Hi, welcome back. In this module we're going to be talking about the use of decision trees in real estate finance projects. So let's get started with this. First of all, what do we mean when we say decision tree analysis? Well, decision tree analysis is a method for looking at to determine the value of a financial project under certain circumstances, specifically when the phases of the project or the tasks of the project happened sequentially and at various time, mutually exclusive choices happen. And also characteristic of decision trees is that the outcomes of some future phases are uncertain. And then finally for each phase we feel that we can estimate the cashflows that we'll get under any outcome and the probability of that outcome. So, any kind of financial problem we can organize like this. It's called a Decision Tree Problem. Decision Tree Problems happen throughout finance and actually also other areas of business for example, real estate development. We're going to look at a real estate problem shortly. In biotech with drug development, in litigation, in general they're applicable to any problem where you have uncertain things happening in multiple stages over multiple time periods. Okay, so now let's get a little bit pedantic and give you a definition here. Formal definition of a decision tree is a graphical representation of a decision tree problem which provides a mathematical solution, in quotes, to the problem. And I have solution in quotes because this is actually going to provide us with one presumed best solution, which under some circumstances, might not actually be the best solution. In any event, a solved decision tree is always going to give us the quote best path through the tree. I put best in quotes because under certain circumstances as we'll see, it might not necessarily be the best path. But what the tree means when it says it's giving us the best path through the tree is that it's the path that maximizes the Expected Value of this Decision Tree, okay? And they gives us the expected value, in dollar of taking "best" path. Its also going to give us the probability of the tree's end points, i.e the probability of ending at any particular branch of the tree. These are called family terminal nodes and it will give us the financial payoff, the net cash we're going to wind up with if we get to that node at the end of the day on the tree. So, a lot to throw at you, but it's all good. It's all going to become clear once we start digging into an example. Okay, as usual the grey slides I'm not covering, If you want to be real pedantic, you can think about decision trees and game theory, context, and look that up on the internet. Okay, I'm going to be working with decision tree software called Tree Plan, which is sold by a company I believe called Tree Plan, it's extremely cheap, it works very well with almost all versions of Excel. If you just Google TreePlan software, you'll find it. You'll find it very quickly. There are other TreePlan decision tree software packages around those are equally find to use. I'm just using TreePlan because I've used it for a long time, and I'm familiar with it. So using the TreePlan format, graphic format, I'm going to go over on this slide. Certainly not everything on this slide, which looks so confusing, but I'm going to look over the important things for us on this slide, okay. So here is a Decision Tree, and the first thing to know about this Decision Tree is that the X axis is always time or stage. Okay. And the y-axis represents various scenarios. Okay. And we always start at the left, at the beginning and we usually start with a decision to make and whenever we have a decision to make, we're going to call that a decision node. So for example, in this decision tree, we're starting with the question do we want to prepare a proposal for this project or not, okay? We might not want to, because if we prepare a proposal for this project, we're going to spend $50,000 here. Okay, so that's what we've got here. So here are two branches to this decision. You can see they are mutually exclusive and if we decide not to prepare a proposal, we don't spend anything and we're done. Very simple end to our tree. We go all the way over to here, to the end and we have nothing. If we decide, to prepare a proposal, we have to spend 50,000. That's what decision tree calls a partial cash flow, but it's essentially what we have to spend or what we get if we make that decision. All right, so let's keep following the tree assuming that we do decide to prepare a proposal because if we don't prepare a proposal, we're done. These triangles represent what are called terminal nodes, and that just means the end of the tree if we choose to follow that path. So let's follow the prepare proposal branch here. We're going to spend the 50,000, and then what's going to happen? We might get awarded our contract, or we might not. Okay, so here's awarded contract, here's not awarded contract. And you notice now at this node, we have instead of a square, we have a circle, okay? And whenever we have a circle, that's called an event node and that means something is happening that is out of our control. Okay, we're going to get the contract, we're not, it's out of our control. So what do we need to know about event nodes? Okay well, event nodes have probabilities associated with them, and these are guesstimated by us. So in this case we're saying eh, we have a 50-50 chance of being awarded the contract. If we're not awarded the contract, we get nothing, okay? And again we're done. And here this shows us at the end at the terminal node what we wind up with net-net if we follow the tree to the end of this branch. So what do we wind up here with net net? Minus 50,000 because we spent 50,000 to prepare the proposal, we didn't get it, and now we're winding up with our minus 50,000. Alright, so let's continue on and say that we are awarded the contract in which case we get awarded 250,000 to help us develop this. And we can use two methods to develop this project, a mechanical method or an electronic method. So what does that mean? It means we have another decision node here, are we going to use the mechanical method or are we going to try the the electronic method? And one thing I'd like to point out now, which applies to all decision nodes, is when we've got all the information we need into the tree the software solves it for us. And it tells us what it believes is the best path for us to try to take through the tree. And it does that with the numbers here in the boxes, okay? So after everything we need is put into this tree, and we'll see how to do that that, okay? The TreePlan software is telling us from its perspective the best thing for us to do is to go ahead and prepare a proposal. One means take the first branch here okay? And then when we get to this decision node if we're awarded the contract we want to try the electronic method. The TreePlan software believes that that's the best thing for us to do. How does the TreePlan software decide which decision is best? Well, the TreePlan software uses this criteria. Always make the set of decisions that maximizes the expected value of this project and our expected value for the project is down here, okay, so that's the criteria that it uses. And we'll see why sometimes that might not be the best thing to do based on our risk criteria, but we'll hold that off for later. So again, just to beat this to death, the tree plan software and other decision tree software decides which decisions to make using the criteria which set of decisions is going to lead to the maximum expected value of this tree. All right, so let's keep going. So let's say we decide to prepare a proposal, 50% probability will be awarded the contract, 50% we won't. Let's say we are awarded the contract. We have to decide whether or not to use the mechanical method or the electronic method and the decision tree is saying choose the electronic method, in which case we're going to have to spend 50,000 of our money to help develop that. And then, what could happen at this point is the electronic method could work, or the electronic method could fail. What does that mean here? It means that we have another event node, with again, in this case 50-50% probability. Okay, if we have electronic success, we don't have to put anything more into this project. And net net, the net cashflow that we end up with including everything we've spent and everything we've received along the tree to this point is 150,000. Okay, and if the electronic method fails, we're going to lose 120,000, but we still wind up with 30,000 at the end of the day. Okay, if we did decide to use the mechanical method, we would wind up with 80,000 here. And the mechanical method is a proven method, so there's no question of mechanical methods success or failure. Okay, so those are the key things. With any decision tree we start somewhere, usually with a decision. Basically, try this project or don't try this project usually, and then as we move along, things may happen that are out of our control like we get awarded the contract or we don't and we have to guess to make probability is for each of those scenarios. And, once we put in all of the cash that we're going to have to spend for every bit of the tree and every amount of cash we're going to at every amount, every branch of the tree, the software will solve this for us and it's going to tell us the expected value of the project if we take the decisions that it recommends and it's going to tell use the terminal net cash we would wind up with for every possible branch of the tree. Okay so that's it. I know this particular image looks pretty crazy but we're going to do an example that is much simpler very soon.