Dr. P.V. Viswanath



Economics/Finance on the Web
Student Interest

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Fall 2014




  • 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.
  • For all quantitative questions, you must provide the formula and show the numerical equivalents of the variables in the formula. You may then use your scientific or financial calculator to compute the answer and put it down on your answer sheet.
  • You must explain all your answers. Answers without explanations may not receive any points.
  1. (23 points) Read the article below and answer the following questions in brief. Rambling answers will get points deducted. Note that stock options are securities that represent the right to buy shares at a fixed price within a specified time period.
    1. (5 points) Why would any firm give stock options to managers as reward for performance? Why would any firm give shares to managers as reward for performance?
    2. (5 points) Explain Warren Buffet's critique of stock option-based compensation.
    3. (5 points) Why would lower-level management get cash-based performance awards and not equity shares?
    4. (8 points) If you were a manager and you were given Coke shares as compensation for superior performance, would you keep the shares or sell them (assuming you were permitted to)? Why?

    Coke Scales Back Executive Equity Compensation, Bowing To Pressure, WSJ, October 2, 2014

    Coca-Cola Co. is overhauling its executive-compensation plan before it goes into effect next year, scaling back stock options and shifting to more cash-based performance awards.

    The reversal by the world's largest beverage company--which championed the original plan at its April shareholder meeting--follows criticism from billionaire investor Warren Buffett and other Coke shareholders who called the equity plan excessive.

    It also coincides with growing efforts by Chairman and Chief Executive Muhtar Kent and other board members to mollify investors impatient with Atlanta-based Coke's recent performance. Coke failed to meet its revenue growth targets last year, pulled down by weak soda sales in the U.S. and elsewhere, and could fall short again this year.

    Coke said Wednesday it isn't altering long-term incentive targets for 6,500 managers and that compensation could remain similar in dollar terms, depending on the company's performance. But it will issue fewer shares to management, replacing equity awards with cash awards for all but about 1,000 managers, or a bit less than 1% of Coke's global staff.

    Annual share dilution will stay below 1% under the new plan, similar to other companies, according to Coke. Executives who receive long-term equity awards will get mostly performance-based share awards, not stock options, it added. Performance-share units are a form of stock in which individuals earn shares based on performance measures.

    The shift from options to performance shares has been a growing trend in recent years, according to Mark Reilly, head of the executive compensation practice for Verisight Inc., a human-resources consultancy. Coke directors, he said, "are late to the party.'' Narrowing the number of executives who qualify for equity awards also makes sense because lower-level managers have less impact on share performance, he added.

    Coke's equity-compensation plan passed easily at the annual shareholder meeting in April, with 83% of votes cast in favor. But "yes'' votes represented just under half of shares outstanding, after including abstentions and non-votes. Two of the top five shareholders, State Street Global Advisors and Capital Group, voted against the plan.

    Mr. Buffett, whose Berkshire Hathaway Inc. is Coke's largest shareholder, with a 9% stake, abstained from voting in April but called the plan "excessive'' afterward. Mr. Buffett has frequently criticized pay plans that rely heavily on stock options as "lottery tickets'' that often generate outsize rewards.

    Mr. Buffett went public with his concerns after a smaller shareholder, David Winters, chief executive at Wintergreen Advisers LLC, began a public campaign against Coke's equity plan in March. Mr. Winters argued the plan, including issuing 340 million new shares and options over four years, could dilute shareholders by up to 16.6% and was more generous than the expiring plan approved in 2008.

    Coke director Maria Elena Lagomasino, chair of the compensation committee, said in a statement Wednesday that shareholder input "has directly led'' to the revised guidelines, which she said "are in line with the long-term interests of shareowners.''

    Coke said equity grants will have an annual "burn rate'' of no more than 0.8% in 2015 and an average of 0.4% for the remainder of the 10-year plan. That compares with 1.7% so far in 2014. Burn rates refer to the number of shares granted as a percentage of shares outstanding. Two thirds of equity awards will be performance shares by 2016, up from 40% currently.

