Dr. P.V. Viswanath
|Courses/ FIN 647|
Fall 2010 Exams, FIN 647
1. (20 points) Answer any five of the following questions:
2. (10 points; take-home to be emailed back to the professor by midnight on Wednesday; no collaboration allowed) Read the following article and answer the questions at the end.
3. (15 points) Problem 23, Chapter 12, page 406
4. (10 points) Problem 43, page 372, Chapter 11
5. (15 points) Problem 47, page 373, Chapter 11
6. (15 points) Problem 18, page 405, Chapter 12
7. (8 points) Problem 24, page 327, Chapter 10
8. (7 points) Problem 18, page 326, Chapter 10
9. (10 points) Problem 26, page 125, Chapter 4
4. Identify each of the following risks as most likely to be systematic risk or diversifiable risk:
5. A big pharmaceutical firm, DRIg, has just announced a potential cure for cancer. The stock price went from $4 to $137 in one day. A friend of yours calls you on the phone to tell you that he owns DRIg. You proudly reply that so do you. Since you have been friends for some time, you know that he holds the market, as do you, and so you both are invested in this stock. Both of you care only about expected return and volatility. The risk free rate is 3%, quoted as an APR based on a 365 day year. DRIg made up 0.07% of the market porftolio before the news announcement.
6. Consider a portfolio consisting of the following three stocks:
The volatility of the market portfolio is 10% and it has an expected reutrn of 8%. The risk free rate is 3%.
7. Stock A has a volatility of 43% and a correlation of 29% with your current portfolio. Stock B has a volatility of 117% and a correlation of 33% with your current portfolio. You currently hold both stocks. Which of the below choices will increase the volatility of your portfolio? Select the best choice and explain your answer.
8. Suppose Johnson & Johnson and the Walgreen Company have expecgted returns and volatilities shown below, with a correlation of returns of 22%.
Assume the portfolio is equally invested in these two stocks. If the correlation between Johnson & Johnson's and Walgreen's stock were to increase,
9. Answer any five of the eight questions below (15 points):
The legal sector’s own Big Bang
By Jane Croft, Michael Peel and Martin Arnold, The Financial Times, September 22 2010
The legal industry is not known for its militancy. So it was unusual to see lawyers – rather than their clients – protesting last year outside London’s High Court. They foisted cans of baked beans, branded with the slogan “Legal services by supermarkets is as ridiculous as lawyers selling beans” at bemused bystanders.
The protesters’ anger was directed at the Legal Services Act, which by next October will make the UK one of the most deregulated legal services markets in the world. The reforms have been described as the legal equivalent of the City of London’s “Big Bang” in 1986. Some lawyers, especially in small, high street firms, fear the changes could lead to intense competition from aggressive new entrants at a time when traditional sources of work such as legal aid and property conveyancing are drying up. There are also concerns that the ability of firms to operate outside the UK might be compromised.
For the first time, the UK’s 10,000 law firms will be able to raise fresh capital by floating on the stock market or to form new business structures by bringing in non-lawyers such as accountants as partners.
The aim of the reforms, brought in by the last Labour government, was to make will-writing and conveyancing as accessible for consumers as buying a can of beans from a supermarket.Hence the act has been dubbed “Tesco law”– although the supermarket chain has itself expressed little interest in the legal market.
Australia, which has already introduced similar reforms, has experienced the first flotation of a law firm. Slater & Gordon, a volume personal injury firm, has used fresh capital to acquire 30 smaller rivals and turn over is up from A$62.5m in 2007 to A$124.7m this year due partly to the acquisitions.
In the UK, the imminent change has resulted in private equity groups eyeing the £25bn domestic legal services market, believing it is dominated by inefficiently run groups that are lagging behind in outsourcing and information technology.
“There’s a nasty storm brewing for traditional law firms,” says Jeremy Hand, managing partner of Lyceum Capital, the UK-based mid-market buy-out group. “The downturn, smart er customers, low-cost outsourcers and IT are major challenges and of course the new laws will open up the market to a host of competitors.
“Private equity brings both capital and expertise, so we expect to see deals done with well-placed firms looking to take advantage of the changes as well as new entrants with a fresh approach,” he says.
