In this workout Target Co's been acquired by a PE fund. And we're told that when the PE fund exits the investments share options that increase management ownership will be granted. And the MOIC has to be above a certain threshold where us to use the capitalization tables to calculate that management and PE fund ownership in each of the scenarios and calculate the total number of shares. So let's have a look at it.

We're told that there'll be an additional management stake for options A of 2%, but when's that going to happen? Well, that's going to happen when the MOIC, the multiple on invested capital is above 1.25. So for instance, if we invested 100 you have to get out at least 125. So the multiple on your invested capital 1.25, there will then be an additional management stake of 4% if we get above a MOIC of 2 and an additional 6%, if we get above stake of 3. So just to check, if we can get above that MOIC of 3 then we'll have 12% ownership for the management just through the options. So let's get those numbers into this table here. So when we're in the diluted A scenario we want to link up to the 2%, I'm going to lock onto that with dollar signs and copy that to the right, because if we have the 1.25 MOIC or above, we'll get those management A options. But if we get into scenario B where the MOICs above 2, we'll get that additional 4% lock onto it and copy it. Right? And if we get to scenario C, the MOIC of 3 times, we'll get that 6% great. But we also have some basic management ownership, management own 250 shares out of 10,000. That gives them 2.5%. They're going to keep that 2.5% under all of the scenarios. So I'll link to that 2.5, lock onto it and copy to the right.

We also noticed the PE funds, they have 9,750 shares out of 10,000. That initially gives them an ownership of 97.5%. However, if we get into the scenario where there are shares being granted, and it's the PE funds that will be diluted, management will keep their basic management ownership. So the way we'll calculate this is we'll take equals 1, so 100% minus the sum of all the other stakes. So at the moment management have the 4.5% in total that will give the PE Funds 95.5%. As I copy that to the right, that percentage comes down and comes down again.

I can then sum up all of the ownership stakes above and I should get to 100% in each scenario.

Great. So that gives us the percentage ownership. We now just want to check how much management gets, and we should see it going up as they manage to exit the business for a higher MOIC.

Now let's just check the total number of shares that each are going to get.

In the undiluted scenario, we'll just have the management shares. For my management shares, they're going to have 250 worth of shares, maybe dollars worth of shares or yen or something like that.

I need to find the total number of shares. So I'll divide it by the share price. And we've got an entry share price of 100. So they'll have 2.5 shares. I'm going to look onto each of those numbers. I can then copy that to the right because we know that they're going to keep those shares.

Now, the PE funds, we saw them being diluted earlier, but their basic shares are going to stay the same. So I'll stick with a 9,750, divide that by the entry share price. I'll lock onto both of those numbers and copy to the right. That feels a bit weird. It feels like they're not being diluted, but we will see them being diluted in just a moment. For the total number of shares, this is where we do something a little bit strange. I'm going to sum up the total number of shares that the management and PE fund already have, but then I'm going to divide that by the sum of the ownerships that they have above.

At the moment, the 100 shares at the bottom, they equal the 100% ownership above. So the total number of shares equal to 100. Great.

But look what happens when I copy this total to the right. Weirdly, the total number of shares goes up to 102.

That's because my 100 shares at the bottom here. They don't equal 100% ownership here. We haven't included the management A shares yet, so let's add them in.

My management shares are going to be 2% of my total number of shares, and I'm going to lock onto that total number of shares at the bottom here so that when I copy to the right it does move to the right, but I want it to be locked onto row 36. There we go. So now I can see that management A options. They give them an extra 2 shares add on the 2.5 and the 97.5, that adds up to 102.

Let's see what happens when we copy the total to the right. Again, the number of shares goes up. This is effectively diluting the PE funds because my management A options, they become worth a bit more, but we're also going to get some management B options. Let's go do them. I'm going to grab the 4%, multiply by the total at the bottom here. I'm going to lock onto row 36. Ah, there we go. We've got some extra shares going to management that increases the total.

Let's copy these to the right and the total to the right.

The total goes up. The A shares go up, the B options go up. But we've now got some C options. We're going to have 6% out of the total down here.

So as a quick recap, my number of management shares the basic number that stays constant, as does the PE fund equity shares. But the management A options gradually go up as the MOIC increases. When we get past that hurdle of 2 times MOIC, the B options come in and they increase as well. And then eventually the C come in.

As we get more management options, the total number of shares goes up and that effectively dilutes the PE fund. And we saw that dilution happening through the PE fund's ownership stake up here.

One last thing you may notice is that as my management options of 2%, 2%, 2%, as they translate into shares, you might notice that 2% actually leads to 2 shares, 2.1 shares, 2.3. That's because my total number of shares is going up. And then the 4%. 4%, which stays constant, leads to an increasing number of shares.

But with the basic management ownership, we've got a constant 2.5%, but that's linking down to a constant 2.5 shares. This is a simplification to avoid a circular here because if I had my basic management ownership leading to an increasing number of shares, that would then lead to a decreasing number of PE fund shares, which would then link back up to changing number of management shares, which then leads to a change in the PE fund shares. So it's a simplification here to avoid a circular.