Dr. P.V. Viswanath



Economics/Finance on the Web
Student Interest

  Courses/ FIN 647  

Fall 2009 Exams, FIN 647





  • If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  • 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.
  • You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
  • You must explain all your answers.

1. (15 points) Read the following letter sent to the WSJ article on September 1, 2009 and answer the questions below:

  1. Mr. Weighell writes: "Risk is defined as the unrealized potential for a negative event." To what extent does standard deviation as a measure of risk satisfy this definition? When would standard deviation of returns suffice to measure "the unrealized potential for a negative event"?
  2. "If markets were good at pricing by risk, then, for example, the collapse of a bank would be preceded by a gradual lowering of its stock price until at the moment of failure the stock price would reach zero. " Comment based on theories and concepts that we have discussed in class.
  3. "If we really want to factor crash risk into pricing then consider: We can say with certainty that, as time passes, the risk of the next crash increases. So market prices should be pushed down as the risk of failure grows with each passing day." Is this true? (Hint: Consider a sequence of coin tosses. Suppose your first toss delivers heads. What is the probability of a tail sometime in the future? Suppose in your sequence of realizations, you keep getting heads. How does the probability of heads change as you keep tossing and keep getting heads?

Markets Always Underprice the Risk of a Crash

As a market-watching professional for 25 years, I cannot let pass Steve Francis's comment that "Over the long term, markets are outstanding evaluators of risk." (Letter to the Editor, August 26). Markets are demonstrably no such thing—although they are undoubtedly excellent setters of asset prices based on known or expected events.

Risk is defined as the unrealized potential for a negative event. In this context, that may be the rapid collapse of asset prices. If markets were good at pricing by risk, then, for example, the collapse of a bank would be preceded by a gradual lowering of its stock price until at the moment of failure the stock price would reach zero. In contrast, however, the stock price of several now failed banks kept rising and only fell after it was revealed that they were in trouble. The problem is always that risk is a hidden but growing bubble that can only be priced by a market after it has surfaced, when it is too late.

To compound the pricing problem, we like to think we can factor calculated, numeric risk, or numeric risk profiles, into price decisions. But we usually fail to factor in the certainty of those risk measurements—a major factor in the recent global debacle. Although we may know that markets fail dramatically every so often, we have no idea of when they will fail. So we can say with 100% certainty that there will be another market crash in the future, but we only know when that crash will occur with 0% certainty—i.e., we have no idea.

If we really want to factor crash risk into pricing then consider: We can say with certainty that, as time passes, the risk of the next crash increases. So market prices should be pushed down as the risk of failure grows with each passing day. Sadly, we don't know if the next crash will be in one year or 1,000 years, so we cannot know by how much we should lower prices each day. So we don't lower the prices and so we don't factor the risk of another crash into the market. A market price then never contains the correct level of risk of the next crash simply because we don't know what that price variation should be. As a result, market prices are generally always a bit higher than they should be.

Unfortunately it is an understandable human failing that the longer the time period since the previous crash, the less likely we are to think the next one is imminent. This, however, is the exact opposite of the underlying risk probability, which grows daily just as we think it recedes daily. The failure of markets to evaluate risk before it becomes certainty explains why markets generally rise gently for long periods and then suddenly fail. Investor confidence in a rising market grows with that rising market but all the time the real risk of the next crash is inexorably growing too—until at some point the risk becomes certainty and the market crashes again.

Far from being a leading indicator of risk then, markets are instead lagging indicators of what has become, by then, the blindingly certain.

Paul J. Weighell
Purley, United Kingdom

2. You are a precocious type and although you just turned 25 (yesterday was your birthday), you have already received your MBA degree. Not only that, you have a great job. Being a far-seeing person, you decide to start saving on a regular basis. Your firm has an investment plan, which requires you to contribute every month, with your first payment being at the end of the current month (it's the first of the month today) and the last payment being the day you turn 59. Your firm's retirement plan invests in a portfolio of securities that have a beta of 0.8. The risk-free rate now is also 5% p.a. and you estimate the market risk premium to be 6% p.a. (not the expected rate of return on the market).