One such new entrant is the Co-operative Group, the supermarket to financial services group that is Britain’s biggest mutual retailer. It is gearing up to offer legal services to non-members. Eddie Ryan, managing director of Co-operative Legal Services, has spent four years building up its legal practice from four people to 330 in preparation. He believes the Co-op has the advantage of being a trusted brand: “People go to solicitors in time of necessity and distress and they provide the service they need.”
Matthew Hudson of law firm MJ Hudson is one of those who believes the changes will be as transformative as the deregulation of Big Bang. He says there are parallels with merchant banks, such as Cazenove, which were privately owned partnerships in the 1980s but have long since abandoned their partnership structures to become public or quoted companies.
A study this year by Smith & Williamson, the accountancy and professional services group, questioned 121 law firms including 60 of the UK’s top 100 legal firms. It found that a fifth of those questioned would consider flotation to raise external fin ance and 43 per cent would look at private equity.
An early indication of private equity interest came in January when UK-based Intermediate Capital Group agreed a £440m buy-out of CPA Global, a patent and legal services group that has won contracts to outsource law work from companies including Rio Tinto.
Mr Hudson explains private equity’s interest in the sector: “This country is a world leader and English law is a world-leading product. It’s high margin, high growth and highly cost generative, and barriers to entry are high as these are specialist skills.”
Linda Lee, president of the Law Society, which represents lawyers in England and Wales, is more cautious: “I’m not expecting a huge rush of outside investment in law firms next October although there might be some.”
Lawyers say the reforms are most likely to affect smaller to mid-sized law firms that specialise in high-volume areas such as personal injury. London’s Magic Circle firms – which include some of the world’s biggest law firms, such as Clifford Chance and Herbert Smith – are unlikely to seek fresh capital. David Morley, senior partner at Allen & Overy, says: “We don’t need the money. People say there must be a price at which the partners would be willing to sell out, but I am not sure any valuations within the range of the plausible would yield value on such a scale that partners would want to give up control.”
However, Mr Morley does believe the act will have a big impact on the sector. “I certainly wouldn’t subscribe to the view that the Magic Circle wouldn’t be affected by any of these changes,” he says. “They are pretty profound ... They will spark ideas. But flotation? No – not for us.”
Stuart Popham, Clifford Chance senior partner, says it has no plans to take advantage of the changes. “There is no shortage of people prepared to make investments. We have been ap proached by a number of people.” But he adds: “I don’t think we see it as a way of attracting further business or further partners into the firm.”
Barristers are cautious. Nicholas Green QC, chairman of the Bar Council, which represents barristers, agrees there will be activity in the more commoditised end of the legal market. But he points out “there are already fundamental changes happening because of the changes to legal aid. We are doing a lot of work in setting up new business models, so I don’t think the [act] will affect the Bar – although we may see some barristers join law firms.”
In Scotland, with its own legal system, feelings among lawyers ran so high this year that Holyrood’s Justice Committee in June accepted the recommendation of the Law Society of Scotland that the act should be significantly watered down.
Concern has also been voiced outside the UK because many international regulators would not be able to permit UK firms to operate outside the UK if they are being funded by private equity or have non-lawyers as partners in the new-style firms – which are being called Alternative Business Structures.
Regulatory changes that will accompany the act have also triggered concerns. A Legal Services Board has been formed to authorise regulatory bodies such as the Solicitors Regulatory Authority, which regulates all solicitors, to become “licensing authorities” for overseeing the new Alternative Business Structures – which will bring in outside capital or non-lawyers such as accountants.
The approach to regulation will be more flexible and less “rules-based”.
Ms Lee says that the Law Society has concerns that the new regime, due to start in October 2011, is being implemented too quickly.
Others point out that in the financial sector, the UK’s Financial Services Authority jettisoned a rules-based system for a risk-based approach at the start of the decade but failed to spot the looming financial crisis.
David Edmonds, a former telecoms regulator who is now chairman of the Legal Services Board, concedes there are parallels but says the legal sector is more robust: “What you’ll see from October next year is a legal service sector which has proper restrictions in terms of protection for consumers but which, I think, will have the most modern and open regulatory structure in the delivery of legal services anywhere in the world.”
