My question pertains to the CFA Level 2 calculation of private equity fees using the first total return method.
I will present two examples to suggest what I am trying to convey about the formula and I hope someone will be able to clarify my reasoning and explain to me why I am wrong. For simplicity let us assume that there are no management fees and the carried interest is equal to 20%. Let the committed capital be equal to 100. Under the first total return method carried interest is paid only when the value of the investment portfolio exceeds committed capital and subsequent carried interest payments are only made if there is an increase in the NAV before distributions
Example 1: Let us assume that in Year 1 the paid in capital is equal to 90 and committed capital is equal to 100. There are no management fees and the operating results generate 10. Therefore, the NAV before distribution is equal to 100. Given the formula for carried interest we can see that the NAV before distribution isn’t greater than the committed capital of 100. Hence according to this formula carried interest should be 0. Now let us say we liquidate our current position and all of the money is paid as distribution to the investors. Therefore distributions equal to 100 and NAV after distribution is 0. In Year 2, let us say we draw down on the remaining committed capital and we invest the remaining 10. Let us assume that there is a blockbuster year and operating results are 90. Therefore NAV before distribution should be equal to 100. Again given the formula for carried interest we can see that the NAV before distribution isn’t greater than the committed capital of 100. Hence carried interest is again 0. At the end of Year 2 now, the 100 is paid as distribution and the firm is closed and liquidated. The NAV after distribution at the end of year 2 is 0. If we break down the results we can see that carried interest is 0 across both years. But if we look at the results cumulatively the private equity firm was able to generate 100 in operating results in two years. Therefore the carried interest should be equal to 20 because 20% off 100 is equal to 20. The investors should be paid back their 100 committed capital and be returned 80 of the operating results. As you can see there seems to be a discrepancy between the actual carried interest that is owed to the private equity firm which is 20 against the 0 that we calculated using the formula. I would like to understand where my mistake is in terms of the calculations.
Example 2: Let us assume that we have an investment portfolio worth 100 at Year 0. At the end of Year 1, the portfolio grows by 10 and becomes worth 110. Therefore given that there are no management fees the NAV before distribution is equal to 110. Now since the NAV before distribution is greater than the committed capital of 100 there should be a positive carried interest payment. This should be equal to 2 because 20% of 10 is 2. Let us also consider that the remaining 8 of profit is paid out as distributions therefore the NAV after distribution is equal to 100 again. In Year 2, let us say that the portfolio grows by 10 again. Since there are no management fees this time as well the NAV before distribution should be equal to 110. However according to the formula for carried interest under the first total return method the carried interest should be equal to 0 since there is no increase in the NAV before distribution between Year 2 and Year 1. Since there is no carried interest payment in Year 2, the profit of 10 is distributed to the investors and the NAV after distribution is equal to 100 again. Let us consider a different scenario where no carried interest payments or distributions are made in Year 1. But we will assume that in each year the value of the portfolio increases by 10. Therefore in Year 1 the value of the portfolio is 110 and the value of the portfolio in Year 2 is 120. Now let us consider that carried interest and distributions are paid at the end of Year 2. The portfolio value has grown by 20 in two years therefore the carried interest should be equal to 4 since 20% of 20 is equal to 4. The remaining 16 of profit can be paid out to the investors as distributions. Again there seems to be a conflict between what should actually be paid out as carried interest versus what the formula given in the curriculum tells us to do.
I am sure that there is some gap in my understanding of the formula and I would like someone to explain to me where I am wrong. I hope my question has been clear and thank you for all your help.