    Under the revised plan, Coke would potentially issue about 200 million shares to managers over 10 years, compared with as many as 340 million over as few as four years under the April version. The company says the reworked plan translates into a potential dilution of less than 5% over the life of the plan for shareholders.

    Mr. Buffett didn't respond Wednesday to requests for comment. He was pleased with the altered plan after Coke briefed him on the changes, according to a person familiar with the situation.

    State Street and Capital Group declined to comment. Each of the investment firms owns between 3% and 4% of Coke's shares outstanding, according to regulatory filings.

    Mr. Winters criticized Coke for moving slowly and said he still wants to see more details about changes to the plan and how they will be implemented. "At this point it's vague and it's just promises. We view this as just more red glitter in the air,'' said Mr. Winters. His Wintergreen fund owns 2.5 million Coke shares, or 0.06% of shares outstanding.

    He said the board and management "haven't done a great job'' running Coke and that Mr. Kent should personally apologize to shareholders for the original equity plan and "probably announce his retirement.''

    The State Board of Administration of Florida, which voted against the equity plan in April, praised the changes. "The changes to Coke's plan are very responsive to investors' prior concerns,'' said Michael McCauley, who oversees corporate governance issues at the fund, which owns 5.9 million Coke shares, according to regulatory filings.

    There are no signs that Mr. Kent has lost the support of Coke's board. He also hasn't signaled any plans to step down anytime soon.

    Mr. Kent said Coke "will continue to provide long-term incentive awards to a broad-based group of employees with performance metrics that drive line-of-sight accountability directly to business results."

  2. (24 points) Answer any four of the following questions:
    1. What is moral hazard? Give an example of moral hazard in the context of corporate governance.
    2. What is the role of the stock market in stock value maximization as a corporate objective?
    3. What is the difference between the sustainable growth rate and the internal growth rate?
    4. How is a discount rate similar to a price?
    5. Stockholders' equity cannot be negative because stockholders have limited liability. True or false? Explain.

  3. (24 points) You are 40 years old and you have decided to save $6000 per year, which you plan to put in a special investment account which pays a guaranteed 5% per annum (starting with your first deposit one year from now). You plan to retire at age 70. During retirement, you plan to withdraw $80000 a year (starting with your 70th birthday, which is also when you will be making your last deposit). You wish to have enough money until your 95th birthday at which time you figure your children will be ready to support you (you wish!) and you don't have to rely on your own resources any more.
    You have just come into a nest egg of $250,000, which you want to spend on a cruise to Alaska. However, you realize that your savings alone might not suffice to finance your retirement, so you are willing to deposit and additional lumpsum from this nest egg to cover any potential shortfall in your retirement needs.
    1. (8 points) How much will you need to have at age 70 to finance your retirement fully, including the withdrawal you will make on your 70th birthday?
    2. (8 points) How much will you have at age 70 from your savings (including the deposit you will make on your 70th birthday)?
    3. (8 points) How much will you have left from the nest egg today for you to spend on the Alaska cruise, after putting aside the requisite amount to cover your requirement needs shortfall?

  4. (16 points) Using the information below, answer the following questions:
    1. (6 points) What is the quick ratio for RSH, as of December 31, 2013? (Treat Other Current Assets similar to inventory.) What is the quick ratio as of December 31, 2012? What would you conclude from these two numbers?
    2. (6 points) Compute the average collection period (also known as Accounts Receivable Days) for the year ending December 31, 2013. Compute the same number for the year ended December 31, 2012. What do you conclude from a comparison of these two numbers?
    3. (4 points) What is RSH's gross profit margin for 2013? For 2014?
    4. (Bonus: 5 points) If Radio Shack has a positive gross profit, why does it have a net operating loss? Don't tell me that it has operating expenses greater than the gross profit; I want you lay out for me a scenario of what these expenses might be. Speculate as to the reasons why RSH might be having an net operating loss.

