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.

Managing Corporate Turnarounds - Part II

Wednesday

Often when things go wrong, people are inclined to fire the management. However, in the real world, things are hardly ever that simple. Firing management, like anything in turnarounds, is decided on whether or not this action will speed up or slow down the turnaround. Besides packages given to executives on exit, there is also a great deal of institutional knowledge that they take with them. There is a counter balance to understanding the value they bring through their experience versus the inertia they create against the changes required. This is particularly true in SMEs as well as family owned enterprises where the institutional knowledge is often not formalized (pricing mechanics, customer relationships etc.)

Also, with the separation of the chairman and CEO roles, it is possible that a power divide coupled with an inappropriate strategy may have smart people being told to chase bad strategies. One remedy which is often used is an immunity period: the idea that employees in a turnaround situation have a window of opportunity to identify any potential problems. This allows an honest analysis of problems without reprimand and realigns expectations (Are we going to make the numbers? Are our margins as good as we expect? Are we doing things right? Are we doing the right things?) Because a new team is put into place to fix previously created problems, it is not appropriate to assign current problems to new management. However, eventually, whether or not these issues were created by you initially you will inevitably begin to wear them if you don’t fix them soon enough or don’t manage expectations of the company and all stakeholders.

Thursday

Like in any business strategy, there are two major things to keep in mind in a restructuring: operations and financing. For operations, it is necessary to check if the overall business strategy works (are people buying your product and do you have a viable business) and if you are able to profitably deliver (are our margins good or are we chasing low quality customers). Also from a financing perspective, it is important to understand the liquidity constraints of the enterprise. For example, what is an appropriate financing structure to keep the company alive while providing adequate and appropriate protection and returns to current and new capital providers?

One such useful tool is the paid-in-kind (PIK) security. It is a type of mezzanine high yield debt that doesn’t pay a coupon. Typically, these types of securities return 14 to 17%. They return higher than senior debt because they are subordinated but they don’t require cash payments which allow the company to maintain its liquidity for short period of time when it’s heavily cash strapped. However, what usually happens is this is coupled with a cash sweep. To use a structure like this in this circumstance is tantamount to saying: “We understand you are strapped for cash now, so you don’t have to pay us immediately, but we want an appropriate return for taking this risk that’s more similar to equity if things recover. However, we still want to be paid sooner rather than later and when you have any excess cash, you will give us everything you have and we’ll consider you less risky and ratchet down your interest rate to reflect the change in risk.”

Managing Corporate Turnarounds

This week, I’m taking a block week course (one week intensive following the 10 week standard course period) at LBS: Managing Corporate Turnarounds. So far this course has actually been really interesting, with us looking at business cases for salvaging distressed companies and learning about the mechanics and considerations of struggling businesses.

Unlike my undergraduate strategy course, which I nicknamed “doom and gloom” because the distressed companies in our cases never seemed to recover, this course talks about different cases that were successfully turned around using a variety of different techniques to improve operational efficiencies and use financial tools like LBOs to capture the upside.

We’ve also had great guest speakers come talk about their specific experiences and their perspective on different aspects of turning companies around (shedding assets for cash, improving operations, recovering debt, how to identify target companies etc.) One of our requirements in class is to summarize some key learnings from the class, and in a similar fashion to the Latin America study tour which had a similar component, I plan on using this blog to jot a few notes for me to recall later as I compile my thoughts:

Monday

In turning a company around, it is important to understand where control lies. Since equity is flirting with bankruptcy, it may lose control to the debt holders. Some debt investors may be holding “grenades”, the intent to liquidate their holdings ASAP when a trigger event happens (broken covenants, default etc), and may not be interested in salvaging the company, even if there is potential to recover equity value because they just want to unwind their positions.