You can withdraw the entire amount of your investments at the age of 60. And since you don't want any risk regarding your retirement expenditures, you plan to withdraw all your investments on your 60th birthday (other than what you will be keeping behind to consume for the coming year) and invest them in riskless Treasury securities, which you expect will yield about 5% per annum when you will retire.

You want to be able to spend $200,000 a year during your retirement. You expect to die at the age of 100 -- which means that your last withdrawal would be when you turn 99, which will carry you until your 100th birthday. Note that withdrawals will be once a year.

  1. (5 points) What is the expected rate at which your retirement contributions will grow?
  2. (10 points) If you want your retirement plan to be fully funded, that is, the present value of your intended withdrawals equals the present value of your contributions to your fund, what should be the amount of your monthly saving while you are employed?
  3. (5 points) Would you be fully protected for your retirement, if you used this strategy? Why or why not?

3. (20 points) Answer any four questions:

  1. What is the purpose of the Annual Meeting from a Corporate Governance point of view?
  2. What are the determinants of expected rates of return on assets in an economy?
  3. Why is better to use data from a longer period to estimate mean returns?
  4. How would you evaluate the multiples approach in relation to the DCF approach to valuation?
  5. According to the Fama-French-Carhart model, do stocks with higher book-to-market ratios earn higher or lower returns, on average? Why do you think such a situation exists?

4. (10 points) Answer either part a) or part b)

  1. Comment on the following excerpt from an Economist (September 7, 2009) article on different ways of setting up company boards (of directors) in different countries. Discuss the relative advantages and disadvantages of the German and American systems in not more than five or six sentences:
    Company boards. The biggest distinction here is between Germany and the rest of the world. The German system has two boards—a supervisory board and a management board—their different roles explained largely by their names. Other countries have only one. But that one can still vary greatly in its composition and its powers. American boards are often stuffed with cronies of the CEO. French boards generally include someone who is or was a senior politician. German management boards, by law, must include workers’ representatives.
  2. Explain why tests of the CAPM might not provide support for the theory even if the theory is, in fact, true.

5. Your firm's R&D department has discovered a fantastic toothpaste. And you're thinking of moving forward with you. You have the following forecasts for two equally likely scenarios.

Scenario R(project) R(S&P500)
1 5% 7%
2 9% 12%
  1. (5 points) What is the required rate of return on the project if the risk-free rate is 5.5%? Would you move ahead with the project?
  2. (5 points) You are given the following additional information on estimated expected monthly returns for three different portfolios:
    Factor Average Monthly Return

    If the betas of the project with respect to the SMB, HML and PR1YR factors are -0.374, -0.255 and -0.53, would you change your mind using the Fama-French-Carhart model?
  3. (5 points) Explain the construction of any one of the SMB, HML or PR1YR factors.

6. You have the following data on end-of-month prices for Walmart (WMT) stock on the NYSE from Yahoo. Dividends are paid at the end of the month.

Date Close Dividend
October 51.22
Sept 49.09
Aug 0.273
Aug 50.87
July 49.88
June 48.44
May 0.273
May 49.74

Assume that prices given are end-of-month prices and that dividends are paid at the end of the month.

  1. (5 points) Using this information, what is your estimate of the expected monthly return on WMT?
  2. (5 points) What is your estimate of the standard deviation of monthly returns on WMT?
  3. (5 points) Provide a 95% confidence interval for the expected monthly return?
  4. (5 points) If you discover that the price at the end of April was $50.4, how would this change your confidence interval? Use the new information to recompute your estimate of the expected monthly return, but assume that the new information does not change your estimate of the standard deviation of monthly returns on WMT stock.

