Nothing Lasts Forever, Perpetuities and Terminal Values

I've done a review previously of geometric sequences and series, as a prelude for explaining perpetuities (the DDM is a form of growing perpetuity to determine a price in today's dollars).

I'll probably be doing a lot of valuation modeling at my equities research position over the next two months, so I though I would posts some thoughts on the techniques and methods regarding the basics of modeling (with my posts becoming more sophisticated as I become more sophisticated).

Technically speaking, a stock is a form of perpetuity (with the incremental value as the earnings per share). Most models assume that the company will exist forever and discount the earnings flows to come up with a price for the asset. In the current climate of bankruptcies, anyone would be naive to believe this is the case any more (if it ever was).

However, in private equity this isn't always the case (in fact it often isn't), as firms will buy undervalued companies (or companies in which they plan on making management or strategy changes) in an attempt to flip the company (buy it, fix it up and sell it) for higher exit multiples.

In modeling, there are different reasons for creating terminal values. It simplifies the valuation process (rather than calculating 10 more years of earnings growth estimates, you can boil it down to one number to represent the value of the earnings of the remaining years) or if you plan on selling the company, you can model a target exit price.

Game Theory Foundations: Production-Possibility Frontiers

The next concept relating to efficiency is the idea of production-possibility frontiers. This is the idea that given a limited amount of resources and accounting for systematic diminishing returns, that there is some limit where you cannot create more of one product without sacrificing another. In the simplest case, this is described as a curve on a graph with two axis each reflecting one product (a more complicated model with more products can be represented with more dimensions in a multi-dimensional model, but is beyond the scope of this discussion).

The most popular form of this model includes the Guns or Butter model as well as the efficient frontier in market portfolio theory.

In the Guns or Butter model, a government has the choice of spending its resource on foreign or defense projects (Guns) versus domestic or civilian projects (Butter). With a limited budget, there is some limit where in order to get more of one, they have to sacrifice production of the other. Plotting the points along this curve produces the production-possibility frontier.
Excusing the violent association with the "Guns" component, it is possible to instead substitue the idea of exportable goods and globalization which affect the balance of trade between countries (a topic for another time).

An efficient frontier in market portfolio theory describes a securities portfolio which includes securities in the most efficient weights and correlations such that the portfolio exhibits no un-systematic risk and is composed entirely of non-diversifiable risk (Capital market line - CML). Here the frontier is presented a little differently with the resource simply being combinations of different securities betas versus their expected return to form the efficient frontier (which intersects with the investor's marginal utility curve to determine the efficient market portfolio).

It seems like everywhere we go we naturally run into these frontier limits. How can we describe them in game theory? As it turns out, there are some models which describe behaviour in different stages of game theory.

Positions on the efficient possibility frontiers can not produce more of one benefit without sacrificing another. In game theory, this manifests as a zero-sum game. That is to say for one participant to gain (show on the production possibility frontier as one axis), another has to lose out).

Points contained within the curve (but not on the curve) allow for gains of one benefit or the other without having to make any sacrifices. This is represented in game theory as a non-zero sum game. That is to say, that at the end of the day, it is possible for both parties to benefit positively without the expense of the other.

You'll notice that the theme here is one of efficiency. In an environment where no more benefit can be extracted from the system with out additional resources (maximum efficiency), it becomes a zero-sum model. However, if production is inefficient, there is potential for a non-zero sum model (recouping the inefficientcy as non-zero sum gains - getting more of A without comprimising B).

This is also an indicator of efficiency and competition. In an industry with a maturing life cycle, transactions, deals and strategy will slowly being to have less non-zero sum models.

Game Theory Foundations: Economies of Scale or Diminishing Returns?

Before we start out foray into game theory, I'd like to do a quick review of economic efficiency framed as economies of scale versus diminishing returns for growing enterprises. In the examples provided by economics textbooks, they will often express diminishing returns as using less efficient resources in order to produce the same task (which reflects a decreasing marginal utility / benefit / revenue).

