Being Made Whole in Bankruptcy

In our discussions in our Managing Corporate Turnarounds class during our financial restructuring session, I got to thinking about what it would take to be made whole in a bankruptcy scenario. While the hard math will tell you that it is impossible in the short term (EV = 80, Net Debt = 100), I began to think back to the PIK and using a high yield to restore value in the future. So my question became this: If I hold the debt of an insolvent company, what can I negotiate to help me restore value? The most obvious solution is to renegotiate the terms of my debt which will probably result in me taking a haircut (discount) on the principal or face value of my debt. However, we’ve acknowledged that in scenarios where people become riskier, obviously the company’s related securities should bear a higher return. So my question then evolved to: If I have to take a discount of X percent, what additional spread Y would I have to earn in order to be made whole in N years. It turns out:

FV x (1 + kd) ^ N = FV x (1 – X) x (1 + kd + Y) ^ N

However, this assumes that you can break even with (or more accurately, catch up to) where your security would have been if the company had not defaulted to begin with. After playing with these numbers, however, it was quite clear that even with a small discount (say 20% discount), the spread Y had to be astronomically (unreasonably) higher in order to have any chance of being made whole relative to the standard debt, so I thought it would be unrealistic not to include a factor which accounts for the value lost:

FV x (1 + kd) ^ N = FV x (1 – X) x (1 + kd + Y) ^ N + Value Lost

In trying to understand what these numbers mean, I looked at Value Lost / FV as a proxy for the default rate of this type of security in distress which is obviously closely tied to the actual economic circumstances of the company. In the graph, it is reflected by the distance between the Standard Debt curve and the PIK (Realistic) curve.

Also, Y can probably be determined by looking at the spread between similar bonds with different credit ratings (dropping from BBB to C for instance).

X is reflective of the economic scenario (so if EV was 80 and Net Debt was 100, X would be 20%). It is also reflective of the negotiations, as well as considering a discount in order to liquidate the current assets of the company.

Another problem is also that once a company switches from PIK to cash sweep, its risk profile drops and it stops earning high yields, dropping the return on capital and therefore making it impossible to “catch up”. Also, a bank which was happy to finance your debt will not be interested in converting neither into a mezzanine structure better suited for hedge funds nor into equity.

This model is similar to the VC model of predicting the failure rate using the discount rate except in reverse. It is also similar to the interest rate parity (IRP) model and boot strapping by using compounding to determine where you would have / should have been otherwise as a benchmark for where you are going.

I guess the real lesson is that bankruptcy is really expensive and that being made whole in this scenario is difficult, regardless of the financial engineering and patience, although these two factors can be used to ease the pain.

FEI Competition

Apparently, our final round presentation for the Financial Executives International Case Competition is now available online. Unfortunately, I can't embed it into the blog, but I can include the link below:

http://www.feicanada.org/cfo-tv.php?vid=22&page=2

Enjoy!

Bid / Ask Curves

At the break in behavioural finance, I was speaking to a prop trader about the mechanics of the market. This reminded me of my short trading exercise in the Rotman Finance Lab with the Trading Simulation software.

In microeconomics, we discuss demand curves and how they are based on individuals with different levels of willingness to pay. So as the price increases due to a supply curve shift right (less supply), the quantity demanded decreases.

In markets, this is a little more transparent if you look at the bid / ask lists. These lists show the prices and volumes people are willing to buy and sell for. The other unique thing about the capital markets, is that there is actually a set number of securities (assuming that banks do not issue or buyback securities in the short term, supply is price inelastic based on total float) and that investors can be both buyers and sellers (short term suppliers and consumers) of securities. Actually, a better way to put it would be they can either hold or release securities (demand based relationship).

If their intrinsic value (IV) of a stock is above the current market price, they will buy the stock. If their IV is less than market, then they will sell. And in an exchange market, that is exactly the case (orders, unless removed before execution, are commitments to buy or sell at the stated price).

Shown here is an illustration of a “complete” market. This assumes that everyone’s IVs are included, that there are no hidden orders and that people’s opinions won’t change with the market price (a snapshot by nature). The current ask price is $8.00 and the bid is $7.75. As people’s sentiments change (or new investors are introduced into the market), orders to buy are satisfied at $8.00 and orders to sell are satisfied at $7.75. If all the potential sellers at $8.00 are taken up, then people can only buy the stock at $8.25 and the stock price goes up. Note that the differential between bid and ask is a proxy for market liquidity, as the lower the transaction fee to enter and exit a position the lower the cost of trading the security.

Also note that the steepness of the curve is a good proxy for potential volatility as well. Because if the slope of the curve is steep over a variety of prices, it means that the market doesn’t necessarily agree on the price. And if a few people cross the line from one side to another, the price can change quickly and dramatically (shown below):

Bridge to Value

One graph I've seen which I thought was clever was a breakdown of change in EV. This brings together many other details I've learned about M&A, LBO's and transactions in general.

