Deutsche Bank: A Greek Tragedy at a German Institution?

This may be a stereotype, but the Germans are a precise people and while that precision often gets in the way of more creative pursuits (like cooking and valuation), it lends itself well to engineering and banking. For decades until the introduction of the Euro and the creation of the European Central Bank, there was no central bank in the world that matched the Bundesbank for solidity and reliability. Thus, investors and regulators around the world, I am sure, are looking at the travails of Deutsche Bank in the last few weeksand wondering how the world got turned upside down. I am sure that there are quite a few institutions in Greece, Spain, Portugal and Italy who are secretly enjoying watching a German entity be at the center of a market crisis. Talk about schadenfreude!

Deutsche Bank's Journey to Banking Hell

There are others who have told the story about how Deutsche Bank got into the troubles it is in, much more creatively and more fully than I will be able to do so. Consequently, I will stick with the numbers and start by tracing Deutsche Bank’s net income over the last 28 years, in conjunction with the return on equity generated each year.

If Deutsche Bank was reluctant to follow more daring competitors into risky businesses for much of the last century, it threw caution to the winds in the early part of the last decade, as it grew its investment banking and trading businesses and was rewarded handsomely with higher earnings from 2000 to 2007. Like almost every other bank on earth, the crisis in 2008 had a devastating impact on earnings at Deutsche, but the bank seemed to be on a recovery path in 2009, before it relapsed. Some of its recent problems reflect Deutsche’s well chronicled pain in investment banking, some come from its exposure to the EU problem zone (Greece, Spain, Portugal) and some from slow growth in the European economy. Whatever the reasons, in 2014 and 2015, Deutsche reported cumulative losses of close to $16 billion, leading to a management change, with a promise that things would turn around under new management. The other dimension where this crisis unfolded was in Deutsche’s regulatory capital, and as that number dropped in 2015, Deutsche Bank's troubles moved front and center. This is best seen in the graph below of regulatory capital (Tier 1 Capital) from 1998 to 2015, with the ratio of the Tier 1 capital to risk adjusted assets each year super imposed on the graph. 

The ratio of regulatory capital to risk adjusted assets at the end of 2015 was 14.65%, lower than it was in 2014, but much higher than capital ratios in the pre-2008 time-period. That said, with the tightening of regulatory capital constraints after the crisis, Deutsche was already viewed as being under-capitalized in late 2015, relative to other large banks early this year. The tipping point for the current crisis came from the decision by the US Department of Justice to levy a $14 billion fine on Deutsche Bank for transgressions related to the pricing of mortgage backed securities a decade ago. As rumors swirled in the last few weeks, Deutsche Bank found itself in the midst of a storm, since the perception that a bank is in trouble often precipitates more trouble, as rumors replace facts and regulators panic. The market has, not surprisingly, reacted to these stories by marking up the default risk in the bank and marking down the stock price, most strikingly over the last two weeks, but also over a much longer period. 

At close of trading on October 4, 2016, the stock was trading at $13.33 as share, yielding a market capitalization of $17.99 billion, down more than 80% from its pre-2008 levels and 50% from 2012 levels. Reflecting more immediate fears of default, the Deutsche CDS and CoCo bonds also have dropped in price, and not surprisingly, hedge funds sensing weakness have moved in to short the stock. 

Revaluing Deutsche Bank

When a stock is down more than 50% over a year, as Deutsche is, it is often irresistible to many contrarian investors, but knee jerk contrarian investing, i.e., investing in a stock just because it has dropped a lot, is a dangerous strategy. While it is true that Deutsche Banks has lost a large portion of its market capitalization in the last five years, it is also true that the fundamentals for the company have deteriorated, with lower earnings and hits to regulatory capital. To make an assessment of whether Deutsche is now “cheap”, you have to revalue the company with these new realities built in, to see if the market has over reacted, under reacted or reacted correctly to the news. (I will do the entire valuation in US dollars, simply for convenience, and it is straightforward to redo the entire analysis in Euros, if that is your preferred currency).

a. Profitability 

As you can see from the graph of Deutsche’s profits and return on equity, the last twelve months have delivered blow after blow to the company, but that drop has been a long time coming. The bank has had trouble finding a pathway to make sustainable profits, as it is torn between the desire of some at the bank to return to its commercial banking roots and the push by others to explore the more profitable aspects of trading and investment banking. The questions in valuation are not only about whether profits will bounce back but also what they will bounce back to. To make this judgment, I computed the returns on equity of all publicly traded banks globally and the distribution is below: 

Global Bank Data

I will assume that given the headwinds that Deutsche faces, it will not be able to improve its returns on equity to the industry median or even its own cost of equity in the near term. I will target a return on equity of 5.85%, at the 25th percentile of all banks, as Deutsche’s return on equity in year 5, and assume that the bank will be able to claw back to earning its cost of equity of 9.44% (see risk section below) in year 10. The estimated return on equity, with my estimates of common equity each year (see section of regulatory capital) deliver the following projected net income numbers. 

Year	Common Equity	ROE	Expected Net Income
Base	$64,609	-13.70%	$(8,851)
1	$71,161	-7.18%	$(5,111)
2	$72,754	-2.84%	$(2,065)
3	$74,372	0.06%	$43
4	$76,017	1.99%	$1,512
5	$77,688	5.85%	$4,545
6	$79,386	6.57%	$5,214
7	$81,111	7.29%	$5,910
8	$82,864	8.00%	$6,632
9	$84,644	8.72%	$7,383
10	$86,453	9.44%	$8,161
Terminal Year	$87,326	9.44%	$8,244

I am assuming that the path back to profitability will be rocky, with losses expected for the next two years, before the company is able to turn its operations around. Note also that these expected losses are in addition to the $10 billion fine that I have estimated for the DOJ.

b. Regulatory Capital 

Deutsche Bank’s has seen a drop in it Tier 1 capital ratios over time but it now faces the possibility of being further reduced as Deutsche Bank will have to draw on it to pay the US DOJ government fine. While the DOJ has asserted a fine of $14 billion, Deutsche will negotiate to reduce it to a lower number and it is assessing its expected payment to be closer to $6 billion. I have assumed a total capital drop of $ 10 billion, leaving me with and adjusted regulatory capital of $55.28 billion and a Tier 1 capital ratio of 12.41%. Over the next few years, the bank will come under pressure from both regulators and investors to increase its capitalization, but to what level? To make that judgment, I look at Tier 1 capital ratios across all publicly traded banks globally: 