Companies need to have good strategies when it comes to M&A, otherwise they can fall victim of a vicious cycle: accretive acquisitions increase EPS (albeit in an inorganic manner) and can give false impressions of growth, which could potentially boost the P/E multiple. A higher P/E multiple gives the company expensive equity which it can use as a better transaction currency for buying other companies (low P/E) and still be accretive. This is a vicious cycle if the M&A is not well integrated with substantial delivery of synergies and/or overpays for targets. This typically occurs in new industries where there are a limited number of potential buyers (targets with low P/Es as there is no other mechanism for exit) and the industry is consolidating into larger players (large strategic buyers displace financial buyers niche shopping).

Another version of the problem above is when companies which are asset-light use M&A as a backdoor for raising leverage. Services companies cannot raise leverage in a traditional manner because they have neither hard assets nor collateral to borrow against, so they can acquire companies which have higher leverage ratios to boost their own ratios. Also, this type of reckless acquisition can divert focus from the core business. In turning around companies which have fallen along this path, one of the immediate remedies is to spin off non-core assets for cash.

Tuesday

When you are on the buyside for any company (not just distressed companies for turnaround), it is important to have multiple targets in the pipe, not just for the more obvious negotiation leverage points, but to prevent yourself from getting too much deal heat over one deal and to avoid negotiating against yourself and your emotions.

Negotiating a transaction involves much more than a “price”. There are terms of payment, the structure of the compensation, workouts, milestones, terms and conditions. A price which is seemingly too high can be restructured to be paid out overtime so that the undiscounted amount remains the same, but the risk and cash outflows can be spread over a longer period with the appropriate covenants and milestones.

Islamic Finance – Executive 3 Day Program

Today, I presented remotely from London at the Islamic Finance Program, hosted at Rotman for the Executive Program in partnership with Bennett Jones. This was the final component of our Islamic Finance ICP. The team lead by Walid included myself, Arash, Shahzad, Khaled, Kashif and Noureen and we presented our materials to the executive program participants.

With the rise of Islamic finance, I’ve had some interesting conversations with people I’ve met while on exchange at LBS regarding Sharia compliant financial structures such as the various types of sukuks we’ve been analyzing.

Our spread analysis drove quite a bit of interest for people who were interested in what a Sharia compliant structure would yield and the market conditions for doing such an issuance. Even before our presentation, I had the opportunity to answer some basic questions regarding the pricing spread between Islamic instruments versus conventional.

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.

ICP Islamic Finance - "Conventional" Analysis

This morning we had a working session for our ICP - Islamic Finance with some lawyers, a corporate banker and professors. The two teams presented their analysis of the conventional financing structure of the primary security instruments used to finnace our projects. Under this conventional analysis, we looked at the costs of capital and the associated terms related to these types of paper with the intent of understanding the requirements need to make them Sharia compliant.

We also had great explanation from a senior lawyer regarding the structuring and "asset-based" (versus "asset-backed") nature of nominating (rather than selling) assets under a Special Purpose Vehicle (SPV) in order to comply with the necessary requirements of Islamic finance. We had considered the capital gains implications of a sale leaseback transaction, as well as understood how an asset and capital intense infrastucture project would look similar under an adjusted EV to EBITDAR metric regardless of the off-balance sheet financing that may potentially be required.

We have a solid understanding of the work requirements due before our next meeting in early January (before I fly off for London). We also had an opportunity to fire questions back at the professionals in the room in terms to learn what were the appropriate resources for generating comparables for analysis and benchmarking of our theoretical capital structures based on similar Sharia compliant instruments and current market conditions.

Some of the best advice we got:

• Understand the difference between "asset backed" versus "asset based" and how that affects your ability to issue Sharia compliant instruments
• Be aware of tax implications of capital gains/losses in a sale leaseback transaction
• Like any financial security, understand the key characteristics of seniority and expected return for a sukuk issuance and understand market appetite for these structured products

Islamic Finance - International Consulting Project

A new initative at Rotman (although you wouldn't know it as it has simply exploded this year) is the International Consulting Project. Laura Wood, Director of International Programs, has started a new research type project that engages students to work with professors on international topics. Some countries involved are the G20, Middle East, Israel, Africa and potentially others.

I myself am participating in the Islamic Finance ICP with Walid Hejazi, the professor who leads the Middle East study tour.

