Scotia in Dubai

Today, Scotia Mocatta gained approval to operate it's own branch in Dubai to provide gold and price hedging services.

This will certainly be an interesting story to follow both for the implications of gold and the region.

The price of gold seems to be particularly noteworthy, having dropped to below 1100 yesterday for the first time in a while.

Dubai Stock Exchanges Merge

Dubai Financial Market announced today that they will be merging with Nasdaq Dubai for $121M. Also, the troubles with their debt might not yet be over as Dubai World may have to continue to restructure their debt.

There are certainly many interesting events in the area with a lot of activity in this market. It will certainly be worth while to see how the restructuring in the market will manifest and effect other markets around the world.

24h Strategy Case Comp

Yesterday at Rotman we had the 24 hour case competition (mandatory as part of our Strategy Class with Anita McGahan, shown above) with all the first year MBAs.

There were 49 teams of 5 or 6 students each in 7 rooms (7 teams per presentation room competiting against each other in the first round). We were assigned teams and asked to work on and present the case in 24 hours with newly assigned teams (not our teams from Q1-Q2).

I got assigned to a great team: Francois, James P., Miranda and Selina and we managed to place third in the competition overall!

Q2 - Done and Done

One way or another, we are done the dreaded Q2. Tonight, we are heading down to Grace O'Malleys and partying with the second years and others. It promises to be a good night. A good good night.

Mechanics of Retirement Planning

A question I posed to some of my classmates who wanted to practice DCF or time value of money questions:

John is 20 years old and is making $100k annually. He plans on retiring at 65 and will require 70% of his current annual income every year thereafter. The general life expectancy is 'til 85. And he can earn 8% on any money he invests.

How much does John need to save per year in order to retire at 65 according to plan?

[Solution]
You would break this question into two parts.

Part I: Nest Egg - Understanding the PV of the money he needs in retirement (aka how much he needs to have saved by 65)
Using a financial calculator:
PV = ?

FV = 0 (Doesn't plan on giving any inheritance when he dies)
PMT = 70,000 (70% of 100k)
P/Y = 1 (1 period per year, NOT semi-annual)
I/Y = 8
N = 20 (Retires and lives for 20 years, 85 - 65)
PV = 687,270.32 (How much his nest egg should be at 65)

Part II: How much he needs to invest every year
PMT = ?

FV = PV @ 65 = 687,270.32 (How much his nest egg should be at 65)
P/Y = 1
I/Y = 8
N = 45 (Works for 45 years, 65 - 20)
PV = 0 (Starts with nothing)
PMT = 1,778.16

John needs to save 1,778.16 per year. Now most people will say: "That seems really low"

That's true, but look at the scenario: John is saving for 45 years and spending for 20 years. For all of those 65 years, John is earning 8% on every dollar he's invested (aka he's not using). This returns to our original point when it comes to personal finance: "You can buy stocks. You can buy bonds. You can even buy good advice. But the one thing you can't buy is time."

Inventory Turnover - An Alternative

I was thinking about Inventory Turnover (and other similar accounts and operating / activity ratios) when I noticed what I thought were some assumptions that were made that might not be appropriate for all business types.

Recall: The formula for Inventory Turnover is: COGS / Average Inventory

For intance, if you look at an annual report this is what you see regarding inventory:
You get only two numbers regarding the ending balance last year (beginning balance this year) and the ending balance this year. The assumption is that the inventory gradually increased from it's last year's value to this year's value. So we take the value of the area under the graph to produce an average Inventory (Area divided by time).
Rather than calculate the area under the graph of an awkward trapezoid, an easy way to do this is to approximate the volume by taking the average of the two points and taking the area of the resulting rectangle (assuming the line above is straight, this is an exact approximation).
However, while this assumption might be a good approximation for most businesses, this inventory model isn't appropriate for many other types of businesses. Which kinds? I would argue businesses where design is important the inventory takes a much different shape (as shown below):Which types of business might exhibit this behaviour? I would suggest two candidates would be clothing stores or automotive dealers. Why? Because they often shift their inventory for new models every year. Their inventory levels will spike starting at the beginning of the year and then towards the end they will sell out all their inventory to reduce carrying costs and get rid of "old" inventory which will be harder to sell (or sell at a discount etc).