      Balance Sheet for Radio Shack (RSH: NYSE)

      As Reported Annual Balance Sheet 
      Report Date 12/31/2013 12/31/2012
      Scale Thousands Thousands
      Cash & cash equivalents
      Accounts & notes receivable, net
      Total other current assets
      Total current assets
      Furniture, fixtures, equipment & software
      Leasehold improvements
      Property, plant & equipment, net
      Goodwill, net
      Other assets, net
      Total assets
      Short-term debt, including current maturities of long-term debt
      Accounts payable
      Total accrued expenses & other current liabilities
      Total current liabilities
      Long-term debt, excluding current maturities
      Total other non-current liabilities
      Total liabilities
      Common stock
      Additional paid-in capital
      Retained earnings (accumulated deficit)
      Treasury stock, at cost
      Accumulated other comprehensive income (loss)
      Total stockholders' equity
      Total liabilities and stockholders' equity 1591200 2299100

      Income Statement for Radio Shack (RSH: NYSE)

      As Reported Annual Income Statement 
      Report Date 12/31/2013 12/31/2012
      Scale Thousands Thousands
      Net sales & operating revenues
      Cost of products sold
      Gross profit
      Total operating expenses
      Operating income (loss)
      Interest income
      Interest expense
      Other income (expense)
      Income tax expense (benefit)
      Income (loss) from continuing operations
      Discontinued operations, net of income taxes
      Net income (loss)

  5. (18 points) Consider the following securities and their prices:
    Security Price Today Cashflow in one year Cashflow in two years
    A 95 100  
    B 88.56   100
    C 50 40 20
    1. (3 points) What is the one year interest rate, i.e. the annualized interest rate on a one-year loan?
    2. (3 points) What is the two year interest rate, i.e. the annualized interest rate on a two-year loan?
    3. (6 points) Is there an arbitrage opportunity? If so, explain exactly what arbitrage strategy you would use to make money. Assume you can buy and sell all securities at the quoted prices.
    4. (6 points) If you could only buy the securities at the quoted prices, but you could only get a price 10% lower if you wanted to sell them, would you still have an arbitrage opportunity? Why or why not? No points without explanation.

Midterm Solutions


  1. The basic problem here is that of moral hazard and incentive alignment. Managers have their own objectives, which might not coincide with stockholder objectives. Issuing shares will increase alignment by making managers shareholders, as well. Stock options are similar in that the prices of stock options increase when share prices go up. However, as long as managers have their own objectives that are inconsistent with shareholder goals, shares and share options are unlikely to resolve the issue completely.
  2. Warren Buffet characterized 'pay plans that rely heavily on stock options as "lottery tickets'' that often generate outsize rewards.' By this, he may have meant two different things. One, the value of the stock and consequently the value of the stock options are unrelated to manager actions; furthermore, bad performance doesn't mean lower pay for the manager, except for forgoing positive rewards. Two, stock options are likely lottery tickets in that they are very risky; increasing the riskiness of the firm actually increases the value of the stock option even if it doesn't increase the share value.
  3. Lower level management have less of an impact on share prices; there are too many other factors that affect stock price. Hence rewarding such managers with shares will not have as much of an incentive effect.
  4. If the manager were allowed to sell them, s/he probably would do so because -- considering that his/her human capital is already tied to the stock price -- holding the shares in addition would lead to an overly undiversified/concentrated portfolio and expose him/her to risks of fluctuation of shares prices of the company. On the other hand, publicly showing that s/he is not selling the stocks could signal the confidence of the manager that s/he will do the right things and that the stock price will rise.