Previously, I mentioned a framework for PE deal success, but it is easy to cut into more detail if necessary and really define and put a mathematical value to "synergies".

For example: After a transaction, we've increased sales by 21%. How does that affect EV? Well on one hand, you've immediately realized a 21% increase in revenue. After you account for associated costs with that increase in revenue (ie. You've sold more widgets, but it still costs you money to make those widgets), what do your future growth prospects look like as a result of this new growth (ie. Should you trade at a higher multiple? Have you gone from "boring" to "exciting"? Or is it just general market conditions?)

Previously, you had:

Market Cap = $100
Shares outstanding = 100
Price per share = $1

Debt = $100 (@ 5%)
Excess Cash = 0

EV = $200

Revenue - $100
COGS - $40
GPM = $60

Op Ex - $20
EBITDA = $40

DA - $10
EBIT = $30

Interest = $5

Tax = 40%

NOPAT = $18
NI = $15

Therefore:

EPS = 15 cents

P/E = ($1/$0.15) = 6.67x

EV/EBITDA = ($200/$40) = 5.00x

Let's tell a story: The 21% increase comes from opening a new line of products. You are selling 10% more products by introducing a new product line and this new product line actually increases your revenue per unit (across the board) by 10% (110% x 110% = 121%). All margins are the same.

What should we do? Bring everything down to the EBITDA level:

Now:
Revenue - $121
COGS - $44 (10% more products at same costs)

GPM = $77

Op Ex - $22

EBITDA = $55

DA - $10
EBIT = $47

Interest = $5

Tax = 40%

NOPAT = $28.20
NI = $25.20

EPS = 25.20c

(Magic happens - Which we will explain shortly)

New Price per share = $1.80

Market Cap = $1.80 x 100 shares = $180
Debt = $100
EV = $280

P/E = ($1.80) / ($0.2520) = 7.14x
EV/EBITDA = ($280 / $55) = 5.09x

Analysis:
So a lot is going on. The price of the equity and the enterprise has changed, but how can we do a cross section such that we know exactly where all the value is being driven from?

How much of this value is because of leverage (hint, we didn't change amount of leverage)?
How much of this value is simply because we are operationally better?
How much of this value is because we have a "brighter future" (better growth prospects)?

Step 1: Value from leverage arbitrage:
No change = 0

Step 2: Value from "synergies":
Total EBITDA level changes: $40 to $55 or $15
At a multiple of 5.00x (previous multiple), value increased is $75

Step 3: Value from "Brighter future"
Brighter future (higher multiple) due to either market conditions or expected future growth:
$55 at 5.00x versus at 5.09x = $55 x (5.09 - 5.00x) = $5

Total value created: $75 + $5 = $80 (note total increase in value of EV / Market Cap)

Next step, look closer at Step 2:
Change of $40 to $55 is created by:
$21 in Revenue (Price +10%, Volume +10%)
$4 in COGS (Volume + 10%)
$2 in Opex (Volume +10%)

For a $21 increase in revenue, keeping margins constant we would have expected an increase of:
$8.4 in COGS (40% of revenue) and $4.2 in Opex (20% of revenue). COGS is lower by $4.4 and Opex is lower by $2.2 versus what is expected.

Note we mentioned we can sell products for 10% more across the board.
This created value for existing product base (at EBITDA level) of
$110 - $40 - $20 or $50 versus $40 creating $10 of additional EBITDA level value (makes sense, increase topline growth by 10% without changing expenses / sales volumes results in increase of EBITDA by 10% of revenue)

Also, selling an additional 10% at old price we would expect:
$10 (additional sales) - COGS ($4) - Opex ($2) or $4

But selling new products at new price: Gain $1 (similar to math shown above)

Total change in EBITDA: $10 + $4 + $1 = $15
At 5.00x
$55 or ($10 + $1) x 5.00x of EV is generated from selling at a higher price
$20 ($4 x 5.00x) of EV is generated from selling new products (higher volume)

Above is what the bridge would look like if a PE firm had 60% ownership and management had 40%.

Note, this framework is iterative and can be applied across multiple product lines to help do a break out and sum of the parts analysis for companies to see where value is hidden in undervalued divisions.

Also note that as an interesting aside, if you were actually to build out a proper DCF model of this (using some basic business assumptions holding margins constant etc.), your short term growth rate would have to be adjusted upwards in order to come to the same intrinsic valuation that would justify the higher multiple.

Back from the Holiday

Well after a well deserved break, all the students are back.

