In this workout, a management team are going to invest 10 million into an LBO transaction for 20% of the common equity. The deal completes with total equity invested of 500 million. Oh, wow. So let's jump down into the assumptions quickly. Our 10 million investments gives management 20%, but we're also going to have the PE funds investing 40 million for 80%, but the total equity invested is 500. Let's go back to the question. Let's check what it says. Any equity funding shortfall is made up of a 10% pick preference shares. Great. Okay. The managements have a ratchet mechanism activating after the PE fund reaches an IRR hurdle of 20%. Any additional proceeds over the hurdle rates are split 50/50. And we're asked, what are the returns to the PE fund? So let's go down to this table and let's work out what each group have invested at entry. The common stock for the management was 10. Common stock for the PE fund was 40. And the preference shares for the PE fund, that's going to be the 500 minus the 10 and the 40 we've already got. So the preference shares or the pik notes 450.

What happens at exit? Well, first of all, let's assume that we get that exit IRR return of 20%, for the PE funds that's going to be made up of two parts. They'll have a return from their preference shares and a return from their common stock.

Let's do the preference shares first. We're told that there's an interest rate on them of 10%, so let's work that out. I'm going to take the initial entry value, multiply it by 1 plus that 10%, but they get that for 4 years to the power of 4.

Great. So the first return they get is a 10% return on their preference shares. But that was not what the ratchet mechanism or hurdle said. It said that they need a 20% return on the full 490 that they've invested. So what we need to do is calculate that 20% on the 490. I'll add up the 40 and the 450. To get the 490. I'll then multiply that by 1 plus the 20% to the power of 4 years.

And that gives them, that gives the PE fund the total return that they receive 1016.1. That gives them the 20% return on the 40 and the 450 preference shares. But hang on, we already gave them some of that 1016 in the return of for the preference shares. So let's subtract that number out.

Great. Those two figures added together, that gives them their total return of 20%. Some of it's been returned in the form of preference shares and the rest returned in the form of common stock.

Okay, so we now move up to the common stock management. They're going to get some of their return under the ratchet as well. Now they could say, ah, we want a 20% return each year for four years on the figure of 10. But then they look at the PE funds and they say, hang on. The PE fund didn't get a 20% return it year for four years on the 40, they got their return on the 490. That's outrageous. We want some of that. So what they're going to say is they'll look at the return that the PE fund has got, and they'll say that was your 80% ownership return. So let's divide that by the 80% and then multiply it by our 20% and we'll work out what management should be getting and they should get 89.3.

So we've got the minimum returns to the PE fund and the minimum returns to management. If we add them all up, it comes to 1105.4, but we've exited for more than that. We've sold the company for 1200. That gives us some extra proceeds that we can share out.

Let's share it to the management first. Let's work out how much we can share out. It's the 1200 minus the 1,105. And the way we're going to share it is it's going to be a 50% of returns over the hurdle. So they get an extra 47.3. My PE fund, pretty much the same thing. I take the 1200 minus the 1,105 and I'm going to multiply it by one minus the 50% to managements. It's the same number. So how much of a return do we see? Well, management's had 89.3, but we now add on those super profits of 47.3. That gives them 136.6. Great for them. They invested 10 and they come out with 136. Great. If I copy that down, we see that the PE funds have come away with 404 of common stock and 658 of preference shares.

So let's work out the total cash flows For the the PE fund. They invested 490 at entry. I'm gonna copy that and paste it into F26.

They exit with 1060 3.4, and I can now calculate their IRR. That's where you take their exit value, divide it by their entry value and put it to the power of 1 over exit year minus 1. And the PE funds, remember their minimum return was 20%. They're actually going to get 21.4. Very good for them. Management have been incentivized to work hard. They've earned some extra money, and the PE fund have given themselves a higher IRR than their minimum required rates.