The pace of change is likely to be slow in this most conservative profession. But judging by what happened following the 1980s Big Bang in the financial sector, some observers believe there may yet be a flurry of mergers among law firms or even a stock market listing.
1. a. Use the future value of an annuity formula, or compute the present value of an annuity of $6000 per period for 38 periods, then compound it at 10% p.a. for 38 years to get the answer of $2184260.61.
b. If you repeat the exercise with n=32 periods, you get $1,333,509.27
2. The present value of a perpetuity is 200/r; if we set r = 0.05, we get $4000. Hence the bank's implied interest rate is 5%.
3. Clearly, you're prefer Bank A, since the loans are all independent and the standard deviation of the amount repaid will be lower, while the average amount repaid will be the same for both banks.
5. a. The return on DRIg is 3325% (137/4-1) on that day. So, if DRIg made up 0.07% of the market, and the rest of the market earned 0%, the return on the market portfolio would be 3325*(0.0007) or 2.3275%. The risk-free rate is 3% on an APR basis, or 3/365 = 0.0082192% per day. If the value of your portfolio went up by 1.1%, then we have 2.2375y + (1-y)0.0082192 = 1.1 or y = 48.97% in the market and the rest in the risk-free asset.
6. The beta of a stock is its correlation with the market times the ratio of the stock's volatility to the market volatility. The E(R) is computed using the CAPM formula. For example, for HEC Corp, it would be 3% + 0.63(8-3) or
c. The beta of the portfolio would be 0.21(0.63) + 0.32(1.701) + 0.47(0.484) = 0.904
d. The expected return on the portofolia can be computed using the CAPM to obtain 3+0.904(8-3) = 7.52%
7. As you increase the proportion in A, the volatility of the portfolio increases at a rate given by Corr(A,P).Stddev(A), which works out to (0.29)(43) for A and (0.33)(117) for B. This means that increasing the amount in B and decreasing the amount in A should increase portfolio volatility. But once we’ve moved a little in this direction, the correlation of B with P should increase and that of A with P should decrease. In other words, if a little movement away from A and towards B is good, a lot of it should be even better. Hence the answer is a. selling 50% of stock A and investing the proceeds in stock B.
8. If the correlation increases, the expected return of the portfolio would not be affected. However, the volatility of the portfolio would increase.
1. Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin's equity beta is 0.81, the risk-free rate is 5%, and the market risk premium is 6%.
a. (5 points) If your firm's project is all equity financed, estimate its cost of capital.
b. (5 points) Assume Thurbinar's debt has a beta of zero. Estimate Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar's unlevered cost of capital.
c. (5 points) Estimate Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these results, estimate Thurbinar's unlevered cost of capital.
d. (5 points) Explain the difference between your estimate in part (b) and part (c).
e. (5 points) You decide to average your results in part (b) and part (c), and then average this result with your estimate from part (a). What is your estimate for the cost of capital of your firm's project?
2. State whether each of the following is inconsistent with an efficient capital market, the CAPM, or both:
a. (5 points) A security with only diversifiable risk has an expected return that exceeds the risk-free interest rate.
b. (5 points) A security with a beta of 1 had a return last year of 15% when the market had a return of 9%.
c. (5 points) Small stocks with betas of 1.5 tend to have higher returns on average than large stocks with betas of 1.5.
3. A hedge fund has created a portfolio using just two stocks. It has shorted $48,000,000 worth of Oracle stock and has purchased $71,000,000 of Intel stock. The correlation between Oracle's and Intel's returns is 0.65. The expected returns and standard deviations of the two stocks are given in the table below:
a. (5 points) What is the expected return of the hedge fund's portfolio?
b. (5 points) What is the standard deviation of the hedge fund's portfolio?
