To some degree, OilFinancier works in the same way. But you can mitigate this rather primitive oil-finding strategy by cooperation, negotiation, and good financial judgment.

Let’s see how a decision tree analysis can work for drilling a shallow well early in the seminar. As we determined in the previous section, drilling one shallow well was not profitable (the negative expected NPV of -$19,000, remember). But if you did discover a shallow oil well, would this not increase our chances of finding another shallow oil well nearby? Of course it would! If you go to OilFinancier Statistics, we find that a square with an adjacent square having a shallow well has a 55% chance of also having a shallow pool underneath. So you go to the owner of the adjacent square and tell him, "I want to drill a shallow well on my square. If my square has oil, your square probably does too. We should partner to develop this play by drilling two wells."

The financier owning the adjacent square may say, "No, I will wait until you drill first, then I will know for sure and drill later without having to deal with you." But if the financier has some smarts, he will realize that he is sitting on an asset that is not producing any revenue. He sure won’t be a successful financier he takes this attitude. So you and he start negotiating a deal that plans to drill a second shallow well if the first one is successful. The two of you will negotiate the subsequent well section in the Oil Financier agreement. For this particular analysis, it is not important whether you and the other financier split the deal 50/50 or 70/30 or whatever; we will do the analysis as the partnership working together.

The Expected NPV of this play is the sum of the Expected NPV of the first well and the second well. The formula is:

E (1+2) = E (1) + P(2) ´ E (2)

where:

E (1+2) = the Expected NPV of the play

E (1) = the Expected NPV of the first well, which we already calculated to be –$19,000.

P (2) = the probability that we will drill the second well, which will be conditional on the success of the first well, which is—as stated earlier—19%.

E (2) = the Expected NPV of the second well, which uses same formula as E (1) but with the improved odds of finding oil. Note that E (2) = P(oil) ´ NPV + P(dry) ´ Cost of Drilling

So plugging in the numbers, we find:

E (1 + 2) = –$19,000+ 0.19 ´ [0.55 ´ $328,000 + 0.45 ´ –$100,000]

= –$19,000 + 0.19 ´ [180,000 – $45,000]

= –$19,000 + $26,000

= $7,000

The Expected NPV is now positive! If you and the other financer find yourselves in this kind of wildcat many times, you should make money at it in the long term. But what is more significant is that drilling a well conditional on drilling a second well on an adjacent is a profitable venture, whereas drilling the first well by itself is not.

Conditional Wells  To make financially sound deals, use conditional wells based on the results of the first well in the deal. When you do the ENPV analysis of conditional well deals, you will find much more profit than the wells drilled by themselves. The more deals you negotiate with conditional wells, the more success you will have in OilFinancier.

The decision tree analysis gets its name from the shape it creates. The two shallow well analyses did not show good tree-shape so we are going use another approach to show you the tree.

Assume that you and another tycoon have two adjacent oil rights and want to work up a play together. The first question you should ask yourselves is: "How deep should we drill our first well?" The answers are shallow, intermediate, and deep. But rather than selecting one of these answers right now, we keep all these options open to consider so that we can analyze each of these "big branches."

The next question we should ask is: "If we drill this kind of well, what are the possible outcomes?" For a shallow well, our outcomes are finding a shallow oil pool or drilling a dry well. For intermediate, the possible outcomes are shallow, intermediate, and dry. For deep, we can have shallow, intermediate, deep, or dry results.

We now have one more question to ask: "How deep should we drill the second well given the result of the first well?" Suppose we discover a shallow oil pool in the first well. It seems the most logical response would be to drill a second shallow well, but we will leave the options open to drill an intermediate and a deep well. Likewise, we’ll analyze shallow, intermediate, and deep wells for the second well if the first well finds oil at the intermediate or deep depth.

At this point in the lecture, I’m going to close off some options right now just so the following diagrams do not become too cluttered. If the first well is dry, you have agreed not to drill the second well. With a dry well, this play is over, your partnership is dissolved, and you starting looking for other oil rights to exploit with a different potential partner.

If you look at the next diagram, you can see our "tree" we have built by listing all the possible outcomes. To the left is the trunk. In the center left are the big branches. The center right shows the little branches, and the far right shows the leaves. We also have some dead branches that represent the first well being dry; i.e. they have no leaves (or do not warrant a financial analysis).