Global Bank Data

I will assume that Deutsche Bank will try to increase its regulatory capital ratio to the average (13.74%) by next year and then push on towards the 75th percentile value of 15.67%. As the capital ratio grows, the firm will have to increase regulatory capital over the next few years and that can be seen in the table below: 

Year	Net Income	Risk-Adjusted Assets	Tier 1 Capital/ Risk Adjusted Assets	Tier 1 Capital	Change in Tier 1 Capital	FCFE = Net Income - Change in Tier 1
Base	$(8,851)	$445,570	12.41%	$55,282
1	$(5,111)	$450,026	13.74%	$61,834	$6,552	$(11,663)
2	$(2,065)	$454,526	13.95%	$63,427	$1,593	$(3,658)
3	$43	$459,071	14.17%	$65,045	$1,619	$(1,576)
4	$1,512	$463,662	14.38%	$66,690	$1,645	$(133)
5	$4,545	$468,299	14.60%	$68,361	$1,671	$2,874
6	$5,214	$472,982	14.81%	$70,059	$1,698	$3,516
7	$5,910	$477,711	15.03%	$71,784	$1,725	$4,185
8	$6,632	$482,488	15.24%	$73,537	$1,753	$4,880
9	$7,383	$487,313	15.46%	$75,317	$1,780	$5,602
10	$8,161	$492,186	15.67%	$77,126	$1,809	$6,352
Terminal Year	$8,244	$497,108	15.67%	$77,897	$771	$7,472

The negative free cash flows to equity in the first three years will have to be covered with new capital that meets the Tier 1 capital criteria. By incorporating these negative free cash flows to equity in my valuation, I am in effect reducing my value per share today for future dilution, a point that I made in a different context when talking about cash burn. 

c. Risk

Rather than follow the well-trodden path of using risk free rates, betas and risk premiums, I am going to adopt a short cut that you can think of as a model-agnostic way of computing the cost of equity for a sector. To illustrate the process, consider the median bank in October 2016, trading at a price to book ratio of 1.06 and generating a return on equity of 9.91%. Since the median bank is likely to be mature, I will use a stable growth model to derive its price to book ratio: 

Plugging in the median bank’s numbers into this equation and using a nominal growth rate set equal to the risk free rate of 1.60% (in US dollars), I estimate a US $ cost of equity for the median bank to be 9.44% in 2016. 

Using the same approach, I arrive at estimates of 7.76% for the banks that are at the 25th percentile of risk and 10.20% for banks at the 75th percentile.  In valuing Deutsche Bank, I will start the valuation by assuming that the bank is at the 75th percentile of all banks in terms of risk and give it a cost of equity of 10.20%. As the bank finds its legs on profitability and improves its regulatory capital levels, I will assume that the cost of equity moves to the median of 9.44%. 

The Valuation 

Starting with net income from part a, adjusting for reinvestment in the form of regulatory capital in part b and adjusting for risk in part c, we obtain the following table of numbers for Deutsche Bank. 

Year	FCFE	Terminal Value	Cost of equity	Cumulative Cost of Equity	PV
1	$(11,663)		10.20%	1.1020	$(10,583.40)
2	$(3,658)		10.20%	1.2144	$(3,012.36)
3	$(1,576)		10.20%	1.3383	$(1,177.54)
4	$(133)		10.20%	1.4748	$(90.34)
5	$2,874		10.20%	1.6252	$1,768.16
6	$3,516		10.05%	1.7885	$1,965.99
7	$4,185		9.90%	1.9655	$2,129.10
8	$4,880		9.74%	2.1570	$2,262.34
9	$5,602		9.59%	2.3639	$2,369.91
10	$6,352	$87,317	9.44%	2.5871	$36,206.88
Total value of equity					$31,838.74
Value per share =					$22.97

Note that the big number as the terminal value in year 10 reflects the expectation that Deutsche will grow at the inflation rate (1% in US dollar terms) in perpetuity while earning its cost of equity. Note also that since the cost of equity is expected to change over time, the cumulated cost of equity has to be computed as the discount factor. The discounted present value of the cash flows is $31.84 billion, which when divided by the number of shares (1,386 million) yields a value of $22.97 per share. There is one final adjustment that I will make and it reflects the special peril that banks face, when in crisis mode. There is the possibility that the perception that the bank is in trouble could make it impossible to function normally and that the government will have to step in to bail it out (since the option of letting it default is not on the table). I may be over optimistic but I attach only a 10% chance to this occurring and assume that my equity will be completely wiped out, if it occurs. My adjusted value is: 

Expected Value per share = $22.97(.9) + $0.00 (.1) = $20.67 

Given my many assumptions, the value per share that I get for Deutsche Bank is $20.67. To illustrate how much the regulatory capital shortfall (and the resulting equity issues/dilution) and overhang of a catastrophic loss affect this value, I have deconstructed the value per share into its constituent effects: 

Unadjusted Equity Value =	$33.63
- Dilution Effect from new equity issues	$(10.66)
- Expected cost of equity wipeout	$(2.30)
Value of equity per share today =	$20.67

Note that the dilution effect, captured by taking the present value of the negative FCFE in the first four years, reduces the value of equity by 31.69% and the possibility of a catastrophic loss of equity lowers the value another 6.83%. The entire valuation is pictured below:

Download Spreadsheet

I know that you will disagree with some or perhaps all of my assumptions. To accommodate those differences, I have set up my valuation spreadsheet to allow for you to replace my assumptions with yours. If you are so inclined, please do enter your numbers into the shared Google spreadsheet that I have created for this purpose and let's get a crowd valuation going!

Time for action or Excuse for inaction? 

At the current stock price of $13.33 (at close of trading on October 4), the stock looks undervalued by about 36%, given my estimated value, and I did buy the stock at the start of trading yesterday. Like everyone else in the market, I am uncertain, but waiting for the uncertainty to resolve itself is not a winning strategy. Either the uncertainty will be resolved (in good or bad ways) and everyone will have clarity on what Deutsche is worth, and the price and value will adjust, or the uncertainty will not resolve itself in the near future and you will be sitting on the side lines. For those of you who have been reading my blog over time, you know that I have played this game before, with mixed results. My bets on JP Morgan (after its massive trading loss in 2012) and Volkswagen (after the emissions scandal) paid off well but my investment in Valeant (after its multiple scandals) has lost me 15% so far (but I am still holding and hoping). I am hoping that my Deutsche Bank investment does better, but I strapped in for a rocky ride!