Solution to Midterm


  1. Standard deviation woudl be able to measure the unrealized potential for a negative event, only if return distributions were symmetric. In this case, the unrealized potential for a positive event is the same as the unrealized potential for a negative event and they can both be measured by the standard deviation. If this were not the case, then we would have to take the skewness into account.
  2. If markets were informationally efficient, then we could not have a "gradual lowering" of the stock price except to the extent that there was a sequence of unexpected negative events (which is unlikely). Hence if markets were good at risk, we would, in general, not have a gradual lowering of the stock price of banks.
  3. What Mr. Weighell says is true if his assumption is true, viz. that as time passes, the risk of a crash increases. If prices were mean reverting, then the more prices kept rising, the greater the chance of a crash. It is not at clear that this should be so. For example, in a sequence of independent coin tosses, if we kept getting heads by chance, we would not say that the probability of a tails goes up -- if the coin is truly unbiased, then the probability of a tails is always 50%. Similarly, in our case, prices could very well increase for a long-time because value increases -- for example, if the average productivity of capital is positive. This would not imply that the price rises were due to bubbles and would need to crash!


  1. The expected rate of return is 5% + 0.8(6%) = 9.8%. On a monthly basis, this works out to 0.7821%.
  2. Since yesterday was your 25th birthday, and you're going to save every month until your 59th birthday, you have 34*12 = 408 payments to make. Suppose you save $C per month; then the present value of your savings would be [(C/0.007821)[1-(1.007821)-408] or $122.5321C. On your 60th birthday, this will have an expected value of [(C/.007821)[1-(1.007821)-408](1.098)35 = 3230.9614C. Excluding the $200K that will be withdrawn on the 60th birthday, there will be 39 annual withdrawals of $200K. Since you will be investing the retirement savings in riskfree securities yielding 5%, in order to have enough, you will have to have accumulated on your 60th birthday, [(200/0.05)[1-(1.05)-39] = 3403.408K. Add to this, the 200K to be withdrawn on the 60th birthday, and the condition for full-funding is [(200/0.05)[1-(1.05)-39]+200 = [(C/.007821)[1-(1.007821)-408](1.098)35 or 3603.208K = 3230.9614C. Solving this, we find C = 1.115212K or $1115.212.
  3. You would not be fully protected because the accumulation on your 60th birthday is only an expected accumulation and if returns are lower during the accumulation period, there may not be enough to allow $200K withdrawals every year.


  1. The purpose of an annual general meeting, from a corporate governance point of view, is to allow shareholders to monitor management and ensure that they are keeping to their true objectives, which is maximizing shareholder wealth.
  2. The determinants of expected rates of return on assets in an economy are:
    • The expected productivity of capital goods
    • The degree of uncertainty about the productivity of capital goods
    • Time Preferences of people
    • Risk Aversion
    • Expected Inflation
  3. It is better to use data from a longer period to estimate mean returns because as long as observations are relatively independent, this increases the reliability of the mean return (i.e. it reduces the standard error).
  4. The multiples approach value a security with respect to its peer group, while the DCF approach values it with respect to the entire market.
  5. They earn higher returns, since the expected return on the HML portfolio has been, on average, positive (0.53% per month, averaged over the past several years). This may be because stocks with higher book-to-market have greater risk of some sort. Alternatively, if the market is inefficient, then higher book-to-market stocks would be underpriced and the higher average return would represent a correction.


  1. The advantage of the German system is that the supervisory board, to the extent that it is independent of management can perform a true monitoring function of management. Furthermore, the presence of workers' representatives on the management board ensures that agency costs between management/shareholders and workers are minimized. On the other hand, having two different boards can make it more difficult for the CEO to get anything done. Flexibility might be lower.
  2. Even if the CAPM is true, empirical tests may not support it. For one reason, it's difficult to get returns on the true market portfolio. This is because price data on art, real estate and even bonds are not that easy to come by. Human capital is also theoretically part of the market portfolio -- markets for human capital are very illiquid, and might not even exist.