  1. Moral hazard refers to the incentives for economic agents who are parties to a contract to take inefficient actions that differ from the actions that they would have taken if they had not been party to the contract. Thus moral hazard leads to a potential waste of resources. For example, persons who have insured their car are likely to worry less about the maintenance of the car knowing well that if there is an accident, they will be at least partially reimbursed by the insurance company.
    In the context of corporate governance, the tendency of managers of a leveraged firm taking excessive risk to benefit shareholders is an example of moral hazard.
  2. Even if stock value maximization is an appropriate goal, it is ncessary to have a reliable and objective way of measuring stock value. The stock market can be used for this purpose. Obviously, if the stock market does not reflect true underlying value properly, that would be a problem.
  3. The sustainable growth rate is the rate at which the firm can grow if it uses no additional equity other than its retained earnings for reinvestment purposes, while keeping the debt-equity ratio constant. That is, there is an assumption that the firm will raise additional debt. The internal growth rate is the rate at which the firm can grow if it uses its retained earnings alone for reinvestment purposes, with no additional outside capital; hence the internal growth rate will be lower than the sustainable growth rate, since the leverage ratio will drop.
  4. A discount rate is simply the rate of return that can be obtained by investing in a primary security at the market price and holding it to maturity. In other words, the discount rate is simply a transformation of the market price of the primary security. Hence it can be used to compute the value of a complex security just like prices can.
  5. The market value of stockholders' equity cannot be negative because stockholders have limited liability. However, the book value of stockholders' equity can very well be negative if the firm has accumulated losses that are lower than the amount initially paid by stockholders for their shares. Even though the book value of equity is negative, the firm need not be bankrupt because the market value could be high, reflecting for example, future profits.


  1. You need $80,000 a year from your 70th birthday to your 95th birthday. The value at the 70th birthday of your income needs for the last 24 years (that is, the 71st birthday withdrawal until the 94th birthday withdrawal; on your 95th birthday, you can turn to your children) is given by the formula [80000/0.05](1-(1.05)-24). Add to that the 80,000 required on the 70th birthday to get a total of 1,103,891.30+80,000 = 1,183,891.30.
  2. You will be saving in 30 instalments of $6000 each, starting one year from now. The present value of these savings is given by the present value of an annuity formula as [6000/0.05](1-(1.05)-30) = 92,234.71. In 30 years, this will be worth 92,234.71(1.05)30= $398,633.09.
  3. Your shortfall will be 1,183,891.30 - 398,633.09 = $785,258.25. In present value terms, this is equal to $785.258.25/(1.05)30= $181,691.05. This means that you can spend 250,000-181,691.05 or $68,308.95 on the Alaska cruise.


  1. For December 31, 2013, the Quick Ratio can be computed as (Current Assets - Inventory - Other Current Assets)/Current Liabilities or [1,333,000-(802,300+139,000)]/584,600 = 0.67; for December 31, 2012, this ratio is [1,981,900-(908,300+85,400)]/978,200 = 1.01. The firm's short-term liquidity situation has deteriorated. They will find more difficult to meet their short term liabilities if they were under pressure to do so.
  2. The average collection period for 2013 can be computed as Average Accounts Receivable/(Sales/365). However, if we did this, we would not be able to compare the 2013 figure for the 2012 figure, since we do not have the 2011 balance sheet. Unfortunately, there is quite a bit of difference between the accounts variable number for 2012 and for 2013, leading us to believe that the 2011 figure may also be quite different from those of 2012 and 2013. However, in this case, we have to make some assumption to allow us to compare. So if we assume that the rate of growth in sales from 2011 to 2012 is about the same as that from 2012 to 2013, then using end-of-year sales will give us comparable ratios. Under this assumption, we can compute the Average Collection period as 211900/(3434300/365) = 22.52 days for 2013 and 452,500/(4257800/365) = 38.8 days for 2012. Clearly, Radio Shack is collecting receivables at a faster pace in 2013 than in 2012.
  3. The gross profit margin for 2013 is 1172200/3434300 = 34.13% for 2013 and 1,561,800/4,257,800 = 36.68%.
  4. Total Operating expenses are clearly very high, leading to a net operating loss. Since direct costs are already taken into account under Cost of products sold, these operating expenses must be expenses such as advertising, rental or building lease expenses and other indirect expenses. These could be high either because Radio Shack expected revenues to be high and maintained high advertising expenses and a large amount of office space and was surprised when revenues were lower. Alternatively, considering that we have the same situation for 2012 and for 2013, there's probably a secular decline in Radio Shack's revenues and Radio Shack has not adjusted to that by cutting indirect expenses. Another possible hypothesis is that Radio Shack is investing in a lot of advertising, but it hasn't borne fruit yet.