The point I'm trying to make is that if you use the previous (generally accepted) model, you will be underestimating your inventory turnover model because your ending reported inventory is not an accurate reflection of your "average" inventory carried throughout the year.

In the same way some people might cheat a stock price by invoking a "window dressing" price (deliberately bidding up the last trade of the day to inflate the close, I think that if you aren't aware of how the inventory moves throughout the year, you might be in danger of accepting a "window dressing" inventory value.

ICUP

I know it's the eve of the finance exam and most people are expecting me to do finance posts. I'm sure I'll oblige later. But first, I need to make a comment regarding exams and people going to the washroom. What is it about exams where people suddenly have weak bladders? During exams, whether they be MBA or CFA, there are always people getting up to go the washroom.

During today's MCV exam, at the 45 minute mark when people were officially allowed to use the rest room facilities, a few hands immediately went up to use the facilities. I have to admit I do find it mildly hilarious. I don't think I've ever used the facilities during an exam. I think it's a bit creepy and childish to have to be escorted by an exam proctor.

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.

Venture Capital - Burn Rate

In preparing for our accounting exam (final exams for this quarter start next week with the rest of the university), I wanted to have a quick look at burn rate. One of the concepts taught in our class is cash flows of companies in different stages. An idea I wanted to look into a bit deeper was the idea of cash flows for start up companies.

Cash flow is the primary metric of financial health. For a start up company, there is a lot of money going out the door, but often little money coming in. Revenues are low or non-existant, R&D (and expenses in general) can often be high, and working capital and CAPEX are growing.

Although I've seen different "interpretations" of burn rate it is essentially an FCF which is negative. An operational definition is how much cash is going out the door excluding what is being replaced through financing activities (CFF). I would say that CFO less CAPEX is generally a good proxy of where burn rate is. The assumption is that other sources of cash flows (selling assets, raising cash through financing etc) are not guaranteed and also not sustainable.

The next important measure of financial health is the actual cash and equivalents account. Between the two values, burn rate and cash, you can approximate how long the company will survive without additional financing activities (cash / burn rate per quarter = approximate longevity in quarters).

The goal, of course, is the hockey stick shaped recovery: eventually investing enough to develop a revolutionary product or service that causes revenue and profits to go through the roof (and provided dramatic long term IRR).

Enterprise Value - Cash, how much is too much?

One interesting note made by our professor, Heather Ann Irwin, was for calculating EV.

I've learned the two basic ways to calculate EV (again in theory they should work out to be the same):

EV = EBITDA x Multiple
or
EV = Market Capitalization + Net Debt

Where
Market Capitalization = Share Price x # of Shares
Net Debt = Long Term Debt + Short Term Debt - Cash and Equivalents

I've been told there are more sophisticated versions of EV which include:
+ Preferred Shares
+ Minority Interest

And that the reason we use EV is to look a the company's value assessed under a capital structure neutral scenario (because the capital structure will change when you acquire it).

What I wanted to focus on is the Net Debt component, specifically cash and equivalents. Heather Ann Irwin mentioned a version of the formula which uses "excess cash" instead of cash. I had an idea what she meant but I asked her to clarify. She confirmed my perspective of her idea:

You subtract cash from net debt (and from EV) because cash has a special relationship as a highly liquid asset, so it is often seen as different from other working capital accounts (such as AR, Inv or Prepaid Exp). However, a company still requires some cash to run. The assumption of removing cash from net debt implies that you are acquiring the company for it's "raw" value. Leaving the cash in the company's EV is like buying cash with cash.

However, Heather Ann Irwin proposed that instead of "cash and equivalents" we should use "excess cash". This subtle difference is rather interesting. Yes, cash has a special relationship and is therefore different than other current accounts and working capital, however, you still need SOME cash in order to operate and maintain liquidity. But you don't want ALL the cash (you don't want to have to raise more funds than you need or else you risk screwing up your WACC when you try to raise too much funds). So rather than cutting out all the cash (or none at all) she is suggesting that you remove the excess cash, cash that is not necessary.

