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After Lyft’s IPO on March 29, 2019, it was only a matter of time before Uber threw its hat in the public market ring, and on Friday, April 12, 2019, the company filed its prospectus. It is the first time that this company, which has been in the news more frequently in the last few years than almost any publicly traded company, has opened its books for investors, journalists and curiosity seekers. As someone who has valued Uber with the tidbits of information that have hitherto been available about the company, mostly leaked and unofficial, I was interested in seeing how much my perspective would change, when confronted with a fuller accounting of its performance.

Backing up!

To get a sense of where Uber stands now, just ahead of its IPO, I started with the prospectus, which weighing in at 285 pages, not counting appendices, and filled with pages of details, can be daunting. It is a testimonial to how information disclosure requirements have had the perverse consequence of making the disclosures useless, by drowning investors in data and meaningless legalese. I know that there are many who have latched on to the statement that "we may not achieve profitability" that Uber makes in the prospectus (on page 27) as an indication of its worthlessness, but I view it more as evidence that lawyers should never be allowed to write about investing risk.

Uber's Business
Just as Lyft did everything it could, in its prospectus, to relabel itself as a transportation services (not just car services) company, Uber's catchword, repeatedly multiple times in its prospectus, is that it is a personal mobility business, with the tantalizing follow up that its total market could be as large as $2 trillion, if you count the cost of all money spent on transportation (cars, public transit etc.)
Uber Prospectus: Page 11
While the cynic in me pushes me back on this over reach (I am surprised that they did not include the calories burnt by the most common transportation mode on the face of the earth, which is walking from point A to point B, as part of the total market), I understand why both Lyft and Uber have to relabel themselves as more than car service companies. Big market stories generally yield higher valuation and pricing than small market stories!

The Operating History
Uber went through some major restructuring in the three years leading into the IPO, as it exited cash burning investments in China (settling for a 20% stake in Didi), South East Asia (receiving a 23.2% share of Grab) and Russia (with 38% of Yandex Taxi the prize received for that exit). It is thus not surprising that there are large distortions in the financial statements during the last three years, with losses in the billions flowing from these divestitures. In the last few weeks, Uber announced a major acquisition, spending $3.1 billion to acquire Careem, a Middle Eastern ride sharing firm. Taking the company at its word, i.e., that the large divestiture-related losses are truly divestiture-related, let’s start by tracing the growth of Uber in the parts of the world where it had continuing operations in 2016, 2017 and 2018:
Uber Prospectus: Page 21
The numbers in this table are the strongest backing for Uber’s growth story, with gross billings, net revenues, riders and rides all increasing strongly between 2016 and 2018. That good news on growing operations has to be tempered by the recognition that Uber has been unable to make money, as the table below indicates:
Uber Prospectus: Pages 21 & 24
The adjusted EBITDA column contains numbers estimated and reported for the company, with a list of adjustments they made to even bigger losses to arrive at the reported values. I convert this adjusted EBITDA to an operating income (loss) by first netting out depreciation and amortization (for obvious reasons) and then reversing the company’s attempt to add back stock based compensation. The company is clearly a money loser, but if there is anything positive that can be extracted from this table, it is that the losses are decreasing as a percent of sales, over time.

The Rider Numbers
One of Uber’s selling points lies in its non-accounting numbers, as the company reported having 91 million monthly riders (defined as riders who used either Uber or Uber delivery at least once in a month) and completing 5.2 billion rides. To break down those daunting numbers, I focus on the per rider statistics to see the engines driving Uber’s growth over time:
Uber Prospectus: Page 21
There is good and bad news in this table. The good news is that Uber’s annual gross billings per rider rose almost 28% over the three year period, but the sobering companion finding is that the billings/ride are decreasing. Boiled down to basics, it suggests that the growth in overall billings for the company is at least partially driven by existing riders using more of the service, albeit for shorter rides. It could also reflect the fact the new riders for the company are coming from parts of the world (Latin America, for instance), where rides are less expensive.  Finally, I took Uber’s expense breakdown in their income statement, and used it to extract information about what the company is spending money on, and how effectively:
Uber Prospectus: F-4 (income statement in appendix)
I make some assumptions here which will play out in the valuation that you will see below.
  1. User Acquisition costs: Using the assumption that user change over a year can be attributed to selling expenses during the year, I computed the user acquisition cost each year by dividing the selling expenses by the number of riders added during the year.
  2. Operating Expenses for Existing Rides: I have included the cost of revenues (not including depreciation) and operations and support as expenses associated with current riders. 
  3. Corporate Expenses; These are expenses that I assume are general expenses, not directly related to either servicing existing users or acquiring new ones and I include R&D, G&A and depreciation in this grouping.
The good news is that the expenses associated with servicing existing users has been decreasing, as a percent of revenues, indicating that not all of these costs are variable or at least directly linked to more rider usage. Also, corporate expenses are showing evidence of economies of scale, decreasing as a percent of revenues. The bad new is that the cost of acquiring new users has been increasing, at least over this time period, suggesting that the ride sharing market is maturing or that competition is picking up for riders.

More than ride sharing?
Uber is a more complicated company to value than Lyft, for two reasons. The first is that Uber is not a pure ride sharing company, since it derives revenues from its food delivery service (Uber Eats) and an assortment of other smaller bets (like Uber Freight). In the graph below, you can see the evolution of these businesses:
Uber Prospectus: Page 114

It is worth noting this table while suggests that while some of Uber’s more ambitious reaches into logistics have not borne fruit, its foray into food delivery seems to be picking up steam. Uber Eats has expanded from 2.68% of Uber’s net revenues to 13.12%. There is some additional information in another portion of the prospectus, where Uber reports its "adjusted" net revenue and gross Billings by business, and it does look like Uber's net take from Uber Eats is lower than its take from ride sharing:
Uber Prospectus: Pages 102 & 103
While it is clear that Uber's ride sharing customers have been quick to adopt Uber Eats, there are subtle differences in the economics of the two businesses that will play out in future profitability, especially if Uber Eats continues to grow at a disproportionate rate.

Unlike Lyft, which has kept its focus on the US and Canadian markets, Uber's ambitions have been more global, though reality has put a crimp on some of its expansion plans. While Uber's initial plans were to be everywhere in the world, large losses have led Uber to abandon much of Asia, leaving China to Didi and South East Asia to Grab, with India being the one big market where Uber has stayed, fighting Ola for market share and who can lose more money. The fastest growing overseas market for Uber has been Latin America, as you can see in the graph below:

Uber does not provide a breakdown of profitability by geographical region, but the magnitude of the losses that they wrote off when they closed their Chinese and South East Asian operations suggests that the US remains their most lucrative ride sharing market, in terms of profitability. 

The Road Ahead : Crafting a story and value for Uber
1. A Top Down Valuation
In valuing Lyft, I used a top-down approach, starting with US transportation services as my total accessible market and working down through market share, margins and reinvestment to derive a value of $13.9 billion for its operating assets and $16.4 billion with the IPO proceeds counted in. Using a similar approach is trickier for Uber, since its decision to be in multiple parts of the logistics business and its global ambitions require assessment of a global logistics market, a challenge. I did an initial assessment of Uber, using a much larger total market and arrived at a value of $44.4 billion for its operating assets, but adding the portions of Didi, Grab and Yandex Taxi pushed this number up to $55.3 billion. Adding the cash balance on hand as well as the IPO proceeds that will remain in the firm (rumored to be $9 billion), before subtracting out debt yields a value for equity of about $61.7 billion.
Download spreadsheet
The share count is still hazy (as the multiple blank areas in the prospectus indicate) but starting with the 903.6 million shares of common stock that will result from the conversion of redeemable convertible preferred shares at the time of the IPO, and adding in additional shares that will result from option exercises, RSUs (restricted stock units issued to employees) and new shares being issued to raise approximately $10 billion in proceeds, I arrive at a value per share of about $54/share, though  that the updated version of the prospectus, which should come out with the offering price, should allow for more precision on the share count.

2. A Rider-based Valuation

The uncertainty about the total accessible market, though, makes me uneasy with my top down valuation. So, I decided to try another route. In June 2017, I presented a different approach to valuing companies like Uber, that derive their value from users, subcribers or members. In that approach, I began by valuing an existing user (rider), by looking at the revenues and cash flows that Uber would generate over the user’s lifetime and then extended the approach to valuing a new user, where the cost of user acquisition has to be netted out against the user value. I completed the assessment by computing the value drag created by non-rider related costs (like G&A and R&D). In the June 2017 valuation, I had to make do with minimalist detail on expenses but the prospectus provides a much richer break down, allowing me to update my user-based valuation of Uber. The valuation picture is below:
Download spreadsheet

This approach yields a value for the equity of about $58.6 billion for Uber’s equity, which again depending on the share count would translate into a share price of $51/share.

Value Dynamics

The benefits of the rider-based valuation is that it allows us to isolate the variables that will determine whether Uber turns the corner quickly and can make enough money to justify the rumored $100 billion value. The value of existing riders is determined by the growth rate in per-user revenues and the cost of servicing a user, with increases in the former and decreases in the latter driving up user value.  The value of new riders, in the aggregate, is determined by the increase in rider count and the cost of acquiring a new rider. One troubling aspect of the growth in users over the last three years has been the increase in user acquisition costs, perhaps reflecting a more saturated market. In the table below, I estimate the value of Uber's equity, using a range of assumptions for the growth rate in per user revenues and the cost of acquiring a new user:
Download spreadsheet
There are two ways that you can read this table. If you are a trader, deeply suspicious of intrinsic value, you may look at this table as confirmation that intrinsic value models can be used to deliver whatever value you want them to, and your suspicions would be well founded. I am a believer in value and I see this table in a different light.

  • First, I view it as a reminder that my estimate of value is just mine, based on my story and inputs, and that there are others with different stories for the company that may explain why they would pay much more or much less than I would for the company. 
  • Second, this table suggests to me that Uber is a company that is poised on a knife's edge. If it just continues to just add to its rider count, but pushes up its cost of acquiring riders as it goes along, and existing riders do not increase the usage of the service, its value implodes. If it can get riders to significantly increase usage (either in the form of more rides or other add on services), it can find a way to justify a value that exceeds $100 billion. 
  • Third, the table also indicates that if Uber has to pick between spending money on acquiring more riders or getting existing riders to buy more of its services, the latter provides a much bigger bang for the buck than the former. 
Put simply, I hope Dara Khoshrowshahi means it when he says that Uber has to show a pathway to profitability, but I think that is what is more critical is that he acts on those words. In my view, this remains a business, whether you define it to be ride sharing, transportation services or personal mobility, without a business model that can generate sustained profits, precisely because the existing model was designed to deliver exponential growth and little else, and Uber, and the other players in this game), have only a limited window to fix it.

Refreshing the Pricing
Having spent all of this time on Uber's valuation, let me concede to the reality that Uber will be priced by the market, and it will be priced relative to Lyft. That is why Uber has probably been pulling harder than almost any one else in the market for the Lyft IPO to be well received and for its stock to continue to do well in the aftermarket. In the table below, I compare key operating numbers for Uber and Lyft, with Lyft's pricing in the market in place:

In computing the metrics, it is worth remembering that Uber and Lyft use different definitions for basic metrics and I have tried to adjust. For instance, Uber defines riders as those who use the service at least once a month and the closest number that I can get for Lyft is their estimate that they had 18.6 million active quarterly riders. Uber is bigger on every single dimension, including losses, then Lyft. I convert Lyft's current market pricing (on April 12, 2019) into multiples, scaling them to different metrics and applying these metrics to Uber:
Download pricing spreadsheet
In computing Uber's equity value from its enterprise value, I have added the cash ($6.4 billion of cash on hand plus the $9 billion in expected IPO proceeds) $ and Uber's cross holdings ($8.7 billion) to the value and netted out debt ($6.5 billion). To get the value per share, I have used the estimated 1175 million shares that I believe will be outstanding, including options and RSUs, after the offering. Depending on the metric that I can scale it to, you can get values ranging from $47 billion to $124 billion for Uber's equity, though each comes with a catch. If you believe that there are no games that are played with pricing, you should think again! Also, as Lyft's price moves, so will Uber's, and I am sure that there are many at Uber (and its investment banks) who are hoping and praying that Lyft's stock does not have many more days like last Thursday, before the Uber IPO hits the market.

I am sure that there are many who understand the ride sharing business much better than I do, and see obvious limitations and pitfalls in my valuations of both Uber and Lyft.  In fact, I have been wrong before on Uber, as Bill Gurley (who knows more about Uber than I ever will) publicly pointed out,  and I am sure that I will be wrong again.  I hope that even if you disagree with me on my numbers, the spreadsheets that are linked are flexible enough for you to take your stories..
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Last week, Lyft became the first of the ride sharing companies to announce plans for an initial public officering, filing its prospectus. It is definitely not going to be the last, but its fate in the market will not only determine when Uber, Didi, Ola and GrabTaxi will test public markets, but what prices they can hope to get. My fascination with ride sharing goes back to June 2014, when I tried to value Uber and failed spectacularly in forecasting how much and how quickly ride sharing would change the face of car service around the world. I have since returned multiple times to the scene of my crime, and while I am not sure that I have learned very much along the way, I have tried to right size my thinking on this business. You can be the judge as bring my experiences to play in my valuation of Lyft, ahead of its IPO pricing.

The Rise of Ride Sharing
The ride sharing business, as we know it, traces its roots back to the Bay Area, with the founding of Uber, Sidecar and Lyft providing the key impetus, and its impact on the car service business has been immense. In a post in 2015, I traced out the growth of ride sharing and the ripple effects it has had on the car service status quo, noting that revenues for ride sharing companies have climbed, the price of a taxi cab medallion in New York city has plummeted by 80-90%. The most impressive statistic, for ride sharing companies, is not just the growth in revenues, which has been explosive, but also how much it has become part of day-to-day life, not just for younger, more tech savvy individuals but for everyone.  While the growth was initially in the United States, ride sharing has taken off at an exponential rate in Asia, with India (Ola), China (Didi) and Malaysia (GrabTaxi) all developing home grown ride sharing companies. The regulatory push back has been strong in Europe, slowing growth, but there are signs that even there, ride sharing is acquiring a foothold.

There are many factors that can explain how and why ride sharing so quickly and decisively disrupted the taxi cab business, but the latter was ripe for the taking for may reasons. First, the taxi business in the 2009 had changed little in decades, refusing to incorporate advance in technology and shifting tastes, secure that it did not have to adapt, because it had a captive market.  Second, in most cities, rules and regulations that were throwbacks in time or lobbied for by special interests handicapped taxi operators and gave ride sharing companies, not bound by the same rules, a decisive advantage. Third, automobiles are underutilized resources for the most part, since most cars sit idle for much of the day, and ride sharing companies took advantage of excess capacity, by letting car owners monetize it. Finally, individuals often under price their time and do not factor in long term costs in their decision making and the ride sharing companies have exploited that irrationality. I think that the MIT study in February 2018 that showed absurdly low hourly wages (less than $4/hour) for Uber and Lyft drivers was flawed, but I also don't buy into the rosy picture that the ride sharing companies paint about the income potential in driving. 

It has not been all good news for ride sharing, as usage has increased. While revenues have come easily, the companies have struggled with profitability, reporting huge losses as they grow. Lyft reported losses of $911 million in 2018, in its prospectus, but Uber's loss was $1.8 billion during 2018, Didi almost matched that with a $1.6 billion loss and the only reason that Ola and GrabTaxi lost less was because they were smaller. Put simply, these company are money losing machines, at least at the moment, and if there are economies of scale kicking in, they are showing up awfully slowly. While some of this can be attributed to growing pains, that will ease as these companies age and grow bigger, a significant portion of the profitability shortfall can be attributed to how these businesses are designed. In my 2015 post, I argued that the low capital intensity (where ride sharing companies don't invest in cars) and the independent contractor model (where drivers are not employees), which made growth so easy, also conspired to make it difficult for these companies to gain economies of scale or stay away from cut throat competition. 

