Kingsford Charcoal Case

For our Managing Customer Value class, myself and Jasmine were warm called to do a presentation on the brand of Kingsford Charcoal case and present an overview of the situation. Vincent and Yijun provided an analysis of the price strategy analysis. Finally Harsh and Kim represented agency 1 and Irina, Mainak and Gang presented as agency 2.

Our professor asked us (Jasmine and I) to ask questions of the two agency groups which was a bit of a unique experience. I drew on the classes' conversation to try to ask intellegent questions to understand how they were positioning Kingsford charcoal relative to it's competitors, what their vision was for differentiating our product and how they planned to build an advertising strategy to drive consumer behaviour.

Harsh and Kim had picked mediums which we thought were in line with the BBQ experience. Agency two, with Irina, Mainak and Gang, showed that they understood Kingsford's position as a market leader and planned to exploit it by emphasizing the advantages of charcoal. However, we felt that their advertising strategy wasn't as focused.

In the end, we had to choose which group we prefered and we went with Agency 1 (Harsh and Kim).

It was an intersting exercise as Jasmine and I had to have a discussion outside of the class while the class came up with it's own selection. I'm told they came up with the same decision, albeit possibly based on different criteria.

Dubai World in Trouble

I've had this article (or variants) sent to me from many different people who are concerned / aware of what is happening in Dubai.

We had just done our Dubai presentation on market entry (our project was done on Sugar Mountain and their positioning with international infrastructure to source confectionaries from around the world) and were looking at different possible locations.

We had discovered Dubai World in our research and commented on how monsterously large it was. It actually dwarfs other famous projects from the same real estate development company, Nakheel, such as the famous World project, which creates small artificial islands on the coast in the shape of the earth.

An interesting point, the financing involve is actually islamicly based, as the bonds are sukuks. But there are interesting implications when it involves default and unwinding financial positions which have islamic components. It will be an interesting lesson in understanding not only islamic financial instruments, but also a pragmatic lesson in how distressed islamic investment instruments.

I wonder how liquidation would work. One of the general tenants (as I understand it) of islamic finance is that there are not many recourses for default, however, bonds do have an equity component so I wonder if the bonds will just naturally "convert" if the bond (sukuk) holders do not agree to delaying / suspending payments.

Strategy with Anita McGahan, Fleck Atrium Part II

In another rare treat, Anita ran another tutorial based on our most recent quiz in the Atrium earlier today (around lunch time). She discussed the answers and rational for the quiz questions as well as what she was looking for in good responses.

This time the tutorial was only for two of the four sections at Rotman. The other two courses are having their tutorial now.

Next week, due to construction in extending the Rotman facilities, we've been told that some of our classes will be in the Royal Ontario Museum (ROM). That plans to be exciting, not only to also be in a large class with all our 265 classmates, but also to be in such an interesting "class room". I hope we don't have to pay additional "admission".

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?"

Semper Fidelis

Once a few years ago, I was having dinner with a friend. This person was certainly very successful in a traditional way and we were having a conversation about the plants around his house as a metaphor for life.

He was talking to the head house keeper about the upkeep of the house. She explained to him how she had been singing to the plants and how she felt that was encouraging them to grow. He took exception: "Why are you singing to the plants? Things grow better under pressure! You shouldn't be singing to them, you should be yelling at them!"

He chuckled as he related the story, and reflected on how history tests and challenges us and how the people who have tasted the peaks of success in life first drank deep from the cup of failure in the depths of despair. Success too easily won, he argued, no matter how tremendous, is not a path to sustained growth. The irony is that success often invokes a sense of accomplishment and complacency although the drive that accompanies true success is never really satisfied.

This is certainly true for those of us who chose to do an MBA at Rotman. We are being put through the wringer now. But most of us know that if things go the way we want, this is just the beginning. Should we be so lucky to achieve the goals we are aiming for, life will only become more challenging, more difficult and more rewarding.