YouTube Videos


Attachments

1. My valuation of Deutsche Bank
2. Global Banks - Data
3. Google Shared Spreadsheet: Crowd Valuation of Deutsche Bank

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Fairness Opinions: Fix them or Flush them!

My post on the Tesla/SCTY deal about the ineptitude and laziness that Lazard and Evercore brought to the valuation process did not win me any friends in the banking M&A world. Not surprisingly, it drew some pushback, not so much from bankers, but from journalists and lawyers, taking me to task for not understanding the context for these valuations. As Matt Levine notes in his Bloomberg column, where he cites my post, "a fairness opinion is not a real valuation, not a pure effort to estimate the value of a company from first principles and independent research" (Trust me. No one is setting the bar that high. I was looking for biased efforts using flawed principles and haphazard research and these valuation could not even pass that standard)  and that "they (Lazard and Evercore) are just bankers; their expertise is in pitching and sourcing and negotiating and executing deals -- and in plugging in discount rates into preset spreadsheets -- not in knowing the future". (Bingo! So why are they doing these fairness opinions and charging millions of dollars for doing something that they are not good at doing? And there is a difference between knowing the future, which no one does, and estimating the future, which is the essence of valuation.) If Matt is right, the problems run deeper than the bankers in this deal, raising questions about what the purpose of a   "fairness opinion" is and whether it has outlived its usefulness (assuming that it was useful at some point).

Fairness Opinions: The Rationale

What is a fairness opinion? I am not a lawyer and I don't play intend to play one here, but it is perhaps best to revert back to the legal definition of the term. In an excellent article on the topic, Steven Davidoff defines a fairness opinion as an "opinion provided by an outsider that a transaction meets a threshold level of fairness from a financial perspective". Implicit in this definition are the assumptions that the outsider is qualified to pass this judgment and that there is some reasonable standard for fairness.  In corporate control transactions (acquisition, leveraged buyout etc.), as practiced today, the fairness opinion is delivered (orally) to the board at the time of the transaction, and that presentation is usually followed by a written letter that summarizes the transaction terms and the appraiser's assumptions and attests that the price paid is "fair from a financial point of view". That certainly sounds like something we should all favor, especially in deals that have obvious conflicts of interest, such as management-led leveraged buyouts or transactions like the Tesla/Solar City deal, where the interests of Elon Musk and the rest of Tesla 's stockholders may diverge.

Note that while fairness opinions have become part and parcel of most corporate control transactions, they are not required either by regulation or law. As with so much of business law, especially relating to acquisitions, the basis for fairness opinions and their surge in usage can be traced back to Delaware Court judgments. In Smith vs Van Gorkom, a 1985 case, the court ruled against the board of directors of Trans Union Corporation, who voted for a leveraged buyout, and specifically took them to task for the absence of a fairness opinion from an independent appraiser. In effect, the case carved out a safe harbor for the companies by noting that “the liability could have been avoided had the directors elicited a fairness opinion from anyone in a position to know the firm’s value”.  I am sure that the judges who wrote these words did so with the best of intentions, expecting fairness opinions to become the bulwark against self-dealing in mergers and acquisitions. In the decades since, through a combination of bad banking practices, the nature of the legal process and confusion about the word "fairness", fairness opinions, in my view, have not just lost their power to protect those that they were intended to but have become a shield used by managers and boards of directors against serious questions being raised about deals. 

Fairness Opinions: Current Practice?

There are appraisers who take their mission seriously and evaluate the fairness of transactions in their opinions, but the Tesla/Solar City valuations reflect not only how far we have strayed from the original idea of fairness but also how much bankers have lowered the bar on what constitutes acceptable practice.  Consider the process that Lazard and Evercore used by  to arrive at their fairness opinions in the Tesla/Solar City deal, and if Matt is right, they are not alone:

What about this process is fair, if bankers are allowed to concoct discount rates, and how is it an opinion, if the numbers are supplied by management? And who exactly is protected if the end result is a range of values so large that any price that is paid can be justified?  And finally, if the contention is that the bankers were just using professional judgment, in what way is it professional to argue that Tesla will become the global economy (as Evercore is doing in its valuation)? 

To the extent that what you see in the Tesla/Solar City deal is more the rule than the exception, I would argue that fairness opinions are doing more harm than good. By checking off a legally required box, they have become a way in which a board of directors buy immunization against legal consequences. By providing the illusion of oversight and an independent assessment, they are making shareholders too sanguine that their rights are being protected. Finally, this is a process where the worst (and least) scrupulous appraisers, over time, will drive out the best (and most principled) ones, because managers (and boards that do their bidding) will shop around until they find someone who will attest to the fairness of their deal, no matter how unfair it is. My interest in the process is therefore as much professional, as it is personal. I believe the valuation practices that we see in many fairness opinions are horrendous and are spilling over into the other valuation practices.

It is true that there are cases, where courts have been willing to challenge the "fairness" of fairness opinions, but they have been infrequent and  reserved for situations where there is an egregious conflict of interest. In an unusual twist, in a recent case involving the management buyout of Dell at $13.75 by Michael Dell and Silver Lake, Delaware Vice Chancellor Travis Lester ruled that the company should have been priced at $17.62, effectively throwing out the fairness opinion backing the deal. While the good news in Chancellor Lester's ruling is that he was willing to take on fairness opinions, the bad news is that he might have picked the wrong case to make his stand and the wrong basis (that markets are short term and under price companies after they have made big investments) for challenging fairness opinions.

Fish or Cut Bait?

Given that the fairness opinion, as practiced now, is more travesty than protection and an expensive one at that, the first option is to remove it from the acquisition valuation process. That will put the onus back on judges to decide whether shareholder interests are being protected in transactions. Given how difficult it is to change established legal practice, I don't think that this will happen. The second is to keep the fairness opinion and give it teeth. This will require two ingredients to work, judges that are willing to put fairness opinions to the test and punishment for those who consistently violate those fairness principles.

