In this workout, we're being asked to calculate the PE fund and management IRR under the following scenario. In this scenario, those two parties have invested 100, but unfortunately the exit value has now gone down below that, it's at 90. Management's invested 5 out of the 100, but we're going to give them a 10% stake to help incentivize them. We're gonna see a weird outcome here. So let's do some numbers. My PE fund value at exit. Well, they had a 90% stake. Multiply that by their 90 value ah, they put in 95, but they now come out with 81. Okay, well that makes sense. That's fair enough. When the exit value is below the initial investment value, you are going to expect some kind of loss. But let's look at what happens to the management. Well, management are going to have 10% out of this exit value of 90, and they, oh, they put in 5, but now they come out with 9.

So we start to see that the interests of these two groups are not quite aligned. Let's check with the IRR. Let's do it for the management first. I need their exit value. Divide that by their entry value, all to the power of 1 divided by the exit year of 4. I'm gonna lock onto that and then subtract one. So their IRR ooh, it's positive. So again, that shows that they're making a return. They invested 5, they come out with 9. They're getting a return of 15.8% every year for 4 years. But let's copy that cell. Let's put it in the cell above and let's see what happens to the PE funds. And ah, yes, they're making a loss. They put in 95 at the beginning, and they came out with 81. That implies a negative IRR of 3.9% every year for 4 years. So we now start to think that their interests are not aligned at all. In fact, management here are incentivized to drive the company into the ground as quickly as possible, sell it for an exit value of 90, and then they can suddenly turn their initial investment of 5 into an exit value of 9. In fact, this happens in year 4, but if we change it to year three or two or one, their IRR would be much higher. They have a good outcome, but the PE fund have a bad outcome. This is management being incentivized very poorly, and we might be able to change this by changing the capital structure and preference shares are a way to help us do that.