  1. The beta of the project is (9-5)/(12-7)=0.8. The expected return on the market is 0.5(7) + 0.5(12) = 9.5%. Hence, using the CAPM, the required rate of return is 5.5%+0.8(9.5-5.5) = 8.7%. The expected return on the project is 0.5(5) + 0.5(9) = 7% < 8.7%. Hence we would not move forward with the project.
  2. The annualized factor premiums for the SMB, HML and PR1YR factors are (1.00176)12 -1 (= 2.1326%), (1.00542)12 (= 6.70143%) and (1.00758)12(= 9.485%). The required rate of return, using the Fama-French-Carhart model, can be computed as 5.5% + 0.8(9.5-5.5) -0.374(2.1326) - 0.255(6.70143) - 0.53(9.485), which comes to 5.6307% < 7%. We would, therefore, accept the project.
  3. The SMB (small-minus-big) portfolio is a self-financing portfolio consisting of long positions in small stocks financed by short positions in large stocks. The HML (high-minus-low) portfolio is a self-financing portfolio consisting of long positions in stocks with high book-to-market ratios financed by short positions in stocks with low book-to-market ratios. The PR1YR (prior 1-yr momentum) portfolio is a self-financing portfolio consisting of long positions in the top 30% of stocks that did well the previous year financed by short positions the bottom 30% stocks.


  1. If we have price data from May to October, we can compute returns for the months June, July, Aug, Sep and October. Thus, the return for August would be (50.87+0.273)/49.88 - 1 or 2.5321%. The expected monthly return is estimated by adding all the returns and dividing by the number of returns,viz. 5.
    The standard deviation is obtained by taking the sum of the five squared deviations and dividing by 4 (i.e. 5-1).

    Date Close Dividend Return Sq Dev from Mean
    October 51.22 0.04339 0.0013
    Sept 49.09 -0.03499 0.0012
    Aug 50.87 0.273 0.025321 0.0006
    July 49.88 0.029727 0.0006
    June 48.44 -0.02614 0.0007
    May 49.74 0.273 -0.00768
    April  50.4
    Average (May to Oct) 0.75%
    Std Devn 0.0334
    Std Error of Mean 0.014923
    Average (Apr to Oct) 0.49%

    The estimate of the expected monthly return is 0.75%
  2. The estimate of the standard deviation of monthly returns is 3.34%
  3. The standard error of the mean is 3.34/sqrt(5) = 1.4923%. Hence the 95% confidence interval (assuming a normal distribution for the expected monthly return is (3.34-1.96(1.4923),3.34+1.96(1.4923) or (-2.179%,3.67%).
  4. If the price at the end of April is $50.4, the realized return for May is (49.74+0.273)/50.4 -1 or -0.768%. The new estimated expected monthly return is computed as before, or by taking (5(0.75)-0.768)/6 = 0.49%.
    The standard deviation is assumed to be the same. The new standard error, therefore, is 3.34/sqrt(6) = 1.36% (there are 6 observations, now). The new confidence interval is (3.34-1.96(1.3623),3.34+1.96(1.3623) or (-2.176%,3.16%), which is tighter than before.

Final Exam


  • If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  • 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.
  • You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
  • You must explain all your answers.
  • Answer all five questions -- parts (c) and (d) on question 5 are bonus questions.

1. In the following article titled "Hilton Debt Load Weighs on Blackstone" from the October 29 issue of the WSJ, we read:

Blackstone Group LP has begun talks with lenders to cut up to $5 billion from the $20 billion debt load carried by Hilton Worldwide, as the private-equity firm seeks to protect its single biggest investment, according to people familiar with the matter.

[hilton debt and blackstone and embassy suites]The talks are part of a restructuring of corporate debt under way across the economy. Companies hold roughly $1 trillion of senior loans and high-yield bonds that mature before 2015, much of it issued in leveraged buyouts from the middle of the decade. Many of those deals were struck at sky-high valuations, and now owners are trying to fix balance sheets to stave off default.

The talks also are another sign of the turmoil in the commercial real-estate industry. Delinquencies on commercial mortgages held by banks more than doubled to 4.7% in the third quarter, according to Foresight Analytics.