However, in the abstract, we are also told about economies of scale, where adding staff and capacity can result in productivity gains beyond what is expected (Specialization of tasks and the Model T assembly line strategy). In evaluating a scenario, how can we tell which stage we are in?

The best way to understand your efficiencies is by understanding the production bottle necks of your current factors of production. That is to say that you can fight off diminishing returns if you add resources to the weakest link of your system (similar to the idea of critical path of a PERT chart). While adding resources in general will cause you to gain diminishing returns in the one production line, it should create synergies that recoup the drop in efficiency.

Now, if you are sensitive to seemingly meaningless buzzwords like "synergy" which tend to be overused, you'll probably recoil a little as I did upon hearing that word so let's break it down to less abstract terms with an example.

Example: A factory has 200 workers working on 20 machines. The optimal ratio of workers to machines is 12 to 1 for the purposes of scheduling and capacity planning. Although adding the 21st machine will bring some benefit (versus not having the machine at all), it is clearly diminishing versus adding the 3rd machine. In this scenario, adding another 40 workers would help bring the worker / machine level up to its target concentration. Note that beyond that, adding another worker begins to diminish the benefit of workers and the value of adding a machine starts to increase again.

Now assume that you have a limited number of resources to apply to your production. What mix of workers to machines will you have?
This introduces the idea of production-possibility frontiers which we will discuss in the next post.

Game Theory - An "Emerging" Field of Study and Interest

While game theory, the study of strategic interactions, has been a field of study in social psychology for sometime, it has become an increasingly important field which on which management science has recently begun to focus on. Particularly, the logical analysis of decision making processes to optimize success as defined within the model.

While the CFA has introduced the idea in the Economics portion of their level I curriculum, I thought that it would be valuable to look beyond what is presented there (including the "optional" sections) and how using game theory can predict strategic level behaviours.

First, the basics, we are familiar with the Hawk-Dove model (a game of chicken) which I used in my investment blog to describe the benefits and pitfalls awaiting investors hoping to gain first movers advantage in the market. I've also used the Prisoner's Dilemma to describe OPEC and Oil.

However, what is what oversimplifies these two examples of game theory is the assumption that they occur only once. That is to say that these models only look at a particular snapshot in time. Whereas we know that the game continues to be played and is modeled by a series of events rather than one discrete iteration. Also, the models used to describe these scenarios are simple 2x2 matrices. As we start to remove some of the assumptions, we will also begin to look at more flexible (and therefore complex) models.

In the next couple of posts and into next week, I will focus on a series of posts aiming to look at more involved cases of game theory and how they can be used to model strategic business behaviour.

Molson Canadiens

One of the preeminent Canadian families (and household names), the Molson family, famous for founding one of the few remaining pure big Canadian brewers (with the purchase of Labatt by InBev a few years ago) recently announced their purchase of the Montreal Canadiens, a legendary hockey team and staple of Canadian hockey and history.

The Provence of Quebec was reported to offer a loan of $100M for any Quebecois who were interested in purchasing the team. I can't blame them. It would be an absolute travesty if the Canadiens were purchased by anyone else.

With all the turmoil, in the markets, one wonders if now is the best time to be buying a hockey team. Maybe people are getting good prices? My former boss, RIM Co-CEO Jim Balsillie is constantly in the papers fighting to try to acquire a team for Hamilton (most recently focused on the Phoenix Coyotes), was turned down by a recent court decision, but encouraged by the judge to pursue other avenues to get his team (according to his legal team's public statements). It seems like he'll get his team eventually... The guy is persistant for certain. We used to joke at RIM that we'll be selling hocket tickets along with BlackBerrys.

While there are the Maple Leafs near by (and I'm not much of a hockey fan) I must sympathize with Toronto hockey fans who aren't getting the team they deserve. Although a good team, the Leafs are notorious for not really getting anywhere because their fan base always fills the seats. There is apparently no motivation for the team (except in the most recent year) to pick up the game a little to keep the fans. The fans feel like they deserve better and maybe Jim B's big has shaken them up a bit. The threat of competition usually does.