A Judicial Check

Many judges have allowed bankers to browbeat them into accepting the unacceptable in valuation, using the argument that what they are doing is standard practice and somehow professional valuation.  As someone who wanders across multiple valuation terrain, I am convinced that the valuation practices in fairness opinions are not just beyond the pale, they are unprofessional. To those judges, who would argue that they don't have the training or the tools to detect bad practices, I will make my pro bono contribution in the form of a questionnaire with flags (ranging from red for danger to green for acceptable) that may help them separate the good valuations from the bad ones.

Question	Green	Red
Who is paying you to do this valuation and how much? Is any of the payment contingent on the deal happening? (FINRA rule 2290 mandates disclosure on these)	Payment reflects reasonable payment for valuation services rendered and none of the payment is contingent on outcome	Payment is disproportionately large, relative to valuation services provided, and/or a large portion of it is contingent on deal occurring.
Where are you getting the cash flows that you are using in this valuation?	Appraiser estimates revenues, operating margins and cash flows, with input from management on investment and growth plans.	Cash flows supplied by management/ board of company.
Are the cash flows internally consistent?	1.     Currency: Cash flows & discount rate are in same currency, with same inflation assumptions. 2.     Claim holders: Cash flows are to equity (firm) and discount rate is cost of equity (capital). 3.     Operations: Reinvestment, growth and risk assumptions matched up.	No internal consistency tests run and/or DCF littered with inconsistencies, in currency and/or assumptions. -       High growth + Low reinvestment -       Low growth + High reinvestment -       High inflation in cash flows + Low inflation in discount rate
What discount rate are you using in your valuation?	A cost of equity (capital) that starts with a sector average and is within the bounds of what is reasonable for the sector and the market.	A cost of equity (capital) that falls outside the normal range for a sector, with no credible explanation for difference.
How are you applying closure in your valuation?	A terminal value that is estimated with a perpetual growth rate < growth rate of the economy and reinvestment & risk to match.	A terminal value based upon a perpetual growth rate > economy or a multiple (of earnings or revenues) that is not consistent with a healthy, mature firm.
What valuation garnishes have you applied?	None.	A large dose of premiums (control, synergy etc.) pushing up value or a mess of discounts (illiquidity, small size etc.) pushing down value.
What does your final judgment in value look like?	A distribution of values, with a base case value and distributional statistics.	A range of values so large that any price can be justified.

If this sounds like too much work, there are four changes that courts can incorporate into the practice of fairness opinions that will make an immediate difference:

1. Deal makers should not be deal analysts: It should go without saying that a deal making banker cannot be trusted to opine on the fairness of the deal, but the reason that I am saying it is that it does happen. I would go further and argue that deal makers should get entirely out of the fairness opinion business, since the banker who is asked to opine on the fairness of someone else's deal today will have to worry about his or her future deals being opined on by others.
2. No deal-contingent fees: If bias is the biggest enemy of good valuation, there is no simpler way to introduce bias into fairness opinions than to tie appraisal fees to whether the deal goes through. I cannot think of a single good reason for this practice and lots of bad consequences. It should be banished.
3. Valuing and Pricing: I think that appraisers should spend more time on pricing and less on valuation, since their focus is on whether the "price is fair" rather than on whether the transaction makes sense. That will require that appraisers be forced to justify their use of multiples (both in terms of the specific multiple used, as well as the value for that multiple) and their choice of comparable firms. If appraisers decide to go the valuation route, they should take ownership of the cash flows, use reasonable discount rates and not muddy up the waters with arbitrary premiums and discounts. And please, no more terminal values estimated from EBITDA multiples!
4. Distributions, not ranges: In my experience, using a range of value for a publicly traded stock to determine whether a price is fair is useless. It is analogous to asking, "Is it possible that this price is fair?", a question not worth asking, since the answer is almost always "yes". Instead, the question that should be asked and answered is "Is it plausible that this price is a fair one?"  To answer this question, the appraiser has to replace the range of values with a distribution, where rather than treat all possible prices as equally likely, the appraiser specifies a probability distribution. To illustrate, I valued Apple in May 2016 and derived a distribution of its values:

Let's assume that I had been asked to opine on whether a $160 stock price is a fair one for Apple. If I had presented this valuation as a range for Apple's value from $80.81 to $415.63, my answer would have to be yes, since it falls within the range. With a distribution, though, you can see that a $160 price falls at the 92nd percentile, possible, but neither plausible, nor probable.  To those who argue that this is too complex and requires more work, I would assume that this is at the minimum what you should be delivering, if you are being paid millions of dollars for an appraisal.

Punishment
The most disquieting aspect of the acquisition business is the absence of consequences for bad behavior, for any of the parties involved, as I noted in the aftermath of the disastrous HP/Autonomy merger. Thus, managers who overpay for a target are allowed to use the excuse of "we could not have seen that coming" and the deal makers who aided and abetted them in the process certainly don't return the advisory fees, for even the most abysmal advice. I think while mistakes are certainly part of business, bias and tilting the scales of fairness are not and there have to be consequences:

1. For the appraisers: If the fairness opinion is to have any heft, the courts should reject fairness opinions that don't meet the fairness test and remove the bankers involved  from the transaction, forcing them to return all fees paid. I would go further and create a Hall of Shame for those who are repeat offenders, with perhaps even a public listing of their most extreme offenses. 
2. For directors and managers: The boards of directors and the top management of the firms involved should also face sanctions, with any resulting fines or fees coming out of the pockets of directors and managers, rather than the shareholders involved.

I know that your reaction to these punitive suggestions is that they will have a chilling effect on deal making. Good! I believe that much as strategists, managers and bankers like to tell us otherwise, there are more bad deals than good ones and that shareholders in companies collectively will only gain from crimping the process.

YouTube Video


Attachments

1. The Fairness Questionnaire (as a word file, which you are free to add to or adapt)

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The School Bell Rings! It's Time for Class!

As most teachers do, I mark time in academic rather than in calendar years and as September dawns, it is New Year's eve for me and a new class is set to begin. In just under a week, on September 7, 2016, I will walk into a classroom and face up to a roomful of students, not quite ready for summer to end, and start teaching, as I have every year since 1984. This semester, I will be back to teaching Valuation to MBAs at Stern, and as I have in semesters past, I invite you to join me on this journey, as we look at the mix of art, science and magic that makes valuation such a fascinating discipline.

