Okay, let's calculate the IRR for this investment. And the first thing to note is that in year zero we've got a cash outflow followed by a number of cash inflows and then another cash outflow. So we've got two changes in direction of the cash flows. Year zero it's out, then it changes to become an inflow. And then in year five it's out again. So it changes direction again. So there's two changes direction. If I use Excel's inbuilt IRR function and grab those cash flows. One thing I would just notice as I'm building the function is it says IRR. The first argument is can you gimme the values which I've done? And then in square brackets you might notice there it says, guess that means there's another argument, but it's an optional argument. Now if we don't give it anything we're not obliged to, then it will uh, it will assume a 10% guess. And what that means is when it calculates the IR its starting point for calculating your RR is 10% and it will feel its way either side of 10% to figure out the discount factor that gives an NPV of zero. So if I hit enter pretty close to 10%, we've got an IRR of 6.8%. Now I'm, because we've got two changes in direction here, I'm assuming that we're gonna have two IRRs. So why don't we say equals IRR exactly the same information feed in these cash flows, but comma, let's give it a guess of 50%. So I'm now saying, Hey Excel, why don't you start at 50% and see if you can find the IRR and it will feel either side of 50%, it finds an IRR at 65.4%. This is problematic. Okay, 'cause we've got two IRRs. So let's try and figure out what's going on here. If we scroll down, um, we've got a section to calculate the NPV. So I'm going to use Excel's inbuilt MPV function. The first thing it says is, Hey, I'd love to have a discount rate, so let's go left and grab 5%, and it then says, I want some cash flows. Now you might remember that what Excel does is, um, the MPV function's first cash flow, it assumes occurs in year one. So that means that we'd also need to take account of the year zero cash flow. Let's do that. Okay? And then we come out, not surprisingly, with a negative MPV, if I copy this down, one cell at a 10% discount rate, we have a positive MPV. And what this suggests at the moment is that the IRR exists somewhere between five and 10%. And in fact, previously we've calculated this at 6.8%. So that seems to be correct. Now, if I copy this down a little bit further, you can see that the MPV is increasing at an increasing discount rate and then somewhere between 25% And 30%. The NPV slight slightly seems to reduce. So if we copy, keep copying this down now all the way down to eight 80%, you can see that eventually, um, at 70% the NPV becomes negative. So somewhere between 75, 70% and 65%, we've got another IRR. And in fact, we'd already suggested that that was at 65.4%. So if we now scroll down, you can see this represented on a graph. And if you think about this graph and the two points of intersection, initially in our function, we said to excel, Hey, why don't you, uh, do the IRR function and start at 10%. Now look at 10% on the graph there. Um, what Excel would do is it would slightly increase the discount rate, slightly reduce the discount rate, and realize that by reducing the discount rate from 10%, the MPV was falling. And so it would iterate that and arrive at the first IRR we calculated. And then if you look towards the right hand side of that graph, what Excel would do is we initially said, uh, well recalculate IRR with a guess of 50%, and it would slightly increase the discount rate and slightly reduce the discount rate and realize that if it increased it, the MPV was falling. And again, it would feel its way until it gets to the second IRR. So the problem is that if cash flows change direction, then we have multiple IRRs.