The Playing Field
In 2015, I argued, with tongue only half in cheek, that one possible model for the ride sharing companies to develop sustainable businesses was the Mafia's mostly successful attempt to stop intrafamily warfare in the 1930s by dividing up New York city among five families, giving each family its own fiefdom to exploit. (I prefer The Godfather version.). While that may have seemed like an outlandish comparison in 2015, it is interesting that in the years since, Uber has extricated itself from China, leaving that market to Didi, in return for a 20% stake in the company and then from South East Asia, in return for a share of GrabTaxi. In fact, the United States may be the most competitive ride sharing market in the world, with Uber and Lyft going head-to-head in most cities.

While Uber and Lyft are ride sharing companies, their evolution over the last decade offers a fascinating contrast in business models, for young companies. In a post in 2015, I drew the contrast between the two companies, as a prelude to valuing them. Uber was the "big story" company, telling investors that it wanted to be in all things logistics, expanding into delivery and moving, and all over the world. Lyft was the "focused story" company, setting itself apart from Uber by keeping its business in the United States and staying with car service, as its primary business.  I argued in 2015, that given how the two companies were priced, I would rather be an investor in Lyft than Uber. 

In the four years since the post, we have seen the consequences for both companies. While Uber's bigger story gained it a much higher pricing from investors, it has also brought the company a whole host of troubles, ranging from being a target for regulators to management over reach. Travis Kalanick, its high profit CEO, left the company in a messy and public divorce, and Dara Khosrowshahi, who replaced him, has scaled Uber's ambitions down, first globally by getting out of China and Southeast Asia, where it was burning through cash at an exponential rate, and then within the logistics business, by focusing on Uber Delivery as the key add on to car service. Lyft has stayed true to its US and car service focus, and it has paid off in a higher market share in the market. Both companies have jumped on the bike and scooter craze, with Uber buying Jump and Lime and Lyft acquiring Motivate. From the looks of it, neither company seems willing to concede to the other in the US market, and this fight will be fought on multiple fronts, in the years to come.

The Lyft Valuation
When valuing young companies, it is the story that drives your numbers and valuation, not historical data or current financials. I have stayed true to this perspective, in all of the valuations that I have done on ride sharing companies. In this section, I will lay out my story for Lyft, drawing on past behavior and the clues that are in their current plans, but it would be hubris to argue that I have a monopoly on the truth and a claim on the "right" story. So, feel free to disagree with me and you can use my valuation spreadsheet to reflect your disagreements.

The Story
Reviewing Lyft's (very long) prospectus, I was struck by the repetition of the mantra that it saw its future as a "US transportation" company, suggesting that the focus will remain primarily domestic and focused on transportation. While the cynical part of me argues that Lyft's use of the word "transportation" is intended to draw attention to the size of that market, which is $1.2 trillion, Lyft's history backs up their "focused" story. While I am normally leery of management stories for companies, I will adopt Lyft's story with a few changes:
  1. It will stay a US transportation services company: The total market that I assume for US transportation services is $120 billion at the moment, well over two and a half times larger than the taxi cab market was in 2009. That is, of course, well below the size of the transportation market, but the $1.2 trillion that Lyft provides for that market includes what people spend on acquiring cars and does not reflect that they would pay for just transportation services.
  2. In a growing transportation services market: One of the striking features of the ride sharing revolution is how much it has changed consumer behavior, drawing people who would normally never have used car service into its reach. I will assume that ride sharing will continue to draw new customers, from mass transit users to self-drivers, causing the transportations services market to double over the next ten years.
  3. With strong market-wide networking benefits: In 2014, when I first valued Uber, I argued that ride sharing companies would have local, but not market-wide, networking benefits. In effect, I saw a market where six, eight or even ten ride sharing companies could co-exist, each dominating different local markets. Observing how quickly the ride sharing companies have consolidated, over the last few years, I think that I was wrong and that the networking effects are likely to be market-wide. Ultimately, I see only two or three ride sharing companies dominating the US ride sharing market, in steady state. In my story, I see Lyft as one of the winners, with a 40% market share of the US transportation services market.
  4. A sustained share of Gross Billings: The concentration of the market among two or three ride sharing companies will also give them the power to hold the line on the percentage of gross billings. That percentage, which was (arbitrarily) set at 20% of gross billings, when the ride sharing companies came into being, has morphed and changed with the advent of pooled rides and how the gross billing number is computed. Lyft, for instance, in 2018, reported revenues of $2,156 million on gross billings of $8.054 million, working out to a 26.77% share. I will assume that as Lyft continues to grow and offers new services, this number will revert back to 20%.
  5. And a shift to drivers as employees: Since their inception, the ride sharing companies have been able to maintain the facade that their drivers are independent contractors, not employees, thus providing the company legal cover, when drivers were found to be at fault of everything from driving infractions to serious crimes, as well as shelter from the expenses that the would ensue if drivers were treated as employees. As the number who work for ride sharing companies rises into the millions, states are already starting to push back, and in my view, it is only a matter of time before ride sharing companies are forced to deal with drivers as employees, causing operating margins in steady state to drop to 15%.
There are some aspects of this story that some of you may find too pessimistic, and other aspects that others may find too optimistic. You are welcome to download the spreadsheet and make the story your own,

The Valuation
The story that I have for Lyft already provides the bulk of the inputs that I need to value the company. To complete the valuation, I add four more inputs related to the company:
  1. Cost of capital: Rather than try to break down cost of capital into its constituent parts for a company that is transitioning to being a public company, I will take a short cut and give Lyft the cost of capital of 9.97%, at the 75th percentile of all US companies at the start of 2019, reflecting its status as a young, money-losing company. I will assume that this cost of capital will drift down towards the median of 8.24% for all US companies as Lyft becomes larger and profitable.
  2. Sales to capital: While Lyft will continue to operating with a low capital-intensity model, its need for reinvestment will increase, to build competitive barriers to entry and to preserve market dominance. If autonomous cars become part of the ride sharing landscape, these investment needs will become greater, I will assume revenues of $2.50 for every dollar of capital invested, in keeping with what you would expect from a technology company.
  3. Failure rate: Given that Lyft continues to lose money, with no clear pathway to generating profits, and that it will remain dependent on external capital providers to stay a going concern, I will assume that there is a 10% chance that Lyft will not survive as a going concern
  4. Share Count: Lyft posits that it will have 240.6 million shares outstanding, including both the class A shares that will be offered to the public and the class B shares, with higher voting rights, that will be held by the founders. It also discloses that it did not include in the share count two share overhangs: (1) 6.8 million shares that are subject to option exercise, with a strike price of $4.68, and (2) 31.6 million restricted shares that had already been issued to employees, but have not vested yet. I will include both of these in shares outstanding, the options because they are so deep in the money that they are effectively outstanding shares and the restricted stock because I assume that the employees that have large numbers of RSUs will stay until vesting, to arrive at a total share count is 279.03 million.
Finally, the company has not made explicit how much cash it hopes to raise from the initial public offering, but I have used the rumored value of $2 billion in new proceeds, which will be kept in the firm to cover reinvestment and operating needs, according to the prospectus. With these assumptions in place, my valuation of Lyft is below:
Download spreadsheet
My story for Lyft leads to a value of equity of approximately $16 billion, with the $2 billion in proceeds includes, or $14 billion, prior to the IPO cash infusion. Dividing by the 279 million shares outstanding, computed by adding the restricted shares outstanding to the share count that the company anticipates after the IPO, yields a value per share of about $59. Any story about young companies comes with ifs, ands and buts, and the Lyft story is no exception. I remain troubled by the ride sharing business model and its lack of clear pathways to profitability, but I think Lyft has picked the right strategy of staying focused both geographically (in the US) and in the transportation services business. I also am leery of the special voting rights that the founders have carved out for themselves, but that seems to have now become par for the course, at least with young tech companies. Finally, the possibility that one of the big technology companies or even an automobile company may be tempted to enter the business remains a wild card that could change the business.

The Lyft Pricing
I am a realist and know that when the stock opens for trading on the offering day, it is not value that will determine the opening bid, but pricing. In the pricing game, investors look at what others are paying for similar companies, scaling to some common operating variable. With publicly traded companies in mature sectors, this takes the form of an earnings (PE), cash flow (EV/EBITDA) or book value (Price to Book) multiple that can then be compared across companies. With Lyft, investors will face two challenges.

  • The first is that it is the first ride sharing company to list, and the only pricing that we have for other ride sharing companies is from venture capital rounds that are sometimes dated (from the middle or early last year). 
  • The second is that every company in the ride sharing business is losing money and the book values have no substance (both because the companies are young and don't invest much in physical assets). 
Notwithstanding these limitations, investors will still try, by scaling to any operating number that they can find that is positive, as I have tried to do in the table below:

It is true that there is substantial noise in the VC pricing numbers and that the operating numbers  for some of these companies are rumored or unofficial estimates. That said, desperation will drive investors to scale the VC pricing to one of these numbers with the gross billings, revenues and number of riders being the most likely choices. Uber has the highest pricing/rider and that the metric is lowest for the Asian companies, which have far more riders than their US counterparts; the revenue per rider, though, is also far lower in Asia than in the US. The companies all trade at high multiples of revenues and more moderate multiples of gross billings. In the table below, I have priced Lyft, using Uber's most recent pricing metrics as well as global averages, both simple and weighted:

To the extent that you accept these metrics, the pricing for Lyft can range from $5 billion to $22 billion, depending on your peer comparison (Uber, Global average, Global weighted average) and your scaling variable (Gross Billings, revenues or riders). In fact, if I bring in the rumored pricing of Uber ($120 billion) into the mix, defying circular logic, I can come up with pricing in excess of $30 billion for Lyft.  I think that they are all flawed, but you should not be surprised to see Lyft and its bankers to focus on the comparisons that yield the highest pricing.

Given the way the pricing game is structured, the pricing of the Lyft IPO is going to be watched closely by the rest of the ride sharing companies, since there will be a feedback effect. In fact, I think of pricing as a ladder, where if you move one rung of the ladder, all of the other rungs have to move as well. For instance, if investors price Lyft at $25 billion, about 12 times its revenue in 2018, Uber will be quicker to go public and will expect markets to attach a pricing in excess of $130 billion to it, given that its revenues were more than $11 billion in 2018. The Asian ride sharing companies, where rider numbers are high, relative to revenues, will try to market themselves on rider numbers, though it is not clear that investors will buy that pitch. Conversely, if investors price Lyft at only $12 billion, Uber may be tempted to wait to go public, and continue to tap into private investors, with the caveat being that those investors will also lower their pricing estimates. The pricing ladder can lead prices up, but they can also lead prices down, and timing is the name of the game.

The Waiting Game
It is still early and there is much that we still do not know. While some of the uncertainties will not be resolved in the near future, we will learn more specifics about the offering itself, including the amount that Lyft plans to raise on the offering day, over the next few weeks. Sometime soon, we will also get the a pricing of the company from the bankers that have been given the task of taking the company public, and I use the word "pricing" rather than "valuation" deliberately. The bankers' job is to price the company for the IPO, not value it. Not only should any talk of value from them be discounted, but if you do see a discounted cash flow valuation from a bank for Lyft, you can almost bet that it will be a Kabuki valuation, where they will go through the motions of estimating valuation inputs, when the ending number has been pre-decided.

YouTube Video
Lyfting Off? The Lyft IPO - YouTube

  1. Prospectus for Lyft
  2. Lyft Valuation
  3. Lyft Pricing
Posts on Ride Sharing (from 2015)
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On February 22, Kraft-Heinz shocked investors with a trifecta of bad news in its earnings report: sub-par operating results, a mention of accounting irregularities and a massive impairment of goodwill, and followed up by cutting dividends per share almost 40%. Investors in the company reacted by selling their shares, causing the stock price to drop more than 25% overnight. While Kraft is neither the first, nor will it be the last company, to have a bad quarter, its travails are noteworthy for a simple reason. Significant portions of the stock were held by Berkshire Hathaway (26.7%) and 3G Capital (29%), a Brazil-based private equity group. Berkshire Hathaway’s lead oracle is Warren Buffett, venerated by some who track his every utterance, and try to imitate his actions. 3G Capital might not have Buffett’s name recognition, but its lead players are viewed as ruthlessly efficient managers, capable of delivering large cost cuts. In fact, their initial joint deal to bring together Heinz and Kraft, two of the biggest names in the food business, was viewed as a master stroke, and given the pedigree of the two investors, guaranteed to succeed. As the promised benefits have failed to materialize, the investors who followed them into the deal seem to view their failure as a betrayal.

The Back Story
You don’t have to like ketchup or processed cheese to know that Kraft and Heinz are part of American culinary history. Heinz, the older of the two companies, traces its history back to 1869, when Henry Heinz started packing and selling horseradish, and after a brief bout of bankruptcy, turned to making 57 varieties of ketchup. After a century of growth and profitability, the company hit a rough patch in the 1990s, and was targeted by activist investor, Nelson Peltz, in 2013. Shortly thereafter, Heinz was acquired by Berkshire Hathaway and 3G Capital for $23 billion, becoming a private company. Kraft started life as a cheese company in 1903, and over the next century, it expanded first into other dairy products, and then widened its repertoire to includes other processed foods. In 1981, it merged with Dart Industries, maker of Duracell batteries and Tupperware, before it was acquired by Philip Morris in 1988. After a series of convulsions, where parts of it were sold and rest merged with Nabisco, Kraft was spun off by Philip Morris (renamed Altria), and targeted by Nelson Peltz (yes, the same gentleman) in 2008. Through all the mergers, divestitures and spin offs, managers made promises of synergy and new beginnings, deal makers made money, but little of substance actually changed in the products.

In 2015, the two companies were brought together, with Berkshire Hathaway and 3G playing both match makers and deal funders, as Kraft Heinz, and the merger was completed in July 2015. At the time of the deal, there was unbridled enthusiasm on the part of investors and market observers, and part of the unquestioning acceptance that the new company would become a force in the global food business was the pedigree of the main investors. In the years since the merger, though, the company has had trouble delivering on expectations of revenue growth and cost cutting:

The bottom line is that while much was promised in terms of revenue growth, from expanding its global footprint, and increased margins, from cost cutting, at the time of the deal, the numbers tell a different story. In fact, if investors were surprised by the low growth and declining margins in the most recent earnings report, they should not have been, since this has been a long, slow bleed.

The Earnings Report
The earnings report that triggered the stock price collapse, for Kraft-Heinz, was released on February 22, and it contained bad news on many fronts:
  1. Flatlining Operartions: Revenues for 2018 were unchanged from revenues in 2017, but operating income dipped (before impairment charges) from $6.2 billion in 2017 to $5.8 billion in 2018; the operating margin dropped from 23.5% in 2017 to 22% in 2018.
  2. Accounting Irregularities: In a surprise, the company also announced that it was under SEC investigation for accounting irregularities in its procurement area, and took a charge of $25 million to reflect expected adjustments to its costs.
  3. Goodwill Impairment: The company took a charge of $15.4 billion for impairment of goodwill, primarily on their US Refrigerated and Canadian Retail, an admission that they paid too much for acquisitions in prior years.
  4. Dividend Cuts: The company, a perennial big-dividend payer, cut its dividend per share from $2.50 to $1.60, to prepare itself for what it said would be a difficult 2019.
While investors were shocked, the crumb trail leading up to this report contained key clues. Revenues had already flattened out in 2017, relative to 2016, and the decline in margins reflected difficulties that 3G faced in trying to cut costs, after the deal was made. The only people who care about impairment charges, a pointless and delayed admission of overpayment on acquisitions, are those who use book value of equity as a proxy for overall value. The dividend cuts were perhaps a surprise, but more in what they say about how panicked management must be about future operations, since a company this attached to dividends cuts them only as a last resort.

