So let's jump right into an example which I think is going to illustrate how decision tree is worked. And how to create a decision tree and tree plan very well. Okay, so let's look at a project that we're calling FirstDealofYear. And this a project being considered by Housing Developers LLC. Okay, so HDL's opportunity cost of capital based on their historical performance doing developments, similar developments over many years is actually, sorry for the typo here. It's actually 4%, okay, not 12%. So I'll make that correction and we'll move on. Now let's get into a specific risk reward policy. HDL's risk reward policy for this project, the first steel of year project is they want to maximize the expected value of the NPV of the project while ensuring that the expected of the NPV is greater than zero, right. And then here is we could call this their reward policy, Sorry that's reward up here and we could call these two the firm's risk policies. Okay, so they want to maximize their expected value. What does that mean? That means that if they pursued this project in the exact same way many, many times over and over and over and over again. And they recorded how much they gained or lost in the project each time on average. Over the long run they would achieve their expected values. So they want to make all the decisions that they can that maximize their expected value. Their long-run average for this project if they could keep repeating it over, and over and over again. From risk they clearly want to make sure that that expected value is greater than zero, right? If it's less than zero over the long haul they're going to lose money on this, that's a loser of a project. Also, they want to say that the probability, that's P stands for probability. The probability that the NPV of the project is less than 40 million is 0. So what do they mean by that. They mean that no matter what they don't want to lose more than 40 million on this project okay. So that's going to be a key component of the risk criteria. Okay, so first remember we're going to solve this without considering time value of money okay? So in this case the risk-reward policy looks like this. They want to maximize the expected value of the project while ensuring that that expected value is s greater than zero. And the probability that the value of the project being less than 40 million is zero. Okay, so that's the way they'd say it without considering any time value. Okay, so here is futures table for HDL as I've put it together. Again, there are different ways to put this together. You just want to think about the whole project. Make sure that you've considered all the decisions you have to make. The things that may happen along the way and their probabilities. So before i start walking us through this completely. I just want to make this correction again. Their opportunity cost of capital is 4% not 12%. And I'm doing this right now for no time value, okay? So we begin. The first thing we need to think about is do we want to try for a zoning variance, yes or no? So to develop this property, thing number one, they're going to have to do is get a zoning variance, okay? So they can decide, if they decide no, this is beginning of the project always end of year or end of period zero. T equals 0. T= 0, here. They decide no, they're not going to spend anything, they're not going to get anything so they get zero, okay? If they try for a variance they're going to have to spend $40,000 on this. That's what it's going to take to pay the lawyers, etc, etc. Get the land platted, all that junk, okay. And then what's going to happen, if they take that try variance path. The variance may or may not be granted, and they think this is going to take about a year to do all the work on the variance and get a decision for it. They feel, based on their past experience and their knowledge of the local authorities etc. They think they have about a 70% probability of getting a variance granted, and a 30% probability that they're going to fail. So that's what we'll put in at that event node, okay? Now we're just going to continue with assuming the variance is granted, because if its not we're done, right? Project is over, okay? So if they get granted here, what can happen is they can decide to develop the property, which is really what these guys are in the business of. They're in the business of. Buying a properties, getting variances as needed and then developing them. But another thing they could do if they feel like the market is about to turn or for any reason. If they just have a capital shortage, they need to raise some cash. What they could do at that point is sell the varianced property and that property, they've added a lot of value to that property just by changing its zoning status. So if they sell the variance property they think they could do that immediately right, after the variance is grounded. And they think they could get 60,000 for it, okay? If they decide to develop the property, they're going to have to invest another 200 million. Sorry, I said thousands a few times, but all of our units here are in millions. Okay, so they try for variances, clearly big properties something like Manhattan, Tokyo, Beijing, something like that. They're going to have to spend 40 million to make that happen. They could sell it, if it does get varianced, immediately for 60 million. If they want to develop, it's going to be 200 million they're going to have to thrown in to get that developed. And for right now we're going to assume they'd throw in all that money at end of year one, okay? And then let's say now if they sell the variance property they're done, so let's continue on the assumption that they're trying to develop this. And they're going to develop it and then they're in the business of selling their developed properties to property managers, operators, asset managers who like to have completed projects with tenants and maintain those properties and enjoy the cash flows from the tenants. So that's the idea of selling here, okay? These guys, HDL are in the business of developing and selling not managing completed cash flow producing properties, okay? So they're going to sell, so it's going to take them a year to do the development they think, which is pretty quick for a $200 million development here. But nonetheless if there is a, there may or may not be a real estate market crash between now and two years from now. And this being recorded in the fourth quarter of 2016 and I thinks that's a appropriate consideration right now certainly for a top tier properties in a top tier city such as New York, Beijing, Tokyo etc. So they believe, that HDL believes that the probability of a market crash in the next two years is 20% and the probability of a localized market crash in the city where they're building this, let's say New York so everything is in dollars. The probability of no crash is 80% and now we need to figure out what they are going to get if they sell the property under both of those circumstances. So if they sell the property to a manager, operator, asset manager and there is no market crash, they're going to get a cool 300 million, that's pretty awesome. And if there is a market crash, they're still going to be able to sell it and again, this is a low class market crash not a crash through a whole real estate industry, it's a low class market crash in New York where they're developing the property. If there is a market crash in New York, they still believe they'll get 150 million, which is not jump change, okay? And just quick note too, for those of you in the pedantic let's think about options, let's think about other things, groups in the audience. Whenever we’re making a decision like do we want to try for a variance, yes, no? The no answer is really considered an option to abandon, it ends the tree at that point. So same thing here. If they get the variance granted, they can choose to develop or not. If they develop not to, that's called their option to abandon.