Class Philosophy

I have always believe that to teach a class well, you have to start with a story and that the class is an extended serialization of the story. I also believe that to teach well, you have to, at least over time, make that story your own and mold the class to reflect it. In fact, the valuation class that I will be teaching this Fall has its seeds in the very first valuation class that I taught in 1986, but the differences reflect not only how much the world has changed since then, but also how my own thinking on valuation has evolved. The class remains a work in progress, where each time I teach it, I learn something new as well as recognize how much I have left to learn.

I could give you an extended essay on what this class is about, but I would repeating what I said at the start of the Fall 2015 semester in this post. In short, I said this class is not an extended accounting class (where you forecast entire financial statements for extended periods), or a modeling class (where you become an Excel Ninja) or a theory class (since there is so little of it in  valuation to begin with). Instead, here are the broad themes that underlie this class, all captured in the picture below:

If you find this picture a little daunting, I did do a Google talk that encapsulated these themes into about an hour-long session. 

In particular, this class is less about the tools and techniques of valuation and more about developing a foundation that you can use to build your own investment philosophy. I know that faith is a word that is seldom used and often viewed with suspicion by many in the valuation community, but it is at the heart of this class, both in terms of how you build up faith in your own capacity to value assets and businesses and how you hold on to that faith when the market price moves away from your value.  Since I still struggle on both of these fronts, I cannot give you a template for success but I will be open about my own insecurities both about my own valuations and about markets.

Class Structure

Since my objective in the class is that by the end of it, you should be able to attach a number to just about any asset, I will roam the spectrum. I will start with the basics of intrinsic value, partly because it is where I am most comfortable and partly because it provides me with ways of dealing with other approach. The mechanics of estimating discount rates, cash flows, growth and terminal value are not just simple, but easily mechanized. It is the specifics that we will wrestle with in this class:

• On risk free rates, usually the least troublesome and more easily obtained input in valuation, we will talk about why risk free rates vary across currencies, what to do about currencies that have negative risk free rates and whether normalizing risk free rates (as many practitioners have taken to doing) is a good idea or a bad one.
• On risk premiums and discount rates, we will wrestle with questions of what risks should and should not be incorporated into discount rates and the different methods of bringing them in. In the process, we will examine how best to estimate equity risk premiums and default spreads, and why even if you don't like betas or portfolio theory, you should should still be able to estimate discount rates and do intrinsic valuation.  
• On cash flows, we will focus on why accounting inconsistencies (on dealing with R&D, leases and other items) can lead to misstated earnings and how to fix those inconsistencies, examine what should and should not be included in reinvestment (capital expenditures and working capital) and what to do about stock based compensation.
• On growth, we will start with the easy cases (where historical earnings growth is a good predictor of future growth) but quickly move on to more difficult cases (of companies in transition) and to what some view as impossible cases (like estimating growth in a start-up)>
• On terminal value, the big number in every DCF,  that can very quickly hijack otherwise well-done valuations, we will develop simple rules for keeping the number in check and put to sleep many myths surrounding it.

We will apply intrinsic valuation to value companies across the life cycle, in different sectors and across different markets. We will value small and large companies, private and public, developed and emerging and discuss how to value movie franchises (like Star Wars), phenomena (Pokemon Go) and sports teams. We will talk about why start ups can and should be valued in the face of daunting uncertainty and how probabilistic tools (simulations and decision trees) can help.

About half way through the class, we will turn our attention to pricing assets/businesses, where rather than build up to a value from a company's fundamentals, we price it, based on how the market is pricing similar companies. Put simply, we will shine a light on the practice of using pricing multiples (PE, EV/EBITDA, EV/Sales) and comparable companies not with the intent of improving how it is done. We will also talk about why, even when you are careful and take care of the details, your pricing of a company can be very different form its value.

In the last segment of the class, we will stretch our valuation muscles by talking about how option pricing models can sometime be used to estimate the additional value in a business, such as undeveloped reserves for a natural resource company or expansion potential for a young growth firm, and sometimes to value equity in deeply distressed companies. We will close by looking at acquisition valuation, where good sense seems to be in short supply, and how understanding value can be critical to corporate managers.

Want to sit in?

If you are intrigued or interested, you are welcome to sit in on the class (online and unofficially). While my immediate attention will be reserved for the Stern MBAs who will be registered in this class, you will have access to all of the resources that they do, starting with the lectures but also extending to lecture notes, quizzes/exams and even emails. The bad news is that I will be unable to grade your work or give you a certificate of completion. The good news is that the price is right. There are three ways in which you can join the class:

1. My website: The most comprehensive and most updated center of all things related to this class at this link. You will find the webcasts, lecture notes, past exams, reading and even the emails I send on this class here.
2. iTunes U: Just as I am not an Excel Ninja, my capacity to deal with html is primitive and my website's design reflects that lack of sophistication. If you prefer more polish, you can try the iTunes U app in the Apple app store. It is a free app that you can download and install on your Apple device. Once you have it installed, click on the add course and enter the enroll code FER-SFJ-AKA. Like magic, the class should pop up on your shelf. If you don't have an Apple device, you can get to the course on your computer using this link. If you have an Android device, you can use a workaround by downloading this app first. Like all things Apple, the set up is amazing and easy to work with.
3. YouTube: The problem with the first two choices is that they presuppose that you don't have a broadband constraint, perhaps a phone internet connection or worse. My suggestion is that you use the YouTube playlist that I have created for this class at this link. The nice thing about YouTube is that it adjusts the image quality to your connection speed. So, it should work in almost any setting.

Since I have made this offer for almost 20 years now, predating the MOOC boom and bust, I can offer some suggestions. First, it is a lot of work to watch two 80-minute lectures a week, try your hand out at working through actual valuations and finish the class in fifteen weeks, if you have other things going on in your life (and who does not?). My suggestion is that you cut yourself some slack and take more time, since the materials will stay up for at least a year after the class ends. Second, watching a lecture online for almost an hour and a half can be painful and for those of you who find the pain unbearable, I do have an alternative. A couple of years ago, I created an online version of this class, shrinking each 80-minute session into 10-15 minute sessions and this class is also available on my website at this link, on iTunes U at this link and on YouTube. Third, whichever version of the class you take will stick more if you pick a company and value it and even more, if you keep doing it. 

