In this workout, we're asked to calculate the IRR for both the PE fund investor and management. If we see what they've invested. The PE fund have invested 95, whereas management have only invested 5. That adds up to 100. So we're giving management a stake in the company that they're gonna help build, but we're going to incentivize them even harder. Instead of giving them just 5%, because it certainly looks like 5% investment here, we're going to give them 10% stake at exit, meaning the PE funds, they'll get one minus that, they'll get 90%.

So management should be super incentivized to help this company grow.

Now, when we get to the exit, we find that the investment, which was initially 100, has now grown to 200. Fantastic. So let's have a look at what's happened for the PE fund. Well, they had 90% out of that 200, they get 180 and management. They had 10% outta that 200, so they get 20.

What's a fantastic result for management? It's grown from an initial investment of 5 up to exit of 20. Let's check out management's IRR for that. I need to take their exit value divided by their entry value, and then all to the power of 1 divided by the number of years that they've invested for. So it's 4 years was the exit year. I'm going to look onto that and subtract one. They got a 41.4% return. IRR. That's amazing. Let's copy and paste into the sell above for the PE fund, and they got a 17.3% return. Now, I'm going to argue that their interests here are aligned when the exit value or 200 was higher than the investment of 100. Both of them have done well. You might argue that the management have done a bit too well. They get 41% return every year for 4 years, whereas the PE fund only gets 17. However, if we look at the absolute numbers, management only put in 5 and they only come out with 20. The PE funds put in 95 and they come out with 180. The PE funds have done fantastically well in absolute terms, and management in absolute terms is very small. But in percentage terms, they've done really well. So their interests are aligned when the exit value 200 is higher than the investment of 100.