End of an Era, RIP Nortel

Yesterday, Nortel announced that it will be selling it's wireless division to Nokia-Siemens for $650 million. It's noted that Nortel's wireless division is it's most valuable asset and that Nortel has plans to sell of it's other divisions as well as it liquidates its assets for bankruptcy.

This is also a good lesson in debt tranches, as although Nortel is liquidating it's assets, there isn't enough to cover the entire debt load (as is usually true with all bankruptcies). As a result, some debt holders will get heavily reduced value back for the Nortel debt they hold (and some none at all - the junior debt holders - preferred shares etc.). In this case, the obvious debt holders (from a finance perspective) are the holders of bonds and preferred shares etc, but also don't forget suppliers to Nortel (for instance, one of the larger holders of Nortel debt is reported a company which buys ad time for Nortel). After all, Accounts Payable is a fairly senior debt tranche.

This is in contrast to a restructuring in which "everyone gets a haircut" and holders of all forms of debt get some reduction. The idea is that there is a hope of recovery and everyone can get "something" back. However, in a bankruptcy, there is no illusions and the company is packing its things and closing shop.

Other notable points is that Nortel has made the sale contingent upon their employees of that division being given jobs with Nokia Siemens. In this scenario, where the division is actually valuable, it's isn't a bad thing. Generally, when buying parts of a failing company, there is usually an option to only take on the parts that you need. It's a fancy and seemingly cruel way of saying that an acquiring company can pick up only what they want in the sale (talent, equipment, intellectual property etc) and I think it makes sense. After all, with all due respect, the reason we are buying your division (especially in bankruptcy) is because there is something in it that doesn't work and we hope to fix (or "synergize" with our existing business). Buying things "as is" is generally not a good idea (especially in bankruptcy). However, as stated, this is one of the best chunks of Nortel, so it's forgivable in this circumstance.

Otherwise, it's usually a good reason to consolidate costs (systems, labour etc) and pick the best talent from both sides of the fence (as Jack Welch is such an avid proponent of). Yes, this implies possibly letting go of some of your own (his fifth sin of M&A - the "conqueror syndrome").

Nortel will be delisted, with it's final stocks closing price at 18.5c from highs in 2000 in the $120s. Look for Nortel stock certificates soon in Toronto convenience stores as souvenirs (just like Bre-X a few years back).

Understanding LIFO Reserve

I'm going to continue to post more CFA related topics from Level I. Although the exam is over, there might be people interested in prepping for Dec, or who possibly stumble upon this blog in later years, but it doesn't hurt for me to try to keep sharp.

If you were like me during the CFA exam, even simple concepts can seem confusing under pressure. One such example for me was the idea of LIFO reserve. Particularly, I often found it confusing to remember when I should use LR or the change in LR to answer questions (when the correct answer is one, the CFA will often have the other as an incorrect answer for those of us not paying attention).

After taking a quick review of the tools to understand the concepts relating to LIFO versus FIFO, some CFA questions require you to understand how the accounting differences of each method affect the balance sheet and income statement and state by how much an account is expected to change or what the ending balance should be.

Firstly, LIFO reserve is defined as the difference in the inventory value if it was stated using FIFO versus LIFO or in other words:

LIFO Reserve (LR) = Inv FIFO - Inv LIFO

Note that LR is cumulative over the life of the company, that is to say that LR is a reflection of financial position which would be reflected in the balance sheet (along with inventory as an asset). So when dealing with financial position, use LR as an absolute value to determine the appropriate adjustment to the inventory.

So when would you use the change in LR? The change in LR reflects what has happened in the year to inventory. For example, if in the most recent year, assume that you purchased 200 units of product but only sold 150 units. Assuming that prices are generally increasing, your LR would go up. Conversely, if you had purchased 150 units, but sold 200 (dipping into your inventory) your LR would go down (selling some of the older, cheaper inventory). Therefore, you can determine that the amount that your LR changes would be reflected by the purchases of inventory versus COGS. Also note:

ΔLR = COGS LIFO - COGS FIFO ✠

✠ Note that the key word here is "change". Anything that involves a "change" (implying activity in the year) it always has to do with the income statement (ie using the change in AP, AR, Inv, WC etc in the indirect method to determine cash flow from Net Income). Same goes with accounting for the LR. Also note that in this formula, the LIFO term is first.