The Value Effects
With the bad news in the earnings report still fresh, let’s consider the implications for the story for, and the value of, Kraft Heinz. The flat revenues and the declining margins, as I see them, are part of a long term trend that will be difficult, if not impossible, to reverse. While Kraft-Heinz may have a quarter or two with positive blips, I see more of the same going forward. In my valuation, I have forecast a revenue growth of 1% a year in perpetuity, less than the inflation rate, reflecting the headwinds the company faces. That downbeat revenue growth story will be accompanied by a matching “bad news” story on operating margins, where the company will face pricing pressures in its product markets, leading to a drop (though a small and gradual one) in operating margins over time, from 22% in 2018 (already down from 2017) to 20% over the next five years. The company’s cost of capital is currently 6%, reflecting the nature of its products and its use of debt, but over time, the benefits from the latter will wear thin, and since that is close to the average for the industry (US food processing companies have an average cost of capital of 6.12%), I will leave it unchanged. Finally, the mistakes of the past few years will leave at least one positive residue in the form of restructuring charges, that I assume will provide partial shelter from taxes, at least for the next two years.
Spreadsheet with valuation
The good news is that, even with a stilted story, Kraft Heinz has a value ($34.88) that is close to the stock price ($34.23). The bad news is that the potential upside looks limited, as you can see in the results of a simulation that I did, allowing expected revenue growth, operating margin and cost of capital to be drawn from distributions, rather than using point estimates.
Simulation Results
The finding the value falls within a tight range, with the first decile at about $26 and the ninth at close to $47 should not surprise you, since the ranges on the inputs are also not wide. As an investor, here are the actions that would follow this valuation. 
  • If you owned Kraft Heinz prior to the earnings report (and I thankfully did not), selling now will accomplish little. The damage has been done already, and the stock as priced now, is a fair value investment. I know that 3G sold almost one quarter of its hold 3 days after Tuesday, but that may say more about 3G than it does about Kraft Heinz.
  • If you don’t own Kraft Heinz, the valuation suggests that the stock is fairly valued, at today’s price, but at a lower price, it would be a good investment. I have a limit buy on the stock at a $30 price (close the 25th percentile of the distribution), and if it does hit that price, I will be a Kraft Heinz stockholder, notwithstanding the fact that I think its future does not hold promise. If it does not drop that low, there are other fish to catch and I will move on.
There are two concerns, though, that investors looking at this stock have to consider. The first is that when companies claim that they have discovered accounting irregularities, but that they have cleaned up their act, they are often dissembling and that there are more shocks to come. With Kraft Heinz, the magnitude of the irregularity is small, and given that they have no history of playing accounting games, I am willing to given them the benefit of the doubt. The second is that the company does carry $32 billion in debt, and while that debt has no toxic side effects today, that is because the company is perceived to have stable and positive cash flows. If the margin decline that I forecast becomes a margin rout, the debt will expose the company to a clear and present danger of default. Put simply, it will make the bad case scenarios that are embedded in the simulation worse, and perhaps threaten the company’s existence. 

The Lessons
There are lessons in the Kraft-Heinz blow-up, but I will tread carefully, since I risk offending some, with talk that you may view as not just incorrect but sacrilegious:
  1. It is human to err: At the risk of stating the obvious, Warren Buffett and 3G’s key operators are human, and are prone to not only making mistakes, like the rest of us, but also to have blind spots in investing that hurt them. In fact, Buffett has been open about his mistakes, and how much they have cost him and Berkshire Hathaway shareholders. He has also been candid about his blind spots, which include an unwillingness to invest in businesses that he does not understand, a sphere that only grows as he gets older and the economy changes, and an excessive trust in the managers of the companies that he invests in. While he is, for the most part, an excellent judge of character, his investments in Wells Fargo, Coca Cola and Kraft-Heinz show that he is not perfect. The fault, in my view, is not with Buffett, but with the legions of investors, analysts and journalists who treat him as an investment deity, quoting his words as gospel and tarring and feathering anyone who dares to question them. 
  2. Stocks are not bonds: In my data posts, I looked at how companies in the United States have moved away from dividends to buybacks, as a way of returning cash. That trend, though, has not been universally welcomed by investors, and there remains a significant subset of investors, with strategies built around buying stocks with big dividends. One reason that stocks like Kraft  Heinz become attractive conservative value investors is because they offer high dividend yields, often much higher than what you could earn investing in treasury or even safe corporate bonds. In effect, the rationale that investors use is that by buying these shares, they are in effect getting a bond (with the dividends replacing coupons), with price appreciation. From the Dogs of the Dow to screening based upon dividend yields, the underlying premise is that investors can count more on dividends than on buybacks. While it is true that dividends are stickier than buybacks, with many companies maintaining or increasing dividends over time, these dividend-based strategies become delusional when they treat dividends as obligated payments, rather than expected ones. After all, much as companies do not like to cut dividends, they are not contractually obligated to pay dividends. In fact, when a stock carries a dividend yield that looks too good to be true, it is usually almost always an unsustainable dividends, and it is only a question of time before dividends are cut (or even stopped) or the company drives itself into a financial ditch. 
  3. Brand Names last a long time, but nothing lasts forever: A major lodestone of conventional value investing is that while technology, cost efficiencies and new products are all competitive advantages that can generate value, it is brand name that is the moat that has the most staying power. Again, that statement reflects a truth, which is that brand names last long, often stretching over decades, but even brand name benefits fade, as customers change and companies seek to become global. The troubles at Kraft-Heinz are part of a much bigger story, where some of the most recognized and valued brand names of the twentieth century, from Coca Cola to McDonalds, are finding that their magic fading. Using my life cycle terminology, these companies are aging and no amount of financial engineering or strategic repositioning is going to make them young again. 
  4. Cost cutting can take you far, but no further: For the last few decades, we have cut a great deal of slack for those who use cost cutting as their pathway for creating value, with many leveraged buyouts and restructurings built almost entirely on its promise. Don’t get me wrong! In firms with significant cost inefficiencies and bloat, cost cutting can deliver significant gains in profits, but even with these firms, those gains will be time limited, since there is only so much fat to cut out. Worse, there are firms that find themselves in trouble for a myriad of reasons that have little to do with cost inefficiencies and cutting costs as these firms is a recipe for disaster. It is true that 3G did a masterful job, cutting costs and increasing margins at Mexico's Grupo Modelo, the Mexican brewer that they acquired through Inbev, but that was because Modelo’s problems lent themselves to a cost-cutting solution. It may even have worked at Kraft-Heinz initially, but at this point, the company’s problems may have little to do with cost inefficiencies, and much to do with a stable of products that is less appealing to customers than it used to be, and cost cutting is the wrong medicine for whatever ails them.
I hope that you do not read this as a hit piece on Warren Buffett and/or 3G. I admire Buffett’s adherence to a core philosophy and his willingness to be open about his mistakes, but I think he is ill served by some of his devotees, who insist on putting him on a pedestal and refuse to accept the reality that his philosophy has its limits, and that like the rest of us, he has an ego and makes mistakes. If you have faith in value investing, you should be willing to have that faith tested by the mistakes that you and the people you admire make in its pursuit. If your investment views are dogma, and you believe that your path is only the correct one to success, I wish you the best, but your righteousness and rigidity will only set you up for more disappointments like Kraft Heinz.

YouTube Video
Investing Idol Worship: The Kraft Heinz Lesson - YouTube

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In my last eight posts, I looked at aspects of corporate behavior from investments to financing to dividend policy, using the data that I collected at the start of 2019, to examine what companies share in common, and what makes them different. In summary, I found that the rise in risk premiums in both equity and bond markets in 2018 have pushed up costs of equity and capital, that companies across the globe are finding it difficult to generate returns on their investments that exceed their costs of funding, and that many of them, especially in mature businesses, are returning more cash, much of it in the form of buybacks. Since all of the companies in my data set are publicly traded, there is one final number that I have not addressed directly in my posts so far, and that is the market pricing of these companies. In this post, I  complete my data update series, by looking at how pricing varies across companies, sectors and geographies, and what lessons investors can draw from the data.

Value versus Price: The Difference
I have posted many times on the between the value of an asset and its' pricing, but I don't think it hurts to revisit that difference. The determinants of value are simple, although not always easy to estimate. Whether you are valuing start-up businesses, emerging market firms, or commodity companies, the values are driven by expected cash flows, growth, and risk. Although a discounted cash flow valuation is often the tool that we used to give form to these fundamentals, in the form of cash flows, growth rates in these cash flows, and discount rates, it is not the only pathway to intrinsic value.  The determinants of price are demand and supply, and while fundamentals do affect both, mood and momentum are also strong forces in pricing. These “animal spirits,” as behavioral economists might tag them, can not only cause price to diverge from value, but also require different tools to be used to assess the right pricing for an asset. With many assets and businesses, pricing an asset usually involves standardizing a price (a multiple), finding similar or comparable assets that are already priced in the marketplace, and controlling for differences. The picture below, which I have used many times before, captures the two processes:

The reason that I reuse this picture so much is because, to me, it is an all-encompassing snapshot of every conceivable investment philosophy that exists in the market:
  1. Efficient Marketers: If you believe that markets are efficient, the two processes will generate the same number, and any gap that exists will be purely random and quickly closed.
  2. Investors: If you are an investor, whether value or growth, and you truly mean it, your view is that the pricing process, for one reason or the other, can deliver a price different from your estimate of value and that the gap that exists will close, as the price converges to value. The difference between value and growth investors lies in where you think markets are most likely to make mistakes (in valuing existing assets or growth opportunities) and correct them. In essence, you are as much a believer in efficient markets as the first group, with the only difference being that you believe markets become efficient after you have taken your position on a stock. 
  3. Traders: If you are a trader, you start off with either the presumption that there is no such thing as intrinsic value, or that it exists, but that no one can estimate it. You play the pricing game, effectively using your skills at gauging momentum and forecasting the effects of corporate news on prices, to buy at a low price and sell at a high price.
Market participants are most exposed to danger when they are delusional about the game that they are playing. Many portfolio managers, for instance, claim to be investors, playing the value game, while using pricing screens (PE and growth, PBV and ROE) and adding to their holdings of momentum stocks. Many traders seem to think that they will be viewed as deeper and more accomplished if they talk the value talk, while using charts and technical indicators in the closet, to make their stock picks.

The Pricing Process
The essence of pricing is attaching a number to an asset or company, based upon how similar assets and companies are being priced in the market. To get insight into how to price an asset, a business or a company, you should break down the pricing process into steps:

You may be a little puzzled by the first step in the process, where I standardize the price, but the reason is simple. You cannot compare price per share across companies, since it is a function of the share count, which can be changed overnight in a stock split. To standardize prices, you scale them to some variable that all of the assets in the peer group share. With real estate properties, you divide the price of each property by its square footage to arrive at a price/square foot that can be compared across properties. With businesses, you scale pricing to an operating variable, with earnings being the most obvious choice, but it can be revenues, cash flows or book value. Note that any multiple that you find on a stock or company is embedded in this definition, ranging from PE ratios to EV/EBITDA multiples to revenue multiples, and even beyond, to market price per subscriber or user. The second step in the process, i.e., finding similar assets and companies, should make clear the fact that this is a process that requires subjective judgments and is open to bias, just as is the case in intrinsic valuation. If you are pricing Nvidia, for instance, you determine how narrowly or broadly you define the peer group, and which companies to deem to be "similar".  The third step int he process requires controlling for differences across companies. Put simply, if the company that you are pricing has higher growth or lower risk or better returns on its investments on it projects that the companies in the peer group, you have to adjust the pricing to reflect it, either subjectively, as many analysts do, with story telling, or objectively, by bringing in key variables into the estimation process.

Pricing the Markets in January 2019
Rather than taking you through multiple after multiple, and overwhelming with pictures and tables on each one, I will list out what I learned by looking at the pricing of all publicly traded stocks around the world, in early 2019, in a series of pricing propositions.

Pricing Proposition 1: Absolute rules don't belong in a relative world!
Paraphrasing Einstein, everything is relative, if you are pricing companies. Is a PE ratio of five low? Not if half the stocks in the market trade at less than five. Is an EV/EBITDA of forty high? Perhaps in some sectors, but not if you are comparing high growth companies in a highly priced sector. Old time value investing is filled with rules of thumb, and many of these rules are devised around absolute values for PE or PEG ratios or Price to Book, at odds with the very notion of pricing. If you want to make pricing statements about what comprises cheap or expensive, you should be looking at the distribution of the multiple across the market. Thus, to form pricing rules on US stocks at the start of 2019, I looked the distribution of current, forward and trailing PE ratios for US stocks on January 1, 2019:

At the start of 2019, a low trailing PE ratio for a US stock would have been 6.09, if you used the lowest decile or 10.36, if you moved to the first quartile, and a high PE ratio, using the same approach, would have been 27.31, with the third quartile, or 53.70, with the top decile. Lest I be accused of picking on value investors, they are not the only or even the biggest culprits, when it comes to absolute rules. Private equity investors and LBO initiators have built their own set of screens. I have lost count of the number of times I have heard it said that an EV to EBITDA less than six (or five or seven) must mean that a company is not just cheap, but a good candidate for leverage, but is that true? To answer the question, I looked at the EV to EBITDA multiples across companies, across regions of the world.
If you wield a pricing bludgeon and declare all companies that trade at less than six times EBITDA to be cheap, you will find about half of all stocks in Russia to be bargains. Even globally, you should hav no trouble finding investments to make with this rule, since almost one quarter of all companies trade at less than six times EBITDA.  My point is not that that you cannot have rules of thumb, since they do exist for a reason, but that those rules, in a pricing world, have to be scaled to the data. Thus, if you want to define the first decile as your measure of what comprises cheap, why not make it the first decile? That would mean that an EV to EBITDA multiple less than 5.16 would be cheap in the US on January 1, 2019, but that number would have to recalibrated as the market moves up or down.

Pricing Proposition 2: Markets have a great deal in common, when it comes to pricing, but the differences can be revealing!
Much is made about the differences across global equity markets, and especially about the divide between emerging and developed market companies, when it comes to pricing, with delusions running deep on both sides. Emerging market analysts are convinced that stocks are priced very differently, and often more irrationally, in their local markets, leaving them free to devise their own rules for their markets. Conversely, developed market analysts often bring perspectives about what comprises high, low or average pricing ratios, built up through decades of exposure to US and European markets, to emerging markets and find them puzzling. The data tells a different story, with pricing ratios around the world having distributional characteristics that are surprisingly similar across different parts of the world:

While the levels of PE ratios vary across regions, with Chinese stocks having the highest median PE ratios (20.63) and Russian and East European stocks the lowest (9.40), they all have the same asymmetric look, with a peak to the left (since PE ratios cannot be lower than zero) and a tail to the right (there is no cap on PE ratios). That asymmetry, which is shared by all pricing multiples, is the reason that you should always be cautious about any pricing argument that is built on comparisons to the average PE or PBV, since those numbers will be skewed upwards because of the asymmetry.  While it is true that markets share common characteristics, when it comes to pricing, the differences in levels are also worth paying attention to, when investing. A global fund manager who ignores these differences, and picks stocks based upon PE ratios alone, will end up with a portfolio that is dominated by African, Midde East and Russian stocks, not a recipe for investing success.