Yesterday, we were invited to attend the kick off event for the Islamic Finance EMBA course which will be offered in Jan 2011. The keynote speaker was David Dodge, Senior Advisor, Bennett Jones and former Governor of the Bank of Canada. He spoke about the growing interest in Islamic finance and how there it is common for people to see Shariah compliant instruments as simply "no interest" and how this superficial understanding does not encompass the fundamental rational for the structure of these products.

I am looking forward to working with my four other colleagues on this research project to look at Islamic financial instruments.

Financial Management Presentation

Yesterday, my team had our presentation for Financial Management with Asher Drory, a professor notorious for not pulling any punches and generally holding all Rotman students to a very high standard. We didn't want to disappoint.

Our case was on securitization as a form of financing. The company was a collections company which bought bad loans for pennies on the dollar and made a profit by collecting on them. However, they were being squeezed on the margins due to banks beginning to charge more for the bad debts as well as the quality and collectability of the debts shrinking.

The company was also looking to grow, and had been previously financing its growth through the securitization of it's uncollected loans (in this specialized financial industry, loans are a form of inventory, rather than as a liability in a traditional company). However, the conditions of the security were almost exactly the same as debt (monthly interest payments and principal flowthrough).

Therefore, in order to properly understand the risk exposure in the company, rather than have the financing sit off the balance sheet, we made adjustments to show what the balance sheet would look like if they were financed with traditional debt (which is not an unreasonable assumption, given the type of business risk that they are exposed to through this financing is not dissimilar). The end result is that suddenly all their solvency ratios and coverage ratios are totally out of whack. Whereas before their company had reasonable ratios (debt to equity of about 0.8x), their ratios were now about 4 to 5x.

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.

Pop Quiz

What is the value of a zero coupon bond with no maturity?

Defined Pension / Benefit Obligations

One of the interesting topics in the CFA Level II material is the mechanics for Defined Pension / Benefit Obligations. Previously, in the Rotman Finance I exam / CFA Level I material, I posted an example of the basic mechanics of how a pension plan would be valued (how much would be the PV of future benefit cash flows based on life expectancy and % of salary expectations and what rate of saving would be required to save the required FV to generate those future CF's).

However, if you notice, the "mechanics" of a pension plan are suspiciously similar to that of a bond. And that should come as no surprise. In the retirement or payout phase of retirement, it is as if the retiree is cashing out a fixed income investment (getting regular payments over time) or similar to amortizing a bond liability for the pension plan. However, when they are still "young and saving money" the pension plan is receiving regular payments overtime. The because the payments are regular and defined, they have all the characteristics of a bond.

This metaphor extends even further when you think about what the worker is doing. First a few contrasting scenarios:

Scenario 1: The worker makes a salary of $100k per year.

Scenario 2: The worker makes a salary of $70k per year, but has a defined benefit plan where the company contributes $30k per year into it.

In both of these scenarios the worker (assuming fair treatment) is being given the same value through salary (note also, the I/S in both scenarios reflects a $100k expense with regards to this worker... the only difference is that the $30k would be recognized as deferred wages or change in pension benefit non-cash expense on the CF/S).

However, let's take a closer look at that $30k. What is another way of looking at this? Well, another perspective is to say that the worker is deferring $30k of salary in the hope of future gain as realized through the defined pension benefit. In essence, the worker is loaning money to the company. Assuming that the DPO/DBO is as risk free as the company can guarantee (it is a contractual obligation) in terms of seniority of capital, this money actually ranks as quite senior (priority claim). This is a topic of particular interest with the recent financial crisis, especially as it related to Chrysler and it's recent financial trouble and relationship with the UAW / CAW.

This answers the next question: What is the appropriate discount rate for these funds? Well if you assume this obligation to be one of the most senior forms of claims against the company, it should have the most risk free rate the company can afford which is usually the same rating as it's highest quality bond.

This also raises an interesting point, if you were a lender or potential acquirer (through M&A or LBO) and you were analyzing a company with a defined benefit plan, would you consider the liability similar to debt? While it is not strictly a form of debt in the same way as a revolving credit facility, debenture, high yield bond, PIK or other, it noticably has many of the same characteristics (and is often modeled as a bond liability).