[Example] Your company makes the following purchases and sales each year (in order):

1. 2009 - Buy 100 units @ $50
2. 2009 - Sell 90 units*
   
3. 2010 - Buy 150 units @ $55
4. 2010 - Sell 155 units*
   
5. 2011 - Buy 200 units @ $60
6. 2011 - Sell 190 units*

What is the COGS, Inv and LR for each year under LIFO and FIFO?

* Just a quick note, we don't really care what the price they are sold at is (we are just accounting for COGS, Inv and LR. If we wanted to know revenue we would want price, but it's out-of-scope for now.

Also note that the number of units in inventory under each method *is the same*. The reason for the difference in inventory value is how you account for their worth.

[Solution]
Dec 2009 (steps 1 and 2)
FIFO
COGS = 90 units x $50 = $4500
Inv = 10 units x $50 = $500

LIFO (same as FIFO)
LR = 0**

**LR is 0 because our inventory is uniform (that is to say we've only paid one price per unit so far so the accounting under LIFO and FIFO is the same).

Dec 2010 (steps 3 and 4)
FIFO
COGS = (10 units x $50) + (145 units x $55) = $500 + $7975 = $8475
Inv = 5 units x $55 = $275

LIFO
COGS = (150 units x $55) + (5 units x $50) = $8250 + $250 = $8500
Inv = 5 units x $50 = $250
(Note you are dipping into your inventory here a little bit).

LR = Inv F - Inv R = $275 - $250 = $25***

***Note also that ΔLR = COGS L - COGS F
(Also note that since LR = 0 last year, ΔLR = LR)

Dec 2011 (steps 5 and 6)
FIFO
COGS = (5 units x $55) + (185 units x $65) = $275 + $11,100 = $11,375
Inv = 15 units x $60 = $900

LIFO
COGS = (190 units x $60) = $11,400
Inv = (5 units x $50) + (10 units x $60) = $250 + $600 = $850

LR = Inv F - Inv R = $900 - $850 = $50 ✝

✝ Note that LR has gone up by $25 from last year. ΔLR = $25 also note ΔLR = COGS L - COGS F = $11,400 - $11,375 = $25. Two different methods. Same result.

[Aside] One question that I wonder is if it's possible to have a negative LR. This could theoretically happen in the case where prices are falling, it's not unreasonable to expect Inv F to be less than Inv R. What happens then? Mathematically, it's possible, but from a regulatory stand point something looks funny. I'd anticipate that there is probably some accounting rule that doesn't allow negative LR (or requires you to restate under FIFO). I'll have to look into it.

New York Internship - Equities Research

I apologize for the lack of updates recently. I've been taking some extended downtime following the CFA exam. Also, I've been offered an internship with an Equities Research firm in New York and I'll be starting in early July staying 'til late August. They've already sent me the training schedule so I am very excited to get started.

Admittedly, however, finding accomodation in NYC has proved quite challenging as I am unable to visit locations before I arrive and people tend to be a bit weary of an international traveller who they've never met who offers to take a room they've never physically seen and pay the rent in full in cash upfront (I don't have a USD checking account and bank drafts cost $7.50 + $13+ to send via Canada Xpress Post).

There have also been a few Rotman events as well as mild preparation for the upcoming school year (I have to do it now as I'll be away for the bulk of the summer).

Demand Elasticity - Who pays?

In high school, through university and even in the CFA, economics is an important field of study. One of my favourite topics is the concept of elasticity.