Pricing Proposition 3: Book value is the most overrated metric in investing
I have never understood the reverence that some investors seem to hold for book value, as revealed in the number of investing adages built around it. Stocks that trade at less than book value are considered cheap, and companies that build up book value are considered to be value creating. At the root of the "book value" focus are two assumptions, sometimes stated but often implicit. The first is that the book value is a measure of liquidation value, an estimate of what investors would get if they shut down the company today and sold its assets. The second is that accountants are consistent and conservative in estimating asset value, unlike markets, which are prone to mood swings. Both assumptions are built on foundations of sand, since book value is not a good measure of liquidation value in most sectors, and accountants are both inconsistent and slow-moving, when it comes to estimating and adjusting book value. Again, to get perspective, let's look at the price to book ratios around the world, at the start of 2019:
If you believe that stocks that trade at less than book value are cheap, you will again find lots of bargains in the Middle East, Africa and Russia, but even in markets like the United States, where less than a quarter of all companies trade at less than book value, they tend to be clustered in industries that are in capital intensive (at least as defined by accountants) and declining businesses.
PBV by Industry (US)
Note that among the US industries with the fewest stocks that trade at less than book value are a large number of technology and consumer product companies, with utilities and basic chemicals being the only surprises. On the list of US industry groups with the highest percentage of stocks that trade at less than book value are oil companies (at different stages of the business), old time manufacturing companies and life insurance. If you pick your stocks based upon low price to book, in January 2019, your portfolio will be weighted with companies in the latter group, a prospect that should concern you.

Pricing Proposition 4: Most stocks that look cheap deserve to be cheap!
There are traders who have little time for fundamentals, arguing that they have little or no role to play in day to day movements of stock prices. That is probably true, but fundamentals do have significant explanatory power, when it comes to why some companies trade at low multiples of earnings or book value and others are high multiples. To understand the link, I find it most useful to go back to a simple intrinsic value model, and with simple algebraic manipulation, make it a model for a pricing multiple. The picture below shows the paths you would take with an equity multiple (Price to Book) and an enterprise value (EV/Sales) to arrive at their determinants:

Now what? If you buy into the intrinsic view of a price to book ratio, it should be higher for firms that earn high returns on equity, have higher growth and lower risk, and lower for firms that earn low returns on equity, have lower growth and higher risk. Does the market price in fundamentals? For the most part, the answer is yes, as you can see even in the tables that I have provided in this post so far. Russian stocks have the lowest PE ratios, but that reflects the corporate governance concerns and country risk that investors have when investing in them. Chinese stocks in contrast have the highest PE ratios, because even with stepped down growth prospects for the country, they have higher expected growth than most developed market companies. Looking at stocks with the lowest price to book ratios, Middle Eastern stocks have a disproportionate representation because they earn low returns on equity and the industry groupings with the lowest price to book (oil industry groups, steel etc.) also share that feature. Pricing, done right, is therefore a search for mismatches, i.e., companies that look cheap on a pricing multiple without an obvious fundamental that explains it. This table captures some of the mismatches:

MultipleKey DriverValuation Mismatch
PE ratioExpected growthLow PE stock with high expected growth rate in earnings per share
PBV ratioROELow PBV stock with high ROE
EV/EBITDAReinvestment rateLow EV/EBITDA stock with low reinvestment needs
EV/capitalReturn on capitalLow EV/capital stock with high return on capital
EV/salesAfter-tax operating marginLow EV/sales ratio with a high after-tax operating margin

Pricing Proposition 5: In pricing, it is not about what "should be" priced in, but "what is" priced in!
In the last proposition, I argued that markets for the most part are sensible, pricing in fundamentals when pricing stocks, but there will be exceptions, and sometimes large ones, where entire sectors are priced on variables that have little to do with fundamentals, at least on the surface. This is especially true if the companies in a sector are early in their life cycles and have little to show in revenues, very little (or even negative) book value and are losing money on every earnings measure. Desperation drives investors to look for other variables to explain prices, resulting in companies being priced based upon website visitors (at the peak of the dot com boom), numbers of users (at the start of the social media craze) and numbers of subscribers.

I noted this phenomenon, when I priced Twitter ahead of its IPO in 2013, and argued that to price Twitter, you should look at its user base (about 240 million at the time) and what markets were paying per user at the time (about $130) to arrive at a pricing of $24 billion, well above my estimate of intrinsic value of $11 billion for the company at a time, but much closer to the actual pricing, right after the IPO.  It is therefore neither surprising nor newsworthy that venture capitalists and equity research analysts are more focused on these pricing metrics, when assessing how much to pay for stocks, and companies, knowing this, play along, by emphasizing them in their earnings reports and news releases.

I do believe in intrinsic value, and think of myself more as an investor than a trader, but I am not a valuation snob. I chose the path I did because it works for me and reflects my beliefs, but it would be both arrogant and wrong for me to argue that being a trader and playing the pricing game is somehow less worthy of respect or returns. In fact, the end game for both investors and traders is to make money, and if you can make money by screening stocks using PE ratios or technical indicators, and timing your entry/exit by looking at charts, all the more power to you! If there is a point to this post, it is that a great deal of pricing, as practiced today, is sloppy and ignores, or throws away, data that can be used to make pricing better.

YouTube Video
January 2019 Data Update 9: Playing the Pricing Game - YouTube

Data Links
  1. PE ratios by industry grouping: USEuropeEmerging MarketsJapanAustralia & CanadaIndia and China
  2. Book Value Multiples by industry grouping: USEuropeEmerging MarketsJapanAustralia & CanadaIndia and China
  3. EV to EBIT & EBITDA by industry grouping: USEuropeEmerging MarketsJapanAustralia & CanadaIndia and China
  4. EV to Sales by industry grouping: US
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In my series of data posts, I had always planned to get to dividends and buybacks, the two mechanisms that companies have for returning cash to stockholders, at this point, but an op ed on buybacks by Senators Schumer and Sanders this week, in the New York Times, will undoubtedly make this post seem reactive. The senators argue that the hundreds of billions of dollars that US companies have expended buying back their own shares could have been put to better use, if it had been reinvested back in their businesses or used to increase wages for their employees, and offer a preview of legislation that they plan to introduce to counter the menace. Like the senators, I am concerned about the declining manufacturing base and income inequality in the US, but I believe that their legislative proposal is built on premises that are at war with the data, and has the potential for making things worse, not better.

The Buyback Effect: Benign Phenomenon, Managerial Short-termism or Corporate Malignancy?
'The very mention of buybacks often creates heated debate, because people seem to have very different views on its causes and consequences. All too often, at the end of debate, each side walks away with its views of buybacks intact, completely unpersuaded by the arguments of the other. The reason, I believe is that our views on buybacks are a function of how we think companies act, what the motives of managers are and what it is that investors price into stocks.

a. Buybacks are benign
If companies are run sensibly, the cash that they return to shareholders should reflect a residual cash flow, making the cash return decision, in terms of sequence, the final step in the process. 

If companies follow this process, buybacks are just another way of returning cash to stockholders, benign in their impact, because they are not coming at the expense of good investments, at least with good defined as investments that generate more than their hurdle rates. In fact, putting restrictions on how much cash companies can return, can harm not only stockholders (by depriving them of their claim on residual  cash flows) but also the economy, because capital will now be tied up in businesses that don't need them, rather than find its way to good ones.

b. Buybacks are short term
The benign view of stock buybacks is built on the presumption that managers make decisions at publicly traded companies with an eye on maximizing value, and since value is a function of expected cash flows over the life of the company, that they have a long term perspective. That view is at odds with evidence that managers often put short term gains ahead of long term value, and if investors are also short term, in pricing stocks, you can get a different picture of what drives buybacks and the consequences:

In effect, managers buy back stock, often with borrowed money, because it reduces share count and increases earnings per shares, and markets reward the company with a higher stock price, because investors don't consider the impact of lost growth and/or the risk of more debt. The argument that buybacks are driven by short term interests is strengthened if management compensation takes the form of equity in the company (options or restricted stock), because managers will be personally rewarded then for buybacks that, while damaging to the company's value (which reflects the long term), push up stock prices in the short term. With this view of the world, buybacks can create damage, especially at companies with good long term projects, run by managers who feel the need to meet short term earnings per share targets.

c. Buybacks are malignant
There is a third view of buybacks, where buybacks are not just motivated by the desire to push up earnings per share and stock prices, but become the central purpose of the firm. With this view, companies try to do whatever they can to generate more cash for buybacks, including crimping on worker wages, turning away good investments and borrowing more, even if that borrowing can put their survival at risk.

This picture captures almost all of the arguments that detractors of buybacks have used, including the ones that Senators Schumer and Sanders present in their article. If buybacks are the drivers of all other corporate actions, instead of being a residual cash flow, the “buyback binge” can be held responsible for a trifecta of America's most pressing economic problems: stagnant wages for workers, the drop in capital expenditures at US companies and the rise in debt on balance sheets. If this buyback shift is being driven by activist shareholders and a subset of "short term" institutional investors, as many argue that it is, you have a populist dream cast of good (workers, small stockholders, consumers) and evil (activists, wealthy shareholders and bankers). If you buy into this description of corporate and investor behavior, and it is not an implausible picture, it stands to reason that restricting or even stopping companies from buying back stock should alleviate and even solve the resulting problems. 

Picking a perspective
The reason debates about buybacks very quickly bog down is because proponents not only come in very different perspectives of corporate behavior, but they use anecdotal evidence, where they point to a specific company that behaves in a way that backs their perspective, and say "I told you so". The truth is that the real world is a messy place, with some companies buying back stocks for the right reasons (i.e., because they have no good investments and their stockholders prefer cash returns in this form), some companies buying back stock for short term price gains (to take advantage of markets which are myopic) and some companies focusing on buying back stock at the expense of their employees, lenders and own long term interests. 

Moneyball with Buybacks

The question of which side of this debate you will come down on, will depend on which of the perspectives outlined above comes closest to describing how companies and markets actually behave. Since that is an empirical question, not a political, idealogical or a theoretical one, I think it makes sense to look at the numbers on dividends and buybacks, not just in the US, but across the world, and I will do so with a series of data-driven statements.

1. More companies are buying back stock, and more cash is being returned in buybacks

Are US companies returning more and more cash in the form of buybacks? Yes, they are, and it represents a trend that saw its beginnings, not ten years ago, but in the 1980s. In the graph below, I look at the aggregate dividends and buybacks from firms in the S&P 500 since 1986, and also report on the percentage of cash returned that takes the form of buybacks, each year:

Starting at a base in the early 1980s, where buybacks were uncommon and dividends represented almost all cash return, you can see buybacks climb through the 1980s and 1990s, both in dollar value terms and as a percentage of overall cash return. That trend has only accelerated in this century, with the 2008 crisis putting a brief crimp on it. In 2018, more than 60% of the cash returned by S&P 500 companies was in the form of buybacks, amounting to almost $700 billion.

2. Cash Returns are rising as a percent of earnings, and it looks like companies are reinvesting less back into their own businesses
If you look at the graph above, you can see that the rise in buybacks has been accompanied by a stagnation in dividends, with growth rates in dividends substantially falling short of growth in buybacks. This shift has had consequences for two widely used measures of cash return, dividend yield, which looks at dividends as a percent of market capitalization or stock prices and the dividend payout ratio, a measure of the proportion of earnings as dividends. The declining role of dividends, as a form of cash return, has meant that a more relevant measure of cash return has to incorporate stock buybacks, resulting in a broader definition of cash yield and cash payout ratio measures:
  • Cash Yield = (Dividends + Buybacks) / Market Capitalization
  • Cash Payout Ratio = (Dividends + Buybacks)/ Net Income
The push back that you will get from dividend devotees that while dividends go to all shareholders, buybacks put cash only in the pockets of those stockholder who sell back, but that argument ignores the reality that the it is still shareholders who are getting the cash from buybacks. (As a thought experiment, imaging that you own all of the shares in a company and consider whether you notice a difference between dividends and buybacks, other than for tax purposes.) Calculating both dividend and cash measures of yield and payout over time, we observe the following for the companies in the S&P 500:
S&P 500: Dividends, Buybacks, Mkt Cap and Net Income
This table reinforces the message from the previous graph, which is that both dividends and buybacks have to be considered in any assessment of cash return. That is why I think that the handwringing over how low dividend yields have become over the last two decades misses the point. The cash yield for US companies, which includes both dividends and buybacks, is much more indicative of what companies are returning to shareholders and that  number has remained relatively stable over time. Using the same logic that I used to argue that cash yields were better indicators of cash returned to shareholders than dividend yields, I computed cash payout ratios, by adding buybacks to dividends, before dividing by net income in the table in the last section, and it does show a disquieting pattern. In fundamental analysis, analysts give weight to the payout ratio and its twin measure, the retention ratio (1- payout ratio) as a measure of how much a company is reinvesting into its own business, in order to grow.  The cash returned to shareholders exceeded net income in 2015 and 2016, and remains high, at 92.12% of net income, and that statistic seems to support the proposition that US companies are reinvesting less.

3. The drop in reinvestment may be real, but it could also be a reflection of accounting inconsistencies and failure to see the full picture on cash return
It is true that companies are returning more of their net income, as measured by accountants, to stockholders in dividends and buybacks, with the latter accounting for the lion's share of the return. Before we conclude that this is proof that companies are reinvesting less, there are two flaws in the numbers that need fixing:
  1. Stock Issuances: If we count stock buybacks as returning cash to shareholders, we should also be counting stock issuances as cash being invested by these same shareholders. Thus, the more relevant measure of cash return would net out stock issuances from stock buybacks, before adding dividends. While this is a lesser issue with the S&P 500 companies, which tend to be larger and more mature companies, less dependent of stock issuances, it can be a larger one for the entire market, where initial public offerings can augment seasoned equity issues, especially for smaller, higher growth companies.
  2. Accounting Inconsistencies: Over the last few decades, the percentage of S&P 500 companies that are in technology and health care has risen, and that rise has laid bare an accounting inconsistency on capital expenditures. If a key characteristic of capital expenditures is that money spent on them provide benefits for many years, accounting does a reasonable job in categorizing capital expenditures in manufacturing firms, where it takes the form of plant and equipment, but it does a woeful job of doing the same at firms that derive the bulk of their value from intangible assets. In particular, it treats R&D, the primary capital expenditure for technology and health care firms, brand name advertising, a key investment for the long term for consumer product companies, and customer acquisition costs, central for growth in subscriber/user driven companies as operating expenses, depressing earnings and rendering book value meaningless. In effect, companies on the S&P 500 are having their earnings measured using different rules, with the earnings for GM and 3M reflecting the correct recognition that money spent on investments designed to create benefits over many years should not be expensed, but the earnings for Microsoft and Apple being calculated after netting those same types of investments. As with the treatment of leases, I refuse to wait for accountants to come to their senses on this question, and I have been capitalizing R&D for all companies and adjusting their earnings accordingly. 
In the table below, I bring in stock issues and R&D into the picture, looking across all US stocks, not just the S&P 500:
All US publicly traded companies; S&P Capital IQ
While the trend towards buybacks is still visible, bringing in new stock issuances tempers some of the most extreme findings. In 2018, for instance, the net cash return (with issuances netted out from dividends and buybacks) represented about 46% of adjusted net profit (with R&D added back), well below the gross cash return.  In fact, there is no discernible decline in reinvestment over time, barring 2008 and 2009, the years around the last crisis. Capital expenditures have grown slowly, but an increasing percentage of reinvestment, especially in the last 5 years, has taken the form of R&D and acquisitions. 

4. Buybacks cut across sectors, size classes and growth categories, but the biggest cash returners are larger, more mature companies.

Before we decide that buybacks are ravaging the economy and should be restricted or even banned, it is also worth taking a look at what types of companies are buying back the most stock.  Staying with US stocks, I looked at buybacks and dividends of companies, broken  down by industry grouping. The full table is at the end of this post, but based upon the dollar value of buybacks, the ten industries that bought back the least stock and the ten that bought back the most are highlighted below:
Dividends and Buybacks: By Industry for US
It should come as no surprise that the industries where you see buybacks used the least tend to be industries which have a history of large dividend payments, with utilities, metals and mining and real estate making the list. Looking at the industries that are the biggest buyers of their own stock, the list is dominated by companies that derive their value from intangible assets, with technology and pharmaceuticals accounting for seven of the ten top spots. While that may surprise some, since these are viewed as high growth businesses, some of the biggest players in both technology and pharmaceuticals are now middle aged or older, using my corporate life cycle structure.