When doing a decision tree analysis, you need to start from the leaves and work towards the trunk. Let’s analyze the expected NPV of the first leaf, which represents the decision to drill a second shallow well if we discover a shallow on the first well.

If you go to OilFinancier Statistics, you will find new probabilities of finding oil. Finding oil at the shallow depth has increased from 19% to 55%. Finding oil at the intermediate depth has decreased from 16% to 10%, and finding deep oil has decreased from 9% to 5%.

So for our second shallow well, we have two outcomes: finding oil at the shallow depth or drilling a dry well. Our expected value equation becomes:

E_2S = 0.55 ´ $328,000 + 0.45 ´ - $100,000

= 180,000 - 45,000

= $135,000

For the second intermediate well (if the first well finds shallow oil), we have:

E_2I = 0.55 ´ $328,000 + 0.10 ´ $545,000 + 0.35 ´ - $200,000

= $164,000

And for the second deep well (if the first well finds shallow oil), we calculate:

E_SD = 0.55 ´ $328,000 + 0.10 ´ $545,000 + 0.05 ´ $871,000 + 0.30 ´ - $300,000

= $188,000

Now these results are quite interesting. Our intuition probably told most of us that if we found oil at the shallow depth, we should drill another shallow well next to it. Instead these calculations, given the 0.5% discount rate and the stated probabilities, tell us that drilling a deep well on the second location is the best investment if we find oil at the shallow depth.

Now we’ll do all the calculations for all the "leaves" which brings us to Diagram #2.

For each little branch, we can select the best leaf. In all cases, the leaves representing the deep drilling for the second well had the highest expected NPV. By using this criterion of highest NPV, we have made our first decision. The second well will be deep whether the first well finds oil at the shallow, intermediate, or deep depth. So we remove the leaves with the lower expected NPV values from the little branches. This brings us to Diagram #3 with each little branch now only having one leaf.

In the last diagram, you will notice I have stated the probabilities of the little branches happening. Although we have determined the best option for drilling the second well, drilling the second well is not a sure thing. The probability of this well is conditional on being successful on the first well.

So if we eventually decide to drill the first well as shallow, we have a 19% chance of finding oil at the shallow depth, which is also the probability we will drill the second well, which has an expected NPV of $188,000. Therefore the expected NPV for the second well, given that the first well was drilled to the shallow depth is as follows:

E_2S = 0.19 ´ $188,000

= $36,000

Note that we need not consider the cost of drilling the second well if the first well is dry—because we are not going to drill that second well in this case.

Likewise for a possible intermediate depth for the first well, we have a 19% chance of implementing the leaf with an expected value of $188,000 and a 16% chance (also the probability of finding oil at the intermediate depth) of implementing the leaf with a value of $255,000.

E_2I = 0.19 ´ $188,000 + 0.16 ´ $255,000

= $76,000

For deep wells, the calculation becomes:

E_2D = 0.19 ´ $188,000 + 0.16 ´ $255,000 + 0.09 ´ $512,000

= $122,000

Here’s how you should interpret these numbers:

• the $36,000 is the best expected NPV of the second well if we drill the first well to the shallow depth,
• the $76,000 is the best expected NPV of the second well if we drill the first well to the intermediate depth,
• the $122,000 is the best expected NPV of the second well if we drill the first well to the deep depth.

You can see that we now have only one more decision to make: whether to drill the first well as shallow, intermediate, or deep.

We calculated the expected NPV of the first well earlier. Remember these values we had calculated earlier: E_S = - $19,000, E_I = $14,000, E_D = $59,000. Now we only need to add the expected NPV of the first and second for all three options (first well being shallow, intermediate, or deep) to find the total expected NPV. Diagram 5 shows this:

By working from the leaves to the trunk, we have reduced 18 options from Diagram #1 into one decision. The greatest NPV is $181,000 which tells us to drill the first well to the deep depth. If we find oil at any depth, we should drill the second well to the deep depth.

Please note that this decision is based on a certain discount rate and certain probabilities. If any of these values change, we could come up with a different decision.