing shareholders or existing management, discretion as to how to file the reorganization plans, bondholders might be willing to forego some of their rights or payments, in order to ensure a speedy conclusion to the bankruptcy proceedings. This is particularly important because the ability to wait is, in itself, a sort of call option that can only be beneficial to stockholders. European Law is, in general, not as debtor-friendly as US law; still the law there is also getting more debtor-friendly over time.

Finally, management can often take actions that expropriate bondholder value because no contract, least of all, a bond indenture, is complete.

b. In this case, even though a large percentage of the shares were diffusely held -- 65% -- still, 35% were held by banks and institutions, and so, only 16% more was needed from the shares held by individuals, in order to vote against the managemetn slate of candidates for the Board of Directors. It is also possible that even though 65% of shares were held by individuals, this percentage may not have been held diffusely -- in other words, there might have been some large blocks amongst the 65%.

2. The expected value of your investment in the private equity fund, after five years is 200,000(1.15)⁵ = $402,271.44. This investment has a beta of 1.5; hence the required rate of return on this investment is 4.5 + 1.5(6) = 13.5%, using the CAPM. Hence the market value of this investment is 402271.44/(1.135)⁵=$213,569.82. The banker will lend 80% of this, or $170,855.86. The APR on the loan is 18%; hence the effective monthly rate is 18/12 or 1.5%.

Payments, however, don't start until 13 months from now; so it is as if we have a loan that will be made in a year's time with monthly payments starting the next month. If we look at it, this way, the value of the loan, in 12 months time, rises to 170,855.86(1.015)¹² = $204,278.37. We can, now, use the annuity formula to find the value of each of the 48 monthly payments, by solving 204,278.37 = (C/0.015)[1-(1/1.015))⁴⁸] or C = $6000.68.

3. a. A stock with a beta of 0.5 is more than half as volatile as the market portfolio, because in addition to market related uncertainty stocks also have idiosyncratic volatility. Of course, this idiosyncratic volatility does not "count" in terms of being priced by the market, but it contributes to the volatility, nevertheless, if not to risk.
b. A low-beta stock is a stock that moves less than the market, in whatever direction the market is moving. Hence, in times of market declines, a low-beta stock would tend to decline less than the market -- and hence outperform the market.
c. The betas in the list below are historical betas, as it says: "they've shown at least twice the volatility of the S&P 500 over the past three years."
d. By referring to beta as the comparison of a companys' share price relative to the fluctuations of the Standard & Poor's 500, the article is implicitly defining the S&P 500 as the market.
e. Tibco Software, which is in the Business Software and Services industry would, obviously, see its sales rise when the rest of the economy is doing well, since it sells to other business. This would imply a positive beta. However, more than that, business would buy software, i.e. invest in new productive assets only if they saw the economy continuing to do well. If the economy were predicted to do moderately well in the future, businesses would not buy new software. Hence, Nvidia's stock would reflect amplified market movements in the case of a robust market, while in the case of a sour economy, Nvidia's stock would plummet as businesses would immediately cut their purchases of business software, which would be seen as contra-indicated "investments." In economic terms, demand for business software is a derived demand.
f. If the report is true, then the stock with the highest beta would be best, which in this case, is FFIV.

4. a. If Philip Morris desires to use its own debt ratio of 25% for all its business, then the computation of the levered beta to be used for its tobacco business is as follows:

1. compute the unlevered beta for firms in the tobacco business. This can be computed as 1.1/[1+(1-0.4)(0.2)] = 0.982
2. lever up this using Philip Morris' debt ratio of 25% to get 1.1784.

Hence the cost of equity is 7 + 1.1784(5) = 12.892. The cost of capital is (0.75)(12.892) + (0.25)8(1-0.4) = 10.869%.

