In this workout, we're asked to calculate the PE fund and management IRR for two exit scenarios. We're told to assume that 50 of the PE fund's capital came in the form of preference shares with an interest rate of 10%. So management are going to invest 5, but we'll give them a 10% stake to incentivize them, meaning the PE fund are investing 95.

However, we now need to calculate their contribution structure. We know that of that 95, 50 will be in the form of preference shares, so the remainder must be equity. Let's take the 95, subtract the 50. Great. They've got 45 of ordinary equity.

Now let's look at the two scenarios, and in the first scenario, we'll have an exit value of 200.

The PE fund will get two different types of return. The first one is the PE fund's exit cash flows on preference shares. They'll get out their initial 50, but there was an interest rate on that of 10% per year. So it will have grown by 10% every year for four years. So let's multiply that by 1 plus the 10%. I'm going to lock onto that to the power of four years, and again, I'll lock onto that and I'll copy the C19 at the beginning. Great. Their other return is the ordinary equity that gives them a 90% stake in any residual amount of money left over. But what's the residual amount of money left over? Well, it's going to be the 200 minus the 73.2 that's already been paid out to them. So 90% of that give them 114.1, giving them a total return of 187.3. Let's copy these numbers to the right and we'll see those numbers in just a minute.

We can now see the PE funds IRR overall, we'll take their exit proceeds, divide it by their entry proceeds, which was the 95 lock onto that, and then put that to the power of 1 over the exit year in which was 4 lock minus1, and they get a very respectable 18.5% IRR.

Now let's calculate the management exit proceeds. Well, we know there's only two investors here and we're splitting this 200 between them. So if I subtract out the 180 7 0.3 that's been Allocated to the PE funds, the residual is what the management gets. Managements receive 12.7. Management's IRR will be their exit value divided by the entry of 5 to the power of 1 divided by the exit year, which is 4 lock subtract 1. They get a return of 26.2%.

Let's copy both to the right. So if we look at the good scenario where the exit value of 200 has gone up compared to the investment value, everyone's looking good. The PE fund have a positive IRR. The managements have a positive IRR. Their interests are aligned.

However, when the exit value goes down to 90, we know that without preference shares, managements can actually do quite well. Whereas the PE fund do badly and their interests are not aligned. The preference shares here have corrected that scenario. The preference shares mean that of this very low exit value, most of it goes out to the PE fund first, then any residual is then shared. 15.1 goes to the PE fund and 1.7 goes to management. This means that both the PE fund and management have a negative IRR, so even when the exit value is quite low, in this case, 90, both parties have interests that are aligned. Neither will try to do the other over by trying to drive the company I the ground. Both will work towards a company growing and having a high exit value.