Harvard Business Case Study : Bidding for the Antamina Mine (Alberto Moel and Peter Tufano)

Salah satu kasus dari Harvard Business School yang sering digunakan di sekolah –sekolah bisnis dalam membahas kajian real options ini adalah kasus proses tender untuk sebuah tambang tembaga oleh pemerintah Peru pada tahun 1996.

Kasus ini menarik untuk dipelajari karena pada proses tender ini, investor diberikan opsi untuk keluar dari proyek tersebut, jika eksplorasi yang dilakukan selama dua tahun tidak menghasilkan apa-apa sebagaimana tergambar dibawah ini.



Jika cadangan yang ditemukan memadai dan investor setuju untuk mengembangkan tambang ini, maka investor harus memberikan komitment berapa investasi yang akan dikeluarkan. Apabila investor nantinya tidak mencapai target investasi yang pernah dijanjikan maka pemerintah Peru akan memberikan penalty kepada investor sebesar 30% atas selisih antara realisasi biaya pengembangan yang terjadi dan komitmen awalnya.

Dalam tender ini, peserta tender diminta untuk mendaftarkan proposal penawarannya yang meliputi jumlah uang yang akan dibayar untuk pengikatan kontrak serta jumlah investasi yang akan mereka janjikan jika tambang itu akan dikembangkan.

Disinilah yang menjadi tantangan bagi peserta tender, apakah akan memperbesar jumlah uang yang harus dibayar awal ataukah jumlah komitmen investasi yang akan mereka bayarkan.
Pada saat pertama kali diumumkan, ada lebih dari 40 perusahaan yang tertarik untuk masuk dalam tahap prekualifikasi. Dari jumlah ini, 12 perusahaan dari Canada, Afrika Selatan, Inggris dan Jepang yang memperlihatkan keseriusan dan melakukan “data room”. Pada tahap akhir, hanya tiga perusahaan yang mendaftarkan proposalnya yaitu RTZ-CRA (sekarang Rio Tinto), Noranda, dan joint venture Inmet Mining – Rio Algom.

Sedikitnya informasi geologi dari tambang ini, menyebabkan tingginya ketidakpastian dari proyek ini. Data yang digunakan untuk penilaian kasus ini adalah sebagai berikut :

Adapun data lainnya diambil dari pasar keuangan yaitu data harian dari London Metals Exchange (LME) untuk periode Septermber 1991 sampai Juli 1996 yang digunakan untuk menentukan parameter dari model harga logam.

Disamping itu dari pasar keuangan diperoleh data korelasi return untuk tembaga dan seng beserta “convenience yields”nya masing-masing. Semua korelasi untuk data harian untuk periode September 1991 - July 1996.

Berdasarkan data-data diatas kita dapat lakukan suatu simulasi model stochastic selama 24 bulan (2 tahun) dari tahun 1996 dimana pada akhir tahun 1998, diasumsikan kita akan masuk dalam kontrak “forward” pada saat kita akan memproduksi mineral ini sehingga kita terlindung dari fluktuasi harga logam ini di pasaran.

Dengan mengambil basis 1996 sebagai tahun evaluasi dan asumsi bahwa probabilitas untuk masing-masing skenario adalah sebagai berikut :
1. Skenario “low” = 20% dengan investasi sebesar $581MM
2. Skenario “base” = 40% dengan investasi sebesar $602 MM
3. Skenario “high” = 20% dengan investasi sebesar $622 MM

maka diasumsikan kita akan mendapatkan hasil NPV pada tahun 1996 sebagai berikut :
1. Jika tidak ada asumsi untuk abandon project ditahun 1998 maka NPV = $1,425 MM
2. Jika ada asumsi untuk abandon project ditahun 1998 maka NPV = $1,525 MM

Dengan melihat kondisi diatas, terlihat bahwa opsi untuk melakukan abandon di tahun 1998 mempunyai nilai sebesar $100 MM.