  1. The one year interest rate can be computed using the information on the pricing of security A as 100/95 - 1 or 5.263%
  2. The two year interest rate can be computed using the information on the pricing of security B as (100/88.56)0.5 - 1 or 6.263%
  3. Using these interest rates as discount rates for the cashflows to security C, we would expect it to be priced as 20/(1.06263)2 + 40/(1.05263) = 20(88.56/100) + 40(95/100) = 17.71+38 = 55.71. It is clear that security C is overpriced. Hence we want to be short security C and long securities A and B. The cashflows for security A are 40 in year 1, which can be replicated by 0.4 units of security A and 20 in year 2, which can be replicated by 0.2 units of security B. Hence the arbitrage strategy would be to buy .4 units of security A, 0.2 units of security B and sell 1 unit of security C. This would give a cashflow of exactly zero in years 2 and 3 and net a total inflow in year 0 of (0.4)95 + (0.2)88.56 - 50 = $5.71.
  4. With these additional restrictive conditions, this strategy would net (0.9)(55.71)-50 = 50.139-50 = 0.139; in other words, there would still be an arbitrage opportunity.


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.
  • For all quantitative questions, you must provide the formula and show the numerical equivalents of the variables in the formula. You may then use your scientific or financial calculator to compute the answer and put it down on your answer sheet.
  • You must explain all your answers. Answers without explanations may not receive any points.

    1. ( points) Read the article below and answer the following questions in brief. Rambling answers will get points deducted. Use no more than one page for each part of question 1.

    1. (7 points) What is the Efficient Markets Hypothesis?
    2. (7 points) Your friend asserts that all market participants need to have a piece of information if that piece of information is to be reflected in market prices. Do you agree with her? Why or why not?
    3. (7 points) If you believe a financial asset is overvalued, how would you act on that belief if you didn't own that asset? If you believed that Medallion Financial's stock was overvalued, and you didn't own any Medallion Financial stock, could you have used this strategy? Why or why not?
    4. (7 points) If you think that Uber is competing successfully for the traditional yellow cab market, what should happen to the value of taxi medallions (these are essentially rights to operate a taxicab in New York and pick up passengers on the street)? Should the value of Medallion Financial be correlated with the change in the value of taxi medallions? Why or why not?

    How Our Taxi Article Happened to Undercut the Efficient Market Hypothesis, NY Times December 3, 2014

    If the stock market is efficient, why would a single Upshot article on taxicab medallion prices help push down Medallion Financial’s stock 7 percent in a single day, when most of the information in that article was already public?

    Medallion Financial is a specialty finance company with about half of its portfolio in loans secured by taxi medallions, mostly in New York, with a significant presence in Chicago and Boston. Last Thursday, with the stock market closed for Thanksgiving, my article about falling taxi medallion prices in those cities went up on the web. The next day Medallion Financial’s stock closed more than 7 percent lower, with nearly all that drop coming in the first minute of trading.

    According to the so-called semistrong form of the efficient market hypothesis, that shouldn’t have happened. Medallion Financial’s stock price shouldn’t have been affected by the story.

    “Semistrong-form efficiency” is the claim that a market price, such as a stock price, takes into account all publicly available information at all times. It’s not a claim that stock prices are always correct; unforeseen events happen. But it does mean that if a piece of information is already known to some market participants, shouting it at all of them (or printing it on the front page of The New York Times) shouldn’t matter for the stock price. The well-informed market participants should have already bid the stock price up or down to the level that correctly reflects that information.

    Medallion Financial’s stock opened down 6 percent last week after an article revealed the declining prices of taxi medallions. Credit Bryan Thomas for The New York Times

    This claim comes reasonably close to being true, which is why the stock market works at all. There are tons of companies and tons of information about all those companies; if every market participant needed to have all that information for prices to reach equilibrium, they would never do so.

    So here’s the odd thing about the Medallion Financial price drop: The pertinent information in my article was already substantially publicly available before I wrote it. I calculated the 17 percent decline in New York City taxi medallion prices from monthly transaction reports published on the city’s taxi commission website. I found the 20 percent decline in Boston prices by examining tables published in a New England taxi trade publication called the Carriage News.