First years are in their Negotiations class which odd for me as I didn’t do this last year due to the Middle East study tour, but now I see what it was like with the Atrium constantly being flooded by ambitious MBA students trying to get better deals in their exercises. There have also been requests for help with preparing for recruitment week which is coming up next week and some postings already up.

Even second years are at school, many having the clever idea of taking an intensive or two to lighten their final term course load.

Yesterday, we did a presentation for our ICP in Islamic Finance. Arash and I did a presentation on two comparable securities, one conventional and one Islamic and we showed they were strategically and operationally comparable (same industry, business model, enterprise value, capital structure, debt ladder, similar maturity, seniority and economic conditions, but different country and terms) and we analyzed the yield, adjusting for country risk and broke down the spread accounting for liquidity risk, minor maturity differences and increased cost of capital related to Sharia compliant terms.

This material will be used as part of Rotman’s new Executive MBA program class on Islamic Finance. While we aren’t quite finished with our work, the next step being to propose a term sheet for what the conventional financing would look like if it were Sharia compliant, I’m very happy with our progress and the insight we were able to bring into this new product class.

DCF

With summer recruiting coming up for first years in the next few months and with many of our second year finance courses requiring us to do some form of valuation (Corp Fin, Financial Management, Mergers and Acquisitions, Business Analysis and Valuation etc.), I thought it might be useful to post an "academic" quality discounted cash flow model as a reference.

There are some basic comments in the cells which explain some of the assumptions.

Discounted Cash Flow Model

Discounted Cash Flow Guide

For a more advanced version of forecasting (including working capital schedule and depreciation schedule), check out my Chapters LBO model.

Multi-Factor Models – Applying the Lessons Learned from the Numbers

In Finance 1 last year, we were introduced to the idea of multi-factor models (MFM) originally explained by Fama and French as an alternative to the traditional Capital Asset Pricing Model (CAPM) for assessing systematic risk. Additional factors include small versus big (SML) and value versus growth (HML).

In our Business Analysis and Valuation class, we discussed a merger case in which a large company acquired a smaller company. We talked about what would be the best way to approximate beta. The method I used (which was the best method I could conceive, I’d be happy to hear criticism or suggestions otherwise) was to weight the betas by market cap and take an average.

However, there was some discussion about the fact that one entity was much smaller than the other. While we were having a conversation of what that would actually mean, I would suggest a mathematical method for expressing the quantitative effect of size, using FF’s MFM.

1. 1. Express both company’s re as a three factor MFM
   Re1 – RFR = beta1 (Rm – RFR) + betas1 (SMB) + betav1 (HML)
   Re2 – RFR = beta2 (Rm – RFR) + betas2 (SMB) + betav2 (HML)
2. Take the larger company’s size beta and apply it to the smaller entity
   betasnew = betas2
3. Recalculate re for both entities
   Re1new – RFR = beta1 (Rm – RFR) + betasnew (SMB) + betav1 (HML)
   Re2new – RFR = beta2 (Rm – RFR) + betasnew (SMB) + betav2 (HML)
4. Take a weighted average (by market cap) as the expected return of the combined entity

By taking the larger company’s size beta for both, what you are saying is that you expect the smaller company to have the size “characteristics” of the larger entity. I might even be more appropriate to add the size factors (Would that be appropriate? As the MFM is a linear regression, is it appropriate to add these factors?) and use that for new return on equity for each entity as it relates to the combined entity.

betasnew = betas1 + betas2

While there are some significant assumptions which are required for this to work, it is the best solution I can conjure based on information given. I would really appreciate any additional ideas for creating a more robust model.

Abnormal Earnings Method – Not Entirely Useless

When we were introduced to the Abnormal Earnings method in Business Analysis and Valuation, I was decomposing the math formula which constructs the value of the equity. As far as I was concerned, it didn’t really tell us anything we didn’t already know through a equity based discounted cash flow (FCFE discounted at re).

However, there was an interesting scenario in which this method actually told us something unique. First the formula:

Market Value = Book Value + (NI1 – re*BV)/re + (NI2 – re*BV)/re^2 + …

Nix is Net Income in year x

BV is book value

While in theory, this formula should return a similar value to an equity based DCF, one unique value is that the valuation is relative to book value, rather than strictly looking at only cash flows. Essentially, what it is saying is, the company is worth it’s book value, PLUS it’s “abnormal earnings” where abnormal earnings are the earnings you get in excess of what you would expect (re).

So in looking at a company that is trading below book value, I used to think that it meant that the market did not believe in the company’s management to perform (the company was burning cash). But it doesn’t just have to be that the company is on a “crash” course. It could also just be that the company is not performing as “expected” that is to say there net income is not necessarily negative, but simply less than what is expected.

Legacy REIT

In our corporate finance class today, we were responsible for presenting our valuation of the Legacy REIT IPO. We used a variety of different valuation methods and multiples to provide a range of potential valuations before recommending a price of $10.50.