In the Hilton negotiations, Blackstone is considering contributing $800 million of new equity to buy back debt at a discount. It also is seeking to extend debt maturing in 2013 to 2016, while converting some junior slices of debt into equity. The $800 million in additional equity would come from funds managed by Blackstone that already have invested in the deal, the biggest equity investment ever made by the 24-year-old firm founded by Stephen Schwarzman and Peter G. Peterson.

Blackstone funds and co-investors originally put up $5.6 billion in equity in the deal, while assuming $20 billion in debt. Because the talks are in the preliminary stage, the people cautioned, it is unclear what the outcome will be. But Blackstone hopes the debt load will be cut by one-fourth, or $5 billion.

A number of issues are complicating the discussions. Roughly $4 billion of Hilton debt is held by the Federal Reserve, which assumed the position from Bear Stearns Cos. as part of a sale of the investment bank to J.P. Morgan Chase & Co. Also, the terms of the debt limit Blackstone's ability to repurchase Hilton debt.

Many debt workouts require borrowers to seek consent from scores of lenders, who bought the debt after it was securitized into bonds. The Hilton situation is different because banks hold nearly all of the debt, an unintended result of the closure of securitization markets soon after the Hilton deal was announced.

A Blackstone spokeswoman declined to comment.

It isn't clear how active the Fed, which is being advised by BlackRock Inc., will be in the talks. A Fed spokeswoman declined to comment.

hilton and england and blackstoneWith the capital markets opening over the past six months, large private-equity firms are using a variety of financial maneuvers, including exchange offers, open-market debt repurchases and tender offers, to push off any financial pain. Kohlberg Kravis Roberts & Co., the most-active investor during the boom, has refinanced and extended the maturities on more than $13 billion of debt at eight of its portfolio companies, including hospital chain HCA Inc. and retailer Toys "R" Us Inc., according to the firm.

In Blackstone's case, President Tony James said on a recent earnings call that "you can effectively rewrite history by changing a company's capital structure and reducing its leverage."

But Blackstone can't rewrite its acquisition of Hilton, a storied hotel chain founded by Conrad Hilton in 1919, which owns or manages 2,900 hotels with some 490,000 rooms throughout the world.

The Beetham Tower, center, in Manchester, England, is home to the Hilton Hotel towers. Since Blackstone's acquisition, the global hotel market has gone into a downturn worse than any since the Great Depression.

hilton and england and blackstoneAt the time, it was lauded as a coup for Blackstone as it was able to line up $20 billion in financing from a group of seven banks, including Bear Stearns Cos., Bank of America Corp., Deutsche Bank AG, Goldman Sachs Group Inc., Morgan Stanley, Merrill Lynch & Co. and Lehman Brothers Holdings Inc. General Electric Co.'s finance arm, GE Capital, wound up buying a $2 billion piece of the senior debt, according to people familiar with the matter.

Representatives at the banks and GE declined to comment.

But the downturn in the hotel market, triggered by reduced business and leisure travel, has sent values tumbling and turned the deal into a burden.

The firm already has written down the value of its investment by two-thirds, a paper loss of about $3.7 billion on the investment.

Hilton has been hit with some bad news since it was acquired by Blackstone. Federal prosecutors are investigating whether the chain and several of its former executives should face charges for allegedly stealing confidential documents from rival Starwood Hotels & Resorts, according to people familiar with the matter.

The Hilton deal also has figured prominently in the insider-trading scandal that erupted this month, with prosecutors alleging Galleon Group used nonpublic information on the Blackstone buyout. Blackstone executives haven't been implicated in either of the investigations.

Blackstone has good reason to be nervous about Hilton. Since its acquisition of the chain, the global hotel market has gone into a downturn worse than any since the Great Depression.

Occupancy at U.S. hotels and average revenue per available room have suffered their worst declines in a one-year period since Smith Travel Research began tracking hotel-industry figures in 1987.