    Investors were already wary of Medallion. The company’s stock had peaked almost exactly a year earlier at $17.74 after a two-year run-up. It had fallen almost 40 percent to close at $10.78 the day before Thanksgiving.

    The interviews I conducted for the article also made clear that people in the taxi industry were already broadly aware of the weakness in the taxi market. Consistently, they told me the same stories: Medallion prices are down, credit is much tighter, sales volume is way off. In Boston and Chicago, they told me taxi fleet owners were having more trouble finding interested drivers to lease their cabs to. Tightening credit was even clear from the ads in the Carriage News: Only two medallion lenders placed ads in this October’s issue, compared with five a year earlier.

    The only truly nonpublic information in my article was the fact that three Chicago medallions changed hands in November at an average price of $298,000. That figure, which clarified Chicago’s 17 percent price decline, hasn’t yet been published by the city; I got it by emailing a city spokeswoman and asking.

    Still, that information wasn’t truly private either; an interested investor could have asked the city the same question I did. And even without the November figures, the complete shutdown of Chicago’s medallion market was apparent from the already published summer data: There were just eight medallion trades in the months of July through September, compared with 110 in the summer of 2013.

    So why wasn’t the market efficient here? Why wasn’t the drop in medallion prices already priced into Medallion Financial shares? There are a few factors that may be at play.

    One is that Medallion Financial is a small company, with a market capitalization of about $242 million. It is the only public company whose main business is tied to the value of taxi medallions. So there isn’t a lot of incentive for stock investors to know the taxi medallion market in the way they might know the market for oil or automobiles or insurance. Market efficiency doesn’t require all or even most investors to understand what they’re trading, but you do need a critical mass of knowledgeable and liquid investors to drive the market. It’s possible that critical mass wasn’t present here, and it took a news article to correct the market perceptions.

    A second factor is that, until September, New York City’s taxi commission published inaccurate reports of average medallion prices, which said prices were flat instead of falling. These reports may have led investors in Medallion Financial astray about the state of the medallion market. Several publications relied on the reports and said medallion prices in New York were flat, including articles in Bloomberg Businessweek and Newsweek in July and one in The New York Times in September.

    The Taxi and Limousine Commission published these reports alongside apparently complete lists of medallion transactions. By reading those complete lists, an investor could (as I did) figure out that the city’s average reports were wrong, and that medallion prices were actually declining. In fact, the T.L.C. commissioner, Meera Joshi, issued a statement to me over the weekend saying several lenders who understood this had asked the city this summer to stop publishing the average reports.

    But just because people could have known the truth about medallion prices doesn’t mean most of them did. For example, even Medallion Financial relied on the false T.L.C. reports in its third-quarter S.E.C. filing, writing:

    A significant portion of our loan revenue is derived from loans collateralized by New York City taxicab medallions. According to New York City T.L.C. data, over the past 20 years New York City taxicab medallions have appreciated in value from under $160,000 to $1,320,000 for corporate medallions and $1,045,000 for individual medallions.

    In fact, as of September, average prices for the two classes of medallions were $1.175 million and $900,000.

    A third factor is that Medallion Financial is essentially the only way to use the stock market to speculate on the Uber vs. taxi fight. You can’t invest in Uber unless you work there or you’re a venture capitalist. Investing directly in taxi medallions is difficult, and there’s no way to short-sell one. Most banks either don’t lend against medallions or it’s a tiny fraction of their business.

    If you want to bet on Uber and against taxis, you have to sell Medallion Financial. And people are: In June, The Wall Street Journal ran an article about short-selling Medallion as a play to bet on Uber in the public markets. That play has intensified; on Tuesday, according to data from Markit, over 90 percent of Medallion Financial shares that were available for short-sellers to borrow and resell had been borrowed.

    But Medallion Financial is an imperfect proxy for the taxi industry; as a lender, it’s not as exposed to risks from falling medallion prices as the actual equity holders in taxi medallions are. (The company does directly own some Chicago medallions, but that’s a small part of its business.) And nearly half its business is commercial and consumer lending, not medallion loans.