Interest Rate Parity Condition

The Interest Rate Parity condition that is in the CFA and discussed in our Global Managerial Perspective (GMP) class talks about.

Long story short, it says: Regardless of what financial mechanisms are used, two countries which are considered to be default free should generate the same real returns for the same period.

For example:
Today:

• You hold $1 USD
• The FX rate is 100 yen per USD
• The Japanse Bonds are yielding 5%

A year from now:

• FX rate is expected to be 103 yen per USD

What does IRP imply the interest rate on the US bond should be?

This can be graphically represented by:


The blue path shows how $1 USD is convered to Japanese Yen, held in a bond, and converted back at the new exchange rate back into USD. IRP states that whether this route is taken or if the USD is just held in a US bond (Red path) should make no difference. It should result in the same amount otherwise there is an arbitrage opportunity.

This is the solution. Note that the US bond rate is reverse engineered from the information given such that the end result produced in the red path is the same as the blue path.

You also note that there is a relationship which is defined by IRP. That is:

Japanese Bond Rate = US Bond Rate + [Appreciation / Depreciation of Foreign Exchange Rate]

Notice that this framework can have a blank in any one cell which can be derived using algebra if the other cells are filled in.

Non-Leveraged Accretive Mezzanine Financing

I was looking over my CFA Level II materials for corporate finance this weekend when I looked at the CFA's definition of different types of risk. For instance:

Sales (Business / Industry risk)
- Operating Expenses (Operating Leverage)
- Interest Expense (Financial Leverage)
_____________
Cash flow

The definition of any type of leverage (operational or financial) is increasing your fixed cost component but reducing your variable component.

It got me thinking, is it possible to have an instrument which doesn't increase leverage and solvency ratios, but also provides accretion for common equity holders? For instance, if you want to deleverage, the general strategy is to purchase debt with equity (which results in dilution because cost of equity is higher than cost of debt due to risk concerns etc). I don't know if this is possible, but I asked myself about a preferred share with very particular characteristics.

Fixed income instruments (coupon paying bonds, dividend paying preferred shares) increase the fixed payments required which technically increase leverage.

Accretive
Is it possible to have a preferred share that, rather than paying a fixed predetermined dividend (similar to dividend yield based on price), that pays a percentage of net income (similar to a stated dividend payout ratio). Because it is more senior than common equity, the cost of this capital would be less than the cost of equity (accretive if used in a refinancing / capital restructuring).

No Leverage
But the payout would also be variable based on NI meaning that it isn't technically leverage according to the CFA definition (plus it would be classed as equity rather than debt on the books). If earnings are low, the payout is low. If the earnings are high, payout is high. It rises and falls as a variable component rather than a stated fixed component.

The problem with this model of an instrument is that I don't think you could get a "senior" level instrument to payout variable to net income with a cost of capital less than common equity because they technically face the same level of risk (percent of NI).

Also, because earnings can be manipulated, perhaps the payout would work if it was stated as a percentage of EBT or some other higher quality form of earnings? At first I thought EBITDA, but then I realized that doesn't make sense. It would have to be paidout after EBIT (because interest should be a more senior form of financing and paid first). However, EBT is often modeled with a fixed tax rate to go to NI (so a % of EBT is really a % of NI since tax rate is usually constant).

Perhaps it could be payed out as a % of EBITDA which is paid out after interest?

This would justify the instrument being more senior and paying a lower cost of capital.

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.

The 4 C's of Credit

I have some friends who are looking at trying to gain positions in Fixed Income so I thought I would have a quick review of the 4 C's of Credit. They are:

1. Character - The management team's record, strategy and internal controls
2. Capacity - Ability to meet debt obligations
3. Collateral - Assets pledged to back the loan
4. Covenants - Restrictions on activities as well as maintenance

Recall that in bankruptcy, there is a hierarchy to how remaining capital, collateral and other assets are distributed relative to tranches. However, in restructuring "everyone gets a haircut".