  1. (10 points) In Blackstone's case, President Tony James said on a recent earnings call that "you can effectively rewrite history by changing a company's capital structure and reducing its leverage." This is a quote from the article. Does this mean that Modigliani-Miller were correct after all? It sounds like Mr. James is saying that you can undo leverage and make the specter of bankruptcy go away. Is he right? Explain using information from the article.
  2. (10 points) In the Hilton negotiations, Blackstone is considering contributing $800 million of new equity to buy back debt at a discount. Why on earth would debtholders be willing to sell their debt back to the firm at a discount?

2. You have recently won a jackpot in your state's lottery.  You have the following options:

  1. You receive $160,000 at the beginning of each year for 31 years.  The income would be taxed at an average rate of 28%.  Taxes are withheld when the checks are issued.
  2. You receive $1,750,000 now, and will be taxed immediately at a tax rate of 28 percent, but you do not have access to the full amount immediately.  You can take $446,000 of the after-tax amount now, while the remaining $814,000 will be placed in a 30-year annuity account that pays $72,664 on a tax-free basis at the end of each year.   
  1. (15 points) Assuming you require an after-tax return of 10 percent, which option should you select?
  2. (5 points) Suppose you weren't given the discount rate, how would you go about figuring it out?

3. (21 points) Answer any three of the following questions (no more than one page for each question):

  1. Why do share prices often go up when a firm announces that it will issue debt?
  2. If a firm with a corporate tax rate of 35% pays $10m. of interest in a given year, its tax payments will be 0.35(10) or $3.5m. less than if it had no debt at all. However, this assumes that investors are indifferent between debt income and equity income from a tax point of view. If the effective tax rate on investors' returns on equity investments is less than the effective tax rate on their bond returns, is the tax benefit of debt to be computed at a rate greater than the corporate tax rate or less? Explain.
  3. A firm that announces an increase in dividends will always be rewarded with an increase in its stock price. True or False? Explain.
  4. What are the agency costs of debt?
  5. Suppose markets are perfect and there are no frictions -- no taxes, no information asymmetry etc. Consider firm A and firm B that have identical investment policies. Suppose firm B has higher debt than firm A. Clearly, firm B's debt must be riskier than firm A's debt. Similarly firm B's equity must also be riskier than firm A's equity, since it is more highly leveraged. Hence firm B must be riskier than firm A. True or False? Explain.

4. You are evaluating the dividend policy of Dollar General (DG). The firm pays no dividends, and you have been brought in to advise the firm's Board of Directors on whether to start paying dividends.

DG's Net Income for the year ended Jan. 30, 2009 was $108.182m. Its capital expenditures for the same period were $205.546m. Depreciation was $247.899m. Current Assets were $1870.125m, while Current Liabilities were $1075.235; for the previous period, the numbers were $1517.744m. and $858.241m. respectively. Using these numbers, it is easy to calculate that working capital was $794.89m and $659.503m. for the two periods. Cash increased from $100.209 on 1/30/2008 to $377.995 on 1/30/2009.

  1. (10 points) How much could DG have paid in dividends on Jan. 30, 2009, using the information on its FCFE?
  2. (5 points) In fact, it paid nothing in dividends. Explain why DG's Board might have decided not to pay any dividends?

5. Your firm is considering building a $500m. plant to manufacture telephone component parts. You expect operating profits (EBITDA) of $125m. per year for the next ten years. The plan will be depreciated on a straight line basis over ten years (assuming no salvage value for tax purposes). After ten years, the plant will have a salvage value of $300m. (which would be fully taxable, since its book value would be zero). The project requires $50m. in working capital at initiation, which will be recovered at the end of the project. The corporate tax rate is 35%. All cash flows are assumed to occur at the end of the year.

  1. (15 points) If the rate of return on 10-year bonds is 4.5%, the expected return on the market portfolio is 11% per annum, the asset beta for the telecommunications industry is 1.75, what is the NPV of the project?
  2. (9 points) Suppose you can finance $400m of the cost of the plant using ten-year, 9% coupon bonds sold at par. This amount represents project financing, i.e. the bondholders have agreed to be paid solely from the cashflows of the project, and the bond issue has not connection with the rest of the firm. What is the value of the project, including the tax shield of the debt?
  3. (Bonus: 5 points) If you learn, in addition, that the Treasury-bill rate is 6%, would you use 4.5% or 6% as the risk-free rate for your calculation in part (a)?
  4. (Bonus: 5 points) In part (a), you were asked to use the asset beta for the telecommunications industry. However, suppose you didn't have this information. Instead, you want to use your own firm's equity beta to compute the asset beta. Suppose your firm's equity beta is 2, and your debt-equity ratio is 1. Compute the asset beta for your firm.