    I spoke with Andrew Murstein, Medallion Financial’s president, before my article ran, and he argued that his company was relatively well positioned to weather a decline in medallion prices. He noted that it had no delinquent medallion loans, and attributed that to lending at a lower percentage of the medallion price than competitors. He even said it was buying portfolios of medallion loans from other lenders who went out of the business.

    So, as the only public taxi play, Medallion Financial may have just become the unfortunate whipping boy for Uber fan investors. The company’s small size gives reason to think that people who want to bet on Uber could push its price around; Uber’s most recent equity raise put its value at $40 billion, 160 times the size of Medallion Financial.

    In time, we may find out if that’s what’s going on; of the three theories of why Medallion Financial’s stock price fell so much on Friday, it is the one that bodes best for its price going back up. And there may not be much more room for shorts to push down Medallion’s price. “Short sellers would find it increasingly difficult to source shares to borrow,” said Joanna Vickers, a spokeswoman for Markit.

    2. Your firm would like to evaluate a proposed new operating division. You have forecasted cash flows for this division for the next five years, and have estimated that the cost of capital is 13%. You would like to estimate a continuation value. You have made the following forecasts for the last year of your five-year forecasting horizon (in millions of dollars):

    Year 5
    Operating Income
    Net Income
    Free Cash flows
    Book Value of Equity
    1. (12 points) You forecast that future free cash flows after year 5 will grow at 2% per year forever. Estimate the continuation value in year 5, using the growing perpetuity formula.
    2. (8 points) You have identified several firms in the same industry as your operating division. The average P/E ratio for these firms is 16. Estimate the continuation value assuming the P/E ratio for your division in year 5 will be the same as the average P/E ratio for the comparable firms today.
    3. (8 points) The average market/book ratio for the comparable firms is 3.6. Estimate the continuation value using the market/book ratio.

    3. Benchmark Metrics, Inc. (BMI), an all-equity finance firm, just reported an EPS of $5.78 for 2013. Despite the economic downturn, BMI is confident regarding its current investment opportunities. But due to the financial crisis, BMI does not wish to fund these investments externally. The Board has therefore decided to suspend its stock repurchase plan and cut its dividend to $1.09 per share (vs. almost $2 per share in 2012), and retain these funds instead. The firm has just paid the 2013 dividend, and BMI plans to keep its dividend at $1.09 per share in 2014 as well. In subsequent years, it expects its growth opportunities to slow, and it will still be able to fund its growth internally with a target 35% dividend payout ratio, and reinitiating its stock repurchase plan for a total payout rate of 64%. (All dividends and repurchases occur at the end of each year.)
    Assume BMI's existing operations will continue to generate the current level of earnings per share in the future. Assume further that the return on new investment is 15%, and that reinvestments will account for all future earnings growth (if any). Finally, assume BMI's equity cost of capital is 10%.

    1. (10 points) Estimate BMI's EPS in 2014 and 2015 (before any share repurchases).
    2. (10 points) What is the value of a share of BMI at the start of 2014 (end of 2013)?

    4. Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%. Also suppose the risk-free rate is 4% per annum.

    1. (5 points) Use the beta of a firm that goes up on average by 40% when the market goes up and goes down by 20% when the market goes down to estimate the expected return of its stock.
    2. (5 points) How does this compare with the stock's actual expected return?
    3. (5 points) What would you infer from this?

    5. Fast Track Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $217,000 per year. Once in production, the bike is expected to generate a profit of $303,800 per year for ten years. Assume the cost of capital is 10%.

    1. (10 points) Calculate the NPV of the investment opportunity, assuming all cash flows occur at the end of each year. Should the company make the investment?
    2. (5 points) Your friend has come to the opposite conclusion to you. Assuming that you and he only differ regarding the cost of capital assumption, is his estimated cost of capital higher than yours or lower?