Also, when building credit ratings, there are various ratios that are looked at, particularly:

• Profitiability Ratios
• Liquidity Ratios (Short Term Solvency)
• Capitalization (Leverage) Ratios (Solvency)

Commitment - Restrictions for Improved Reward

Wow. What an oxymoron. We had briefly heard about this in game theory in Economics way back in Q1 and now it's coming up again in Q3 in finance.

First in game theory and dominant strategies. Look at the following example of the prisoner's dilemma:

So in the typical fashion, the dominant strategies for both players show that they will end up in the lower right corner with a return of 3 each. This is unfortunate, as there is a potential to get 5 each if they could only credibly commit to Strategy A each. But because of the conditions of the prisoner's dilemma, it's impossible.

To change the parameters of the game, what if it was possible for Player 1 and 2 to commit to impairing their own return matrix? For instance, what if Players 1 and 2 could reduce their returns in the cells AB and BA to 4 instead of 7 (as shown below)? Suddenly, the dominant strategy changes and the end game to a return of 5 each rather than 3.
We achieve a counter intuitive result. By placing restrictions on their own returns, both players can achieve a higher return.

In our finance class today, we talked about a different scenario with similar characteristics. First, an overly simplified example. Because equity holders are only liable for capital at risk (what money they put in), with the effects of leverage, they can increase their upside with a bottom of bankruptcy. This will encourage them to take on projects even if they have a stand-alone negative NPV (but a positive NPV with regards to the equity holder's return and relationship in bankruptcy - equity holders don't lose more money then they put in).

However, the debt holders will require a larger return on their debt to compensate them (make them whole) and offset the risk. This in turn can make projects unattractive and become prohibitive.
However, shareholders can introduce debt covenants in order to restrict the their own flexibility (preventing them from taking on too much risk and inflating their upside) to secure financing and ensure debt holders that they won't have to bear the dead weight loss of projects which fail.
Again, a counter intuitive result: You can do better by restricting your choices.

Country Risk Premium

Previously, I was talking about the risks associated with bonds and how yield prices are constructed based on different types of risk.


I wanted to take a moment to have a peek at bonds. First is the US 10 year bond which is a proxy for the Risk Free Rate (RFR). Next, I wanted to look at the equivalent instruments available in different countries and their respective yields. If I'm not mistaken, the difference in yield prices should be accounted for by country risk only (having your bond issued by one country versus another). This should in theory account for both foreign exchange risk as well as sovereign risk.


Let's have a look:

Bond yields source: Bloomberg

A few interesting notes: While the US bond is considered risk free, there are some countries which have yields which are lower (Canada, Germany, Swedish, Swiss, and Japan). Other countries with bond yields at a premium include: Italian, Spanish and Australian. French and Dutch seem to be about par.

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.

Companies Investing in Securities

Our professor, Francesco Bova, has the honour / misfortune of having us for our Friday afternoon Financial Accounting class. It's usually a good time (yes, you read that correctly).

Just now, he was asking us what types of securities would be considered as being classed as "held to maturity". He jokingly hinted that the only securities with maturities are bonds. The best question of the day:

"Does a zero coupon bond have a maturity?"

Islamic Finance

Additionally in this Middle East International Study Tour class, we had professor Mohammad Fadel come in and describe the details, mechanics and rational of Islamic Finance.

While most people are familiar with Islamic Finance as simply "not charging interest" there are many more details which make up the rich tapestry of Islamic Finance.


The first note is that conformity with Islamic finance is voluntary. I think this might have been a point many members of my class (myself chief among them) got hung up on. Especially when we asked questions about how this law affected goodwill for M&A, sale of IP or brand equity or options or sale of receivables.


Some of the key takeaways for understanding Islamic Finance include:

• a strong association with tangible assets
• a general prohibition against floating or uncapped risk elements
• an emphasis on partnership, ownership and charity

There are certainly going to be more study before I can even begin to understand the find details, but this is certainly an interesting consideration for global finance.