The End Game

I would love to tell you that I live a life of serenity and that I am sharing for noble reasons, but that would not be true. I am sharing my class for the most selfish of all reasons. I am a performer (and every teacher is) and what performer does not wish for a bigger audience? If I am going to prepare and deliver a class, would I not rather have thirty thousand people watch the class than three hundred. If you get something of value from this class, and you feel the urge to repay me, I will make the same suggestion that I did last year. Learning is one of those rare resources that is never diminished by sharing. So, please pass it on to someone else! See you in class!

Links

1. Entry Page for the Valuation Spring 2016 (on my website)
2. Webpage for the Valuation Spring 2016 class webcasts (on my website)
3. iTunes U for the Valuation Spring 2016 class (Enroll code on device: FER-SFJ-AKA)
4. YouTube Playlist for the Valuation Spring 2016 class
5. Webpage for Valuation Online class (short sessions)
6. iTunes U for the Valuation Online class (short sessions)
7. YouTube for the Valuation Online class (short sessions)

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DCF Myth 3.2: If you don't look, its not there!

In this, the last of my three posts on uncertainty, I complete the cycle I started with a look at the responses (healthy and unhealthy) to uncertainty and followed up with an examination of the Margin of Safety, by taking a more extended look at one approach that I have found helpful in dealing with uncertainty, which is to run simulations. Before you read this post, I should warn you that I am not an expert on simulations and that the knowledge I bring to this process is minimalist and my interests are pragmatic. So, if you are an expert in statistics or a master simulator, you may find my ramblings to be amateurish and I apologize in advance. 

Setting the Stage

The tools that we use in finance were developed in simpler times, when data was often difficult (or expensive) to access and sophisticated statistical tools required machine power that was beyond the reach of most in the finance community. It should come as no surprise then that in discounted cash flow valuation, we have historically used point estimates ( single numbers that reflect best judgments at the time of the valuation) for variables that have probability distributions attached to them. To illustrate, in my valuation of Apple in February 2016, I used a revenue growth rate of 2.2% and a target operating margin of 25%, to arrive at my estimate of value per share of $129.80.

It goes without saying (but I will say it anyway) that I will be wrong on both these numbers, at least in hindsight, but there is a more creative way of looking at this estimation concern. Rather than enter a single number for each variable, what if I were able to enter a probability distribution? Thus, my estimate for revenue growth would still have an expected value of 2.2% (since that was my best estimate) but would also include a probability distribution that reflected my uncertainty about that value. That distribution would capture not only the magnitude of my uncertainty (in a variance or a standard deviation) but also which direction I expect to be wrong more often (whether the growth is more likely to be lower than my expected value or higher).  Similarly, the expected value for the operating margin can stay at 25% but I can build in a range that reflects my uncertainty about this number.

Once you input the variables as distributions, you have laid the foundations for a probabilistic valuation or more specifically, for a simulation, where in each run, you pick one outcome out of each distribution (which can be higher or lower than your expected values) and estimate a value for the company based on the drawn outcomes. Once you have run enough simulations, your output will be a distribution of values across simulations. If the distributions of your variables are built around expected values that match up to the numbers that you used in your point estimate valuation, the expected value across the simulations will be close to your point estimate value. That may seem to make the simulation process pointless, but there are side benefits that you get from simulations that enrich your decision process. In addition to the expected value, you will get a measure of how much variability there is in this value (and thus the risk you face), the likelihood that you could be wrong in your judgment of whether the stock is under and over valued and the potential payoffs to be right and wrong. 

Statistical Distributions: A Short Preview

It is a sad truth that most of us who go through statistics classes quickly consign them to the “I am never going to use this stuff” heap and move on, but there is no discipline that is more important in today’s world of big data and decision making under uncertainty. If you are one of those fortunate souls who not only remembers your statistics class fondly but also the probability distributions that you encountered during the class, you can skip this section. If, like me, the only memory you have of your statistics class is of a bell curve and a normal distribution, you need to expand your statistical reach beyond a normal distribution, because much of what happens in the real world (which is what you use probability distributions to capture) is not normally distributed. At the risk of over simplifying the choices, here are some basic classifications of uncertainties/ risks::

1. Discrete versus Continuous Distributions: Assume that you are valuing an oil company in Venezuela and that you are concerned that the firm may be nationalized, a risk that either occurs or does not, i.e., a discrete risk. In contrast, the oil company's earnings will move with oil prices but take on a continuum of values, making it a continuous risk. With currency risk, the risk of devaluation in a fixed exchange rate currency is discrete risk but the risk in a floating rate currency is continuous.
2. Symmetric versus Asymmetric Distributions (Symmetric, Positive skewed, Negative skewed): While we don't tend to think of upside risk, risk can deliver outcomes that are better than expected or worse than expected. If the magnitude and likelihood of positive outcomes and negative outcomes is similar, you have a symmetric distribution. Thus, if the expected operating margin for Apple is 25% and can vary with equal probability from 20% to 30%, it is symmetrically distributed. In contrast, if the expected revenue growth for Apple is 2%, the worse possible outcome is that it could drop to -5%, but there remains a chance (albeit a small one) that revenue growth could jump back to 25% (if Apple introduces a disruptive new product in a big market), you have an a positively skewed distribution. In contrast, if the expected tax rate for a company is 35%, with the maximum value equal to the statutory tax rate of 40% (in the US) but with values as low as 0%, 5% or 10% possible (though not likely), you are looking at a negatively skewed distribution.
3. Extreme outcome likelihood (Thin versus Fat Tails): There is one final contrast that can be drawn between different risks. With some variables, the values will be clustered around the expected value and extreme outcomes, while possible, don't occur very often; these are thin tail distributions. In contrast, there are other variables, where the expected value is just the center of the distribution and actual outcome that are different from the expected value occur frequently, resulting in fat tail distributions.

I know that this is a very cursory breakdown, but if you are interested, I do have a short paper on the basics of statistical distributions (link below), written specifically with simulations in mind. 