Solution to Final Exam


  1. If it were possible to undo leverage, then bankruptcy would be irrelevant in evaluating the capital structure of a firm and Modigliani-Miller would be correct, as far as this issue is concerned (i.e. they may still be wrong because of other "leakages.")
    However, the problem is that even if one could undo leverage, it is not a costless process at all. Since not all information is possible, there could be a lot of gaming and posturing between the parties before a deal ensues. Such gaming could be costly because the ultimate deal won't necessarily be the deal that would have happened, had all parties had the same information. Furthermore, the parties would expend resources in trying to obtain more information.
    For example, as the article explains, Blackstone is involved in trying to buy back debt from Hilto, as well as extending debt matuing in 2013 for another three years, as well as converting junor debt into equity. Since the value of the debt depends on information available to Hilton management (such management not being available to Blackstone), the negotiations can be protracted and costly Even when it is an issue of swapping one kind of security for another, the value of the deal depends on non-public information -- the value of equity is much more sensitive to information than the value of debt, for example.
    Furthermore, as we learn, $4 of Hilton debt is held by the Federal government and the objectives of the Federal Government have to be taken into account. Finally, Blackstone is not allowed to repurchase Hilton debt.
    Although not an issue in this case, an additional complication is that debt workouts often require consent from scores of lenders -- this is not an issue here, since banks hold most of the debt and the complexity of the negotiations is a lot less, given that the number of debtholders is smaller plus all the banks would be interested in coming to some kind of an arrangement -- private bondholders sometimes don't even respond to financial incentives.
    What Tony James means is true -- it is possible to undo leverage; doing so would reduce the cost of a suboptimal capital structure and lower the costs of financial distress; however, it is not costless and that's why Modigliani-Miller is not true in spite of the truth of Mr. James's statement.
  2. The value of the debt is less than its original issue price because Hilton is in much worse shape than it was when the debt was issued. However, there may be a holdout problem, here. That is, bondholders, recognizing that the value of the firm would go up if it bought up the debt or otherwise converted it into equity, might hold for a share of the increased value from reorganization.

2. The present value of option a) can be computed as an annuity with an annual flow of 160,000(1-0.28) = $115,200.  This works out to $1,091,982.30.  This would be the PV if the flows occurred at the end of the year; however, we need to consider that the flows will occur at the beginning of the year.  This means that we need to multiply by 1.1 in order to account for the increased value: this works out to $1,201,180.50.

 Option b) can be evaluated as follows: 1,750,000(1-0.28) = $1,260,000 is the amount that will be available after payment of taxes.  Of this, $446,000 is available immediately; the remaining $814,000 (1,260,000-446,000) will be placed in an annuity paying $72,664 a year for 30 years.  The present value of this flow, using the 10% discount rate is $684,997.31 (computed as (72664/.1)(1-(1.1)-30).  To this, we add the $446,000 that is immediately available, for a total PV of $1,130,997.30.

Hence option a) is more valuable.