Given that there are often wide differences in size and growth, within each industry grouping, I also broke companies down by market cap size, to see if smaller companies behave differently than larger ones, when it comes to buybacks:
Market capitalization, as of 12/31/18
It is not surprising that the largest companies account for the bulk of buybacks, but you can also see that they return far more in buybacks, as a percent of their market capitalizations, then smaller firms do. 

Finally, I categorized companies based upon expected growth in the future, to see if companies that expect high growth behave differently from ones that expect low growth.
Expected revenue growth in the next two years
While companies in every growth class have jumped on the buyback bandwagon, the biggest buybacks in absolute and relative terms are for companies that have the lowest expected growth in revenues, returning 4-5% of their market capitalization in buybacks each year. Companies in the highest growth class, in contrast, return only 0.95% of their buybacks. That said, there are companies in higher growth classes that are buying back stock, when they should not be, perhaps for short term pricing reasons, but they represent only a small portion of the market, accounting collectively for only 10.56% of overall market capitalization.

I may be guilty of letting my priors guide my reading of these tables, but as I see it, the buyback boom in the United States is being driven by large non-manufacturing firms, with low growth prospects. If you restrict buybacks, expecting that this to unleash a new era of manufacturing growth and factory jobs, I am afraid that you will be disappointed. The workers at the firms that buy back the most stock, tend to be already among the better paid in the economy, and tying buybacks to higher wages for these workers will not help those who are at the bottom of the pay scale.

5. Investing back into businesses is not always better than returning cash to shareholders, when it comes to jobs, economic growth and prosperity.
Implicit in the Schumer-Sanders proposal to restrict buy backs is the belief that while shareholders may benefit from buybacks, the economy overall will be more prosperous, and workers will be better served, if the cash that is returned to shareholders is invested back in the businesses instead. Incidentally, this seems to be a shared delusion for both ends of the political spectrum, since one of the biggest sales pitches for the tax reform act, passed in 2017, was that the cash trapped overseas by bad US tax law, would, once released, be invested into new factories and manufacturing capacity in the US. I believe that both sides are operating from a false premise, since investing money back into bad businesses can make both economies and workers worse off. In a prior post, I defined a bad business as one where it is difficult to generate a return that is higher than the risk adjusted rate that you need to make to break even on your investment. 
Data Update 6 on excess returns
Using the return on capital, a flawed but still useful measure, as a measure of return and the cost of capital, with all of the caveats about measurement error, I found that approximately 60% of companies, both globally and in the US, earn less than their cost of capital. Forcing these companies to reinvest their earnings, rather than letting them pay it out, will only put more more money into bad businesses and create what I call "walking dead" companies, tying up capital that could be used more productively, if it were paid out to shareholders, who then can find better businesses to invest in. 

6. Some companies may be funding buybacks with debt, but the bulk of buybacks are still funded with equity cash flows
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Debt is a hot button issue, viewed as destructive to businesses by some at one end of the spectrum and an easy value creator by some at the other. The truth, as is usually the case, falls in the middle. In this post, I will look not only at how debt loads vary across companies, regions and industries, but also at how they have changed over the last year. That is because last year should have been a consequential one for financial leverage, especially for US companies, since the corporate tax rate was reduced from close to 40% to approximately 25%. I will also put leases under the microscope, converting lease commitments to debt, as I have been doing for close to two decades, and look at the effect on  profit margins and returns, offering a precursor to changes in 2019, when both IFRS and GAAP will finally do the right thing, and start treating leases as debt.

The Debt Trade Off
Debt is neither an unmixed good nor an unmitigated disaster. In fact, there are good and bad reasons for companies to borrow money, to fund operations, and in this section, I will look at the trade off, and look at the implications for what types of businesses should be the biggest users of debt, and which ones, the smallest.

The Pluses and Minuses
There are only two ways you can raise capital to fund a business. One is to use owner funds, which can of course range from personal savings in a small start up to issuing shares to the market, for a public company. The other is to borrow money, again ranging from a loan from a family member or friend to bank debt to corporate bonds. The debt equity trade off then boils down to what debt brings to the process, relative to equity, in both good and bad ways.

The two big elements driving whether a company should borrow money are the tax code, and how heavily it is tilted towards debt, on the good side and the increased exposure to default and distress, that it also creates, on the bad side. Simply put, companies with stable and predictable earnings streams operating in countries, with high corporate tax rates should borrow more money than companies with unstable earnings or which operate in countries that either have low tax rates or do not allow for interest tax deductions. For financial service firms, the decision on debt is more complex, since debt is less source of capital and more raw material to a bank. As a consequence, I will look at only non-financial service firms in this post, but I plan to do a post dedicate to just financial service firms.

US Tax Reform - Effect on Debt
If one of the key drivers of how much you borrow is the corporate tax code, last year was an opportunity to see this force in action, at least in the US. At the start of 2018, the US tax code was changed in two ways that should have affected the tax benefits of debt:
  1. The federal corporate tax rate was lowered from 35% to 21%. Adding state and local taxes to this, the overall corporate tax rate dropped from close to 40% to about 25%.
  2. Restrictions were put on the deductibility of interest expenses, with amounts exceeding 30% of taxable income no longer receiving the tax benefit.
Since there were no significant changes to bankruptcy laws or costs, these tax code changes make debt less attractive, relative to equity, for all US companies. In fact, as I argued in this post at the start of 2018, if US companies are weighing the pros and cons correctly, they should have reduced their debt exposure during the course of 2018.

While I have data only through through the end of the third quarter of 2018, I look at the change in total debt, both gross and net, at non-financial service US companies, over the year (by comparing to the debt at the end of the third quarter of 2017).
Download debt change, by industry
In the aggregate, US non-financial service companies did not reduce debt, but instead added $434 billion to their debt load, increasing their total debt from $6,931 billion to $7,365 billion between September 2017 and September 2018. That represented only a 6.26% increase over the year, and was accompanied by a decline in debt as a percent of market capitalization, but that increase is still surprising, given the drop in the marginal tax rate and the ensuing loss of tax benefits from borrowing. There are three possible explanations:
  1. Inertia: One of the strongest forces in corporate finance is inertia, where companies continue to do what they have always done, even when the reasons for doing so have long since disappeared. It is possible that it will be years before companies wake up to the changed tax environment and start borrowing less.
  2. Uncertainty about future tax rates: It is also possible that companies view the current tax code as a temporary phase and that the drop in corporate tax rates will be reversed by future administrations.
  3. Illusory and Transient Benefits: Many companies perceive benefits in debt that I term illusory, because they create value, only if you ignore the full consequences of borrowing. I have captured these illusory benefits in the table below: Put simply, the notion that debt will lower your cost of capital, just because it is lower than your cost of equity, is widely held, but just not true, and while using debt will generally increase your return on equity, it will also proportionately increase your cost of equity.
I will continue tracking debt levels through the coming years, and assuming no bounce back in corporate tax rates, we should get confirmation as to whether the tax hypothesis holds.

Debt: Definition
The tax law changed the dynamics of the debt/equity tradeoff, but there is an accounting change coming this year, which will have a significant impact on the debt that you see reported on corporate balance sheets around the world, and since this is the debt that most companies and data services use in measuring financial leverage. Specifically, accountants and their rule writers are finally going to come to their senses and plan to start treating lease commitments as debt, plugging what I have always believed is the biggest source of off balance sheet debt.

Debt: Definition
In my financing construct for a business, I argue that there are two ways that a business, debt (bank loans, corporate bonds) and equity (owner's funds), but to get a sense of how the two sources of capital vary, I looked at the differences:

Specifically, there are two characteristics that set debt apart from equity. The first is that debt creates a contractual or fixed claim that the firm is obligated to meet, in good and bad times, whereas equity gives rise to a residual claim, where the firm has the flexibility not to make any payments, in bad times. The second is that with debt, a failure to meet a contractual commitment, will lead to a loss of control of the firm and perhaps default, whereas with equity, a failure to meet an expected commitment (like paying dividends) can lead to a drop in market value but not to distress. Finally, in liquidation, debt holders get first claim on the assets and equity gets whatever, if any, is left over. Using this definition of debt, we can navigate through a balance sheet and work out what should be included in debt and what should not. If the defining features for debt are contractual commitments, with a loss of control and default flowing from a failure to meet them, it follows that all interest bearing debt, short term as well as long term, bank loans and corporate bonds, are debt. Staying on the balance sheet, though, there are items that fall in a gray area:
  1. Accounts Payable and Supplier Credit:  There can be no denying that a company has to pay back supplier credit and honor its accounts payable, to be a continuing business, but these liabilities often have no explicit interest costs. That said, the notion that they are free is misplaced, since they come with an implicit cost. To make use of supplier credit, for instance, you have to give up discounts that you could have obtained if you paid on delivery. The bottom line in valuation and corporate finance is simple. If you can estimate these implicit expenses (discounts lost) and treat them as actual interest expenses, thus altering your operating income and net income, you can treat these items as debt. If you find that task impossible or onerous, since it is often difficult to back out of financial reports, you should not consider these items debt, but instead include them as working capital (which affects cash flows).
  2. Underfunded Pension and Health Care Obligations: Accounting rules around the world have moved towards requiring companies to report whether their defined-benefit pension plans or health care obligations are underfunded, and to show that underfunding as a liability on balance sheets. In some countries, this disclosure comes with legal consequences, where the company has to set aside funds to cover these obligations, akin to debt payments, and if this is the case, they should be treated as debt. In much of the world, including the United States, the disclosure is more for informational purposes and while companies are encouraged to cover them, there is no legal obligation that follows. In these cases, you should not consider these underfunded obligations to be debt, though you may still net them out of firm value to get to equity value.
The table below provides the breakdown of debt for non-financial service companies around the world.
Debt Details, by Industry (US)
As you browse this table, please keep in mind that disclosure on the details of debt varies widely across companies, and this table cannot plug in holes created by non-disclosure. To the extent that company disclosures are complete, you can see that there are differences in debt type across regions, with a greater reliance on short term debt in Asia, a higher percent of unsecured and fixed rate debt in Japan and more variable rate, secured debt in Africa, India and Latin America than in Europe or the US. You can get the debt details, by industry, for regional breakdowns at the link at the end of this post.

Debt Load: Balance Sheet Debt
Using all interest bearing debt as debt in looking at companies, we can raise and answer fundamental questions about leverage at companies. Broadly speaking, the debt load at a company can be scaled to either the value of the company or to its earnings and cash flows. Both measures are useful, though they measure different aspects of debt load:

a. Debt and Value
Earlier, I noted that there are two ways you can fund a business, debt and equity, and a logical measure of financial leverage that follows is to look at how much debt a firm uses, relative to its equity. That said, there are two competing measures of value, and especially for equity, the divergence can be wide.
  • The first is the book value, which is the accountant's estimate of how much a business and its equity are worth. While value investors attach significant weight to this number, it reflects all of the weaknesses that accounting brings to the table, a failure to adjust for time value of money, an unwillingness to consider the value for current market conditions and an inability to deal with investments in intangible assets. 
  • The second is market value, which is the market's estimate, with all of the pluses and minuses that go with that value. It is updated constantly, with no artificial lines drawn between tangible and intangible assets, but it is also volatile, and reflects the pricing game that sometimes can lead prices away from intrinsic value.
In the graph below, I look at debt as a percent of capital, first using book values for debt and equity, and next using market value.
Debt ratios, by industry (US)
In the table below, I break out debt as a percent of overall value (debt + equity) using both book value and market value numbers, and look at the distribution of these ratios globally:

Embedded in the chart is a regional breakdown of debt ratios, and even with these simple measures of debt loads, you can see how someone with a strong  prior point of view on debt, pro or con, can find a number to back that view. Thus, if you want to argue as some have that the Fed (which is blamed for almost everything that happens under the sun), low interest rates and stock buybacks have led US companies to become over levered, you will undoubtedly point to book debt ratios to make your case. In contrast, if you have a more sanguine view of financial leverage in the US, you will point to market debt ratios and perhaps to the earnings and cash flow ratios that I will report in the next section. On this debate, at least, I think that those who use book value ratios to make their case hold a weak hand, since book values, at least in the US and for almost every sector other than financial, have lost relevance as measures of anything, other than accounting ineptitude.

b. Debt and Earnings/Cashflows
Debt creates contractual obligations in the form of interest and principal payments, and these payments have to be covered by earnings and cash flows. Thus, it is sensible to measure how much buffer, or how little, a firm has by scaling debt payments to earnings and cash flows, and here are two measures:
  • Debt to EBITDA: It is true that EBITDA is an intermediate cash flow, not a final one, since you still have to pay taxes and invest in growth, before you get a residual cash flow. That said, it is a proxy for how much cash flow is being generated by existing investments, and dividing the total debt by EBITDA is a measure of overall debt load, with lower numbers translating into less onerous loads.
  • Interest Coverage Ratio: Dividing the operating income (EBIT) by interest expenses, gives us a different measure of safety, one that is more immediately tied to default risk and cost of debt than debt to EBITDA. Firms that generate substantial operating income, relative to interest expenses, are safer, other things remaining equal, than firms that operate with lower interest coverage ratios. 
In the table below, I look at the distributions of both these numbers, again broken down by region of the world:
Debt ratios, by industry (US)
Again, the story you tell can be very different, based upon which number you look at. Chinese companies have the most debt in the world, if you define debt as gross debt, but look close to average, when you look at net debt. Indian companies look lightly levered, if you look at Debt to EBITDA multiples, but have the most exposure to debt, if you use interest coverage ratios to measure debt load.

Operating Leases: The Accounting Netherworld
Going back to the definition of debt as financing that comes with contractually set obligations, where failure to meet these obligations can lead to loss of control and default, it is clear that focusing on only the balance sheet (as we have so far) is dangerous, since there are other claims that companies create that meet these conditions. Consider lease agreements, where a retailer or a restaurant business enters into a multi-year agreement to make lease payments, in return for using a store front or building. The lease payments are clearly set out by contract, and failing to make these payments will lead to loss of that site, and the income from it. You can argue that leases providing more flexibility that a bank loan and that defaulting on a lease is less onerous, because the claims are against a specific location and not the business, but those are arguments about whether leases are more like unsecured debt than secured debt, and not whether leases should be treated as debt. For much of accounting history, though, accountants have followed a different path, treating only a small subset of leases as debt and bringing them on to the balance sheet as capital leases, while allowing the bulk of lease expenses as operating expenses and ignoring future lease commitments on balance sheets. The only consolation prize is that both IFRS and GAAP have required companies to show these lease commitments as footnotes to balance sheets.

