One of the most salient features of investing in early early-stage firms is the fact that many of those firms fail. So we need to now think about that explicitly and how we account for that fact when we're doing valuation. So the first question I want to pose here is, suppose that rather than, as in our case where we developed the Kiln Kombucha case where we said cash flows are a certain amount, I expect that the cash flows will be a certain amount each year. Suppose that instead I tell you that, in fact, cash flows could be very high with a 50 percent probability or zero with 50 percent probability. How does that change the whole valuation framework that we have been using up until now? If you remember what we've said so far, the answer to this question is, it doesn't change the problem. It doesn't change the problem because everything that we've said so far, when we said that prices are the present value of future cash flows, what we really mean is that prices are the present value of the expected cash flows that we will obtain in the future. So really, if in fact, the firm cash flows could be high with 50 percent probability or very low at zero with a 50 percent probability, all that we would do is take the average of those two outcomes and then NPV applies as before. All of our evaluation framework is still valid as long as; risk is idiosyncratic and investors hold a diversified portfolio. So if cash flows are high or low, because of some specific reasons to that firm. No matter what it is, you can think of various examples for why for some reason sometimes cash flows could be high or cash flows could be low, think of that as a coin flip. As long as that coin flip is not correlated with what's going on in the rest of the market, then all we would do is build projections based on the mean outcomes, so the expected outcomes for the cash flows, and then NPV would apply unchanged. So the implications for startup funding that I want to make very clear now, so that then you can see what changes as we go forward, is that if investors hold diversified portfolios and startups are evaluated using expected cash flows, nothing changes. Everything that we've said so far applies exactly the same. We would use free cash flows, we would use our standard discount rate, sometimes referred to as the weighted average cost of capital. If you're funding your company with equity and debt, but that will not be the focus of this class. We are thinking mostly of companies that are purely funded with equity, then nothing changes. You have your free cash flows, you have your discount rate, and you would discount everything the way we have described so far.