There are many people here who are exceptionally bright and hard working. Everyone is being put under pressure. Everyone is being "rattled" as we are being pushed to our limits to see how far we can go. But I'm very impressed with the resilience and strength of my classmates. Clearly, they are made of strong yet malleable stuff. You can tell that in 10 years time (if not sooner) they will be rock stars and will look back and smile at "the good ol' days at Rotman".

Dany Shehab Wins Spelling Bee

On Tuesday evening, Rotman hosted its annual Spelling Bee in the Atrium where students, faculty and staff were challenged to spell different words in front of their friends and colleagues.

Section 2's very own Dany Shehab rocked the Rotman world with his stunning win at the Rotman Spelling Bee with a word I will not attempt to reproduce here.

Roger Martin Launches New Book

Roger Martin launched his new book on earlier this week in the Atrium at Rotman. "The Design of Business: Why Design Thinking is the Next Competitive Advantage".

Although many companies strive to be innovative, very few often are. Roger Martin offers an interesting explaination in that companies focus on analytical thinking at expense of design thinking. His book investigates the topic further and promises to be an interesting read.

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.

Level 5 Marketing with Peter Drumond

In our Middle East International Study Tour class, Peter Drummond from Level 5 came in to discuss how marketing affects strategy, which is particularly cructial to how we will conduct our market entry strategy projects for bringing companies into the Middle East.

I was fortunate enough to ask him a question relating to how to focus our approach in bringing our company into Dubai. He focused on the emotional aspects of our company's product, which was particularly relevent and discussed Cirque de Soleil (our second choice) as an example.

He talked about Second Cup, and how the core value of similar companies was items such as "sensory experiences", "another place" (similar to what we discussed in the SBUX case). An interesting point was that each of these points never used the word "coffee" in them. And building from this base, there was some importance of understanding his framework of table stakes, key drivers, limitations of operations and hidden value.

With his background, he emphasized the value of intangible assets and how the emotional connections that individuals have can drive additional value add beyond standard economic value creation (the lesson we are learning in Managing Customer Value this term).

Strategy in The Atrium

We have a strategy quiz coming up on Thursday and our professor decided to book out the atrium yesterday evening in order to accommodate all four sections at once. This was probably one of the best lectures we've had in a while if only for the fact that this was the one time all 270 students were able to be in the "same" class.

As with all Atrium speakers, there were some curious on lookers and some students were observing from the second floor and balcony areas.

Anita went through all of the key take aways from each of the cases we've studied so far and reiterated how we are to look at and apply framework to have a better understanding of how strategy affects the profitability of a company.

It's too bad we can't have all our classes like this.

Lunch With Chad

If being outbid was a down point today, then lunch with Chad was certainly a good up point. We eventually decided to forego sushi and head out for lunch at Noodle Bowl on Bloor a little past Spadina.

We had a great chat about what it's like to be in the MBA, what we want to do in the summer and when we are finished here. It was good to see a class mate outside of the class as too often we have hectic whirlwind lives bound within the Rotman bubble.

It seems like this is the first week this quarter has been "reasonable" meaning a hectic pace rather than earlier this quarter (only two or three weeks ago) which have been progressing at break neck speed. We were promised by our second year peers that quarter 2 would probably be the toughest and we are certainly seeing that now.

In the spirit of keeping interesting content coming, I'll be thinking about other great questions to post and see what answers I get. Stay tuned!

United Way Auction - Outbidding Maddness

The Outreach club at Rotman was running an auction to sell items in order to raise funds for the United Way. There were certainly interesting items being auctioned, most of which were meals with professors or second year students, gift sets or even a name card decorating session.

I had put together a small syndicate of bidders to bid on the Capital Markets night out with a fairly healthy max bid. Just before 1 pm, it was pure chaos as there were groups of students sitting out in the atrium trying to outbid each other by different increments for different items. Unfortunately, we got booted below our maximum bid at $1450 because I lost my wifi connection.



However, I'm really impressed with the group of students that I came to bid with. Although everyone was commenting that it "wasn't really worth it", the eventual selling price was only at about a 45% premium over the projected cost and it is for charity and a good cause. Who ever won certainly deserves rock star status.

No one really knows who won yet, but everyone is poking around trying to find out who it is.