The cost of capital for the food business is computed similarly. The unlevered beta for firms in the food business is 0.645; lever up this using Philip Morris' debt ratio of 25% to get 0.774. The cost of equity is 7 + 0.774(5) = 10.87%. The cost of capital is (0.75)(10.87) + (0.25)8(1-0.4) = 9.353%

b. The average cost of equity for Philip Morris can be computed as 7 + 0.95(5) = 11.75, and the cost of capital as (0.25)(8)(1-0.4) + (0.75)(11.75) = 10.0125%

c. One might argue that litigation risk is diversifiable, and should not be included in the costs of capital. If litigation risk is not diversifiable, then the cost of that has to be added on, perhaps by an increase in the estimated beta, assuming that the beta is a historical beta. If the betas are, indeed, historical betas, then it may be difficult to argue that the beta estimate already includes the effect of litigation risk because the nature of litigation risk in the past is probably different from that in the future.

Final Exam

Notes:

1. If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
2. If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
3. You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
4. You must explain all your answers. Answers without explanations may get no points or be heavily penalized.
5. There are ten questions below. You must attempt the six questions for which point values have been assigned, ranging from 5 points to 20 points. Four other questions are marked "optional." Do any two of these optional questions for 15 points each. Any additional optional question that you attempt will be graded out of 10 points. Hence you can obtain a maximum of 120 points if you attempt all questions and all your answers are perfect.

Using the information in items A-F (except where indicated to the contrary) to answer the questions below:

1. (15 points) What sort of capital structure would you expect Lennar Corporation to have? High on debt or low? Use only the information in "Key facts about Lennar from WSJ Online" to make your case.
2. (optional) Why (in the Dow Jones article) does Fitch include the debt and equity from Lennar's off balance-sheet operations (partnerships and joint ventures) to compute an overall debt-to-capitalization ratio of 46.9%? If Lennar doesn't have to consolidate those operations for reporting purposes, why should they be incorporated in the computation of its debt ratios?
3. (optional) Why does Lennar used off balance-sheet financing for those joint ventures (see Dow Jones article)?
4. (5 points) The net debt to capitalization ratio is defined as "Net debt in relation to total shareholders' equity (including minority) and net debt;" and net debt is defined as "Short- and long-term interest bearing liabilities and related derivatives, less cash and cash equivalents," according to http://www.autoliv.com. Compute the net debt to capitalization ratio as of February 28, 2005, using the data from Yahoo (item B). Is this number the same as the one in the Dow Jones article?
5. (5 points) The WSJ.com website has the following information regarding Lennar Corportation's balance sheet for Feb. 28, 2005, which differs somewhat from the information in Yahoo. Long term debt is given as $2,002,867, while "cash and cash-equivalents" are $509,068. Using this information, compute the net debt to capitalization ratio, once more. Which number is more correct, do you think? Why?
6. (10 points) Define the debt-equity ratio as the ratio of the market value of long-term debt to the market value of equity. Correspondingly, define the debt-to-assets ratio as the ratio of long-term debt to the sum of long-term debt and the market value of equity. Using these definitions, and using the February 28, 2005 balance sheet, compute the unlevered beta for Lennar. Note that Yahoo.com reports Lennar's beta as 0.544. Use any other information provided, as needed. (Ignore the off-balance sheet ventures for the purpose of this question.)
7. (optional) According to Yahoo, Lennar's beta is 0.544; that is, it reacts in a dampened fashion to market moves. Your friend, Jane, argues that this beta is probably an underestimate. "If the economy improves, demand for housing will probably go up quite a bit because homeowners will expect the improvement to continue and spend more on homes in anticipation of that improvement. On the other hand, if the economy tanks, homeowners will probably get worried and cut their home purchase plans sharply. I think Lennar's true beta is probably about 1.8," says Jane. Comment. Also, what information is there in the article that supports the idea of a lower beta?
8. (15 points) Compute the cost of long-term capital for Lennar Corporation. (Think carefully about what number you use for the cost of debt capital.) Justify all the rates that you use. Assume a market risk premium of 5.5%. (Ignore the off-balance sheet ventures for the purpose of this question.) The US Treasury 10-year bond rate is 4.18% (as of May 5, 2005).
9. (20 points) If Lennar announces plans to issue new debt of $1billion and use it to pay a special dividend of $1 billion to stockholders, estimate the increase or decrease in the value of Lennar's equity. Assume that the before-tax required rate of return on Lennar's debt would jump by 100 basis points.
10. (optional) Justify the use of the debt-to-assets ratio, as defined in part 6., to compute the weighted average cost of capital instead of the net debt to capitalization ratio used in parts 4. and 5.? Why does the Dow Jones article use the net debt to capitalization ratio?