1. a. The cost of capital can be computed using the CAPM as 5+0.81(6) = 9.86%
b. Thurbinar's total value is 19(16) + 117 = 304 + 117= 421. Thurbinar's asset beta is a weighted average of its stock and debt betas; hence it equals (117/421)(0) + (304/421)(1) = 0.72209; using the CAPM, we get the required rate of return for unlevered Thurbinar equity to be 5 + 6(0.72209) = 9.3325%.
c. Thurbinar's equity cost of capital is 5+6(1) = 11%. Hence its unlevered cost of capital is (117/421)(4.3) + (304/421)(11) = 9.138005%
d. The answer in b. assumes that the debt is riskless; hence it provides an overly low beta estimate for the unlevered equity of Thurbinar and hence an overly low required rate of return for Thurbinar's unlevered equity; the answer in c. is also an underestimate because Thurbinar's debt yield is less than the risk-free rate; since the expected rate of return is less than the yield (which is the return if there is no bankruptcy), this number must be in error, assuming that Thurbinar's debt is risky. Hence this is probably also too low an estimate.
Another possibility is that Thurbinar's debt has a negative beta. Hence the estimate in (d) is too high because it uses a yield, while the estimate in c. is too low since it assumes that the debt is totally riskless.
e. If you average the two, you get 9.235. Averaging this with my original estimate in a. gets me 9.5476%.
2. a. The expected return should be the same as the riskfree rate; hence the answer is B.
b. The answer is A; it could have a return different from that of the market because of the idiosyncratic component.
c. It's inconsistent with the CAPM because according to the CAPM, the size of the company is irrelevant; however, the CAPM could be wrong in an efficient capital market and firm size could be relevant; hence the statement could be correct. The correct choice is D.
3. a. The weights are (-48/(71-48) = -2.087 for Oracle and +3.087 for Intel. The expected return is given by (-2.087)(12) + (3.087)(14.5) = 19.7175%
b. The variance of the portfolio is given by (-2.087)2452 + (3.087)2402 + 2(-2.087)(3.087)(0.65)(40)(45) = 8991.726; taking the square root, we get 94.82%
Read the article entitled "Loehmann’s Files for Chapter 11" below from the WSJ of Nov. 15, 2010 and answer the following questions:
The parent company of Loehmann's, one of the early names among discount retailers of designer apparel, filed for bankruptcy protection, with a plan to reduce its debt by $115 million and recapitalize its balance sheet.
Loehmann's Holdings Inc. was acquired in 2006 by Istithmar World, an arm of the Dubai government's investment fund, for $300 million.
During the past year, Loehmann's has been hit with declining sales and financial constraints stemming from a "highly leveraged capital structure," Joseph Melvin, the retailer's chief operating officer, said in court papers filed Monday.
Founded in 1921 and based in New York City, Loehmann's currently runs more than 45 stores in 12 states and Washington, D.C. Its operations are expected to continue as normal during the reorganization process.
The bankruptcy filing is the latest blow for Istithmar World, a unit of Dubai World. After splurging on trophy assets under former Chief Executive David Jackson, Istithmar has struggled to meet debt obligations on some of its showpiece assets. Last year, Istithmar lost control of the W Hotel Union Square in Manhattan, and this year it lost the former Knickerbocker Hotel near Times Square. Mr. Jackson left the company in January.
Istithmar World bought upscale retailer Barneys in 2007 for $942 million, or 13 times earnings, making it the most expensive retail deal of the recent luxury boom.
The restructuring plan has the backing of Whippoorwill Associates Inc., which is the agent for discretionary funds and accounts representing approximately 70% of senior secured notes.
An affiliate of Loehmann's owes $110 million under notes, according to court documents. Under the restructuring plan, one group of noteholders will receive 42.4% of the reorganized equity, another group of noteholders will receive 8.6% of the reorganized equity, and Istithmar World and Whippoorwill will get 49.1% of the equity, subject to dilution for any new equity issued as part of a management-incentive plan.
The company said it doesn't have an estimate for how much unsecured creditors will recover at this time because it is waiting for these creditors to file claims.
In its bankruptcy petition filed Monday with the U.S. Bankruptcy Court in Manhattan, Loehmann's listed having between $100 million and $500 million in assets. Its debts were listed in the same range.
Crystal Financial has offered to provide $45 million in bankruptcy financing. And Istithmar World and Whippoorwill have agreed to invest $25 million once Loehmann's emerges from bankruptcy, "in the form of convertible preferred equity stake."
The plan and financing arrangements are subject to bankruptcy-court approval. Loehmann's expects to complete its restructuring and emerge from Chapter 11 during the first quarter of 2011.