  1. There could be two reasons for this: one, issuing debt reduces discretionary free cashflow, so that managers have less of an opportunity to misuse cash; two, the market could see the issue of debt as a signal that the firm is in better shape than expected -- else, the issue of debt would expose the firm to a greater probability of bankruptcy.
    Could share prices go up when a firm announces that it will buy back debt? This is likely only if the firm is overleveraged, but the market believed that the firm did not have the ability to raise funds to buy back debt and reduce leverage. The announcement of the debt buyback would, then, be good news because the firm is demonstrating that it's better off than the market believed by showing that it can raise equity financing.
  2. If the effective tax rate on investors' debt returns is higher than the tax paid on equity returns, they would require a higher rate of return on debt to compensate them for the higher tax that they would be paying. Hence the effective tax benefits of debt would be lower than what it would be if debt and equity returns were taxed at the same effective rate.
  3. This will not always be true. If the market interprets the dividend increase as an acknowledgement that the firm does not have profitable investment opportunities, then the stock price could drop.
  4. The agency costs of debt are the deadweight costs due to the tendency of managers of levered firms to take suboptimal actions to dispossess bondholders -- such as taking excessive risk, excessive leverage and paying excessive dividends. Furthermoe, they might pass up profitable investment opportunities because of the problem of debt overhang. There would also be costs of monitoring and compliance with reporting requirements that are due to the existence of debt.
  5. This statement is false -- if markets are perfect, the firm cannot become riskier because of capital structure. The argument as described is fallacious because even though both debt and equity become riskier, debt is always less risky and the increase in leverage increases the relative weight of debt in the capital structure.

4.a. FCFE for 2009 can be computed as Net Income + Depreciation - Capital Expenditures - Change in Noncash Working Capital. Using the numbers given in the problem, the FCFE works out to $292.93. This is the amount that could have been paid out in dividends.

  2009 2008
Net Income 108.182
Capex 205.546
Depreciation 247.899
Current Assets 1870.125 1517.744
Current Liabs 1075.235 858.241
Working Capital 794.89 659.503
Cash $378.00 100.209
Change in cash $277.79
Change in WC 135.387
Change in non-cash WC ($142.40)
FCFE $292.93

b. The FCFE only looks at the cashflow for the current year. If the firm intended to step up capital expenditures next year, or if it expected to have lower cashflows next year, it might feel the need for holding on to some of the cashflow this year. In the case of DG, it had an IPO only on Nov. 12, 2009, so there was no question of paying dividends on common stock previously. It is not known if dividends were paid to the private equityholders prior to the IPO.
The reason could not have been that the firm found positive NPV projects for this year because we are given the Capex number for this year, and FCFE>0 after taking those investments into account.

5. a. The present value of the project can be computed as the present value of after-tax EBITDA plus the tax savings from depreciation minus the adjustment for the use of working capital over the ten years plus the after-tax value of the salvage.

This approach is essentially the FCFF approach. Hence we take the cashflows to the entire firm and discount it at the cost of capital to the entire firm. This cost of capital is computed as 0.045+1.75(.11-.045) or 15.875%.

The present value annuity factor for ten years is (1/0.1)[1-(1.15875)-10] = 4.855806; the present value factor for a $1 realized after ten years is (1.15875)-10 = 0.229141.

The net present value of the project works out to -$14.3497, as shown below, in millions:

Investment 500
Depreciation 50
Salvage Value after 10 yrs 300
Tax rate 0.35
Working Capital 50
Present Value of a 10yr. annuity 4.855806
Present Value of $1 after 10 yrs 0.229141
After tax EBITDA 394.5342
Tax savings from depreciation 84.9766
After tax value of Salvage 44.68247
Working Capital Cost -38.543
Present Value or Project 485.6503
NPV of project -14.3497

b. The value of the tax shield is equal to the present value of an annuity of the tax benefits from the bond financing for ten years. Yearly interest payments are $400(0.09) = $36m. and the savings in tax, therefore, $36(0.35) = $12.6m. Discounting these at 9%, which is the required rate of return for the riskiness of the interest payments and hence of the tax savings, we get a tax shield value of 36(1/0.09)[1-(1.09)-10](0.35) = $231.03568m.(0.35) = $80.86249m.

c. We would use the 10 yr. T-bond rate as the risk-free rate in our computations since the project is a 10-year project.

d. We can compute the beta of the assets as the weighted average of the beta of debt and equity. If the debt-equity ratio of the firm is 1, debt and equity are weighted equally. Assuming a zero beta for debt and the given equity beta of 2, we'd get a beta of 1 for the assets of the firm.


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