1. Article from Dow Jones Newswires, April 22, 2005
2. Balance Sheet Information from Yahoo (in '000s) (http://www.yahoo.com)
3. Key facts about Lennar from WSJ Online
4. Income and Loss Statement (from http://www.yahoo.com)
5. Senior Notes and Other Debts Payable
6. Excerpt from Press Release filed with the SEC

A. Article from Dow Jones Newswires, April 22, 2005

Fitch Assigns 'BBB+' To Lennar Corp.'s $300MM Debt Issue
DOW JONES NEWSWIRES, April 22, 2005 4:53 p.m.

The following is a press release from Fitch Ratings:
Fitch Ratings-New York-April 22, 2005: Fitch Ratings has assigned a 'BBB+' rating to Lennar Corp.'s (NYSE: LEN) $300 million 5.60% senior notes due May 31, 2015. The Rating Outlook is Stable. The issue will be ranked on a pari passu basis with all other senior unsecured debt. Proceeds from the new debt issue are expected to be used for general corporate purposes.

The ratings and Outlook reflect the company's continuing solid financial performance and the expectation that Lennar's credit profile will be maintained as it executes its business model and continues to grow. The ratings also reflect the company's very strong track record over the past 30 years and through many past homebuilding cycles, management's sound operating and financial policies, the company's well positioned, low-basis landholdings in attractive growth markets, and its capacity to withstand a meaningful housing downturn. Lennar's extensive balance sheet liquidity and external liquidity sources position the company to weather a meaningful cyclical downturn and to absorb acquisitions, consistent with its diversified growth strategy. Under a severe housing contraction scenario, the company is expected to generate sufficient cash relative to its financial obligations, allowing the company to manage its capital structure easily within its investment-grade rating.

The rating incorporates the expectations that leverage may periodically spike outside of management's targeted range of 35%-45% as a result of opportunistic acquisitions and that it will be prudently and quickly managed down within that range thereafter (as was the case with the large U.S. Home acquisition in May 2000). The rating also considers the off balance sheet financing of its longer dated land supply and the concentration of deliveries in Florida, Texas, and California (the three largest and among the most supply-constrained state markets in the country). Fitch views Lennar's partnerships and joint ventures (JVs) to be strategically and financially material to the company's operations. However, the manageable leverage levels and the extensive supply of land in attractive markets held in the partnerships mitigate this risk to some extent. In addition, pulling the off balance sheet debt back on balance sheet does not materially alter Lennar's consolidated capital structure. Nevertheless, as these unconsolidated entities grow further and provide an increasing source of Lennar's land needs, it may prove more difficult for Lennar to distance itself from them should they become financially distressed. Although the company derives approximately 68% of deliveries from California, Florida, and Texas, the many significant metropolitan markets within those states with their own unique economic and demographic characteristics and the company's product and price point diversity reduce the state geographic risk.

Lennar has been active in improving homebuilding margins and return on capital during much of this upcycle for housing and especially during the past half dozen years, ranking near the top of its industry peer group with regard to most financial and operating metrics. The company's predominantly build-to-order strategy minimizes speculative inventory and allows management the opportunity to adapt its land reinvestment decisions relative to fluctuation in demand levels in its markets.

As this relatively robust housing cycle continues, creditors benefit from Lennar's financial flexibility supported by $1.89 billion in liquidity as of Feb. 28, 2005 (zero outstanding on its $1.4 billion revolving credit facilities and $495.57 million in unrestricted cash and equivalents), less $250.7 million of letters of credit collateralized against certain borrowings available under the credit facilities. Homebuilding debt to capitalization was 32.5% at the end of the fiscal 2005 first-quarter, while net debt to capitalization was 26.4%. The balance sheet of Lennar's unconsolidated entities (partnerships and JVs) had a debt to capitalization ratio of 51.1% and net debt to capitalization ratio of 46.9% as of Feb. 28, 2005. Assigning Lennar's share of the off balance sheet debt and equity to Lennar's consolidated numbers would only raise its leverage ratio to 36.9%. Under the most extreme (and unlikely) scenario, that of Lennar absorbing all of the partnerships/JVs debt, its consolidated leverage ratio would rise to 49.9%.