My team was fantastic to work with. As we are also responsible for the RioCan valuation next week, we opted to split the group work down the middle and sort out our presentation. My team mates produced a robust DCF model which had it's assumptions firmly grounded in the economic realities of the industry. When it came to question and answers, my team mates were resilient in answering questions about reconciling the various valuation methods to resolve model tensions (the DCF says we should price higher, but yield analysis shows that we aren't generating a high enough yield to attract potential investors relative to other REITs).

In the end, it took all the strength I could muster to stop grinning like a Cheshire Cat as my team mates hammered back answers to questions by pulling up pre-emptive appendix slides and presenting a well founded case for our valuation.

As an interesting note, our professor had worked on this deal and mentioned that they had priced the deal at $10 (and that apparently, for mathematical simplicity, these units are generally priced at $10 and that the sources of funds are changed through the number of units issued - like bonds at $1000 or preferreds at $25).

Levering and Unlevering Beta - Mechanics of the Model

It occurs to me that I didn't really describe the formula for levering and unlevering Beta and why it works. Let's have a closer look:

First think of any given industry. There are some major assumptions required to get levering and unlevering beta to work. For instance, a dollar invested in an industry will give a constant return proportional to it's risk (beta). This is one of the fundamental assumptions in CAPM.

Levering beta is the idea that I can amplify the result of a deal by using debt. Let's look at an example:

I'm in an industry that has a beta of 1.2

ERP is 5%

RFR is 4%

ke = RFR + beta * ERP = 4% + (1.2) 5%

= 10%

So if I invest a dollar, I can expect to get a return of 10%.

However, I can use leverage (borrow money) so that I want to experience an amplified result:

I'll invest 1 dollar, but allow borrow another dollar to invest with. So I have two dollars in play, but only one of those is mine. My return? Well, assuming you can borrow at RFR (a huge assumption), you'll gain another 10% on that additional dollar, but have to pay 4% (RFR) so you'll gain another 6% on top of your original 10% for a total of 16%. You've doubled your systematic risk by having two dollars in play. Let's check with CAPM:

Beta = 2*1.2 (twice as much exposure)

ke = RFR + beta * ERP

= 4% + 2.4 * (5%) = 16%

This makes sense. For every additional dollar you borrow at RFR and invest in the industry, you will make the spread between their returns (or the beta * ERP).

So if you borrow D, dollars (D in this case stands for Debt), versus E dollars of your own money (Equity), and because CAPM is a linear function, you can expect:

• Your exposure will be based off of D+E dollars (total capital in the game - systematic risk, exposure)
• But off a base of E dollars invested (the money you have invested yourself, or Equity)

So if an industry has a beta of Ba, and you use leverage D on your initial investment E, you can expect your new beta of Be, to be:

Be = Ba * (E+D)/E

Note, however, that (E+D)/E = 1 + (D/E)

Look familiar? It's the levering formula:

Be = Ba * (1 + D/E)

But there is still one piece missing. The (1-t) portion of the formula is to simply account for the fact that debt that you borrow provides a tax shield, so the final version of the formula replaces D with (1-t)*D to get:

Be = Ba * (1 + (1-t)*D/E)

Hope this decomposition helps. I noticed this relationship is very prevalent in financial calculations as Anita McGahan clarified in one of her lectures on Starbucks in first year when talking about Operating Strategy versus Financial Strategy in the Dupont Decomposition. This was something I had also wondered about previously.

Unlevered Beta

A quick recap:
Beta of a company is determined by a statistical regression of returns of a given security against returns of the market.

As a result, "beta" usually refers to a company's equity beta or observable beta. Using CAPM, we can calculate the expected cost of equity (ke) using:

ke = RFR + beta * ERP

Where ERP is Equity Risk Premium

So what is unlevered beta and why is it important?

Well, recall from CAPM that you can change a company's capital structure in order to add leverage to increase beta and thereby increase expected return of equity (with a company's cost of equity being the investors return on equity).

Unlevered beta tells you how much a company's industry is expected to return, regardless of the leverage employed by looking at the systematic risk of an industry regardless of the financing decisions. Theoretically, the unlevered beta should be constant across companies in an industry.

Why is this important? Here is one example. You are trying to determine the cost of equity (so you can determine WACC for DCF) of a new company in an industry. However, because it is a new company, there is no previous history in terms of what they can be expected to return relative to the market. So it is impossible to calculate its equity beta. So what can you do?

You can look at a variety of other companies in the space, unlever all their betas to get asset betas and average them (as they should be theoretically the same, but will most likely differ slightly) and then relever it to the new company’s capital structure to approximate its expected equity beta. Armed with its equity beta, you can calculate its cost of equity using CAPM.

