Ship of Theseus as a Metaphor for Replacement Cost

Looking at the Parthenon being restored, it reminds me of another Greek concept: the ship of Theseus. It is essentially an identity dilemma: If you take care of something, but are forced to replace parts due to decay over time, is that object still the same? This is something I’m sure archeologists wrestle with when they rebuild replica parts to restore murals or structures for which the original parts are long gone. Even if they use the same material, artistry and methods, the original has lost something ineffable.

This concept has been extended several times with several unique spins, my favourite being Plato’s carriage, where Socrates and Plato exchange parts on their carriages until finally “Socrates’” carriage is made entirely of Plato’s original carriage and vice versa. At what point did the identity of the carriage change?

In a vain attempt to bring all my philosophizing back into the MBA realm of finance, it’s sort of interesting when you think about it in the context of the idea in accounting principle of replacement cost or M&A. While accounting will capture the physical quantities contained within a company’s finances, there also exists value beyond the sum of its parts in the same way you would expect an M&A transaction’s synergies to broaden the qualities of the combined entities: that seemingly ineffable quality.

Parthenon and the Golden Ratio

Today I visited the Parthenon which is one of my favourite buildings and the preeminent landmark of Athens and located in the Acropolis. And yet, many people are unaware of the beautiful mathematical design it holds in plain view. Built into the Parthenon’s design you will often discover that many porportions are designed to the golden ratio, also known as the divine proportion, the ratio that many Greek’s believed to be the source of proportional mathematical beauty.

Shown above: Parthenon

Many believed that this ratio occurred often in nature and was the basis for beautiful proportions (for example it appears in Leonardo Da Vinci’s Vitruvian Man as the ratio between the length of the arms and legs).  Another occurance is with Fibonacci numbers as the ratio between them is an approximation of this same ratio (Fibonacci numbers are numbers in a sequence in which the next number is the sum of the previous two numbers). The approximation becomes more accurate the further out you go. Note: It's only an approximation because the first two numbers are one and one.

The golden ratio is mathematically defined as follows:

(A + B) / A = A / B

Or in layman’s terms, the proportion between two measures is the same as the proportion of their combined length and the larger length. Note that this definition can be recursive and applied over multiple lengths repeatedly.

Also note, that the proof for the actual ratio is self is quite elegant:

(A + B) / A = A / B (Multiplying both sides by A x B we get)

AB + B^2 = A^2

0 = A^2 – AB – B^2

= A^2 – AB + 1/4 B^2 – 1/4 B^2 – B^2

= (A – 1/2 B)^2 – 5/4 B^2

Now assume that B is 1.

= (A – 1/2)^2 – 5/4

5/4 = (A – 1/2)^2

Sqrt(5) / 2 = A – 1/2

Therefore, the golden ratio, A = [1 + sqrt (5)] / 2

Note that this makes A approximately 1.62. (it is an irrational mathematical constant)

Intricate in its beauty, elegant in its simplicity.

Near the Parthenon was once the statue of Athena overlooking the city.

Shown above: Athena's perch from which she offered Victory to the Athenians, now long vacant.

Previously, this building was home to statue of the grey-eyed goddess who watched over her namesake and in her raised hand held Nike, the winged goddess of victory. While the statue is long gone, perhaps it is time for the Greeks to look after her and her fellow Olympians as they recover and protect artifacts of the past.

Athens Metro

The Athens Metro is one of the newest and most beautiful metro systems in the world despite (or rather because) it took an immensely long time to build. This is because as they dug, they had to stop because they often ran into old archeological ruins. Then they would stop digging with machines and archeologists would dig with toothbrushes. The metro plan was equal parts archeological dig as it was construction site.

However, the result is a brilliantly new metro system that includes exhibits and finds from their digs and the duality continues: it is both museum and metro station.

The fare is 1.40 euro for a 90 minute multi-trip ticket which needs to be validated. A day pass is 4 euro.

Greek Hospitality

I tend to have a recklessly casual travel style when it comes to recreational travel (e.g. going to Mt Olympus when it’s closed because I won't be back for a few years). While this often tends to get me lost, I'd be lying if I didn't also admit that this has led to some of my best experiences while travelling.

Having said that, it can also lead to me being at the mercy of the locals. While I'd like to think I have the street smarts to get by, I also have to admit that the kindness inherent in the Greek culture makes it particularly easy.

Maybe it’s because they have had a seafaring culture for centuries / millennia and are accustomed to disoriented visitors arriving from around the world, but I have always had a deep respect for Greek hospitality, an important theme in the Odyssey by Homer, one of my favourite books. This also reminds me of one of my favourite scenes: Book VIII – The Games, when Ulysses meets Euryalus.

Context: Ulysses is lost. It's the whole premise of the book. And throughout, he experiences either kindness or evil from different characters. In this book, he arrives on the shore of the House of Alcinous. During the feast, the blind poet, Demodocus, sings songs of Ulysses' exploits, ironically, not knowing he is in the room. Ulysses' weeping is noticed only by Alcinous, who proceeds to distract his guest by suggesting they compete in athletic competitions instead.