Simulation Tools

I was taught simulation in my statistics class, the old fashioned way. My professor came in with three glass jars filled with little pieces of paper, with numbers written on them, representing the different possible outcomes on each variable in the problem (and I don't even remember what the problem was). He then proceeded to draw one piece of paper (one outcome) out of each jar and worked out the solution, with those numbers and wrote it on the board. I remember him meticulously returning those pieces of paper back into the jar (sampling with replacement) and at the end of the class, he proceeded to compute the distribution of his solutions.

While the glass jar simulation is still feasible for simulating simple processes with one or two variables that take on only a few outcomes, it is not a comprehensive way of simulating more complex processes or continues distributions. In fact, the biggest impediment to using simulation until recently would have been the cost of running one, requiring the use of a mainframe computer. Those days are now behind us, with the evolution of technology both in the form of hardware (more powerful personal computers) and software. Much as it is subject to abuse, Microsoft Excel has become the lingua franca of valuation, allowing us to work with numbers with ease. There are some who are conversant enough with Excel's bells and whistles to build simulation capabilities into their spreadsheets, but I am afraid that I am not one of those. Coming to my aid, though, are offerings that are add-ons to Excel that allow for the conversion of any Excel spreadsheet almost magically into a simulation.

I normally don't make plugs for products and services, even if I like them, on my posts, because I am sure that you get inundated with commercial offerings that show up insidiously in Facebook and blog posts. I am going to make an exception and praise Crystal Ball, the Excel add-on that I use for simulations. It is an Oracle product and you can get a trial version by going here. (Just to be clear, I pay for my version of Crystal Ball and have no official connections to Oracle.) I like it simply because it is unobtrusive, adding a menu item to my Excel toolbar, and has an extremely easy learning curve.

My only critique of it, as a Mac user, is that it is offered only as a PC version and I have to run my Mac in MS Windows, a process that I find painful. I have also heard good things about @Risk, another excel add-on, but have not used it.

Simulation in Valuation

There are two aspects of the valuation process that make it particularly well suited to Monte Carlo simulations. The first is that uncertainty is the name of the game in valuation, as I noted in my first post in the series. The second is that valuation inputs are often estimated from data, and that data can be plentiful at least on some variables, making it easier to estimate the probability distributions that lie at the heart of simulations. The sequence is described in the picture below:

Step 1: Start with a base case valuation
The first place to start a simulation is with a base case valuation. In a base case valuation, you do a valuation with your best estimates for the inputs into value from revenue growth to margins to risk measures. Much as you will be tempted to use conservative estimates, you should avoid the temptation and make your judgments on expected values. In the case of Apple, the numbers that I use in my base case valuation are very close to those that I used just a couple of months ago, when I valued the company after its previous earnings report and are captured in the picture below:

Download spreadsheet

In my base case, at least, it looks like Apple is significantly under valued, priced at $93/share, with my value coming in at $126.47, just a little bit lower my valuation a few months ago. I did lower my revenue growth rate to 1.50%, reflecting the bad news about revenues in the most recent 10Q.

Step 2: Identify your driver variables

While there are multiple inputs into valuation models that determine value, it remains true that a few of these inputs drive value and that the rest go along for the ride. But how do you find these value drivers? There are two indicators that you can use. The first requires trial and error, where you change each input variable to see which ones have the greatest effect on value. It is one reason that I like parsimonious models, where you use fewer inputs and aggregate numbers as much as you can. The second is more intuitive, where you focus on the variable that investors in the company seem to be most in disagreement about. My Apple valuation is built around four inputs: revenue growth (growth), operating margin (profitability), the sales to capital ratio (investment efficiency) and cost of capital (risk). The graph below captures how much value changes as a function of these inputs:

As you can see the sales to capital ratio has little effect on value per share, largely because the base case growth rate that I use for Apple is so low. Revenue growth and operating margin both affect value significantly and cost of capital to a much lesser degree. Note that the value per share is higher than the current price though every single what-if analysis, but that reflects the fact that only variable at a time in being changed in this analysis. It is entirely possible that if both revenue growth and operating margins drop at the same time, the value per share will be lower than $93 (the stock price at the time of this analysis) and one of the advantages of a Monte Carlo simulation is that you can build in interconnections between variables. Looking at the variables through the lens that investors have been using to drive the stock price down, it seems like the front runner for value driver has to be revenue growth, as Apple reported its first year on year negative revenue growth in the last quarter and concerns grow about whether the iPhone franchise is peaking. Following next on the value driver list is the operating margin, as the competition in the smart phone business heats up.

Step 3: The Data Assessment

Once you have the value drivers identified, the next step is collecting data on these variables, as a precursor for developing probability distributions. In developing the distributions, you can draw on the following:

1. Past data: If the value driver is a macroeconomic variable, say interest rates or oil prices, you can draw on historical data going back in time. My favored site for all things macroeconomic is FRED, the Federal Reserve data site in St. Louis, a site that combines great data with an easy interface and is free. I have included data on interest rate, inflation, GDP growth and the weighted dollar for those of you interested in US data in the attached link. For data on other countries, currencies and markets, you can try the World Bank data base, not as friendly as FRED, but rich in its own way.
2. Company history: For companies that have been in existence for a long time, you can mine the historical data to get a measure of how key company-specific variables (revenues, operating margin, tax rate) vary over time. 
3. Sector data: You can also look at cross sectional differences in key variables across companies in a sector. Thus, to estimate the operating margin for Amazon, you could look at the distribution of margins across retail companies.: If the value driver is a macroeconomic variable, say interest rates or oil prices, you can draw on historical data going back in time. My favored site for all things macroeconomic is FRED, the Federal Reserve data site in St. Louis, a site that combines great data with an easy interface and is free. I have included data on interest rate, inflation, GDP growth and the weighted dollar for those of you interested in US data in the attached link. For data on other countries, currencies and markets, you can try the World Bank data base, not as friendly as FRED, but rich in its own way.