Elasticity is literally defined as the percentage change in quantity over the percentage change in price and has several flavours (negative elasticity, positive elasticity for substitutes, negative cross elasticity for complements etc)

Elasticity = %ΔPrice / %ΔQuantity
%ΔPrice = ΔPrice / Pavg = P1 - P2 / Pavg
%ΔQuantity = ΔQuantity / Qavg = Q2 - Q1 / Qavg

Mathematically, note that as you move up and down the curve, the elasticity changes because percentage is affected by the absolute value of the average price. If the average price falls, the elasticity increases because the change becomes larger relative to the average to which it is compared for percentage purposes.

Another way of looking at elasticity is flexibility or bargaining power. If you review Michael Porter's five forces, you can see that elasticity for suppliers or customers increases their bargaining power. That is to say, the more competition and choices available means more options.

Let's look at a good which exhibits perfect inelasticity. This means that regardless of the price, consumers will always consume a constant amount (they set the quantity demanded). This manifests in a horizontal demand curve as shown below:

Note that the determining factor of the price is the supply curve. If there are more suppliers, the supply curve shifts right and the price drops. If there are less suppliers, the supply curve shifts left and the price rises. This is similar to what happens with oil and the "prisoner's dilemma" in OPEC's oligopoly.

Next, look at a perfectly elastic curve. This means that given the slightest change in price, the consumers will dramatically change their spending habits (that is to say, that consumers set the price). This manifests as a horizontal demand curve (at the price they set).
The only power suppliers have here is to set the quantity sold (they are price takers). If there are more suppliers, the supply curve shifts right and there is more quantity sold. Visa versa, if there are less suppliers the supply curve shifts left and there is less quantity sold.

This is important when determining how price changes will affect measures like total revenue, quantity consumed etc. This also applies regardless of whether you are talking about goods sold, wages paid, taxes paid etc.

[Example] The government is thinking of applying a tax on a good which exhibits perfectly elastic demand. Who bears the cost?

1. The supplier
2. The customer
3. The supplier and the customer share the tax burden

[Solution] One way to look at this is that if the good exhibits perfectly elastic demand, then the customers have all the bargaining power. This means that if any supplier were to simply "pass along the tax" and make the consumer pay, the consumer would just go to a different supplier. This means the supplier is forced to take on all the tax. The solution is 1. Notice this also means it eats into the producer surplus.

If the good were perfectly demand inelastic, the suppliers have all the bargaining power then the customer would bear all the tax and the solution would be 2. This would eat into the consumer surplus.

If the good were neither perfectly demand elastic or inelastic, the supplier and customer would split the difference in fractions based on who had more relative bargaining power. Both producer and consumer surplus would diminish. The solution would be 3.

Cash Flow and Operating Cycle

I've written about cash flow with queuing theory as the lifeblood of business in my blog, as well as activity (operations) ratios in my financial profitability analysis series on my investment blog, but I wanted to review an interested concept in the CFA level I regarding the cash conversion cycle.

First let's do a review of the tools and topic. Firstly, what affects operations from a cash flow perspective? Using the direct method, the operating items which affect cash flow is change in working capital and the three items that affect that is Accounts Payable (AP), Accounts Receivable (AR) and Inventory (Inv). Now let's look at a standard process for how changes in each affect the operating cycle.

Order of Operations (like the BEDMAS of elementary arithmetic):

1. Purchase supplies from vendor on credit (AP up, Inv up)
   
2. Process supplies into goods for sale
3. Sell products on credit (Inv down, AR up)
4. Pay back supplier (AP down, cash down)
5. Receive payment from customers (AR down, cash up)

Notice that you don't actually receive any cash until step 5, but you have to pay it back in step 4. This means that you have a negative cash flow until you complete the cycle.