"We look forward to working constructively through this process and achieving a consensual restructuring," said Andy Watson, Istithmar World's acting CEO, in a statement.
Dubai World recently reached a deal with creditors over nearly $25 billion in debt, after announcing a debt standstill almost a year ago that shook global investors and triggered a financial bailout from Dubai's richer neighbor, Abu Dhabi. Both are semiautonomous emirates of the United Arab Emirates. Dubai World's restructuring deal doesn't include Istithmar debt.
1. (15 points) Read the following article, "Film financing: Hedge funds say it's a wrap, but should they?" which appeared in the May 2009 issue of Euromoney and answer the questions below. Keep in mind that simplistic answers will not be sufficient. I will be looking to see if you have done any research as well as whether you have thought about the matter. Appropriate quotations from sources will be appreciated; you may want to also look at the article by Edward Fee, “The costs of outside equity control: Evidence from motion picture financing,” Journal of Business, Oct. 2002, vol. 75, n. 4, pp. 681 ff.
Investing in studios' slates of films had become big business for hedge funds and banks over 2005 to 2008 with the two side partnering up to create vehicles. Studios, strapped for cash and keen to offload some risk of flops in return for shares in DVD and TV sales profits, had turned to Wall Street to help them. Deals were put together whereby hedge funds and banks invested alongside the studio in seven to 25 films to be made in the future. About $15 billion is estimated to have been invested in slates of films over the three-year period ending 2008. Merrill Lynch, Credit Suisse, Deutsche Bank, Goldman Sachs, Citigroup and JPMorgan all arranged co-financing deals with studios raising money from hedge funds and private equity firms. Hedge funds such as Dune Capital and Clark Investments also created co-financing vehicles.
Last year, though, the banks started backing out of film financing, with some, such as Citi, pulling out altogether. Gordon Clark of the Movie Portfolio Fund says he is not surprised. A former CFO of a bank, Clark says he knows all too well that Wall Street and films do not always go well together. "Investing in film is a long-term commitment, and banks are notoriously short-term in their judgments. They only started getting in to slate financing deals in 2005 and already they have pulled out."
Clark's firm looks to invest over at least a five-year period. "It can take two years to begin earning revenue from a movie, and then about five to seven years to collect the bulk of the revenue," he says.
Breaking commitments halfway through a slate of films is damaging for the studios, which end up without partners, and can be costly for the hedge funds and banks, which might face lawsuits for breach of contract. Instead, Wall Street is trying to find speciality partners who can take over their side of the contract, often at a discount. It is good news for smaller funds with expertise in film financing.
Indeed, Clark says now is a good time to be in film finance. Films tend to do well in both good and bad economic situations and provide a hedge and diversification to investors. "The returns are uncorrelated with markets -- 2009 has been a record year so far for the film industry," he says. "Box office sales in January this year were the highest in any January on record for example."
The hedge funds and banks failed in their investments because of lack of expertise, Clark suggests. "The studios managed to construct the deals on their terms, often including the banks and hedge funds on films that were deemed to have less potential," he says. Sequels to best-selling films such as Spiderman were left out of deal contracts, while less attractive films, such as flop Poseidon Adventure, were included, for example. "People tend to jump in when there is a boom without truly knowing what they are getting into," says Clark. "There was a lack of real understanding but those who have a long-term interest in investing in movies stand to make good returns."
2. Mercer Corporation is an all-equity firm with 10 million shares outstanding and $96 million worth of debt outstanding. Its current share price is $66. Mercer's equity cost of capital is 8.5%. Mercer has just announced that it will issue $370 million worth of debt. It will use the proceeds from this debt to pay off its existing debt, and use the remaining $274 million to pay an immediate dividend. Assume perfect capital markets.
3. Garnet Corporation is considering issuing risk-free debt, or risk-free preferred stock. The tax rate on interest income is 35%, and the tax rate on dividends or capital gains from preferred stock is 25%. However, the dividends on preferred stock are not deductible for corporate tax purposes, and the corporate tax rate is 35%.
4. Zymase is a biotechnology startup. Researchers at Zymase must choose one of three different research strategies. The payoffs (after-tax) and their likelihood for each strategy are shown below. The risk of each project is diversifiable.