B. Balance Sheet Information from Yahoo (in '000s) (http://www.yahoo.com)

C. Key facts about Lennar from WSJ Online

Lennar Corporation (Lennar) operates as a homebuilder and a provider of financial services in the United States. The Company's homebuilding operations include the sale and construction of single-family attached and detached homes, as well as the purchase, development and sale of residential land directly and through unconsolidated partnerships. The Company's financial services subsidiaries provide mortgage financing, title insurance, closing services and insurance agency services for both buyers of Lennar's homes and other buyers, and sell the loans they originate in the secondary mortgage market. Through these financial services operations, the Company also provides high-speed Internet access, cable television and alarm installation and monitoring services to residents of communities the Company develops, as well as other communities.

D. Income and Loss Statement (from http://www.yahoo.com)

E. Senior Notes and Other Debts Payable (From Notes to Financial Statements in the 10-K filed with the SEC on Feb. 14, 2005.

F. Excerpt from Press Release filed with the SEC:

LENNAR COMPLETES $300 MILLION 5.60% 10-YEAR SENIOR NOTES OFFERING

MIAMI, April 28, 2005 — Lennar Corporation (NYSE: LEN and LEN.B) announced that it has completed an offering of $300 million of 5.60% Senior Notes due 2015. The Senior Notes were priced to yield 5.629%. Lennar expects to use the proceeds from this offering for general corporate purposes.