In other works, there is some cash which should be treated like working capital because it is actively employed in keeping the company running. The other "cash and equivalents" which are relatively stagnant should be excluded from the EV calculation. When I asked her what constitutes "excess cash" and how would you determine it, she had a great answer: Look at the liquidity ratios and do comps analysis. I'd have to think that it would also be prudent to look at the cash cycle.

I guess this is one of those subtle points that would probably come up in the negotiation of an M&A deal if someone was thinking of acquiring a company. It would probably come up as a point of discussion in terms of the strategic nature of the acquisition and the target capital structure after the deal was done.

Terminal Valuations - Theory and Practice

Yesterday, we had another Capital Markets Technical Prep session. We were looking at valuation methods including DCF, multiples, book value and precedent transactions.

In DCF, we talked about how to value a company's terminal value and discussed how in theory the values should be the same. This a concept I talked about at the Analyst Exchange when I was giving my lecture on geometric series (the math behind DCF's perpetuity formula). In the video, I briefly mentioned how our Hedge Fund Manager commented how it was a coincidence that the numbers were so similar. In theory, as our professor, Heather Ann Irwin mentioned, they should be the same and I just wanted to have a quick look at what the implication is.

There are two methods for valuing a companies terminal value are using a perpetuity method and EBITDA multiples.

The first method, the Terminal Value calculation using a perpetuity formula is: TV = FCF / (WACC - g).

The second method, the TV using EBITDA multiples is: TV = EBITDA x Multiple.

However, if in theory, they are supposed to be the same:

FCF / (WACC - g) = EBITDA x Multiple

I wanted to express the multiple in terms of the perpetuity formula so I rearranged the equation to get:

Multiple = (FCF/EBITDA) / (WACC - G)

This is exactly the point I was trying to make in my lecture in New York when I said that the two formulas and methods were related (except I forgot to highlight the "correction factor" between FCF and EBITDA which is essentially the same as a cash flow to operating profit margin - a factor which adjusts for the difference between FCF and EBITDA - just because EBITDA is often a proxy for FCF doesn't mean it's exact).

Another way of looking at this is as a mathematical proof for why comps valuation works. From an Integrative Thinking perspective, it is essentially looking at two different models for valuation which are looking at the same object and producing different results. Even though in theory both models look at the identical object, they will produce different values, yet I think this is a good integrative solution for understanding what is salient and causal in both models (and how they are related despite their differences).

In this way, if you could have perfect information, assuming that other analysts did comprehensive DCF, you could take a similar company and use the comps multiples to value that company.

Revisiting History - "Pricing the upside derivative"

Our finance professor, Kent Womack, was just describing the model for pricing derivatives and it is almost exactly what I suggested the best method for pricing options would be based on my intuition in January (and was the topic of my Peter Godsoe Scholarship Award in Financial Engineering). He even asked the same questions I was looking into when I was studying for the CFA exam regarding the profit profiles for different put options and call options and why you would enter into different positions.

In his slide, he even mentions the idea of the distribution of stock prices influencing the expected outcome. I think the only difference in our models is that he used a distribution called Geometric Brownian Motion. It's similar to my normal distribution assumption, however, it accounts for an upward drift (which I didn't account for). However, I wonder if it can be approximated with a shifted normal distribution (mean greater than zero).

Also, to actually determine his option price prof. Womack used simulations whereas my model was based more on mathematical calculations. I'm sure both methods to determine the price are acceptable as it's more the model for describing the final underlying price that is more important.

Another improvement from his model is the inclusion of the time value of money as he discounts the future gains back to the present value.

Bova @ the ROM

Due to construction, renovation and expansion at Rotman being disruptive, we've moved our classes to the Royal Ontario Museum theater.

Our accounting professor, Francesco Bova, had the honour of being the first prof to teach us in the ROM. He gave us a warm morning welcome (shown above). It was another rare class where all four sections were together.

At the end of class, Francesco thanked the PSO and the class reps: Myself, Amit, Thi and Katie. Anita McGahan had also done the same in our last Strategy class. What classy profs.