5. If it is managed efficiently, Remel Inc. will have assets with a market value of $50.8 million, $101.3 million or $149.3 million next year, with each outcome being equally likely. However, managers may engage in wasteful empire building, which will reduce the market value by $5.3 millino in all cases. Managers may also increase the risk of the firm, changing the probbability of each outcome to 48%, 10% and 42% respectively.
6. On Monday, November 15, 2004, TheStreet.Com reported: "An experiment in the efficiency of financial marktes will play out Monday following the expiration of a $4.10 dividend privilege for holders of Moft Industries." The story went on: "The stock is currently trading ex-dividend both the special $4 payout and Moft Industries' regular 10-cent quarterly dividend, meaning a buyer doesn't receive the money if he acquires the shares now." Moft Industries stock ultimately opened for trade at $27 on the ex-dividend date (November 15), down $4.10 from its previous close.
7. You are on your way to an important budget meeting. In the elevator, you review the project valuation analysis you had your summer associate prepare for one of the projects to be discussed:
Looking over the spreadsheet, you realize that while all of the cash flow estimates are correct, your associate used the flow-to-equity valuation methods and discounted the cash flows using the company's equity cost of capital of 11%. However, the project's incremental leverage is very different from the company's historical debt-equity ratio of 0.20: for this project, the company will instead borrow $80 million upfront and repay $20 milliion in year 2, $20 million in year 3, and $40 million in year 4. Thus the project's equity cost of capital is likely to be higher than the firm's, not constant over time -- invalidating your associate's calculation.
Clearly, the FTE approach is not the best way to analyze this project. Fortunately, you have your calculator with you, and with any luck you can use a better method before the meeting starts.
8. (15 points) Answer any three of the following questions:
2.a. Note that capital markets are perfect. Therefore the announcement of an recapitalization without any change in the assets will not affect the stock price. Of course, in this case, this is true by virtue of the Modigliani-Miller hypothesis. However, even in the real world, i.e. one where Modigiliani-Miller does not hold, it is instructive to see what Koller, Dobbs and Huyett say in the McKinsey Company publication "The Four Cornerstones of Corporate Finance": Value is created ... not by rearranging investors' claims on [companies'] cash flows.
b. Once the transaction is completed, the total amount of debt is $370m. The amount of equity is the original $660m. less the $274m. dividend, i.e. $386m. The number of shares outstanding is still 10m.; hence the price per share is $386m./10m. or $38.60.
c. From Modigiliani-Miller, we know that the WACC will not change after the recapitalization. The WACC before the recapitalization was 8.5(660/756)+4.54(96/756) = 8%. The new cost of equity capital will, therefore, satisfy 8% = re(386/756)+5.04(370/756). We find that re = 10.83%.
3.a. The assumption, here, is that the adjustment will take place on the demand side for corporate securities. An investor's after-tax return will be 8(1-0.35) on debt, while it will be rp(1-0.25) on preferred stock. In equilibrium, the rates of return will adjust so that investors are indifferent on an after-tax basis to buying preferred stock or debt. So setting 8(1-0.35) = rp(1-0.25), we find that rp= 6.93%.
b. The after tax debt cost of capital for the firm is 8(1-tc) = 8(1-0.35) = 5.2%; obviously, since 5.2% < 6.93%, debt is cheaper for the firm than preferred stock.
Note that (1-t*) = [(1-tc)(1-ti)]/(1-te) = (1-0.35)(1-0.25)/(1-0.35) = 0.75. The after-tax debt cost of capital is 5.2%, while the preferred stock cost of capital multiplied by (1-t*) = 6.93(0.75) = 5.2%; hence we see that the after-tax debt cost of capital is simply equal to (1-t*) multiplied by the preferred stock cost of capital. Since preferred stock has the same tax consequences as common equity, this fact demonstrates that the implicit tax benefit of debt with respect to equity is really t*.