While this is how it would work in theory, there are some major problems with this model, the most obvious being:

• How do you do “comps”? How do you define “a variety of companies in the space”, especially if few or none of the companies are exactly the same?
• CAPM has its own issues which make it a less than perfect model
• As a new company, they will probably not behave in the same manner as more mature companies in the space.

Here is an example:

There are four companies with different betas and leverage levels. By unlevering all the equity betas, you can have various approximations for what the asset beta should be. An average of all four gives you a decent approximation for the beta of the industry.


Now assume we have a new company in this space that will have a D/E of 50% at the same tax rate. We can use the leverage formula to calculate what the beta equity should be:

Equity Beta = Asset Beta * (1+(1-Tax)*D/E)

In this case, the equity beta would be approximately 1.3, which makes sense as it has a leverage between B and C and therefore should have an equity beta in between.

Excess Cash isn't always just from cash

Putting together the last few posts (House analogy for EV, FCFF and NOWC and N[O]WC as a source of funds), let's look at an example of how they are all interrelated.

Target Company:
Total Assets = $100M
AR = $10M
Inventory = $15M
AP = $10M

Industry Average
Total Assets* = $100M
AR = $5M
Inventory = $10M
AP = $20M

* Total Assets for each company are deliberately the same to make percentage calculations convenient.

Let's also assume that looking only at the company's operations, you are planning on bringing the balance sheet accounts closer in line with industry average. Implicitly, you are improving the company's operations (reducing days receivable, days on hand and increasing days payables).

Therefore:
Change in AR = -5M (cash inflow)
Change in Inventory = -5M (cash inflow)
Change in AP = +10M (cash inflow)

Total cash inflow from Operating Working Capital = +5M +5M + 10M = +20M

This change in accounts reflects a type of excess which can be converted into "excess cash". These changes would be manifested in operations through:

• Collecting on debts sooner, reducing credit terms
• Selling out of inventory without replenishment (reducing inventory size and implicit days on hand)
• Taking longer to pay our suppliers, using more supplier credit
• Essentially, running "leaner"

This excess cash would be captured in a financial DCF model as a change in net operating working capital in the first year of operation and built into the company's EV calculation.

Enterprise Value - House Analogy with Excess Cash

Another common question that comes up is related to enterprise value, particularly as it relates to excess cash. Recall that enterprise value is the value of the entire company and should be capital structure neutral.

EV = Equity + Debt - Excess Cash
or
EV = DCF Value + Excess Cash

The initial reaction is: "Wait, how can that be?" How is it that in one formula excess cash detracts from EV whereas in the other it increases? Does that make sense? In explaining, I find that a house analogy is helpful for understanding how to calculate EV.

Scenario 1:
Imagine Steve ownes a house worth $100k. Over the years, Steve has paid down his mortgage to $50k. Therefore, Steve's house's capital structure is $50k debt and $50k equity.

Dave is interested in buying Steve's house. For simplicity, let's say the house hasn't appreciated in value and is still worth $100k. Dave doesn't care what Steve's mortgage is, how much he's paid down etc. After all, that is Steve's capital structure. Dave is a new home buyer and is starting with a $20k downpayment and $80k mortgage.

The main point is that it doesn't matter who is buying the house (over simplified assumption), the house is worth $100k. It is an attempt to understand an unbiased (unlevered) way of looking at value of the company.

Scenario 2:

Let's assume a few changes:

• The $100k price of the house includes $10k in cash which is sitting on the floor of a room
• The house is being rented out as an investment property for $4k per year forever and the appropriate discount rate is 5%

Using the following formula:

EV = Equity + Debt - Cash = $100k - $10k = $90k

Does this make sense? Dave buys the house with $80k of debt, $20k of equity for a total price of $100k. However, immediately upon buying the house, Dave takes the $10k sitting on the floor and pays down his mortgage. Effectively, Dave has only paid $90k for the house.

Using the alternate formula (using a perpetuity formula for DCF):

EV = DCF Value + Excess Cash = $4,000 / 5% + $10k = $80k + $10k = $90k

That is to say, forgetting the cash, the house is worth $80k only from the income it generates. However, because the cash sitting on the floor is not integral to operating the house, it can be taken out of the house without affecting the income stream.

While it isn't an entire conicidence that the end numbers are the same (I've deliberately selected convenient numbers), it should hopefully demonstrate how excess cash in one formula decreases EV whereas in another in increases EV.

Free Cash Flow to Firm and Net Change in [OPERATING] Working Capital

A few of my classmates have been asking me a very common question so I thought I would post the answer. Particularly because I think it is a fantastic question and is something I’ve wrestled with for sometime.