Dari proses tender ini ada tiga perusahaan yang mendaftarkan proposal penawarannya yaitu :
RTZ-CRA Ltd, menawarkan $17.5 M sebagai pembayaran awal dan $900 M sebagai komitment investasi
Noranda menawarkan dengan jumlah yang sama yaitu $17.5 M sebagai pembayaran awal dan $1,900 M sebagai komitment investasi
Perusahaan kecil, Aliansi Rio Algom/Inmet menawar dengan $20.0 M sebagai pembayaran awal dan $2,500 M sebagai komitment investasi

Berdasarkan proposal dari tiga bidder maka pemerintah Peru akan menerima bid sebagai berikut :

Dari 3 penawaran diatas, terlihat bahwa Aliansi Algom/Inmet berhasi memenangkan tender ini dengan harga tawar yang paling tinggi.
Sekarang mari kita analisa apakah pemenang tender ini memberikan penawaran yang tidak wajar.

Jika kita asumsikan nilai PV diluar investasi dan penalti serta investasi yang terjadi adalah sebagai berikut :

Jika kita lihat hasil akhir keekonomian dari tiga proposal bidder ini adalah :

Dilihat dari hasil akhirnya terlihat bahwa hasil yang diharapkan Rio Algom/Imment adalah 50% lebih kecil dibandingkan dengan RTZ-CRA, namun demikian keuntungan ini masih diatas $1,000 MM.

Yang menarik adalah pernyataan dari eksekutif Rio Algom/Imment pada hari yang sama saat diumumkan jadi pemenang, bahwa mereka hanya akan membelanjakan sekitar $1,000 MM untuk mengembangkan tambang Antamina. Pernyataan mereka adalah "If it does not prove viable, we just lose our up-front investment”.
Disini jelas bahwa, mereka sangat mengenal adanya “options” yang ada dalam aturan tender tersebut. Ini mengindikasikan mereka tidak akan berencana berinvestasi sebesar $2,500 MM melainkan hanya sekitar $1,000 MM termasuk didalamnya penalty. Mereka tampaknya ingin memberikan pemahaman kepada analist sekuritas bahwa mereka tidak “overpaid” pada tambang tersebut. Mereka secara jelas mengerti bentuk opsi dari penawaran ini.

Enclave

It figures that that the makers of the dying breed of vehicles known as SUV's have given one model the name Enclave.

enclave (n) : a distinct territorial, cultural, or social unit enclosed within or as if within foreign territory

Soon to come: the Garrison, the Fortress, the Anchor, the White Elephant.

The Shock Model in Action

Brown warns of global oil 'shock'


Radio talker Mike Malloy spent some time talking peak oil recently. As always, he had some interesting takes, especially concerning the religious right's belief in abundant oil. His response was "Well the Lord giveth, and the Lord taketh away".

Similar to what Aldo Leopold said: "the Lord giveth, and the Lord taketh away, but he is no longer the only one to do so."

Oil has become a despised personality

Jim Quinn, rabid right wing talk show host: "Somebody said this -- We can't make up for lack of oil by drilling more. That's as crazy as saying we can't make up a shortage of food by growing more"

Gold Rush dynamics, the Dispersive Discovery sanity check

Dynamics such as those that lead to extinction events and of boom-bust periods first motivated me to generalize discovery dynamics in terms of dispersive effects.

If we look into an extinction event such as passenger pigeons in the 1800's, we find a steadily accelerating harvest per year until culling hit a critical point and then fell precipitously. The harvests went spectacularly to zero and so, unfortunately, did the pigeon population.

I can say the same for boom-bust cycles, such as happened during the gold-rush days of the 1800's. In most cases, a boom occurred on the onset of an isolated discovery as many prospectors joined the search, enough time passed to enable the building of a huge infrastructure and then suddenly everything dried up with the infrastructure left standing in place.

But that hasn't happened with the discoveries of fossil fuel around the world. Although discoveries did increase at an accelerating pace until about the mid-part of the 20^the century, reaching a peak a little after 1960, many discoveries continue to occur and the bottom did not fall out, unlike the cases of extinction and nini-boom-busts. We explain this by considering the role of dispersion in the discoveries. The following figure shows a non-dispersed discovery function, which reaches a sharp peak and then drops to zero as prospectors finish searching an isolated volume of potential finds.



This basically happens when a highly localized search takes place, as with the case of the blanket coverage of passenger pigeon flyways with an efficient army of hunters (often equipped with explosives!). Its also happens with prospectors sifting everything with the equivalent of a fine-tooth comb in some localized gold strike area.