In my experience, waiting for accountants to do the right thing will leave you twisting in the wind, since it seems to take decades for common sense to prevail. Consequently, I have been treating leases as debt for more than three decades in valuation, and the process for doing so is neither complicated nor novel. In fact, it is the same process that accountants use right now with capital leases and it involves the following steps:
  1. Estimate a current cost of borrowing or pre-tax cost of debt for the company today, given its default risk and current interest rates (and default spreads).
  2. Starting with the lease commitment table that is included in the footnotes today, discount each lease commitment back to today, using the pre-tax cost of debt as your discount rate (since the lease commitments are pre-tax). Most companies provide only a lump-sum value for commitments after year 5, and while you can act as if this entire amount will come due in year 6, it makes more sense to convert it into an annuity, before discounting.
  3. The sum total of the present value of lease commitments will be the lease debt that will now show up on your balance sheet, but to keep the balance sheet balanced, you will have to create a counter asset. 
  4. To the extent that the accounting has treated the current year's lease expense as an operating expense, you have to recompute the operating income, reflecting your treatment of leases as debt:
Adjusted Operating Income = Stated Operating Income + Current year's lease expense - Depreciation on the leased asset

Capitalizing leases will have large consequences for not just debt ratios at companies (pushing them for companies with significant lease commitments) but also for operating profitability measures (like operating margin) and returns on invested capital (since both operating income and invested capital will be changed). The effects on net margin and return on equity should either be much smaller or non-existent, because equity income is after both operating and capital expenses, and moving leases from one grouping to another has muted consequences. In the table below, I report on debt ratio, operating margin and return on capital. before and after the lease adjustment :
Lease Effect, by Industry, for US
You can download the effects, by industry, for different regions, by using the links at the bottom of this post.  Keep in mind, though, that there are parts of the world where lease commitments, though they exist, are not disclosed in financial statements, and as a consequence, I will understate the else effect, While the effect is modest across all companies, the lease effect is larger in sectors that use leases liberally in operations, and to see which sectors are most and least affected, I looked at the ten   sectors, among US companies, and not counting financial service firms, that saw the biggest percentage increases in debt ratios and the ten sectors that saw the smallest in the table below:
Lease Effect, by Industry, for US
Note that there are a large number of retail groupings that rank among the most affected sectors, though a few technology companies..
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In my last post, I looked at hurdle rates for companies, across industries and across regions, and argued that these hurdle rates represent benchmarks that companies have to beat, to create value. That said, many companies measure success using lower thresholds, with some arguing that making money (having positive profits) is good enough and others positing that being more profitable than competitors in the same business makes you a good company. In this post, I will look at all three measures of success, starting with the minimal (making money), moving on to relative judgments (and how best to compare profitability across companies of different scales) and ending with the most rigorous one of whether the profits are sufficient to create value.

Measuring Financial Success
You may start a business with the intent of meeting a customer need or a societal shortfall but your financial success will ultimately determine your longevity. Put bluntly, a socially responsible company with an incredible product may reap good press and have case studies written about it, but if it cannot establish a pathway to profitability, it will not survive. But how do you measure financial success? In this portion of the post, I will start with the simplest measure of financial viability, which is whether the company is making money, usually from an accounting perspective, then move the goal posts to see if the company is more or less profitable than its competitors, and end with the toughest test, which is whether it is generating enough profits on the capital invested in it, to be a value creator.

Profit Measures
Before I present multiple measures of profitability, it is useful to step back and think about how profits should be measured. I will use the financial balance sheet construct that I used in my last post to explain how you can choose the measure of profitability that is right for your analysis:

Just as hurdle rates can vary, depending on whether you take the perspective of equity investors (cost of equity) or the entire business (cost of capital), the profit measures that you use will also be different, depending on perspective. If looked at through the eyes of equity investors, profits should be measured after all other claim holders (like debt) and have been paid their dues (interest expenses), whereas using the perspective of the entire firm, profits should be estimated prior to debt payments. In the table below, I have highlighted the various measures of profits and cash flows, depending on claim holder perspective:
The key, no matter which claim holder perspective you adopt, is to stay internally consistent. Thus, you can discount cash flows to equity (firm) at the cost of equity (capital) or compare the return on equity (capital) to the cost of equity (capital), but you cannot mix and match.

The Minimal Test: Making money?
The lowest threshold for success in business is to generate positive profits, perhaps the reason why accountants create measures like breakeven, to determine when that will happen. In my post on measuring risk, I looked at the percentages of firms that meet this threshold on net income (for equity claim holders), an operating income (for all claim holders) and EBITDA (a very rough measure of operating cash flow for all claim holders). Using that statistic for the income over the last twelve month, a significant percentage of publicly traded firms are profitable:
Data, by country
The push back, even on this simplistic measure, is that just as one swallow does not a summer make, one year of profitability is not a measure of continuing profitability. Thus, you could expand this measure to not just look at average income over a longer period (say 5 to 10 years) and even add criteria to measure sustained profitability (number of consecutive profitable years). No matter which approach you use, you still will have two problems. The first is that because this measure is either on (profitable) or off (money losing), it cannot be used to rank or grade firms, once they have become profitable. The other is that making money is only the first step towards establishing viability, since the capital invested in the firm could have been invested elsewhere and made more money. It is absurd to argue that a company with $10 billion in capital invested in it is successful if it generates $100 in profits, since that capital invested even in treasury bills could have generated vastly more money.

The Relative Test: Scaled Profitability
Once a company starts making money, it is obvious that higher profits are better than  lower ones, but unless these profits are scaled to the size of the firm, comparing dollar profits will bias you towards larger firms. The simplest scaling measure is revenues, a data item available for all but financial service firms, and one that is least likely to be affected by accounting choices, and profits scaled to revenues yields profit margins. In a data update post from a year ago, I provided a picture of different margin measures and why they might provide different information about business profitability:

As I noted in my section on claimholders above, you would use net margins to measure profitability to equity investors and operating margins (before or after taxes) to measure profitability to the entire firm. Gross and EBITDA margins are intermediate stops that can be used to assess other aspects of profitability, with gross margins measuring profitability after production costs (but before selling and G&A costs) and EBITDA margins providing a crude measure of operating cash flows.

In the graph below, I look at the distribution of pre-tax operating margins and net margins globally, and provide regional medians for the margin measures:

The regional comparisons of margins are difficult to analyze because they reflect the fact that different industries dominate different regions, and margins vary across industries. You can get the different margin measures broken down by industry, in January 2019, for US firms by clicking here. You can download the regional averages using the links at the end of this post.

The Value Test: Beating the Hurdle Rate
As a business, making money is easier than creating value, since to create value, you have to not just make money, but more money than you could have if you had invested your capital elsewhere. This innocuous statement lies at the heart of value, and it is in fleshing out the details that we run into practical problems on the three components that go into it:
  1. Profits: The profit measures we have for companies reflect their past, not the future, and even the past measures vary over time, and for different proxies for profitability. You could look at net income in the most recent twelve months or average net income over the last ten years, and you  could do the same with operating income. Since value is driven by expectations of future profits, it remains an open question whether any of these past measures are good predictors.
  2. Invested Capital: You would think that a company would keep a running tab of all the money that is invested in its projects/assets, and in a sense, that is what the book value is supposed to do. However, since this capital gets invested over time, the question of how to adjust capital invested for inflation has remained a thorny one. If you add to that the reality that the invested capital will change as companies take restructuring charges or buy back stock, and that not all capital expenses finds their way on to the balance sheet, the book value of capital may no longer be a good measure of capital invested in existing investments.
  3. Opportunity Cost: Since I spent my last post entirely on this question, I will not belabor the estimation challenges that you face in estimating a hurdle rate for a company that is reflective of the risk of its investments.
In a perfect world, you would scale your expected cashflows in future years, adjusted for time value of money, to the correct amount of capital invested in the business and compare it to a hurdle rate that reflects both your claim holder choice (equity or the business) but also the risk of the business. In fact, that is exactly what you are trying to do in a good intrinsic or DCF valuation. 

Since it is impossible to do this for 42000 plus companies, on a company-by-company basis, I used blunt instrument measures of each component, measuring profits with last year's operating income after taxes, using book value of capital (book value of debt + book value of equity - cash) as invested capital:

Similarly, to estimate cost of capital, I used short cuts I would not use, if I were called up to analyze a single company: 

Comparing the return on capital to the cost of capital allows me to estimate excess returns for each of my firms, as the difference between the return on invested capital and the cost of capital. The distribution of this excess return measure globally is in the graph below:
I am aware of the limitations of this comparison. First, I am using the trailing twelve month operating income as profits, and it is possible that some of the firms that measure up well and badly just had a really good (bad) year. It is also biased against young and growing firms, where future income will be much higher than the trailing 12-month value. Second, operating income is an accounting measure, and are affected not just by accounting choices, but are also affected by the accounting mis-categorization of lease and R&D expenses. Third, using book value of capital as a proxy for invested capital can be undercut by not only whether accounting capitalizes expenses correctly but also by well motivated attempts by accountants to write off past mistakes (which create charges that lower invested capital and make return on capital look better than it should). In fact, the litany of corrections that have to be made to return on capital to make it usable and listed in this long and very boring paper of mine. Notwithstanding these critiques, the numbers in this graph tell a depressing story, and one that investors should keep in mind, before they fall for the siren song of growth and still more growth that so many corporate management teams sing. Globally, approximately 60% of all firms globally earn less than their cost of capital, about 12% earn roughly their cost of capital and only 28% earn more than their cost of capital. There is no region of the world that is immune from this problem, with value destroyers outnumbering value creators in every region.

From a corporate finance perspective, there are lessons to be learned from the cross section of excess returns, and here are two immediate ones:
  1. Growth is a mixed blessing: In 60% of companies, it looks like it destroys value, does not add to it. While that proportion may be inflated by the presence of bad years or companies that are early in the life cycle, I am sure that the proportion of companies where value is being destroyed, when new investments are made, is higher than those where value is created.
  2. Value destruction is more the rule than the exception: There are lots of bad companies, if bad is defined as not making your hurdle rate. In some companies, it can be attributed to bad managed that is entrenched and set in its ways. In others, it is because the businesses these companies are in have become bad business, where no matter what management tries, it will be impossible to eke out excess returns.
You can see the variations in excess returns across industries, for US companies, by clicking on this link, but there are clearly lots of bad businesses to be in. The same data is available for other regions in the datasets that are linked at the end of this post.

If there is a consolation prize for investors in this graph, it is that the returns you make on your investment in a company are driven by a different dynamic. If stocks are value driven, the stock price for a company will reflect its investment choices, and companies that invest their money badly will be priced lower than companies that invest their money well. The returns you will make on these companies, though, will depend upon whether the excess returns that they deliver in the future are greater or lower than expectations. Thus, a company that earns a return on capital of 5%, much lower than its cost of capital of 10%, which is priced to continue earning the same return will see if its stock price increase, if it can improve its return on capital to 7%, still lower than the cost of capital, but higher than expected. By the same token, a company that earns a return on capital of 25%, well above its cost of capital of 10%, and priced on the assumption that it can continue on its value generating path, will see its stock price drop, if the returns it generates on capital drop to 20%, well above the cost of capital, but still below expectations. That may explain a graph like the following, where researchers found that investing in bad (unexcellent) companies generated far better returns than investing in good (excellent) companies:
Original Paper: Excellence Revisited, by Michelle Klayman
The paper is dated, but its results are not, and they have been reproduced using other categorizations for good and bad firms. Thus, investing in the most admired firms generates worse returns for investors than investing in the least admired and investing in popular (with investors) firms under performs investing in unpopular ones. While these results may seem perverse, at first sight, that bad (good) companies can be good (bad) investments, it makes sense, once you factor in the expectations game

Finally, on the corporate governance front, I feel that we have lost our way. Corporate governance laws and measures have focused on check boxes on director independence and corporate rules, rather than furthering the end game of better managed companies. From my perspective, corporate governance should give stockholders a chance to change the way companies are run, and if corporate governance works well, you should see more management turnover at companies that don't earn what they need to on capital. The fact that six in ten companies across the globe earned well below their cost of capital in 2018, added to the reality that many of these companies have not only been under performing for years, but are still run by the same management, makes me wonder whether the push towards better corporate governance is more talk than action.

YouTube Video
Data Update 6 for 2019: Profitability, Growth and Value - YouTube

Data Links
  1. Profit Margins: USGlobalEmerging MarketsEuropeJapanIndiaChinaAus & Canada
  2. Excess Returns to Equity and Capital: USGlobalEmerging MarketsEuropeJapanIndiaChinaAus & Canada
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In the last post, I looked at how to measure risk from different perspectives, with the intent of bringing these risk measures into both corporate finance and valuation. In this post, I will close the circle by converting risk measures into hurdle rates, critical in corporate finance, since they drive whether companies should invest or not, and in valuation, because they determine the values of businesses. As with my other data posts, the focus will remain on what these hurdle rates look like for companies around the world at the start of 2019.

A Quick Introduction
The simplest way to introduce hurdle rates is to look at them from the perspectives of the capital providers to a business. Using a financial balance sheet as my construct, here is a big picture view of these costs:

Thus. the hurdle rate for equity investors, i.e., the cost of equity, is the rate that they need to make, to break even, given the risk that they perceive in their equity investments. Lenders, on the other hand, incorporate their concerns about default risk into the interest rates they set on leans, i.e., the cost of debt. From the perspective of a business that raises funds from both equity investors and lenders, it is a weighted average of what equity investors need to make and what lenders demand as interest rates on borrowing, that represents the overall cost of funding, i.e., the cost of capital.

I have described the cost of capital as the Swiss Army Knife of finance, used in many different contexts and with very different meanings. I have reproduced below the different uses in a picture:
Paper on cost of capital
It is precisely because the cost of capital is used in so many different places that it is also one of the most misunderstood and misused numbers in finance. The best way to reconcile the different perspectives is to remember that the cost of capital is ultimately determined by the risk of the enterprise raising the funding, and that all of the many risks that a firm faces have to find their way into it. I have always found it easiest to break the cost of capital into parts, and let each part convey a specific risk, since if I am careless, I end up missing or double counting risk. In this post, I will break the risks that a company faces into four groups: the business or businesses the company operates in (business risk), the geographies that it operates in (country risk), how much it has chosen to borrow (financial leverage risk) and the currencies its cash flows are in (currency effects). 

Note that each part of the cost of capital has a key risk embedded in it. Thus, when valuing a company, in US dollars, in a safe business in a risky country, with very little financial leverage, you will see the 10-year US treasury bond rate as my risk free rate, a low beta (reflecting the safety of the business and low debt), but a high equity risk premium (reflecting the risk of the country).  The rest of this post will look at each of the outlined risks.

I. Business Risk
In my last post, where I updated risk measures across the world, I also looked at how these measures varied across different industries/businesses. In particular, I highlighted the ten most risky and safest industries, based upon both price variability and earnings variability, and noted the overlap between the two measures. I also looked at how the perceived risk in a business can change, depending upon investor diversification, and captured this effect with the correlation with the overall market.  If you are diversified, I argued that you would measure the risk in an investment with the covariance of that investment with the market, or in its standardized form, its beta.

To get the beta for a company, then, you can adopt one of two approaches.
  • The first, and the one that is taught in every finance class, is to run a regression of returns on the stock against a market index and to use the regression beta. 
  • The second, and my preferred approach, is to estimate a beta by looking at the business or businesses a company operates in, and taking a weighted average of the betas of companies in that business. 
To use the second approach, you need betas by business, and each year, I estimate these numbers by averaging the betas of publicly traded companies in each business. These betas, in addition to reflecting the risk of the business, also reflect the financial leverage of companies in that business (with more debt pushing up betas) and their holdings in cash and marketable securities (which, being close to risk less, push down betas). Consequently, I adjust the average beta for both variables to estimate what is called a pure play or a business beta for each business. (Rather than bore you with the mechanics, please watch this video on how I make these adjustments). The resulting estimates are shown at this link, for US companies. (You can also download the spreadsheets that contain the estimates for other parts of the world, as well as global averages, by going to the end of this post).

To get from these business betas to the beta of a company, you need to first identify what businesses the company operates in, and then how much value it derives from each of the businesses. The first part is usually simple to do, though you may face the challenge of finding the right bucket to put a business into, but the second part is usually difficult, because the individual businesses do not trade. You can use revenues or operating income by business as approximations to estimate weights or apply multiples to each of these variables (by looking at what other companies in the business trade at) to arrive at value weights. 

