Questions:
Kyle is a fund manager who manages wealth for high-worth investors in Iowa. One of his private equity funds which he manages as a general partner has $500 million of committed capital. The limited partners included a hurdle rate of 10% in the initial contract along with a full catchup clause. Moreover, there is no management fee. The limited partners are going to get 80% and Kyle will only get carried interest of 20% above the preferred return of the investors. Furthermore, the fund has a deal-by-deal structure with a clawback provision and the fund distribution cannot take place before six years.

In the past 6 years from 2017 to 2023, Kyle has made 5 investments which have performed as follows:

| Investment | Invested Amount | Year Invested | Year Sold | Sale Amount |
|------------|------------------|----------------|------------|--------------|
| 1          | $100 million     | 2017           | 2020       | $120 million |
| 2          | $150 million     | 2019           | 2020       | $160 million |
| 3          | $60 million      | 2018           | 2022       | $88 million  |
| 4          | $90 million      | 2019           | 2023       | $67 million  |
| 5          | $100 million     | 2022           | 2023       | $90 million  |

How much is kyle's total carried interest (performance fees) from 2017 to 2023?

What is the annual geometric rate of return for the limited partners over this six year period (ignoring taxes or fees other than the performance fee)?

Reference answers:
# Investment 1:
Investment: $100 million
Sold for: $120 million
Gain: $20 million
Geometric Mean: ($120m - $100m) / $100m * 100 = 20%

The return is above the hurdle rate so the profit will be shared according to 80/20.

Share of Limited Partners = 80% of $20 m = $16m
Share of General partner (Kyle) = $20m - $16m = $4m


# Investment 2:
Investment: $150 million
Sold for: $160 million
Gain: $10 million
Percentage: ($160m - $150m) / $150m * 100 = 6.67%

The return is above the hurdle rate so the profit will be shared according to 80/20.

Share of Limited Partners = 80% of $10 m = $8m
Share of General partner (Kyle) = $10m - $8m = $2m


# Investment 3:
Investment: $60 million
Sold for: $88 million
Gain: $22 million
Percentage: ($88m - $60m) / $60m * 100 = 36.67%

The return is above the hurdle rate so the profit will be shared according to 80/20.

Share of Limited Partners = 80% of $22 m = $17.6m
Share of General partner (Kyle) = $22m - $17.6m = $4.4m


# Investment 4:
Investment: $90 million
Sold for: $67 million
Loss: $23 million
Percentage: ($67m - $90m) / $90m * 100 = - 25.56%

Since the return is negative, it fails to meet the hurdle rate requirement. Therefore, the clawback provision will get activated and the gains of the general partner (Kyle) will be reduced according to the 80/20 division rule. Since the fund cannot be distributed before six years, the accumulated carried interest of the general partner (Kyle) will have accumulated will get reduced.

Share of Limited Partners = 80% of $(-25.56m) = -($20.45m)
Share of General partner (Kyle) = 20% of $(-25.56m) = (-$5.11m)

# Investment 5:
Investment: $100 million
Sold for: $90 million
Loss: $10 million
Percentage: ($90m - $100m) / $100m * 100 = (-10%)

Since the return is negative, it fails to meet the hurdle rate requirement. Therefore, the clawback provision will get activated and the gains of the general partner (Kyle) will be reduced according to the 80/20 division rule. Since the fund cannot be distributed before six years, the accumulated carried interest of the general partner (Kyle) will have accumulated will get reduced.

Share of Limited Partners = 80% of $(-10m) = (-$8m)
Share of General partner (Kyle) = 20% of $(-10m) = (-$2m)


Total Carried Interest of the general partner
Investment 1: $4m
Investment 2: $2m
Investment 3: $4.4m
Investment 4: -$5.11m
Investment 5: -$2m

Total = $4m + $2m + $4.4m + (-$5.11m) + (-$2m) = $3.29m 

The General Partner (Kyle) will have earned $3.29m in performance fees.

We can compute the geometric rate of return here with:

GRR = (Final Value / Initial Value)^{1/n} - 1

The investors all put in $500 million in capital. The total fund value was 120 + 160 + 88 + 67 + 90 = $525 million. From this we need to subtract Kyle's carried interest of $3.29 million to get $521.71 million. This would then mean the geometric mean of these returns would be:

GRR = (521.71 / 500)^(1/6) - 1 = 0.71%

The geometric return of the investors was 0.71%. Nice job Kyle.