So now we're ready to start thinking about incorporating time value into this analysis. We've done the whole thing without time value, it looks pretty good to me. In particular, we verified that the expected value of the project, that the software computes is the same thing that we compute manually. So that gives me a warm, fuzzy feelings. And we want to go on and improve this analysis by incorporating time value. So why do want to consider time value? Well the project goes over four years. As we say the rocc is high, I would say anything above zero is high and worth considering at 4%. And so time value, I think, is going to make a difference. And let's go through and check this out with time value and see about that, okay. So how do we want to handle time value? We need some simple way to compute all of our cash flows for this project for when a player considering time value. And there's actually a really simple way to make this happen, okay. Remember, as we learned in our review chapter and as you learned with Professor Dan, mathematics of money, to evaluate the cash flows of any project for one player when the cash flows are function of time. Step number one is we want to discount individually all of those cash flows back to a convenient time, usually t=0. Once we've got that, all our cash flows for the project now are on an apples to apples basis and we can combine them in any way we need to, to evaluate the project. So that's our next step is to add them up, add, subtract them, whatever we need to do to help evaluate the project. Compute NPVs, IRRs et cetera, et cetera. So that's all we're going to do with the decision tree. We take every cash flow for the project and get its equivalent at T equals 0 and then start putting those equivalent numbers into our decision tree. So if you're mathy and you want a mathematical formula for that, here is how to do this to get the expected value of the tree with time value considered, that makes it of course the expected value of the NPV of the project for one player who is the developer or the sponsor. Okay, so now with time value, we've got to first of all, individually get the present value of each cash flow. So the 40 million that put in to get the property variance, that happens at t equals 0, so that's going to remain, present value 40 million. The 60 million, we have to discount back by one year at 40%. And as you can see here, if I do that, I get 57.69. I do the same thing with the 200 million here. And I get 192 and etc, etc, with my 3 million, I have to discount this back two years. So I have 300 divided by 1.04 squared gives me 277 million and change, some more sort of the thing with my 150. Okay, so now I've got our futures table with all of our cash flows included here. And it looks exactly like it did before except now the numbers I have here are my equivalence at t equals 0. So I can add them up, I can subtract them etc, etc, to help me get NPVs. All right, so what I do next and I'm going to go ahead and show you these in the Excel, is I'm going to replace all the numbers in my tree. I'm not going to make any other changes except to a place this numbers with the numbers discounted back to t=0 at 4%, and we'll see what that does to the tree. Once again, I'm going to jump to Excel. I'm going to, I'll just type in the numbers directly here. So I want to go number by number here for our inputs. The 40 million we have to put in here to try for a variance, that happens at t equals 0. So I'm not going to muck around with that, but clearly the cell or develop the variance property. I am going to have to change these guys so, I'll just look back quickly at my futures table with the PVs put in 57.69 here. Okay, and for the present value of amount, we'd have to put in to develop is 192. Okay, and what else happens here if there is no market crash we get 300,000. If there's a market crash, we get 150,000 in those 1,000 units. Discounting both of those numbers back to their apples to apples equivalent values at t equals 0, I get 277370. And I get here, instead of 150, 138680. Okay, that was easy right? Pretty straight forward. And I want to show you a few important things about this. Okay first of all, the expected value number of the project has changed radically from $9 million to $383,000 when we have made this change, okay. The other thing that's very interesting is that, now our optimum decision, if we want to maximize the expected value of the NPV of this project, we should sell the variants property and not bother developing that at all. So our optimum decision has changed here, okay and so what does that mean? Well I got to go through and redo all my probabilities now. Okay, so now what's my probability of getting to the sell the variance property after we've tried for a variance and it's been approved? That's going to be equal to what? Just my 70%, probability of approval. I'm going to make this one develop with no market crash zero because we're choosing not to go the developer we're selling various property. So similar way, develop with market crash. I'm going to make the probability equal to zero and I still have a 30% probability from over here of not getting the project approved. I add up my probabilities, I still have 100%. I have my expected value, of the now what is this really? This is expected value of the NPV of the project, and this is expected value of the NPV of the project over here. So the work that we did, confirms what the software is telling us, and it's all looking good, okay.