An Evening of Hope for Ghana

Saturday certainly wasn't over after RFA's Super Saturday. My good friend, Rich Wiltshire, who had previously worked in Ghana, was organizing a charity event to raise money for this worthy cause. He raise his goal of $5000 for SMIDO which will be used to "improve their training center and give the people in the Suame Magazine community a little bost to have a better life."

It was an interesting evening as I met some people I haven't seen in a while (as far back as our CFES days when Rich and I were organizing Congress events for the Canadian Federation of Engineering Students in Toronto). Ironically, many of them have gone on to do their MBA at Rotman (myself included of course).

It was my conversation with Rich in Malaysia which helped me make the decision to come back to Canada to do my MBA at Rotman. He is certainly one of the ambassadors I was previously referring to. He was on exchange at National University of Singapore (NUS) and he was travelling around and visited me in Kota Kinabalu, Sabah. We climbed Mt. Kinabalu, visited Jalan Gaya and took the whirlwind tour (he was only there for a few days). I remember our conversation sitting in one of the few Starbucks in the city, located at Times Square mall when we were chatting about our futures and where we saw ourselves going.

Later, he would talk to me about his time spent in Ghana and how he was going there to work to do international / business development work. In looking at his photos, I have to admit there were some striking similarities in the context he was working in compared to Kota Kinabalu despite the geographic distance.

Currently, Rich and Fayaz Manji (my official Rotman GBC buddy) are currently trying to build a stronger program to entice Rotman MBAs to do development work in Ghana. If you are interested you should certainly get in contact with them and look into it.

RFA Super Saturday

This past saturday was Rotman's Finance Super Saturday. We had a host of speakers from all the major banks talk about some of the different flavours of finance including investment banking, equity research and sales and trading.

There were a series of live interviews with Joe, Katie and Carl. They were asked questions ranging from "Why investment banking?" to "How would you value a mining company?" with live realtime critiquing on how to best craft our answers to deliver maximum impact in a short amount of time.

Other great questions included: "What types of valuation methods are there?" "Which ones will produce the highest value?" etc.

It's great to see the connections that Rotman has in industry as current alumni were telling us about their roles and offered us insight into how to best compose our application materials and prepare for interviews.

ROA as a Proxy for WACC

I was thinking about the previous brilliant question asked at the Rotman Stock Pitch and I wanted to extend the idea a bit further. While I know there are some obvious short comings in the analysis (and idea of proxies) I would like to make the following proposal:

ROA is a proxy for WACC

Most people know that ROA has to be greater than WACC in order to be profitable. Also, the accounting in the proof highlights an idea I've been struggling with:

A as a proxy for D + E VERSUS L + E

First WACC is calculated as:

WACC = ke (E / (D+E)) + kd (1-t) (D / (D+E))

= [ke * E + kd (1-t) * D] / (D+E)

And ROA is defined as:

ROA = [NI + Int Exp (1-t)] / A

However, recall that ROE is a proxy for ke so:

WACC = [ROE * E + kd (1-t) *D] / (D + E)

Note that ROE * E = NI and
kd * D = Int Exp

Therefore (with some assumptions and proxies):

WACC = NI + Int Exp (1-t) / (D+E)

So we can see that WACC is strikingly similar to ROA. What's the difference? This is the original problem I was having before.

The difference between WACC and ROA is that WACC has a denominator of (D+E) whereas ROA has a denominator of A.

What's the difference? A is L + E, not technically D+E. So what's the difference between Liabilities (L) and Debt (D)?

Debt is technically only Long term debt + Short Term debt (and perhaps minus cash, depending on the financial model?)

L is ALL the liabilities, including Current Liabilities (CL) and "Other long term liabilities".

Periods and Terminal Values

If you look at financial models that people have put together, Terminal Value usually accounts for a monstrous portion of Price (above 50%).

I wanted to ask myself:

[Question] How far into the future do I have to model into the future to make sure that TV is less than x% of the price?