But the discovery of oil differs as dispersion in the rates of discovery in various parts of the world lead to a broad smearing of the bust peak. In fact, the effective bust peak (equal integrated volume) only lines up on the backside of the dispersed profile. This all makes consistent sense and provides a further argument against the use of the Logistic function to model any of these kinds of search processes, dispersed or not.

In other words someone has to explain why a symmetric Logistic function (ala the classic Hubbert curve) does not explain the steep drop-off displayed in many culling-forced extinction examples and of the bust drop-off in gold-rush cases.

Of course, this all gets the hand-wave treatment by the classically trained Hubbert modelers that use the Logistic function. Which I find really and truly odd as the Verhulst birth-death equations theoretically apply most effectively in localized Petri dish style experiments. Translation: analysis by Logistic approaches does not meet yet another sanity check and only serves as a cheap heuristic.

The Sigmoid Fraud

Unlike Sigmund Freud, I don't do psychology as a career but I do see something seriously disturbing about the fact that a majority of depletion analysts view the Logistic Function as something that contains some deep and significant meaning.

On the contrary, the Sigmoid curve --as the simplest manifestation of the Logistic-- remains a cheap empirical relationship that describes a value that increases and then saturates below some constrained limit. It indeed does follow from the solution of a non-linear differential equation, but this equation describes the temporal dynamics of a simplistic birth-death model used to describe interacting entities. One can choose populations of biological creatures or concentrations of chemical reagents to plug in to the equation. But you don't insert oil molecules into the equation and expect it to make any sense.

Take a look at this post at TOD on whale oil harvesting in the 1800's. Although the original poster does not bring up the Logistic to describe the saturation, plenty of commenters do. Fair enough, whales do fall into a biological classification, and they do give birth and die. But whale oil harvesting never tracked a population rise in whales themselves. It actually tracked the reverse. So, instead of calling it a "birth-death" model we should refer to it as a "death-birth" model. The parameter "death" represents the culling of the whale population for oil and any residual "birth" comes about because the whales can reproduce themselves based on the size of their population. Then as an exercise for the reader, one can plug some values into the birth-death equations as described here: Derivation of Logistic Growth.

But then we get to the real twist. Since whales do reproduce, if we play our cards right, then the amount of whale oil that we can harvest has no limit! The URR of whale oil essentially becomes infinite since the cumulative never abates. And unless we harvest the whales to extinction, the Logistic Function will fail miserably in describing whale oil production. (In actuality, cumulative whale oil production likely saturated because crude oil replaced whale oil as a harvestable resource.) See passenger pigeons if you want to get closer to a saturated harvest driven to extinction.

This whole analysis when incorrectly applied to oil exploration and production can induce early psychosis. On the one hand, oil does not reproduce like a biological entity nor does it act like a chemical reagent. So the equations themselves make no sense. But since oil only gets consumed and obeys the rules of a finite resource (abiotic-oil-mental-midgets notwithstanding), it will eventually saturate. So the Sigmoid falls into our lap in spite of itself. The fraud survives in effect only because it looks like an S-curve !

To avoid this mental anguish, I prefer to use the Dispersive Discovery formulation for discoveries and the Oil Shock model for extraction/production dynamics. This approach makes intuitive sense, the math falls out naturally, and you don't have to continue to psychoanalyze insane ramblings of people that live in some freakish world where square pegs fit into round holes and empiricism has the dynamic range of a stupid heuristic. The rise and fall of the oil culture deserves a better understanding than the Logistic can ever offer.

End promised rant;

Same: More Of

Kevin Phillips

What more can I say but that the inflation numbers and the dynamics therein remind me a lot about the essentially corporate and government cover-up behind the truth in oil reserves. We can easily figure this out if we had more committed and numerate people.

Unless you believe that growth consists in how many songs you can put into an mp3 player or the accelerating absurdity of Grand Theft Auto, money doesn't buy as much as it used to.

Scaling and the Dispersive Discovery growth function

The search growth function I use for the Dispersive Discovery model follows a T⁶ time dependence. The derivation comes from a quadratic growth term on top of a single dimension of volume. When the quadratic gets multiplied along the three dimensions of volume, the T⁶ dependence results.