II. Financial Leverage
You can run a company, without ever using debt financing, or you can choose to borrow money to finance operations. In some cases, your lack of access to new equity may force you to borrow money and, in others, you may borrow money because you believe it will lower your cost of capital. In general, the choice of whether you use debt or equity remains one of the key parts of corporate finance, and I will discuss it in one of my upcoming data posts. In this post, though, I will just posit that your cost of capital can be affected by how much you borrow, unless you live in a world where there are no taxes, default risk or agency problems, in which case your cost of capital will remain unchanged as your funding mix changes.  If you do borrow money to fund some or a significant portion of your operations, there are three numbers that you need to estimate for your cost of capital:
  1. Debt Ratio: Th mix of debt and equity that you use represents the weights in your cost of capital.
  2. Beta Effect: As you borrow money, your equity will become riskier, because it is a residual claim, and having more interest expenses will make that claim more volatile. If you use beta as your measure of risk, this will require you to adjust upwards the business (or unlettered) beta that you obtained in the last part, using the debt to equity ratio of the company. 
  3. Cost of Debt: The cost of debt, which is set by lenders based upon how much default risk that they see in a company, will enter the cost of capital equation, with an added twist. To the extent that the tax law is tilted towards debt, the after-tax cost of borrowing will reflect that tax benefit. Since this cost of debt is a cost of borrowing money, long term and today, you cannot use a book interest rate or the interest rate on existing debt. Instead, you have to estimate a default spread for the company, based upon either its bond ratings or financial ratios, and add that spread on to the risk free rate:
I look at the debt effect on the cost of capital in each of the industries that I follow, with all three effects incorporated in this link, for US companies. The data, broken down, by other regional sub-groupings is available at the end of this post.

III. Country Risk
It strikes me as common sense that operating in some countries will expose you to more risk than operating in others, and that the cost of capital (hurdle rate) you use should reflect that additional risk. While there are some who are resistant to this proposition, making the argument that country risk can be diversified by having a global portfolio, that argument is undercut by rising correlations across markets. Consequently, the question becomes not whether you should incorporate country risk, but how best to do it. There are three broad choices:
  1. Sovereign Ratings and Default Spreads: The vast majority of countries have sovereign ratings, measuring their default risk, and since these ratings go with default spreads, there are many who use these default spreads as measures of country risk. 
  2. Sovereign CDS spreads: The Credit Default Swap (CDS) market is one where you can buy insurance against sovereign default, and it offers a market-based estimate of sovereign risk. While the coverage is less than what you get from sovereign ratings, the number of countries where you can obtain these spreads has increased over time to reach 71 in 2019. 
  3. Country Risk Premiums: I start with the default spreads, but I add a scaling factor to reflect the reality that equities are riskier than government bonds to come up with country risk premiums. The scaling factor that I use is obtained by dividing the volatility of an emerging market equity index by the volatility of emerging market bonds. 
To incorporate the country risk into my cost of capital calculations, I start with the implied equity risk premium that I estimated for the US (see my first data post for 2019) or 5.96% and add to it the country risk premium for each country. The full adjustment process is described in this picture:

I also bring in frontier markets, which have no sovereign ratings, using a country risk score estimated by Political Risk Services. The final estimates of equity risk premiums around the world can be seen in the picture below:

You can see these equity risk premiums as a list by clicking here, or download the entire spreadsheet here. If you prefer a picture of equity risk around the world, my map is below:
Download spreadsheet
I also report regional equity risk premiums, computed by taking GDP-weighted averages of the equity risk premiums of the countries int he region.

IV. Currency Risk
It is natural to mix up countries and currencies, when you do your analysis, because the countries with the most risk often have the most volatile currencies. That said, my suggestion is that you keep it simple, when it comes to currencies, recognizing that they are scaling or measurement variables rather than fundamental risk drivers. Put differently, you can choose to value a Brazilian companies in US dollars, but doing so does not make Brazilian country risk go away.

So, why do currencies matter? It is because each one has different expectations of inflation embedded in it, and when using a currency, you have to remain inflation-consistent. In other words, if you decide to do your analysis in a high inflation currency, your discount rate has to be higher, to incorporate the higher inflation, and so do your cash flows, for the same reason:

There are two ways in which you can bring inflation into discount rates.  The first is to use the risk free rate in that currency as your starting point for the calculation, since risk free rates will be higher for high inflation currencies. The challenge is finding a risk free investment in many emerging market currencies, since even the governments bonds, in those currencies, have default risk embedded in them. I attempt to overcome this problem by starting with the government bond but then netting the default spread for the government in question from that bond to arrive at risk free rates:
Download raw data
These rates are only as reliable as the government bond rates that you start with, and since more than two thirds of all currencies don't even have government bonds and even on those that do, the government bond rate does not come from liquid markets, there a second approach that you can use to adjust for currencies. In this approach, you estimate the cost of capital in a currency that you feel comfortable with (in terms of estimating risk free rates and risk premiums) and then add on or incorporate the differential inflation between that currency and the local currency that you want to convert the cost of capital to. Thus, to convert the cost of capital in US $ terms to a different currency, you would do the following:

To illustrate, assume that you have a US dollar cost of capital of 12% for an Egyptian company and that the inflation rates are 15% and 2% in Egyptian Pounds and US dollars respectively:
The Egyptian pound cost of capital is 26.27%. Note that there is an approximation that is often used, where the differential inflation is added to the US dollar cost of capital; in this case your answer would have been 25%. The key to this approach is getting estimates of expected inflation, and while every source will come with warts, you can find the IMF's estimates of expected inflation in different currencies at this link.

General Propositions
Every company, small or large, has a hurdle rate, though the origins of the number are murky at most companies. The approach laid out in this post has implications for how hurdle rates get calculated and used.
  1. A hurdle rate for an investment should be more a reflection the risk in the investment, and less your cost of raising funding: I fault terminology for this, but most people, when asked what a cost of capital is, will respond with the answer that it is the cost of raising capital. In the context of its usage as a hurdle rate, that is not true. It is an opportunity cost, a rate of return that you (as a company or investor) can earn on other investments in the market of equivalent risk. That is why, when valuing a target firm in an acquisition, you should always use the risk characteristics of the target firm (its beta and debt capacity) to compute a cost of capital, rather than the cost of capital of the acquiring firm.
  2. A company-wide hurdle rate can be misleading and dangerous: In corporate finance, the hurdle rate becomes the number to beat, when you do investment analysis. A project that earns more than the hurdle rate becomes an acceptable one, whether you use cash flows (and compute a positive net present value) or income (and generate a return greater than the hurdle rate). Most companies claim to have a corporate hurdle rate, a number that all projects that are assessed within the company get measured against. If your company operates in only one business and one country, this may work, but to the extent that companies operate in many businesses across multiple countries, you can already see that there can be no one hurdle rate. Even if you use only one currency in analysis, your cost of capital will be a function of which business a project is in, and what country it is aimed at. The consequences of not making these differential adjustments will be that your safe businesses will end up subsidizing your risky businesses, and over time, both will be hurt, in what I term the "curse of the lazy conglomerate".
  3. Currency is a choice, but once chosen, should not change the outcome of your analysis: We spend far too much time, in my view, debating what currency to do an analysis in, and too little time working through the implications. If you follow the consistency rule on currency, incorporating inflation into both cash flows and discount rates, your analyses should be currency neutral. In other words, a project that looks like it is a bad project, when the analysis is done in US dollar terms, cannot become a good project, just because you decide to do the analysis in Indian rupees. I know that, in practice, you do get divergent answers with different currencies, but when you do, it is because there are inflation inconsistencies in your assessments of discount rates and cash flows.
  4. You cannot (and should not) insulate your cost of capital from market forces: In both corporate finance and investing, there are many who remain wary of financial markets and their capacity to be irrational and volatile. Consequently, they try to generate hurdle rates that are unaffected by market movements, a futile and dangerous exercise, because we have to be price takers on at least some of the inputs into hurdle rates. Take the risk free rate, for instance. For the last decade, there are many analysts who have replaced the actual risk free rate (US 10-year T.Bond rate, for instance) with a "normalized' higher number, using the logic that interest rates are too low and will go up. Holding all else constant, this will push up hurdle rates and make it less likely that you will invest (either as an investor or as a company), but to what end? That uninvested money cannot be invested at the normalized rate, since it is fictional and exists only in the minds of those who created it, but is invested instead at the "too low" rate. 
  5. Have perspective: In conjunction with the prior point, there seems to be a view in some companies and for some investors, that they can use whatever number they feel comfortable with as hurdle rates. To the extent that hurdle rates are opportunity costs in the market, this is not true. The cost of capital brings together all of the risks that we have listed in this section. If nothing else, to get perspective on what comprises high or low, when it comes to cost of capital, I have computed a histogram of global and US company costs of capital, in US $ terms.

    You can convert this table into any currency you want. The bottom line is that, at least at the start of 2019, a dollar cost of capital of 14% or 15% is an extremely high number for any publicly traded company. You can see the costs of capital, in dollar terms, for US companies at this link, and as with betas, you can download the cost of capital, by industry, for other parts of the world in the data links below this post.
In short, if you work at a company, and you are given..
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I think that all investors would buy into the precept that investing in equities comes with risk, but that is where the consensus seems to end. Everything else about risk is contested, starting with whether it is a good or a bad, whether it should be sought out or avoided, and how it should be measured. It is therefore with trepidation that I approach this post, knowing fully well that I will be saying things about risk that you strongly disagree with, but it is worth the debate.

Risk: Basic Propositions
I. Risk falls on a continuum: Risk is not an on-off switch, where some assets are risky and others are not. Instead, it is better to think of it on a continuum, with investments with very little or close to no risk at one extreme (riskless) to extraordinarily risky investments at the other.

In fact, while most risk and return models start off with the presumption that there exists a riskless asset, one in which you can invest for a guaranteed return and no loss of principal, I think that a reasonable argument can be made that there are no such investments. In abstract settings, we often evade the question by using government bond rates (like the US treasury) as risk free rates, but that assumes:
  1. That governments don't default, an assumption that conflicts with the empirical evidence that they do, on both local currency and foreign currency borrowings
  2. That if the government delivers it's promised coupon we are made whole again, also not true since inflation can be a wild card, rendering the real return on a government bond negative, in some periods. A nominal risk free rate is not a real risk free rate, which is one reason that I track the inflation indexed treasury bond (TIPs) in conjunction with the conventional US treasury bond; the yield on the former is closer to a real risk free rate, if you assume the US treasury has no default risk.
If there is one lesson that emerged from the 2008 crisis, it is that there are some periods in market history where there are truly no absolutely safe havens left and investors have to settle for the least stomach churning alternative that they can find, during these crises.

II. For a company, risk has many sources: Following up on the proposition that investing in the equity of a business can expose you to risk, it is worth noting that this risk can come from multiple sources. While a risk profile for a company can have a laundry list of potential risks,  I break these risks into broad categories:
Note that some of these risks are more difficult to estimate and deal with than others, but that does not mean that you can avoid them or not deal with them. In fact, as I have argued repeatedly, your best investment opportunities may be where it is darkest.

III. For investors, risk standing alone can be different from risk added to a portfolio: This is perhaps the most controversial divide in finance, but I will dive right in. The risk of an investment can be different, if it is assessed as a stand-alone investment, as opposed to being part of a portfolio of investments and the reason is simple. Some of the risks that we listed in the table above, to the extent that they are specific to the firm, and can cut in either direction (be positive or negative surprises) will average out across a portfolio. It is simply the law of large numbers at work. In the graph below, I present a simplistic version of diversification at play, by looking at how the standard deviation of returns in a portfolio changes, as the number of investments in it goes up, in a world where the typical investment has a standard deviation of 40%, and for varying correlations across investments.

If the assets are uncorrelated, the standard deviation of the portfolio drops to just above 5%, but note that the benefits persist as long as the assets in your portfolio are not perfectly positively correlated, which is good news since stocks are usually positively correlated with each other. Furthermore, the greatest savings occur with the first few stocks that are added on, with about 80% of the benefits accruing by the time you get to a dozen stocks, if they are not all in the same sector or share the same characteristics (in which case the correlation across those stocks will be higher, and the benefit lower).

I know that I am now opening up an age old debate in investing as to whether it is better to have a concentrated portfolio or a diversified one. Rather than argue that one side is right and the other wrong, I will posit that it depends upon how certain you feel about your investment thesis, i.e., that your estimate of value is right and that the market price will correct to that value, with more certainty associated with less diversification. Speaking for myself, I am always uncertain about whether the value that I have estimated is right and even more so about whether the market will come around to my point of view, which also means that it is best for me to spread my bets. You can be a value investor and be diversified at the same time.

IV. Your risk measurement will depend on how and why you invest and your time horizon: Broadly speaking, there are three groups of metrics that you can use to measure the risk in an investment. 
  1. Price Measures: If an asset/investment is traded,  the first set of metrics drawn on the price path  and what you can extract from that path as a measure of risk. There are many in investing who bemoan the Markowitz revolution and the rise of modern finance, but one of the byproducts of modern portfolio theory is that price-based measures of risk dominate the risk measurement landscape. 
  2. Earnings/Cashflow Measures: There are many investors who believe that it is uncertainty about earnings and cash flows that are a true measure of risk. While their argument is that value is driven by earnings and cash flows, not stock price movements, their case is weakened by the fact that (a) earnings are measured by accountants, who tend to smooth out variations in earnings over time and (b) even when earnings are measured right, they are measured, at the most, four times a year, for companies that have quarterly reporting, and less often, for firms that report only annually or semi-annually.
  3. Risk Proxies: Some investors measure the risk of an asset, by looking at the grouping it belongs to, arguing that some groupings are more risky than others. For instance, in the four decades since technology stocks became part of the market landscape, "tech" has become a stand in for both high growth and high risk. Similarly, there is the perception that small companies are riskier than larger companies, and that the market capitalization, or level of revenues, should be a good proxy for the risk of a company.
While I will report on each of these three groups of  risk measures in this post, you can decide which measure best fits you, as an investor, given your investment philosophy.

Price Risk Measures
The most widely accessible measures of risk come from the market, for publicly traded assets, where trading generate prices that change with each trade. That price data is then used to extract risk measures, ranging from intuitive ones (high to low ranges) to statistical measures (such as standard deviation and covariance). 

Price Range 
When looking at a stock's current price, it is natural to also look at where it stands relative to that stock's own history, which is one reason most stock tables report high and low prices over a period (the most recent 12 months, for instance). While technical analysts use these high/low prices to determine whether a stock is breaking out or breaking down,  these prices can also be used as a rough proxy for risk. Put simply, riskier stocks will trade with a wider range of prices than safer stocks.

HiLo Risk Measure
To compute a risk measure from high and low prices that is comparable across stocks, the range has to be scaled to the price level. Otherwise, highly priced stocks will look more risky,  because the range between the high and the low price will be greater for a $100 stock than for a $5 stock. One simple scalar is the sum of the high and the low prices, giving the following measure of risk:
HiLo Risk = (High Price - Low Price)/ (High Price + Low Price)
To illustrate, consider two stocks, A with a high of $50 and a low of $25 and B with a high of $12 and a low of $8. The risk measures computed will be:
  • HiLo Risk of stock A = (50-25)/ (50+25) = 0.333
  • HiLo Risk of stock B = (12-8)/ (12 +8) = 0.20
Based upon this measure, stock A is riskier than stock B.

I compute the HiLo risk measure for all stocks in my data set, to get a sense of what would be high or low, and the results are captured in the distribution below (Q1: First Quartile, Q3: Third Quartile):
Data at country level 
Embedded in the distribution is the variation of this measure across regions, with some, at first sight, counterintuitive results. The US, Canada and Australia seem to be riskier than most emerging market regions, but that says more about the risk measure than it does about companies in these countries, as we will argue in the next section. If you want to see these risk measures on a country basis, try this link.