During the competition, Alcinous's son, Laodamas, the best boxer, thinks to invite Ulysses to participate and Euryalus foolishly insults him when Ulysses politely declines due to the ravages of “infinite trouble” he’s experienced making his heart heavy for home. Ulysses proceeds to throw the heaviest disc the furthest distance (without even taking off his jacket) and proceeds to challenge anyone and everyone to any contest of their choosing (except for running due to his old age, and except for Laodamas, Alcinous' son, of course, respecting the role of the host's family). Alcinous politely calls Euryalus an idiot and calls for more festivities, hoping to prove to Ulysses that while the Phaeacians were not known for their athletic prowess, he was hoping to prove that they are exceptionally hospitable: “extremely fond of good dinners, music, and dancing”.

After acknowledging the spectacle of dancing, Ulysses compliments Alcinous, to which Alcinous responds by asking the twelve chief men (thirteen with himself) to give him “a clean cloak, a shirt, and a talent of fine gold”. Having disrespected Ulysses by supposing him to be unathletic and breaking the Greek code of hospitality to foreigners, Euryalus apologizes by giving him a gift: a beautiful bronze sword. Ulysses, making peace with his new friend, accepts the gift graciously, remarking that he hopes Euryalus will never have need of it.

(Read the original as this paraphrasing doesn’t do justice to the original poetry. Plus, there is a hilarious adulterer's story of warning told by Demodocus of Hephaistos, Venus and Aries)

As my highschool english teacher once explained, the concept of gift giving was important in Greek culture in that it emphasized the role of both gift giver and acceptee. It symbolized the greatness of the giver to be able to offer a gift as well as the importance of the recipient by being shown respect through the offer of a gift.

Climbing Mount Olympus

This is an instruction guide for anyone who might be interested in visiting Mount Olympus on a student budget. I thought I should write this down as I had unusual difficulty getting details and will probably be back here again sometime. After arriving in Thessaloniki, I got instructions, searched the internet and otherwise asked around for how to climb Mount Olympus:

Getting to Litohoro from Thessaloniki

1. From Thessaloniki airport, take the 78 bus into the city (it goes along Tsimiski street), buy the two ride ticket which costs 1 euro (allows two trips within 90 minutes if I read the instructions correctly)
2. From Thessaloniki, take the 31 bus from Egnatias street (one major street north of Tsimiski)
3. Take the 31 bus to the end of the line to Makedonia bus station
4. Go to the booth for KTEL (Greece public transit, similar to Greyhound) Platform 4 – Litohoro (or Litochoro, multiple spellings)
5. Buy a ticket (student fair is for Greek students only), one way was 8 euro, return was 14
6. Go to Platform 4 and take the bus (it is quite frequent, between one or two hours per bus)
7. The bus stops at Katerini (Don’t get off)
8. The ride to Litohoro is about an hour and drops you off in the city center

Note: There is a KTEL bus from Athens to Litohoro too. I don’t know where it leaves from, but I’ll find out tomorrow when I go to Athens from Litohoro.

Litohoro

The entire climb is along the E4 International Walking trail. Here you have two choices:

Choice 1: Scenic climb From Litohoro to Prionia

From the city center (the water fountain where the KTEL bus drops you off), walk straight past the Hotel Aphrodite and go right, past the residential housing, school and cemetery and past the power / utility plant (There are some dual language signs pointing the way to Olympus National Park).

You will reach the first gate which has signs saying “Olympus National Park”. The climb from Litohoro to Prionia is through the gorge of Olympus, and takes between 4.5 to 5 hours (or more if you take your time, relax and take photos) to go up. There are beautiful cliff faces and crystal clear waterfalls.

 

Choice 2: Skip with Taxi to Prionia (cost 25 to 30 euro one way, 20 minute drive)

If you come to Litohoro in the off season (season this year starts May 13th), then the refuges will be closed and your best bet is to climb the gorge. It is absolutely beautiful and mildly challenging. I promise you will enjoy it's undulating terrain. However, many people "cheat", take a taxi to the top and climb down or climb up and hitchhike down. It is a 5 hour hike one way afterall.

Above: Like Mount Kinabalu in Kota Kinabalu, Sabah, Malaysia (which I plan on doing again with a friend of mine this summer), you can expect to see a lot of this on your way up.

If you come to Litohoro when the refuges are open, then take the taxi to Prionia as it will be taxing enough just to make it to the refuge which is the midpoint from Prionia to the peaks of Mt. Olympus.

People often give advice to “book in advance”, but I was unable to find any good websites or information on ANYTHING, transport to Litohoro from Thessaloniki, accommodation etc.

I’m currently staying in the Hotel Mirtos in Litohoro which is charging me 30 euro a night (keep in mind this is the off season, I think I’m the only guest and they are currently under construction so I have no idea how much it costs when the tourists come in the on season). Tel 23520 81398.

Apparently, Refuge A (which from what I gather is the best one to be in) can be reached at 23520 81800. They spoke English when I called.

Good luck!

Cheerio!

Later tonight (or, more accurately, early tomorrow morning) I will be flying out of London for Thessaloniki, Greece for my last course: Service Management Field trip, a consulting based project where we work with local companies. While the class doesn’t start until the third week of April, I’ll be in Greece and surrounding countries travelling.

So I apologize in advance if there are few posts between now and then. But who knows? In the country that spawned famous philosophers and mathematicians, maybe there will be some inspiration. Plus, I still have a few small assignments to complete for MCT.

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.