In Corporate Finance, Financial Management and Mergers & Acquisitions, one of the most important metrics of a company’s performance is it’s free cash flow. Or more specifically, it’s free cash flow to firm (aka. Unlevered free cash flow). This is the cash flow metric that is used to value the entire enterprise. It’s defined as:

FCFF = EBIT (1 – tax) + DA – NWC – Capex

Where:
EBIT is Earnings Before Interest and Tax (otherwise known as operating income)
DA is Depreciation and Amortization (which is actually a place holder for all non-cash expenses, but DA is the largest and most common one)
NWC – Change in net working capital (*NOTE* This is the tricky part that people are asking about)
Capex – Capital Expenditures

So while this formula is not new to most, what I want to focus on is NWC. If you have read my post on the difference between OPERATING working capital and working capital will know what I’m getting at.

First, before we even get to that, I want to emphasize a lesson taught in Anita McGahan’s first year strategy course relating to Dupont analysis (one of my favourite frameworks). Dupont analysis looks at Return on Equity and Anita made a fantastic point about how to look at the formula:

ROE = NI / Equity

ROE = (NI / A) * (A / E)

ROE = ROA * FLA

Where:
ROA is return on assets (Operational Strategy)
FLA is financial leverage (Financial Strategy)

In a discounted cash flow, a company’s value is calculated as it’s enterprise cash flows discounted at the appropriate enterprise cost of capital (it’s weighted average cost of capital).

In other words: In the summation formula, the numerator is operating (FCFF) and the denominator is financial (WACC).

This is another good way to think about the difference between OPERATING working capital (OWC) and working capital (WC) as I explained previously.

While the commonly accepted formula for FCFF is as explained above, anyone who has done a proper financial model is quick to learn that it isn’t change in net working capital which is important, but rather change in OPERATING net working capital (excluding financing items such as cash and short term debt).

FCFF = EBIT (1 – tax) + DA – NOWC - Capex

But the next logical question is what is the difference between something like short term debt (a quantifiable liability) and accounts payable (also a quantifiable liability which is equally a debt of sorts – a debt to a supplier). The answer? Interest.

The reason why something would be considered OPERATING working capital (or particularly an operating current liability) versus a normal working capital (or current liability) is that a financial current liability *bears interest* whereas an operating liability does not.

This raises the next interesting question: How do you treat pension liabilities? As you may recall, I mentioned previously how the CFA treat’s pensions as if they are interest bearing liabilities (or specifically, debts of the company owed to it’s workers which is expected to grow at the company’s cost of debt). This is a perfect example of a judgment call. Some of the top equity research analysts will consider pensions to be part of operating a business (not included in enterprise value as a financial consideration) whereas others will consider pensions to be a type of financing (don’t take my word for it, check out the research reports of companies with sizable pensions and see how different analysts treat different companies). Some will consider current pension obligations as debt (as it has to be financed to be paid out) whereas others will treat the entire long and short term obligation as debt.

Flight of Fancy: What If...? A Market for Bid Points

One common theme I've heard is that MBA's are often upset when they don't get all the elective courses that they want. While I certainly can't complain, it brings up an interesting question: "What if someone like me was able to sell their bid points? What would I get for them? And how would you value them?"

For example, my course choices weren’t very restrictive, I got 500 points to bid on four courses, most of which I could have gotten with a zero bid. Whereas, Mr(s). Ambitious was trying to take TMP and Value Investing while going on Exchange (physically impossible, Value Investing is a year long course and Exchange means you are physically gone). If there existed a mechanism (and therefore a market) for me to transfer my points for a price, what would I get for them? What should they be worth? Clearly, there is currently some "market inefficiency" as we are both unsatisfied: Mr(s). Ambitious because they didn't get all the courses they wanted [net deficiency] and me because I didn't realize the full value of my bid points because I had more than I could use - [net surplus].

Well let’s make some assumptions:

• Rotman tuition is C$35k per year (let’s not include first year as it’s common, or you can adjust the value of points accordingly if you feel second year courses are more / less important)
• You take 10 elective courses in your second year
• You are given 1000 points with which to bid

A “book value” of the points would simply be C$35k / 1000 points or about $35 per point.

But keep in mind that when something is inherently useful, especially in a scenario where a few points margin can mean the difference between getting the course you really want versus having to settle for a less popular course, there can potentially be bidding wars from “oversubscription” (points trade at a multiple above their book value) especially if they were in limited supply.

While people are paying C$70+k to go to school, for a marginal $35 x 100 points (a rough approximation of the average points allocated per student / course) or $3500 you can get any course you want (including the highly coveted TMP and Value Investing – which includes a trip to visit Warren Buffet – one of the reasons why this course is so wildly popular).