Recall that in the indirect method (calculating CFO from NI):

• If more inventory is made than sold, some "cash value" is retained in Inventory (Inv up, cash down)
• Alternately, if more inventory is sold than made, then you are liquidating your inventory (Inv down, cash up)
• An increase in AP means that you owe your supplier more money. This means that instead of paying with cash, you paid with credit so your cash flow goes up
• A decrease in AP therefore means you paid back your debts
• An increase in AR means that your customers paid you with credit so your cash flow goes down
• A decrease in AR therefore means you were paid back (collected on sales on account)

This next little diagram illustrates the relationship between Operating Cycle, DOH, DSO, Days Payables and Cash Conversion Cycle:
Operating cycle is simply the time it takes from when you purchase supplies to when you collect the cash and is composed of two components, Days Inventory on Hand (DOH) and Days Sales Outstanding (DSO).

• Days Inventory on Hand includes the manufacturing process, as well as storage. In accounting terms, this means works-in-progress (WIP), finished goods, sales cycle.
• Days Sales Outstanding is the time between sales on credit and the collection of cash.
• Cash conversion cycle is the time between when you pay your vendor to when you yourself collect cash. It is the difference between operating cycle and Days Payables.

In looking at which company is more likely to have cash flow problems, cateris paribus, it would be the company with the largest cash conversion cycle. That is to say, it has a low Days Payables (bills due sooner - cash out), but a long Operating Cycle (takes really long to produce and sell goods as well as collect on credit - cash in). So the larger the cash conversion cycle, the worse the operational and implicit structural liquidity.

CFA Exam Results

Now that I've written the CFA exam, I'm awaiting the results (which apparently take as much as 60 days to release for the level I exam). Under the assumption that I've passed, I had a peek at the Level II material shown on the website based on the learning outcome statements (LOS) outline as well as the sample questions and mock exam sample provided on the website.

Suddenly, the level I looks easy, as the level II concepts are quite involved, including even such topics as multi-variate regression analysis (reminds me of Math 3K03 and Comp Eng 3SK4 in university which were both pretty challenging).

I now have to make the decision as to whether I will register to be a Level II candidate in June. I would really like to progress on, but don't want to over load myself during my MBA. Knowing me, though, I'll probably end up signing up almost immediately after I get my results.

Meet the Dean - Roger Martin and Integrative Thinking

I figure I'll take a short CFA study break to write about an encounter I had at the Meet the Dean session at Rotman early last week. I thought it was an invitational event for those of us who were accepted, but it turns out there were some people who were still applying, waiting for acceptances or deciding.

Dean Martin spoke about how Rotman is different from other MBA programs and for once, I was actually impressed with the Rotman presentation. This may seem kind of odd, coming from someone who has already "sampled" the proverbial kool-aid so to speak by accepting my offer letter to start in September, but the truth of the matter is that I was more sold on Rotman by my colleagues and friends currently enrolled (or graduated) than I was from the Faculty administration. I'm quite embarrassed to say that the admin simply made it seem like just an MBA program whereas my friends were raving about their experiences.

The reason I bring up this point is that Dean Roger Martin brought it up and addressed it as well. Now from ANY MBA program, you would expect some pomp and circumstance regarding why their program is so fantastic. One of the major issues facing MBA programs today is their incremental value add. For instance, there are some top schools for which recruiting companies have stated they would rather hire students who were accepted, rather than students that had graduated. The reason? Top schools who accept good candidates are simply validating their position as top performers, whereas the marginal benefit of attending a top school doesn't necessarily justify the exorbitant increase in salary.

Dean Martin reframed this postulate as top schools resting on their laurels and not affecting the changes required by society in light of the financial crisis in the markets. He put up a rather simple diagram of a three dimensional box with the dimensions described as depth, breadth and flexibility. He called the current state of MBA education, shallow, narrow and static where it should be deep, broad and dynamic. I can't remember who he was quoting off hand, but he mentioned: "There aren't marketing or finance problems. Only business problems" (reflecting the interdisciplinary relationships).

He used the example of the Blacks-Scholes models for derivatives valuation and that stated limitations in the model made it inappropriate for use in many circumstances. However, this model is widely used in ALL derivatives valuations and therefore leaves models with large vulnerabilities in their assumptions.

The punch line?

Integrative thinking is a framework which systematically creates people who ask the right questions to make the right decisions.