4. a. The expected payoff of project A is $85m and that of project B is 0.5(150) = $75m. The expected payoff of project C is (0.1)350+(0.9)30 = 62. Hence project A has the highest payoff.
b. If Zymase has debt of $35m. due at the time of the project's payoff, the revised payoffs to the equity holders will be Max(Original payoff - 35, 0). Using this information, we see that the expected payoff to equity holders from project A is 85-35 = $50; from project B is 0.5(150-35) = $57.5; from project C is 0.1(350-35) = $31.5. Hence project B will be preferred by equity holders.
c. Using the same approach, the respective cash flows to equity holders from the three projects are 0; 0.5(30) = $15; and 0.1(220) = $22. Hence project C will now be preferred.
d. In this case, the amount of agency costs would be the loss in NPV due to the choice of the suboptimal project, i.e. $85 (the NPV of project A) less $75, the NPV of project B, i.e. $10m.
5.a. If managers run the firm efficiently, the firm would be worth (50.8+101.3+149.3)/3 = 100.47. If there is no debt, then according to the assumptions, managers will engage in wasteful empire building, and the value of the firm would be 100.47 - 5.3 = $95.17m.
b.i. The first thing to note is that a non-zero probability of bankruptcy is what leads managers to take on additional risk. Under these circumstances, if managers did increase the risk of the firm, the value of the firm would be 0.48(50.8) + 0.1(101.3) + 0.42(149.3) = $97.22m. If the debt due in one year is $41.5m., then the managers would not go bankrupt in any state of nature, hence the existence of debt would not affect their decision regarding the level of risk of the firm. In this case, engaging in wasteful expenditure would also not increase the probability of default, since the state with the lowest value, $50.8 is still greater than the amount of debt due, $41.5 by more than the $5.3, which is the cost of empire building. Hence in this case, the expected value of Remel's assets would be $95.17m. as in part a. The managers would empire-build, but would not increase risk.
b.ii. In this case, also, the firm would not go bankrupt due to the existence of debt; hence the managers would not increase the amount of risk. However, now, the managers would not engage in empire building, because this would then cause the firm to go bankrupt in the first state. Hence the expected value of Remel's assets would be $100.47. The managers would not empire build and would not increase risk.
b. iii. In this case, the firm would go bankrupt in state 1; hence the expected value of the firm to equity holders would be 0.33(101.3-90.1) + 0.33(149.3-90.1) = $23.232m. But if the managers increased the riskiness of the firm, the expected value would rise to 0.1(101.3-90.1) + 0.42(149.3-90.1) = $25.984m. Hence the managers would take on additional risk. In state 1, the firm would definitely go bankrupt; in state 2, it would not go bankrupt even if the managers engaged in empire building (101.3-90.1-5.3>0); and the same is the case for state 3. Hence, the managers would engage in empire building. The expected value of the assets would therefore by 97.22-5.3 = 91.92m. The managers would increase risk and empire-build.
b.iv. In this case, again, the managers would choose to engage in risk. However, now, empire building would cause the firm to go bankrupt in state two, since (101.3-97.4-5.3<0); hence managers would not empire-build, and the expected value of the firm's assets would be $97.22m. The managers would increase risk, but would not empire build.
c. In this case, we are not assuming the level of debt to begin with. Managers have to decide what level of debt to choose. Note that the payment of the amount of the debt and the tax savings as an immediate dividend should not have an impact on the decision to take on risk or not, since once the debt has been issued, the dividend payment is to be considered as a "sunk cost." Hence the managers would take the same decisions. The expected value of the firm in one year would still be $95.17, $100.47, $91.92 and $97.22, without considering the tax savings.
The expected payoff the debt will be $41.5 in case 1 and $47.9 in case 2, since there won't be any bankruptcy. However, in case 3, the payoff will be only 50.8-5.3 or 45.5 in state 1, but the entire 90.1 in states 2 and 3; hence the expected payoff to debt will be 0.48(45.5) + 0.52(90.1) = 68.692. In case 4, the payoff in state 1 will be the entire 50.8 value of the assets without any losses due to empire-building, but in the other two states, bondholders will be paid in full; hence the expected value of the payoff to bondholders will be 0.48(50.8) + 0.52(97.4) = 75.032.
The expected value of the firm in one year including tax savings would, therefore, be $95.17 + 0.09(41.5), $100.47 + 0.09(47.9), $91.92 + 0.09(68.692) and $97.22 + 0.09(75.032); this works out to $98.905m., $104.781m., $98.102m. and $103.973 respectively. The optimal amount of debt is therefore for case 2, viz. $47.9m.