High-order growth terms such as T⁶ have some similarity to exponential growth terms as a particular order in the Taylor's series polynomial expansion dominates over a certain interval. The following chart shows the cumulative dispersive discovery using T⁶ plotted alongside an e^kT growth term inserted into the Dispersive Discovery equation. I normalized the two curves via an affine transformation so they intersect at T=1.

Note that the doubling time for the exponential is about 10% of T at T=1, which roughly coincides to the doubling time for the T⁶ growth.

For world crude oil discoveries, the T=1 time point scales to approximately 100 years (the time period from 1858 to the early 1960's when we observed a global peak). This means that the discovery growth doubling time equated to roughly 10 years in historical terms -- premised on that you believe the Dispersive Discovery model applies. If you look closely at the two curves beyond T=1, the exponential reaches the asymptote much more quickly than the T⁶ growth curve. This makes perfect sense as the higher order polynomial terms in the Taylor's expansion of the exponential take over, and push to the asymptote more quickly, and thus minimizing the effects of dispersion.

Some might find the exponential growth model more understandable or intuitive, as this emulates technological advances such as those described by Moore's law (i.e. which shows doubling of microprocessor speed every two years), or approximates population growth and the demand and acceleration in prospecting effort that this implies.

Whether the exponential growth actually provides a more realistic picture of the dynamics, I can't say but know for certain that it requires a much stronger growth stimulus -- thus implying that a doubling of search effort must occur every 10 years for the foreseeable future. On the other hand, a high-order function such as T⁶, though it continues to accelerate, will show progressively longer doubling periods as T increases.

We know that Moore's Law has recently shown signs of abating. This could result from an abatement of technological progress as researches start to give up on scaling techniques¹, which in the past has guaranteed speed increases as long as the research fabs could continue to reduce circuit dimensions. Or it could stem from a hard limit on the scaling itself, due to parasitics and losses as the electrical properties encounter quantum limits. I have a feeling that something similar to a "dispersive discovery" in the research growth advances will allow Moore's Law to continue to limp along, as researchers will continue to find niches and corners in the ultimately constrained and finite "volume" of semiconductor combinations available to us.

So what happens to oil prospecting effort as we start hitting the walls remains unknown. We may want to pay close attention to how Moore's Law shakes out just out of curiosity and to see how a "smooth landing" applies in that technology area². In any event, it definitely will pay to start using the exponential growth model in conjunction with the T⁶ growth term as the two complementary cumulative dispersive discovery curves don't show a significant amount of difference, and moreover demonstrates that the underlying model shows a certain amount of robustness in terms of parametric variation. In particular, the exponential provides a good way of calculating differential margins should we want to assume a stronger post-peak discovery search pressure.

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¹ Years ago, I sat in an adjacent office to Robert Dennard, a really nice guy by the way. The scaling theory that he formulated, along with his invention of DRAM, had a lot to do with the correctness of Gordon Moore's predictions. I would find it fascinating if I could get Dennard's opinion (or Moore's for that matter) on how the Dispersive Discovery "scaling" theory could apply in a macro sense. I bet they would both admit that the endless doubling would not continue indefinitely, both in classical semiconductor scaling and likely in oil discoveries as well.

² The key area of research interest looks like a focus on multi-threading and concurrent functionality. Building more parallelism into microprocessors allows them to continue on an upward performance path, even though the speed improvement turns into a "virtual" or ephemeral achievement. And that assumes that we can get our arms around creating algorithms that take advantage of multi-threading -- not the easiest or most amenable idioms to formal techniques that programmers would prefer to encounter. But some researchers do have grand hopes; in an EE Times article titled "Berkeley researcher describes parallel path", one professor thinks he has discovered unity energy savings on this path:

Energy and the environmental issues are also driving work in ubiquitous computing, said S. Shankar Sastry, dean of engineering at Berkeley.

"We need to think about a building OS that handles all the heating and cooling systems and controls elevators," he said, describing work that could make these large energy consumers into generators. "We need to create buildings that not only consume zero net energy but have zero net cost," he added.

Incredible.


Next: Stay tuned for a final skewering of the Logistic production model.