TV is calculated as
CF (1+g)^n / (r-g)
And the PV of TV is TV / (1+r)^n

x% of the price is calculated as
x% * CF (1+g) / (r-g)

So if I want the TV to represent x% of the total price:
TV = x% * PV

Simplifying we get:
x% = (1+g)^n / [(1+r)^n*(1+g)]
x% (1+g) = [(1+g)/(1+r)]^n

Solving for n:
n = ln [x%/(1+g)] / ln [(1+g)/(1+r)]

While hardly a clean solution, this formula can be used to find out how far you need to model in order to have TV represent a given percentage of your price.

For instance, let's say growth of 2% and discount at 8% (standard "long term" numbers), and you want TV to represent 50%, then n should be about 12.5 periods.

Or:
Percent PV @ 2%
40% 16.4 periods
50% 12.5 periods
60% 9.3 periods
70% 6.6 periods
80% 4.3 periods

Dogdeball in the Atrium

Shown here: Jeff McCabe against the world!

Also: Prof. Kent Womack is a dodgeball champ!
Sent from my BlackBerry device on the Rogers Wireless Network

Predicting Venture Cost of Capital with Failure Rate (or Visa Versa)

I just did a little more math and came up with an amazing (in my opinion) result.

Question: Can I use the failure rate to determine an appropriate cost of capital (or visa versa)?

Imagine our previous company, but let's simplify it:

Cash Flow: $10 (it doesn't matter - We'll see why shortly)
Regular discount rate: 8%
Venture discount rate: 20%
Failure Rate: ???

Let's look at a given cash flow in period (n) in isolation:

Well using Method 1 - Venture capital discounting @ 20%:
PV1 = $10 * (1 + g)^n / (1 + 20%)^n

Using Method 2 - Regular equity discounting @ 8%, but undetermined failure rate:
PV2 = $10 * (1 + g)^n * (1 - f)^n / (1 + 8%)^n

Note that PV1 = PV2 according to the law of one price.

Also note: for any given period, you can cancel the effect of:

• period because the failure and discount rate affect the PV in the same way,
• the value of the actual cash flow doesn't matter, and
• the growth factor

All of these factors cancel out algebraically.

So we now know that:
1 / (1.20) = (1 - f) / (1.08)

Solving for f = 10%

[Solution]

So we can see that there is a general relationship:

• ke, "normal" cost of equity
• kv, cost of venture capital
• f, failure rate

(1 + ke) / (1 + kv) = (1 - f)
f = 1 - [(1 + ke) / (1 + kv)]
f = (kv - ke) / (1 + kv)

Similarly:

kv = (ke + f) / (1 - f)

Why does Venture Capital Require High Returns?

Intuitively, we can understand how venture capital requires high discount rates because of the high potential of failure of ventures and speculative projects. However, I wanted to see if it was possible to build a model to describe and bridge the gap between "traditional" valuation modeling and modeling for venture capital firms. What do I mean? I wanted to price a theoretical company using two methods:

1. A traditional venture capital method which accounts for failure in the high discount rate.
2. A variation of a standard method which uses a lower discount rate, but uses probability to account for failure in the cash flow itself.

Company Details (Assumptions):

Next Year's Cash Flow per stock: $10
Super Normal Growth for 3 years: 15%
Perpetual Growth: 2%

Note - Raw Cash Flow Would be:

Year 1 2 3 4 5 (2% - Growth)

Raw Projected Cash Flows $10.00 $11.50 $13.23 $15.21 $15.51

Method 1: Typical Venture Capital Model

Use a high discount rate to account for the failure rate, but assume project will work.
Venture cost of capital (ke) = 20%

Using DCF, the value of the stock is:

Year 1 2 3 4 TV Price

Raw Projected Cash Flows $10.00 $11.50 $13.23 $15.21 $5.07
Method 1 (PV) $8.33 $7.99 $7.65 $7.33 $2.44 $33.75**

Method 2: New model using standard discount rates, but also accounting for possibility of failure (not collect cash flow).