In the case of Apple, I isolated my data assessment to three variables: revenue growth, operating margin and the cost of capital.  To get some perspective on the range and variability in revenue growth rates and operating margins, I started by looking at the values for these numbers annually from 1990 to 2015:

This extended time period does distract from the profound changes wrought at Apple over the last decade by the iPhone. To takes a closer look at its effects, I looked at growth and margins at Apple for every quarter from 2005 to the first quarter of 2016 :

Superimposed on this graph of gyrating revenue growth, I have traced the introduction of the different iPhone models that have been largely responsible for Apple's explosive growth over the last decade. There are a few interesting patterns in this graph. The first is that revenue growth is clearly driven by the iPhone cycle, peaking soon after each new model is introduced and fading in the quarters after. The second is that the effect of a new iPhone on revenue growth has declined with each new model, not surprising given the scaling up of revenues as a result of prior models. The third is that the operating margins have been steady through the iPhone cycles, with only a midl dip in the last cycle. There is good news and bad news in this graph for Apple optimists. The good news is that the iPhone 7 will deliver an accelerator to the growth but the bad news is that it will be milder that the prior versions; if the trend lines hold up, you are likely to see only a 10-15% revenue growth in the quarters right after its introduction. 

To get some perspective on what the revenue growth would look like for Apple, if it's iPhone franchise fades, I looked at the compounded annual revenue growth for US technology firms older than 25 years that were still listed and publicly traded in 2016:

Of the 343 firms in the sample, 26.2% saw their revenues decline over the last 10 years. There is a sampling bias inherent in this analysis, since the technology firms with the worst revenue growth declines over the period may not have survived until 2016. At the same time, there were a healthy subset of aging technology firms that were able to generate revenue growth in the double digits over a ten-year period. 

Step 4: Distributional Assumptions
There is no magic formula for converting the data that you have collected into probability distributions, and as with much else in valuation, you have to make your best judgments on three dimensions.

1. Distribution Type: In the section above, I broadly categorized the uncertainties you face into discrete vs continuous, symmetric vs skewed and fat tail vs thin tail. At the risk of being tarred and feathered for bending statistical rules, I have summarized the distribution choices based on upon these categorizations. The picture is not comprehensive but it can provide a road map though the choices:
   
2. Distribution Parameters: Once you have picked a distribution, you will have to input the parameters of the distribution. Thus, if you had the good luck to have a variable be normally distributed, you will only be asked for an expected value and a standard deviation. As you go to more complicated distributions, one way to assess your parameter choices to look at the full distribution, based upon your parameter choices, and pass it through the common sense test.

In the case of Apple, I will use the historical data from the company, the cross sectional distribution of revenue growth across older technology companies as well as a healthy dose of subjective reasoning to pick a lognormal distribution, with parameters picked to yield values ranging from -4% on the downside to +10% on the upside. On the target operating margin, I will build my distribution around the 25% that I assumed in my base case and assume more symmetry in the outcomes; I will use a triangular distribution to prevent even the outside chance of infinite margins in either direction.

Note the correlation between the two, which I will talk about in the next section.

Step 5: Build in constraints and correlations
There are two additional benefits that come with simulations. The first is that you can build in constraints that will affect the company's operations, and its value, that are either internally or externally imposed. For an example of an external constraint, consider a company with a large debt load. That does not apply to Apple but it would to Valeant. If the company's value drops below the debt due, you could set the equity value to zero, on the assumption that the company will be in default. As another example, assume that you are valuing a bank and that you model regulatory capital requirements as part of your valuation. If the regulatory capital drops below the minimum required, you can require the company to issue more shares (thus reducing the value of your equity).  The second advantage of a simulation is that you can build in correlations across variables, making it more real life. Thus, if  you believe that bad outcomes on margins (lower margins than expected) are more likely to go with bad outcomes on revenue growth (revenue growth lower than anticipated), you can build in a positive correlation between the variables. With Apple, I see few binding constraints that will affect the valuation. The company has little chance of default and is not covered by regulatory constraints on capital. I do see revenues and operating margins moving together and I build in this expectation by assuming a correlation of 0.50 (lower than the historical correlation of 0.61 between revenues and operating margin from 1989 to 2015 at Apple).

Step 6: Run the simulations

Using my base case valuation of Apple (which yielded the value per share of $126.47) as my starting point and inputting the distributional assumptions for revenue growth and operating margin, as well as the correlation between the two, I used Crystal Ball to run the simulations (leaving the number at the default of 100,000) and generated the following distribution for value:

The percentiles of value and other key statistics are listed on the side. Could Apple be worth less than $93/share. Yes, but the probability is less than 10%, at least based on my assumptions. Having bought and sold Apple three times in the last six years (selling my shares last summer), this is undoubtedly getting old, but I am an Apple shareholder again. I am not a diehard believer in the margin of safety, but if I were, I could use this value distribution to create a more flexible version of it, increasing it for companies with volatile value distributions and reducing it for firms with more stable ones.

The most serious concern that I have, as an investor, is that I am valuing cash , which at $232 billion is almost a third of my estimated value for Apple, as a neutral asset (with an expected tax liability of $28 billion). Some of you, who have visions of Apple disrupting new businesses with the iCar or the iPlane may feel that this is too pessimistic and that there should be a premium attached for these future disruptions. My concern is the opposite, i.e., that Apple will try to do too much with its cash, not too little. In my post on aging technology companies, I argued that, like aging movie stars in search of youth, some older tech companies throw money at bad growth possibilities. With the amount of money that Apple has to throw around, that could be deadly to its stockholders and I have to hope and pray that the company remains restrained, as it has been for much of the last decade.

Conclusion

Uncertainty is a fact of life in valuation and nothing is gained by denying its existence. Simulations offer you an opportunity to look uncertainty in the face, make your best judgments and examine the outcomes. Ironically, being more open about how wrong you can be in your value judgments  will make you feel more comfortable about dealing with uncertainty, not less. If staring into the abyss is what scares you, take a peek and you may be surprised at how much less scared you feel.

YouTube video


Attachments

1. Paper on probability distributions
2. Apple valuation - May 2016
3. Link to Oracle Crystal Ball trial offer

Uncertainty Posts

1. DCF Myth 3: You cannot do a valuation, when there is too much uncertainty
2. The Margin of Safety: Excuse for Inaction or Tool for Action?
3. Facing up to Uncertainty: Probabilities and Simulations

DCF Myth Posts
Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. The most critical input in a DCF is the discount rate and if you don’t believe in modern portfolio theory (or beta), you cannot use a DCF.
5. If most of your value in a DCF comes from the terminal value, there is something wrong with your DCF.
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

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