If you could some how do it, you could see how much additional probability you have of getting into the classes you wanted and put a dollar value on how badly you wanted to be in that class (regression analysis), you can determine a price you’d be willing to pay to attend that class. For example: Would there be a correlation between the number of points you consumed to get into classes of your choice against your overall earning power once out of university (thinking along the lines of DCF to value bid points like common shares).

And also imagine if this market had a “market maker”. For example, the PSO will (create and) sell you points for a certain value (either regulated and pre-determined or floating with the market). Students could liquidate their points at market value and get money back or buy points of the market to be more competitive for course selection and the school could potentially get revenue from selling points.

And since you have a market with underlying assets, imagine if you created financial instruments for those assets (shorts, puts, and calls for bid points, futures).

And imagine if other schools had market systems (I’m told that bidding systems are not uncommon at other MBA schools), you could trade between these. Or even other programs!

Of course, these points would inherently have an “expiry” as to their value (you wouldn’t want to be holding (take delivery of) 5000 MIT Engineering points if you were going to Stanford Law School).

There are some interesting implications. For instance, a new ranking system for schools where the relative value of a course is determined by the market value (determined by students taking courses there) in real time with comparisons to year over year values. Example: Would an engineering calculus class go for more at Waterloo or Toronto? Could you couple this with flexibility between schools (accreditation programs) which allow students to take equivalent courses at other schools and what do you get?

It would be a more sophisticated and real-time version of tuition regulated by the market. Taken to the extreme, here is another idea: drop the original tuition completely and have students buy bid points for classes. And then what if you were able to connect this market to actual financial markets? An S&P Index of Undergraduate studies to benchmark the valuation of your individual class’ performance.

Another thought: If the value of courses in a particular faculty started to "overheat" would that be a leading indicator of oversupply of labour in a particular industry in 4 years time?

Valuing Commodities Companies - Looking at P/NAV

Recently, I've been trying to learn more about commodities companies building on what we've learned in class as well as discussions with colleagues. Especially as Canada is a strong resource based economy (with a currency heavily influenced by the price of oil, I'm told), it is important to understand how these companies are valued.

Shree was previously very kind to explain why commodities companies provide leveraged exposure to the underlying commodity. In fact, I'm told that this is the reason why companies trade a P/NAV multiples greater than 1.

When I inquired as to what exactly Net Asset Value (NAV) was composed of, I was told that it is essentially the Asset Value (value of the commodity "in the ground") netted by the cost it took to get that asset out of the ground. So if you had to take a snap shot of what that company was worth, you'd intuitively assume that the value of the company was it's NAV.

However, as Shree demonstrated, the markets are always moving and the price of the commodity which the company bases its value on will change. This produces option like behaviour in the price of the company. While not a perfect explaination, I was told to think of it this way:

The value of the company is related to it's NAV PLUS a premium associated with the volatility of the commodity and the probability that the price of that commodity will increase. This is analogous to Intrinsic Value (NAV) + Time Value of a call option.

Obviously, there are a host of complicated relationships related to volatility, future price expectations, supply and demand, hedging and speculation which make this basic generalization a little too simple. However, I think it serves as a good starting point for how to think about and model the price.

This is similar to what we learned in Finance II when our professor explained the example of land that contained 1M barrles of oil which could be extracted at a price of $70 per barrel when the market price of oil was $60 per barrel. While a naive NPV calculation at today's rates would imply a negative NPV, the potential for the price of oil to top $70 provides real value to the land.

Sustainable FCFF (UFCF)

One of the most important measures of value for a company is Sustainable (Terminal) FCFF so I wanted to review some of the ideas which go into calculating it. As the finance saying goes:

"Turnover is vanity,
Earnings is sanity,
but Cash is reality"

Also, because Terminal Value represents somewhere between 70 to 80% of the calculated Enterprise Value in a DCF, the assumptions that go into developing and FCFF have a major impact on the final valuation.

First a recap of what composes FCFF (a slightly more educated view since my first encounter with this measure on the CFA Level I exam):

FCFF = NI + Dep - WCInv - Capex + Int (1-t)

To build up to FCFF, we

1. take NI from the Income Statement
2. add depretiation to get Cash Flow (CF) as a non cash expense (we'll ignore others like change in deferred tax liability for now although for a "sustainable" cash flow they'd net out at 0 anyways)
3. Subtract Working Capital Investment (change in working capital) to get Cash Flow from Operations (CFO)
4. Subtract Capex to get Free Cash Flow (FCF)
5. Finally, since we are looking for cash flows to all stakeholders (including debt holders) we add back the net value of debt after tax to get FCFF

Now let's break down each of these components. First of all, in real terms we'll project zero growth. However, some terms are susceptible to inflation growth (marginal nominal growth).

As a result, even with zero real growth, there will be some marginal incremental growth in WCInv and Capex to reflect this inflation. The best way to model it is as a percentage of sales according to the CFA.

