In this workout, we're looking at Mr. Smith who's investing 1 million dollars into a hedge fund and after a year, the net asset value or the nav of that fund has increased by 10%. We're assuming this is before any fees.

We're then assuming that the fund operates a 2 and 20 structure, 2% management fees, and 20% performance fees. And that performance fees are calculated after accounting for management fees. We're asked to calculate what will be the net asset value of the fund and the return to investors after fees, if the hurdle rate is 0% per annum in this first example, essentially saying there's no hurdle rate. So our first calculation is to figure out what the ending nav of the fund is before any fees. And to do that, we're going to take the beginning net asset value of the million dollars and multiply that by one plus the 10% rate of return giving us not a huge surprise, an ending value of $1.1 million. This is the basis for the management fee. So the management fee is 2% of the assets under management at the end of the year giving us 22,000 of management fees to be paid. The performance fee is 20% of the return generated for investors, but after management fees have been deducted. So first of all, we take the ending portfolio value. We then take away from that the initial portfolio value saying we've made gain of a hundred thousand to begin with. We then need to deduct from this the management fees, which leaves us with a gain of 78,000.

This is the return against which the performance fee is payable. Now for completeness, if we then just say, well let's take away any hurdle rate. The hurdle rate is going to be the 0% hurdle rate multiplied by the initial value for the portfolio. So we've gotta generate at least 0% return over which we're gonna be able to start earning those performance fees.

This doesn't change anything because there's a 0% hurdle rate. But then we need to take that gain, the 78,000 that we've got so far, and then multiply it by the performance fee rate of 20%, which in this example, is gonna give us a performance fee payable of 15,600. As a result, the value of the fund after those fees have been paid is gonna be the 1.1 million, minus the 22,000 of management fees and the 15,600 of performance fees leaving 1,062,400 for the investor. This equates to a return, taking that ending value after fees and dividing it by the beginning value For the period and then taken one away of 6.2% return. In terms of what this means for the investor, the fund has generated 10% return. 2% of that pretty much has been taken away as management fees and an additional 1.8% taken away as a performance fee, leaving the investor with only 6.2% of the return that was generated with the assets at the disposal of the investor of 10%.

If we then move on to have a look at workout two, we can look at the same situation, but where we have a performance fee level of 5%, the numbers are all the same otherwise. So a million dollars invested, a 10% return before fees, 2 and 20 structure, but now a 5% hurdle rate. We can go through these numbers relatively quickly because they're the same as before. So it's the 1 million multiplied by one plus the 10% return, the management fee won't change. It is still 2% of the ending portfolio value.

The performance fee formula won't change as well. So I'm just gonna pick up that formula that we had before and copy it down into out two. And you can see here that the performance fee drops substantially when we have this performance fee hurdle rate up here in workout one. This performance fee is based on the entire 78,000 return above the initial investment amount because there's no hurdle rate. Whereas now for workout two, the performance fee level drops because the fund needs to generate 5% return on the money invested. Initially, that's $50,000 only. On the excess above that are we generating any performance fees. As a result, we end up with a much greater value left in the fund for the investor because the initial 5% of return isn't subject to 20% going to the investment manager. The return to the investor therefore grows where we have this hurdle rate in place being here, 7.2% rather than the 6.2% that we had in out one.

Having hurdle rates in place adds to the return to the investor. Workout three goes one step further and asked us to calculate the performance fees and management fees payable in the second year where we're given a ending year value before fees at the end of the second year rolling on from workout two of 1,145,000 before any fees. So again, the beginning net asset value is the closing net asset value from the previous year.

The ending value, we can just type in 1,145,000 management fees as previously calculated as 2% of the closing value management fees calculated as before. 2% of the closing net asset value giving us 22,900 here. So the performance fee as before ending net asset value before fees, take away the beginning value for this second year, so that we're now only looking at the gain made in the second year. We need to take off the management fees paid and also take off the performance fee level hurdle rate of 5%. So that would be 5% of the initial value for the year as well. What we get here is a negative number, which tells us that the return generated for the year after fees hasn't beaten the hurdle rate of return. As a result of this, no performance fee is gonna be payable. So we just need to put a max function in here to say that the performance fee is gonna be based on the greater of this value or zero, and then multiplied by that 20% performance fee level. In this instance, because the fund hasn't generated enough return after fees to cover the hurdle rate, there's no performance fee payable. As a result, the ending value for the portfolio only subtracts the management fee, and as a result, the return generated for the investor equates to 4.6%. As you can see, the investor didn't get enough return after the management fees were taken into account to exceed that 5% hurdle level. And as such, no performance fees were payable.