Answers to Final

1. Lennar Corporation is really a combination of two businesses -- one, a homebuilder, that holds land; and two, a provider of financial services. The homebuilding operation, since it holds land and constructed homes in its asset portfolio, can take on debt. The provider of financial services, since it does not have any assets, as such to support its operations would not be able to take on much debt. In addition, the cashflows from its operations are probably volatile, in keeping with overall economy movements.
2. It makes sense for Fitch to include Lennar's off balance-sheet operations in its computation of an overall debt-to-capitalization ratio. This is because these operations are really part of Fitch's overall business, and Fitch's shareholders would be able to take advantage of the debt supported by Lennar's off-balance operations. To the extent that Fitch has responsibility for the debt issued by the joint ventures, etc., again, those operations should be taken into account in computing ratios that reflect Lennar's liabilities. GAAP may not require consolidation of off-balance sheet operations for various reasons -- one, it may desire some sort of comparability across companies, and while off-balance sheet operations may be intrinsic to some companies' operations, such as Lennar, this may not be true for other companies; two, GAAP is subject to political pressures, and while it may very well be moving in the direction of requiring consolidation of currently off-balance operations, it may not require that at the moment because of conflicting pressures from different constituencies. Fitch and other rating agencies don't have those same issues.
3. There are several reasons why Lennar might use off-balance sheet finacing -- one, for window-dressing purposes; since GAAP rules do not currently require inclusion of those numbers, the ratios computed without them might look better; two, it may be easier for Lennar to meet its requirements vis-a-vis ratios for satisfaction of debt covenants, since again, debt covenant ratios are based on GAAP numbers; three, it may want to issue non-recourse debt, supported only by the assets of the joint ventures, etc. Isolating certain streams of cashflow in this fashion may allow it to raise funds overall in the cheapest manner.
4. Interest bearing liabilities, in this case, simply includes the long term debt. So, using the Yahoo numbers, we get net debt equal to 2626308-616139 or 2010169; hence net debt to capitalization works out to 2010169/(2010169+4161508) or 32.57%, since stockholders' equity equals 4161508.
5. Using the WSJ information, we get net debt equal to 2002867-509068 or 1493799; hence net debt to capitalization works out to 1493799/(1493799+4161508) or 26.41%. The WSJ.com site may be more trustworthy, since it sells its data by subscription, and would have more competitive pressure to provide correct numbers.
6. The levered beta for Lennar is 0.544. The marginal tax rate can be computed from the Income Statement for the fiscal year ended 30 Nov. 2004 as Income Tax Expense / Income Before Tax, i.e 573448/1519067 as 37.75%. The debt-equity ratio works out to 2626308/4161508 or 0.63. (Although the definition calls for market values, there is no information on that available to us, hence we are forced to use book value numbers.). Using these data, the unlevered beta works out to 0.544/[1+(1-0.3775)0.63] = 0.391
7. I wouldn't agree with Jane for several reasons -- first of all, it's not clear that her evaluation of the sharp movements in demand for homes is correct; second, Lennar's has a lot of liquidity, as pointed out in the article. The article also points out that even on the homebuilding side, Lennar is geographically diversified and the busines cycle in different states is not perfectly correlated; this reduces the volatility of cashflows from Lennar's homebuilding operations.
8. The cost of debt should be 5.629%, given the information in the recent press release filed with the SEC. After tax, this works out to 5.629(1-0.3775) or 3.504%. The cost of equity works out to 4.18 + 0.544(5.5) = 7.172%. Since we're compute the cost of long-term capital, it would be appropriate to use the D/E ratio computed in part 6, i.e. 0.63 to compute the debt and equity weights; this would be 0.63/1.63 or 0.3865 for debt and 1/1.63 or 0.6135 for equity. The cost of capital, therefore is (0.3865)(3.504) + (0.6135)(7.172) = 5.754% (Note: to be absolutely correct, one should really factor the new debt into the computation of the firm's stock beta, as well as on the correct debt-equity ratio. However, I have not taken that into account, here, in order to simplify the calculations -- also, it will not affect the results greatly.)
9. With the capital structure modifications, the debt-to-equity ratio would become (2626308+1000000)/(4161508-1000000) or 3626308/3161508 = 1.147. Hence the new levered beta becomes 0.391[1+(1-0.3775)(1.147)] = 0.67. The new cost of equity is 4.18 + 0.67(5.5) = 7.866%. The new after-tax cost of debt is 6.629(1-0.3775) = 4.127%. The new debt and equity weights are 1.147/2.147 = 0.534 and 0.466. The new weighted average cost of capital equals (0.534)(4.127) + (0.466)(7.866) or 5.869%. Hence the cost of capital has increased by 0.00115 (i.e. 0.05869-0.05754). If we use the total value of the firm as 8,753,494 in thousands of dollars from the latest balance sheet, the decrease in firm value, and hence the decrease in equity value becomes (0.00115)(8753494)/0.05869 = $171,520,000.
10. One might argue for the use of the debt-to-assets ratio, rather than the net debt-to-capitalization ratio to compute the WACC, since cash has to be financed as well. The issue really is what would happen to cash if the firm's operations were to be scaled up; if the firm would need to scale up its cash as well, then the weights used to compute WACC would need to reflect that, and it would not be appropriate to use the net debt-to-capitalization ratio. However, if the cash would not need to be scaled up, then it would be appropriate to simply subtract that from the debt to get a net debt figure; this could then be used to compute the weights for the WACC. To get a better picture of this, suppose debt were equal to cash in the company's balance sheet, then net debt would be zero, and the net debt-to-capitalization number would work out to zero. If the company were financing a new project, should we only use the cost of equity capital to compute the hurdle rate? If there were going to be no need to add to cash, that would make sense; if the new project would need additional cash for working capital purposes, then it would not make sense to talk of the hurdle rate for the new project as simply being the cost of equity capital.
    The Dow Jones article uses the net debt to capitalization ratio because they want to capture the probability of bankruptcy and the extent of flexibility that the firm has. Obviously, the greater the amount of cash the less the impact of debt on the likelihood of bankruptcy; therefore, this measure reduces debt by the amount of cash. Also, for the same reason, only interest bearing debt is included.