Failure rate: 55% every year
Typical discount rate (ke): 8% (exclude effects of leverage - assume venure can't raise debt)

Year 1 2 3 4 TV Price

Method 2 (Undiscounted)* $10.00 $5.18 $2.68 $1.39 $23.56
Method 2 (PV) $9.26 $4.44 $2.13 $1.02 $17.32 $34.16**

* Cash flow in this method is calculated as Raw cash flow * (1 - Failure Rate)^(Years in Operation - 1) - Note this assumes the company's first year is guaranteed (Big assumption)

** The price is about the same (same ballpark) using both methods, which makes sense with the law of one price.

The difference between the two methods is that Method 1 accounts for the chance of failure in the high discount rate, but Method 2 accounts for the chance of failure as a probability of receiving the cash flow. The same concept would apply with junk / high yield bonds.

The point I'm trying to investigate is the idea that there is an intrinsic relationship (possibly even isomorphic in the same way Womack called Price isomorphic to yield with bonds) between a high required rate of return and high failure rate.

Winner: Chad - Perpetuity Formulas

Congrats to the winner: Chad!

The answer to last night's question is: Infinite

If you calculated the value using the Gordon Growth model (or cash flow perpetuity model), you would get -20.11 (which is what Darshan got).

[Solution - Finance Answer]
If your cash flows grow faster than you discount, each cash flow continues to contribute more and more in terms of present value when calculating the price. With a perpetuity, you are adding an infinite number of values which don't converge.

The perpetuity formula is calculated by using a geometric series of cash flows which include the growth rate and discount rate.

[Solution - Calculus Answer]
Another way to look at this question is what happens when the cost of capital (k) is equal to the growth rate (g). If you use Gordon's Growth model, you get a divide by zero. Or if you look at values of g which are trivially smaller than k, you get astronomical prices (if k = 8% and g = 7.99999%). If you take values of k and g such that g incrementally approaches k in the manner shown above, you can see the astronomical effect it has on the stock price.

If you graph price as a function of g (holding k constant), you can see that there is some crazy behaviour when g is close to k (take the limit as g approaches k).

[Why this question is tricky]
Most people could understand that the numbers didn't look right, but let's look at why.
k is usually pegged at about 8% to reflect the opportunity cost of capital (traditionally it is pegged at historical year-over-year returns in the stock market).

g is usually pegged at inflation or GDP growth and is realistcally 2% (for those of us doing Womack's homework yesterday, he had us do a sensitivity test with ranges between 1 to 4%). Even if a company has phenominal growth, you have to remember that a perpetuity formula is the company's performance ever after. And over time, everyone starts to look "the same". Basic economic theory says that over time overly profitable industries will have entry and become more competitive and you have to consider this when doing a terminal value calculation.

Therefore, the best criticism of the problem I've got is that the growth rate is too high. But the reason it's too high is because most people will only use a growth rate of 3% (at most).

Also, note that ke and kd are both less than g so there is no weighting of capital such that WACC is greater than g (no calculation needed to solve this problem).

Chad: Let me know when you want to go eat!

CONTEST: Free Lunch / Dinner at Sushi On Bloor

I was thinking of (deliberately tricky) questions that might get asked in investment banking interviews and I created this one myself:

What is the theoretical value of a company's stock that:

• has earnings of $1.50 per share,
• Dividend payout ratio of 33%,
  
• has a perpetual earnings growth rate of 9%,
  
• Cost of equity of 9%,
  
• After-tax Cost of debt of 5%, and
  
• Financial Leverage of 2.1x

Hint (Question Variant): What would its PE ratio be?

First person who comments on this blog post with the right answer wins a free lunch / dinner at Sushi on Bloor on me. If you are outside of Toronto, we can think of some other prize of approximately equivalent value (let's say $20 CND).

Comment on the blog for your official submission.

Using Proxies: M&A Accretion or Dilution

Another phenomenal question that was asked at the Rotman stock pitch was this:
Company A is trading at a PE of 10.
Company B is trading at a PE of 15.
Company A acquires B using only debt at an after tax rate of 5%.

Is the deal accretive or dilutive?

This was a brilliant question and the trick was this:

PE is calculated as EPS / Price per Share and is a per share approximation of NI / E which is a proxy for cost of capital. This is the same result as when I was wondering about PEG ratios to find an appropriate discount rate for equity.