Pluses and Minuses
The high/low risk measure is simple to compute and requires minimal data, since all you need is the high price and the low price for the year. It is even intuitive, especially if you track market prices continuously. It does come with two problems. The first is the flip side of its minimal data usage, insofar as it throws away all data other than the high and the low price. The second is a more general problem with any price based risk measure, which is that for the price to move, there has to be trading, and markets that are liquid will therefore see more price movements, especially over shorter time period, than markets that are not. It is therefore not surprising that US stocks look riskier than African stocks, simply because liquidity is greater in the US. So, why bother? If you are comparing stocks within the same liquidity bucket, say the S&P 500, the high-low risk measure may correlate well with the true risk of the company. However, if your comparisons require you to look across stocks with different liquidity, and especially so if some are traded in small, emerging markets, you should use this or any other price-based measure with caution.

Standard Deviation/Variance
If you have data on stock prices over a period, it would be statistical malpractice not to compute a standard deviation in these prices over time. Those standard deviations are a measure, albeit incomplete and imperfect, of how much price volatility you would have faced as an investor, with the intuitive follow up that safer stocks should be less volatile.

Returns on Stocks
As with the HiLo risk measure, computing a standard deviation in stock prices, without adjusting for price levels, would yield the unsurprising conclusion that higher prices stocks have higher standard deviations. With this measure, the scaling adjustment becomes a simpler one, since using percentage price changes, instead of prices themselves, should level the playing field. In fact, if you wanted a fully integrated measure of returns, you should also include dividends in the periods where you receive them. However, since dividends get paid, at most, once every quarter, analysts who use daily or weekly returns often ignore them.

To compute and compare standard deviations in stock returns across companies, I have to make some estimation judgments first, starting with the time period that I plan to look over to compute the standard deviation and the return intervals (daily, weekly, monthly) over that period. I use 2-year weekly standard deviations for all firms in my sample, using the time period available for companies that have listed less than 2 years, and the distribution of  annualized standard deviations is in the graph below.
Data at country level  
As with the HiLo risk measure, and for the same reasons, the US, Canada and Australia look riskier than most emerging markets. Again, I report on the regional differences in the table embedded in the graph, with country-level statistics available at this link.

Pluses and Minuses
It is Statistics 101! After all, when presented with raw data, one of the first measures that we compute to detect how much spread there is in the data is the standard deviation. Furthermore, the standard deviation can be computed for returns in any asset class, thus allowing us to compare it across stocks, high yield bonds, corporate bonds, real estate or crypto currencies. To the extent that we can also compute historical returns on these same assets, it allows us to relate those returns to the standard deviations and compute the payoff to taking risk in the form of Sharpe ratios or information ratios.
Sharpe Ratio = (Return on Risky Asset - Risk free Rate)/ Standard Deviation of Risky Asset
That said, the flaws in using just standard deviation as a measure of risk in investing have been pointed out by legions of practitioners and researchers.
  1. Not Normal: The only statistical distribution which is completely characterized by the expected return and standard deviation is a normal distribution, and very little in the investment world is normally distributed. To the extent that investment return distributions are skewed (often with long positive tails and sometimes with long negative tails) and have fat tails, there is information in the other moments in the distribution that is relevant to investors.
  2. Upside versus Downside Variance: One of the intuitive stumbling blocks that investors have with standard deviation is that it will higher if you have outsized returns, whether they are higher or lower than the average. Since we tend to think of downside movements as risk, not upside, the fact that stocks that have moved up strongly and dropped precipitously can both have high standard deviations makes some investors queasy about using them as measures of risk.
  3. Liquidity effects: As with the high low risk measure, liquidity plays a role in how volatile a stock is, with more liquid stocks being characterized with higher standard deviations in stock prices than less liquid ones.
  4. Total Risk, rather than risk added to a portfolio: The standard deviation in stock prices measures the total risk in a stock, rather than how much risk it adds to a portfolio, which may make it a poor measure of risk for diversified investors. Put differently, adding a very risky stock, with a high standard deviation, to a portfolio may not add much risk to the portfolio if it does not move with the rest of the investments in the portfolio.
In summary, the combination of richer pricing data and access to statistical tools has made it easier than ever to compute standard deviation in prices, but using it as your sole measure of risk can lead you to make bad investment decisions.

In the graph on the effect of diversification on portfolio risk, I noted that the key variable that determines how much benefit there is to adding a stock to portfolio is its correlation with the rest of the portfolio, with higher and more positive correlations associated with less diversification benefit. Building on that theme, you can measure the risk added by an investment to a diversified portfolio by looking at how it moves in relation to the rest of the portfolio with its covariance, a measure that incorporates both the volatility in the investment and its correlation with the portfolio.
This equation for added risk holds only if the investment added is a small proportion of the diversified portfolio, but if that is the case, you can have a risky investment (with a high standard deviation) that adds very little risk to a portfolio, if the correlation is low enough.

Standardized Measure (Beta)
The covariance measure of risk added to a portfolio, left as is, yields values that are not standardized. Thus, if you were told that the covariance of a stock with a well diversified portfolio is 25%, you may have no sense of whether that is high, low or average. It is to obtain a scaled measure of covariance that we divide the covariance of every investment by the variance of the portfolio that we are measuring it against:

If you are willing to add on whole layers of assumptions about no transactions costs, well functioning markets and complete information, the diversified portfolio that we will all hold will include every traded asset, in proportion to its market value, the capital asset pricing model will unfold and the betas for investments will be computed against this market portfolio. Note though, that even if you are unwilling to go the distance and accept the assumptions of the CAPM, the covariance and correlation remain measures of the risk added by an investment to a portfolio.

If you already are well versed in financial theory, and find the lead in to beta in this section simplistic and unnecessary, I apologize, but I think that any discussion of the CAPM and betas very quickly veers off topic into heated debates about efficient markets and the limitations of modern finance. I think it is good to revisit the basics of the model, and even if you disagree with the model's precepts (and I do not think that there is anyone who fully buys into all of its assumptions), decide what parts of the model you want to keep and which ones you want to abandon. Since the key number that drives the covariance and beta of an investment is its correlation with, I report on the global distribution of this statistics:
Data at country level 
Unlike the high low risk measure and the standard deviation, where my estimation choices were limited to time period and return interval, the correlation coefficient is also a function of the index or market that is used to compute it. That said, the distribution yields some interesting numbers that you can use, even as a non-believer in the CAPM. The median correlation for a US stock with the market is about 20%, and if you check the graph for savings, that would imply that having a portfolio of ten, twenty or thirty stocks yield substantial benefits. As you move to emerging markets, where the correlations are even lower, especially if you are a global investor, the benefits become even larger. Again, if you want to see this statistic on a country-by-country basis, try this link.

Pluses and Minuses
If you have bought into the benefits of diversification and have your wealth spread out across multiple investments, there is a strong argument to be made that you should be looking at covariance-based measures of risk, when investing. If you use a beta or betas to measure risk in an investment, you get an added bonus, since the number is self standing and gives you all the information you need to make judgments about relative risk. A beta higher (lower) than one is a stock that is riskier (safer) than average, but only if you define risk as risk added to a portfolio.

I use covariance based measures of risk in valuation but I recognize that these measures come with limitations. In addition to all of the caveats that we noted about liquidity's effect on price based measures, the most critical ingredient into covariance is the correlation coefficient and that statistic is both unstable and varies over time. Thus, the covariance (and beta) of the stock of a company that is going through a merger or is in distress will often decrease, since the stock price will move for reasons unrelated to the market. As a result, the covariance measures (and this includes the beta) have substantial estimation error in them, which is one reason that I have long argued against using the beta that you get for one company with one pass of history (a regression beta) in financial analysis.  What can you do instead? Since covariance and beta are measures of risk added to a portfolio, they..
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I am convinced that each of us is granted moments of grace, where, if we are open to the possibility, we find out what we are meant to do with our lives. For me, one of those moments occurred in the second year of my MBA program at UCLA, when, cash poor, I decided to be a teaching assistant for a quarter to earn some money. At the time I made that decision, my plans were typical of many of my MBA cohort, to get a job in consulting or investment banking, and to make my work up the corporate ladder, but the day that I walked in to teach my first session, I knew that I had found my calling. I was going to be a teacher, though I was not sure what I would be teaching, or to whom. As fate would have it, I found myself fascinated by finance, and I ended up as a finance professor at NYU's business school. I have never regretted that choice, but when asked to describe what I do, I still tell people that I am a teacher, not a professor, a researcher or an academic.

Back to the Classroom!
Starting in 1986, I have been teaching almost every semester at Stern, but I have had a break of almost a year and a half from my class room teaching, the first year representing a long-delayed sabbatical and the last half year reflecting a choice that I made to do all my teaching in one semester this academic year (2018-19). During that period, I continued to teach my short-term (2 to 3 day) classes in different parts of the globe, and while I have enjoyed these visits immensely, I have missed my regular classroom. I am therefore looking forward to a new semester and three new classes this spring, a corporate finance class that I teach, primarily to first year MBAs, a valuation class, an elective for mostly second year MBAs, and another valuation class for undergraduates in their sophomore, junior and senior years. If you are not at Stern, you will not be able to sit in the class  but through the wonders of technology, you can still take these classes. With no further ado, let me describe them and offer you the choices.

Corporate Finance (MBA)
If there is one class in finance that everyone, no matter what their paths in life or business may be, should take, it is corporate finance. Corporate finance is a class that covers the first principles that govern how a business should be run and its reach is complete. Every decision that a firm makes is ultimately a corporate finance decision, no matter which functional area (marketing, production, personnel) it originates from, and that is the perspective I take in the class. I teach the class around what I call my big picture page, where I classify business decisions into investing, finance and dividend groupings and frame how to make those decisions with an end objective of increasing the value of the business.
Class webpage
You will notice chapter numbers and sessions under each topic, with the chapters representing chapters in my Applied Corporate Finance book, a book that I loved writing but one that is so hopelessly over priced that I do not require it for my own class, and the sessions showing the sequence of the class through the 26 sessions that start on February 4, 2019 and end on May 13, 2019. The class meets every Monday and Wednesday during this period, barring the break week of May 16-23, and the syllabus for the class can be found at this link. If you cannot be in these classes in person, don't fret since the classes will be recorded and be available for you to watch, not in real time, but about 2-3 hours after each class is done. To follow along with the webcasts (each about 80 minutes long), you can also access the slides that I use for each class, as well as additional material. Finally, I demand a great deal of my class (weekly puzzles, add on videos, exams and a project) and if you want, you can also do the puzzles, take the exams and do the project, though you will have to grade yourself (with a template that I will put online). You can even read the emails I send my class, and I send about a hundred over the course of a semester, at this link. If you prefer your videos on YouTube, you can try the playlist for the class, and if your preference is for an iTunes U version, this link should take you to the site. The good news is that it will cost you nothing (other than your time and perhaps a few relationships) but the bad news is that you will not get any official certification, if that is what you are looking for.

Valuation (Undergraduate and MBA)
I have a fondness for this class, since I created and taught the first full-semester version of it, at any business school, in 1987.  I was told then that there was not enough "stuff" in valuation to fill a class, and while that might have been true at that time, I have found plenty to fill in the gaps since. As the title of the class indicates, this is a class about valuation. Valuing what, you might ask, and my answer would be "just about everything" from stocks to bitcoin to the Kardashians. The picture below captures the broad reach of the class:
Class webpage
As I teach it, this is a class that is not only about valuing assets but also pricing them (I am afraid that you have to sit in on the class to find out the difference) and it looks at valuation/pricing from a variety of perspectives (investors looking at a stock, managers using value to guide decision making and even accountants writing disclosure and accounting rules). As those of you who read my blog know, my fidelity is to intrinsic value, but I try to keep an open mind on different perspective and approaches in this class.

As with the corporate finance class, we will meet every Monday and Wednesday for 14 (15) weeks, starting February 4 (January 28) for my MBA (undergraduate) class. If you are wondering which version to follow, I will save you the trouble, since the classes are identical in content and delivery, since I don't believe that there is any reason why I should challenge a bright 21-year old less than a bright 28-year old; age and work experience can give the latter more perspective but this is often offset by the extra energy and curiosity that youth brings to the table. The links that you can use to follow the class are in the table below for both versions of the class:

Webcast pageYouTube PlaylistiTunes U classStartsEnds# Sessions
MBA Valuation
Undergraduate Valuation

With both versions of the valuation class, I will also be posting what I call my valuation of the week, a company that I will value, with links to the excel spreadsheet and the story behind the value. I encourage you, if you are taking the class, officially or unofficially, to take my valuation and make it your own, changing the story and the inputs, and then recording your valuation in a shared Google spreadsheet. In a world where crowds decide what movies are successes (Rotten Tomatoes) and which restaurants we eat at (Yelp reviews), we can create our version of crowd valuations. It is an optional exercise, but the more people who participate, the more fun that we can have.

Other Options
I am under no illusions that you are sitting around, wherever you are in the world, with nothing better to do than watching two long sessions each week from February through May. Watching long lecture videos on my tablet is not my idea of fun and while some of you will start with the objective of sitting in on the class, life will get in the way. There are three options that you can consider, depending upon your constraints:
  1. If time is your constraint: One of the advantages of taking the class or classes online is that you do not have to do finish the class in May 2019. In fact, the webcasts for the class will stay on for at least another year after the class ends. So, if you like the long class format, you can stretch the class out for longer, if all you need is more time.
  2. If format is your concern: If you find your attention lagging or your brain decomposing because the lectures are too long, I have created online versions of both classes (plus a third one on investment philosophies), where I have compressed my 80 minute sessions into 12-15 minutes each. Without giving away any trade secrets, and at the risk of discounting the value of an MBA, it was not difficult to do. As with the regular classes, these are still free, still come with slides and post class quizzes but offer no official certification.
  3. If you want accreditation: Even if you take my classes online religiously, mastering every nook and cranny of the topic, and acing every quiz, I do not have the bandwidth or the authority to hand out accreditation or certificates. Three years ago, I remedied this, with the help of NYU, by creating certificate versions of the online classes (with shorter duration videos). The pluses are that the videos are more polished than the ones I created for the free version, there is more administrative support and an active message board where you can chat with others taking the class and you will get a certificate at the end of the class. I will also, at least for the foreseeable future, also do live hourly WebEx sessions once every two weeks and grade your  projects.  The minus is that NYU does not give away certificates for free and if you get sticker shock, please don't make me your target. The decision on whether the certificate is worth the fee is yours to make, and the links to both the free and the NYU certificate versions are below.

Online classNYU Certificate Online class
Corporate Finance
Investment Philosophy

Finally, you are always welcome to pick the parts of each class that interest you and ignore the rest. The end game is learning, and what interests me may not interest you.

Bottom Line
I know that there are some who say that those who can, do, and those who cannot, teach, and I have been told that or variants of it multiple times. I don't mind the insult, since I have a thick skin, but I know that there is nothing else in the world I would rather do. I answer to no one (other than my wife), pick when or where I work (for the most part), get to chance to change how people think and make a decent living. If your desire is to manage other people's money, be an equity research analyst or investment banker, or to start and run your own company, I wish you the very best, but I am lucky to be doing what I love, and I would be foolish to trade it in for more money or prestige. At the risk of recycling a cliche, I have only one life to live!

YouTube Video
Back to Class: A Teaching Manifesto! - YouTube

Class Links
a. Full Semester Classes (Spring 2019) (Free)
  1. MBA Corporate Finance Class (Spring 2019) (Free)
  2. MBA Valuation Class (Spring 2019) (Free)
  3. Undergraduate Valuation Class (Spring 2019) (Free)
b. Online Classes (Free)
  1. Online Corporate Finance Class (Free)
  2. Online Valuation Class (Free)
  3. Online Investment Philosophies Class (Free)
c. NYU Online Certificate Classes (Not free!)

  1. NYU Online Corporate Finance Certificate Class
  2. NYU Online Valuation Certificate Class
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