We need to keep in mind two things. One, the proceeds from the debt will not be the same as the face value of the debt; the market will take into account both the discount rate, as well as the probability of bankruptcy. Two, we must assume that the 9% number refers to the value of the tax savings in one year's time; else, we would not be able to add the expected value of the assets without the tax savings and the tax savings to make a decision on the optimal level of debt!
The table below summarizes all the information, above.
6. a. The effective dividend tax rate must be 0%, since the price drop was exactly the amount of the dividend.
b. Based on this information, pension funds are most likely to be the marginal investors because they are tax-exempt and it makes no difference to them whether they receive their returns in the form of dividends or capital gains.
7.a. The tax rate for the firm seems to be 40% based on the ratio of taxes to EBIT. Hence the tax savings due to debt would be 4(0.4), 4(0.4), 3(0.4) and 2(0.4) or $1.6, $1.6, $1.2 and $0.8 in the four years. We discount these at the same rate as the debt to obtain a present value of tax savings of 1.6/(1.05) + 1.6/(1.05)2 + 1.2/(1.05)3 + 0.8/(1.05)4 = 4.67m.
b. The FCF can be computed as 10.1(0.6)+25; 9.9(0.6)+25; 9.7(0.6)+25 and 9.8(0.6)+25+20 (recoupment of NWC), which works out to 31.06, 30.94, 30.82 and 50.88. Keep in mind that these are the free cash flows to the firm -- not to equity!
c. These free cash flows have to be discounted at the project cost of capital, which is (0.2/1.2)(0.05) + (1/1.2)(0.11) = 10%. Discounting these cashflows at the project cost of capital of 10%, we get $111.714. Subtracting from this, the initial investments of 100 in Capital Expenditures and 20 in Net Working Capital, we get 111.714-120 or -8.286. To this, we must add the 4.67, which are the tax benefits of debt for a total positive NPV of -3.616.
8. a. Growth industries using the web to deliver services, like the entertainment delivery industry (e.g. Netflix) do not have much debt because earnings are volatile and tangible, liquid assets are low. Industries like software development also have low debt, partly for similar reasons, but also because the agency costs of debt would be high -- leverage could create an incentive to take on excessive debt.
b. The underinvestment problem refers to the fact that equity investors in a leveraged firm often do not have an incentive to invest in the firm because proceeds from the investment would go first to bondholders. If bankruptcy is likely, then the effect of the investment might simply be to increase the payoff to bondholders in these states of the economy, where the firm would be bankrupt and equity holders would anyway get little or nothing from the investment. The net result is that the investment might look like a negative NPV investment to equity holders, even though from the point of view of total cash flows, it might have a positive NPV.
c. Stock prices drop on the ex-dividend date. However, the amount of the drop is often less than the amount of the dividend because investors are taxed higher on dividends than on capital gains. Hence the amount of the drop is equal to the after-tax value of the dividend to the stock holder. However, if some investors are taxed at the same rate on dividends as on capital gains/losses, they might not mind receiving the dividend. In this case, they would buy the stock just before the ex-dividend date, receive the dividend, suffer the price loss which would cancel out the dividend causing a zero tax impact for them.
However, the former investors, instead of receiving the dividend and paying taxes at a higher rate would, instead, buy the stock on the ex-dividend date and hold it until just before the next ex-dividend date; they would end up paying taxes at a lower rate on the capital gains that they would accrue. The net result would be a loss of tax revenue to the IRS. The actual sharing of gains between the two parties need not be as shown in this example, however. In general, both parties would benefit.
d. This statement is not strictly true as it reads. Some firms might have higher volatility. Such firms would not be able to exploit their tax deductions in each year, if they don't have enough taxable income. This may lead to a less advantageous time distribution of tax benefits.
e. One advantage is that shareholders that need to obtain the funds can sell their shares to the firm and would not have to suffer the transaction costs of selling a small number of shares on the market to obtain those funds. Also, those investors with the greatest tax advantage to selling can choose to sell. In the case of dividends, all shareholders have to receive dividends and pay taxes on them. Of course, capital gains often are taxed at a lower rate than dividends; this is an additional advantage.