Well now having said all that about approaches to option valuation. I would like to shift focus a little bit and talk about what is the most important in applying this option valuation approach for us the people who study real investment projects. So I'll put it real investment projects. Well this is not our focus only because we fail to come up with a more advanced models for listed options. This is just not our core focus. But see what's important here. We know that first of all in analyzing any evaluation of an investment project, we have to come up with some models of cash flows. And if we ignore options, those will be just forecasts about how much money we are expected to receive in terms of revenues, then our cost forecast, and that's the way we proceed. And that's sort of a zero approach. But on top of that, equipped with the idea of option valuation, we sort of adjust that and we will put that like value of active management. And that will include, I'll put just a few examples, options for future investments. Then abandonment options. This is the, sort of the other way around. And then, let's say options for optimal, Timing of investments. So basically the idea is as follows. So we start with the approach that we have studied over the first four weeks of our course, and then we say maybe if we take into account these things or some of them, then our valuation will be more correct. And in the idea of valuing these options, we have to basically do the following. We analyze first of all the qualitative idea how this contributes to the value of the project. And then, we're trying to find some proxies for the value drivers of a corresponding option. So if we are able to identify the option, and to ascribe some of the future forecasts as value drivers of a corresponding options, then we can use the option validation approach and find the additional, or maybe a subtracted value of the fact that this option exists. So it all sounds great, and it is really, it's quite clear that it's important and contributes significantly. However, the key story here, and I'll put it in red, this is the identification of an option. Oftentimes it is really difficult to find out what exactly that these opportunities mean and not always they can be perfectly associated with the corresponding option. And that is the key challenge in this whole weekend, the overall idea of the use and option theory in fine tuning the values of investment projects. To the extent we are able to identify them, then it's an easier job to find these proxies, and then to use the option pricing theory. Now in what follows, I will give you an example how that can be used. And although this example will be quite clear, if we do not use the word option, as soon as we introduce that, we will see these analogies and these proxies. So we are all set for the next example.