FCFF = NI + Dep - WCInv - Capex + Int (1-t)

Another consideration is dividing up capex along two dimensions - 1. Maintenance capex and 2. Investment capex. Maintenance capex is defined as the capex required to maintain your operations. By definition, it is equal to depreciation. Therefore:

FCFF = NI + Dep - WCInv - [Maintenance Capex + Investment Capex] + Int (1-t)

= NI - WCInv - Investment Capex + Int (1-t)

Also, investment capex is related to expanding to new opportunities. However, again, since we are modeling a "sustainable" cash flow rather than a perpetually growing cash flow, investment capex is 0 by definition. This generates a further interesting result:

FCFF = NI - WCInv + Int (1-t)

Next I'd have a look at WCInv. If WCInv is stable, then it should produce a marginal change in the cash flow.

Note also that FCFF = FCFE + Int (1-t) + Net Principle Repayment

This shows that NI is a decent (though not perfect) proxy for sustainable FCFE and that by tacking on the interest net of tax effect, we can arrive at a good proxy for sustainable FCFF.

Ian Schnoor - Financial Modeling 3, LBO's

Just arrived back from March Break and "warming up" to classes again in Ian Schnoor's third financial modeling module: LBO's. Before leaving for the break, he had come and done his second module: Valuations which talked about understanding the operations and finances of a company.

While module 1: Buiding a Financial Model, was a free lesson (I believe it's paid for by PACE at Rotman), Module's 2 and 3 cost $100 each, well worth the cost (again, I believe it's subsidized by PACE at Rotman).

The CFA charges quite a bit more if I'm not mistaken (but I'm lead to suspect that the CFA courses are also subsidized, though maybe not as much).

Having these financial modeling courses under your belt gives you a very good practical understanding of how to apply financial concepts learned in class beyond purely theoretical or academic textbook knowledge.

Tax Implications of Bankruptcy

One thing that I've always been fascinated with (and need to look into more) is mergers and acquisitions. However, in this environment of post-financial crisis recovery, the M&A environment is very different that what it was previously. Particularly, there was a good window recently of purchasing companies at a 50% off sale with equity prices so low if only you had the cash to do it.

One thing we discussed in financial modeling courses I've taken looks at modeling Tax Loss Carry Forwards (TLCF, Canadian) and Net Operating Loss (NOL, American).

As a financial acquirer (rather than a strategic acquirer), I wonder if there are any vulture funds which specialize in purchasing bankrupt companies if only to get their hands on their TLCF / NOLs. Obviously, there are some concerns, including the laws, regulations and transfer rules for obtaining these credits as well as what the capital structure of the acquiring company looks like. I'd imagine that the equity would be worthless (or trading like an option) and the debt would be trading for pennies on the dollar.

Especially with so many failed entrepreneurial ventures, there must be a sea of dead companies which should at least be as valuable as their potential tax credits. This could also potentially reduce the exit cost of early stage companies (for early investors to at least recoup the cost of the tax credits for all losses taken).

Having said that, would it be a potentially good idea to go out looking for strong companies to purchase distressed companies if only to utilize their tax credits? That is to say to purchase these companies only for their deferred tax assets. Or some other metric like break up value or price to book.

Annuity Formula - How it Works

One formula I wanted to have a look at (just in time for both the accounting exam tomorrow and the finance exam on Friday) the annuity formula. While the math looks rather convoluted, I wanted to strip it down to it's parts to understand how (and why) it works.

First let's look at a few things. Assume that you've already explained how a perpetuity formula works (without growth), you know that the value of a perpetuity is:

(Assume it goes forever beyond period 7).

PV = CF / r

Where:

• PV is the present value
• CF is the cash flow per period
• r is the rate per period

The next question I would propose is this, what is the value of the perpetuity in period n at time 0? Well, it would be:

Well it would be the same as the PV's value at time n, discounted back to 0. Since the cash flows at time n would look the same as now, the PV at time n should be the same as the PV now.

PV @ n = PV / (1+r)^n

= CF / [r x (1+r)^n]

Now the last question, what is th value (both of the cash flows and the PV) of the perpetuity now minus the perpetuity at time n? Well, if you draw a diagram, the answer is an annuity from 0 to n. And the math shows the same:
(Note this graph is merely the first graph minus the second graph in the same way the math is the first PV minus the second.)

PV - PV @ n = PV - PV / (1+r)^n
= PV (1 - 1/(1+r)^n)
= CF (1 - 1/(1+r)^n) / r

This is the annuity formula for a cash flow CF, to period n at discount rate r, which is much easier than doing a DCF for each of the cash flows (imagine doing a DCF for 30 even cash flows mechanically).

This is a slight variation on the question that Kent Womack presented to us at our review session in the ROM and also highlights how the formula for annuities is constructed.