So using PE, the reciprocal of 15 is 6.67%. If the deal is paid entirely in debt at a kd(1-t) of 5%, then the cost of capital raised is cheaper than the return on capital used (the returns from the investment instrument we are buying outstrip the costs of the investment instrument we use to raise capital). Think of profiting from a financing transaction.

Another way of thinking of it is that (assuming that equity is always more expensive than debt) is that the change to the capital structure in this transaction is that the two entities are being combined and there is more debt being added to the capital strucure (more leverage, ceteris paribus).

In this case, the deal is accretive. This was absolutely a brilliant question.

A variation of this question could have been: "What if only equity was used to raise capital?"

Then the cost of capital for this incremental deal would be the ke of the acquiring company (Company A). The cost of capital would be the inverse of a PE of 10 or 10%. 10% is greater than the 6.67% of Company B and would therefore be dilutive.

Logically, the next question that follows would be: "Why would a company ever do a deal that's dilutive?"

One possible solution is that we're looking at the original formula for PE and PEG, a company that trades at a high PE ratio (keeping most other characteristics constant and assuming perfectly efficient markets) may have some growth build into the price.

For instance, Company B could be a young upstart company with a really strong product with potential for growth, whereas Company A is more mature but with good distribution networks. Company A might acquire Company B to have access to it's high growth product which it can distribute on it's network for high earnings growth (synergies).

In this case, a short term dilutive transaction might lead to much stronger future earnings growth for the combined entity.

2x Gold Exposure Without Leverage?

Today was the first Rotman stock pitch competition where the second year students gave the first years a chance to practice their skills in valuing and pitching companies. It was an interesting experience for all of us and there were many lessons learned.

In talking to other people doing pitches for companies in different industries, there was a lot of learning between groups. I though I would write about some of the more interesting lessons.

This post is focused on gold (or mining exposure to raw materials). Gold and copper have very important attributes and characteristics which are highly correlated to the health and confidence of the economy, especially as it relates to Canada. As a result, most portfolios will have some exposure in these areas depending on the strategy. Gold is often used as a hedge against inflation, but copper is associated as a leading indicator for the health of the economy.

However, in order to make larger hedges in the market based on these commodities, portfolios will utilize instruments which promise 2x exposure to these materials. When I first heard this, I asked, "How is it possible to have 2x exposure without employing some form of leverage?"

As Shree explained to me, this is how it works:
Imagine gold is selling for $1000 per ounce.
Imagine a company can mine gold for $500 per ounce.
It's profit is $500 per ounce (and let's exclude all other costs for now, or assume that the $500 per ounce includes all expenses).

Now imagine gold rises in price to $1100 per ounce.
The company can still mine it for $500 per ounce.
The profit is now $600.

Gold has only gone up 10%, but the companies earnings have gone up 20%! It's a 2x exposure without any leverage.

The Calculus of Duration

We have been discussing bonds and spot rates in finance as a fairly "simple" investment vehicle (no default risk for government bonds and steady and predictable cash flows).

While I had technically learned the math behind bond duration, it was after the homework assignment that we were assigned in finance that I began to get a better understanding of exactly what this means and why it's important.

As I had mentioned before, duration is defined as the percent change in price for a given change in yield. You'll notice that the definition of the formula is strikingly similar to elasticity calculations.

However, rather that jump in at that level, let's talk about it from the first principles of calculus:

P = C + C/(1+y) + C/(1+y)^2 + C/(1+y)^3 + ... + C/(1+y)^n + M/(1+y)^n

Where P is the price of the bond, C is the coupon and y is the YTM and M is the face value. So far nothing new. But the next idea is to take the derivative of the Price, P, with respect to y to understand how the price will be affected for any give change in y. We can re-write the formula as:

P = C + C (1+y)^-1 + C (1+y)^-2 + C (1+y)^-3 + ... + C (1+y)^-n + M (1+y)^-n

dP/dy = - C (1+y)^-2 + -2 C (1+y)^-3 + -3 C (1+y)^-4 + ... + -n C (1+y)^-(n+1) + -n M (1+y)^-(n+1)
= -1/(1+y)[ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n