Final Solutions


  1. The Efficient Markets Hypothesis asserts that all relevant information is incorporated in security prices. The semi-strong version of the Efficient Markets Hypothesis says that all publicly available information is incorporated in security prices.
  2. All market participants need not have the information for it to be reflected in security prices; the reason is that informed traders would have an incentive to buy up undervalued securities or (short)sell overvalued securities. Hence, as long as the informed market participants have the ability to trade on their information, it is not necessary for all market participants to be informed.
  3. If I believed that a financial asset were overvalued, and I didn't own it, I would try to short sell it. That is, I would borrow units of that asset, sell them, wait until the price moved down to a more "correct" value, then buy them back and return them to the lender, thus making an arbitrage profit. In the case of Medallion Financial, this is difficult because the number of shares trading is low and finding somebody to borrow the stock from is more difficult.
  4. The value of taxi medallions should drop if Uber is competing successfully. Medallion Financial does not own medallions per se, it makes loans to medallion buyers or medallion owners. Hence the value of its existing loans to such borrowers would become riskier and this might cause Medallion Financial's stock to drop. However, it seems that Medallion's portfolio is somewhat diversified; hence the impact on its stock may not be very high. According to the article, nearly half of its business is commercial and consumer lending, not medallion loans. On the other hand, Medallion Financial itself noted in its SEC filings that "a significant portion of our loan revenue is derived from loans collateralized by New York City taxicab medallions."


  1. Free cashflows in year 5 are $91.8m. They are growing at 2%p.a. forever and the discount rate is 13%. Hence the continuation value, i.e. the value of the firm at the end of year 5 is 91.8(1.02)/(0.13-0.02) = $851.2364m.
  2. The earnings in year 5 are 40.5m. If the P/E ratio is assumed to be 16, the continuation value will be 40.5(16) = $648m.
  3. The book value of equity is 166.9. If the market/book ratio is assumed to be 3.6, the estimated market value of equity will be 166.9(3.6) = $600.84m.


  1. Dividends in 2013 are 1.09 with EPS of 5.78; hence the retention ratio is 1-1.09/5.78 or 81.14%. The growth rate in earnings, thus, is 0.8114(0.15) = 12.17%. Earnings in 2014 will, therefore, be 5.78(1.1217) = 6.4835.
    Dividends in 2014 will be 1.09; hence the retention ratio will be 1-1.09/6.4835 or 83.19%. The growth rate in earnings, thus, is (0.8319)(0.15) or 12.478%. Earnings in 2015, therefore, will be 6.4835(1.12478) = $7.292525.
  2. The growth rate, thereafter will be (1-0.64)(0.15) or 5.4%. The payout in 2015 will be (0.64)(7.292525) or 4.6672. Hence the continuation value at the end of 2015 will be 4.6672(1.054)/(0.10-0.054) or $106.94.
    The stock price at the end of 2013 (beginning of 2014) will be 1.09/1.1 + (4.6672+106.94)/1.12 = $93.2284
    Alternatively, the continuation value at the end of 2014 will be (payouts in 2015)/(0.1-0.054) = 4.6672/(0.046) = 101.4609. Hence the price at the end of 2013 will be (1.09+101.4609)/1.1 = $93.2284, once more.


  1. The expected return on the market is (30%-10%)/2 = 10%. The beta of this firm will be (0.4-(-0.2))/(0.3-(-0.1))=0.6/0.4 = 1.5. The expected return according to the CAPM is 4+1.5(10-4) = 13%.
  2. The stock's actual expected return is (40%-20%)/2 = 10%.
  3. We cannot infer much from this. In any actual situation, the actual return is going to be different from the expected return by chance.


  1. At the end of six years, the present value of subsequent profits from the investment opportunity will be (303,800/0.1)(1-(1.1)-10) =(303,800)x 6.1446= 1,866,719.5. The present value of this is 1,866,719.5/(1.16) or 1,053,714.5.
    The present value of the yearly outlay of 217,000 for six years is (217,000/0.1)(1-(1.1)-6) = 945,091.57. Hence the NPV is 1,053,714.5 - 945,091.57 = $108,622.93.
  2. His estimated cost of capital must be higher, so that the present value of the future profits will be lower. Although with a higher cost of capital, the present value of the costs in the first six years are also lower, the impact of a higher discount rate is greater in years further away.





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