Recall that dP/dy describes the change in P with respect to y. In order to get percentage change, we divide both sides by P. This gives us the term dP/dy * 1/P which is a precursor to understanding % change in P or modified duration:

dP/dy * (1/P) = (1/P)[ -1/(1+y)][ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n]

There is a special definition for the monstrous summation term above called the Macaulay duration which is defined as:

Macaulay duration = [ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n] / P

Modified Duration = -Maccaulay duration / (1 + y)
= dP/dy * (1/P)

That's a lot of complicated math with calculus. What is the value of this exercise? Well if you can understand how your bond liabilities will move with interest rates, you can construct a portfolio of bonds which can insulate (immunize) you from changes in the price due to changes in the yield even if the bond's structure you are using to immunize is not of the same construction as the original liability buy matching face values and durations.

Therefore any change in the percentage value of your liability will be offset by a similar change in the percentage value of your bond portfolio (a hedging asset).

Capital Markets Technical Prep

"They" have always said that preparing for recruitment is like taking another class. That was certainly the case this morning as the CCC prepared a morning session entitled: "Capital Markets Technical Overview". The session was fully booked and Heather-Anne Irwin was teaching us about how to ramp up our learning for capital markets beyond what we were taught in our classes.

She gave us the opportunity to try to discuss complex finance terms in layman's terms appropriate for a technical interview scenario as well as a quick review of key financial indicators and what the implications were for movement in either direction. It was certainly a good primer for us to go about doing our own homework to learn more and form our own opinions of what's happening in the market.

While we are not officially graded on this course, perhaps our "grade" is the most important grade of all, the stamp of approval in the form of a summer job offer.

Tell Me The Story

In preparing to enter the business world, we were told that it would be a good idea to read the paper daily. We were promised that it would become natural and, even in the extreme, that there are some people that look forward to that morning paper.

As of today, I'm am now in that place. I've been regularly reading the paper to understand the key business stories of the day, but I'm starting to feel a sense of withdrawal since there was no Sunday paper today at Rotman. I actually find myself craving reading tomorrow's paper to see what has been happening in the business world and around the globe. I caught myself browsing through the internet looking for news stories about some of the major companies that have been in the news lately and the latest related developments.

We've also be given our companies for the RFA stock pitch competition and my partner and I have reviewed our company and although it presents its unique challenges it is also paired with unique and highly profitable earnings growth opportunities (a healthy CAGR), we believe we have a compelling story for a long position.

This bring me to my point. Most people who know me know that I am comfortable with numbers (a quant by nature and training). But doing the CFA and MBA has reminded me (or rather, highlighted in my personality) that I want to know the story behind the numbers. In reading the paper and analyzing the company we were assigned for the competition, I've found that I really enjoy the discussion that follows thoughtful analysis.

Porter's Five Forces and Basic Economic Theory

In our strategy class last week, we were discussing Porter's Five Forces by extending the idea beyond just a static analysis of the industry as is, but looking at the trends in movement for each of the five forces.

I suspected that there would be a pattern that industries with forces which have a rating of "low" would naturally have a trend of "increasing" whereas forces with "high" ratings would have trends of "decreasing" assuming efficient markets. While not a perfectly isomorphic, I would expect this relationship to at least have a high correlation coefficient in terms of regression if you had to build a model for prediction.

When it comes to Buyer or Supplier Power (a recursive framework which can be applied forwards or backwards with regards to vertical integration / value add or creation), I've always enjoyed using elasticity as a measure of bargaining power. However, in economics, there is the axiom that over time there is more "flexibility" for substitution which I would suggest directly results in increased elasticity.

In the same way that a buyer might not have flexibility or bargaining power in the short term, the natural inclination would be for substitutes to enter into an industry with low price elasticity in order to capture producer surplus (in the case of inelastic demand).

In more pragmatic terms, while it might be academically sound (and necessary) to look at historic values to understand how we got to where we are, it doesn't really become as useful (and it is hardly sufficient) until we understand not only our position, but where we are going.