Valuation of Carried Interest Using a DCF – A Step-by-Step Guide

Author: Ross Slutsky, Business Valuation

In venture capital (VC) and private equity (PE) funds, general partners receive two primary forms of compensation: a management fee, which is calculated based on the fund’s assets under management (AUM), and carried interest, which is a performance-based fee. To accurately value the carried interest, it’s essential to estimate the fund’s distributable cash flows for each year and allocate these cash flows according to the limited partnership agreement (LPA). This process is intricate due to the non-linear nature of carried interest, which adds layers of complexity to the valuation. In this step-by-step guide, we’ll show you how to use a Discounted Cash Flow (DCF) model to navigate these complexities and determine the present value of carried interest with precision.


Background Information to Estimate Cash Flows

Our example will have a fund with the following attributes:

  • Committed capital of $300,000
  • Gross expected investment returns of 10%.
  • Management fees of 2%
  • Fund expenses of .1%
  • LP return of 5% compounded.

The investment and divestment schedule will be as follows:




Estimating Distributable Cash Flows

To map out the available cash flows we must simulate the investment, growth, and divestment of the committed capital throughout the term of the fund. We start by setting up seven rows dictating:

  • Starting period NAV – equals the ending NAV of the prior period (will be zero for the first period)
  • Called capital – equals the committed capital * investment rate.
  • Management fee expense – equals the starting period NAV * 2% (2% is the management fee) + called capital * 2% *.5 (the .5 reflects the assumption the called capital is invested equally throughout the year)
  • Fund expense – equals the starting period NAV * .1% (.1% is the fund expense) + called capital * .1% * .5.
  • Market returns – equals the starting period NAV * 10% (10% is the gross investment returns)+ called capital * 10% * .5.
  • Distributions – equals (the sum of (starting period NAV, called capital, market returns) minus management fees minus fund expense) * divestment rate.
  • Ending NAV – equals the sum of (starting period NAV, called capital, market returns) minus distributions minus management fee expense minus fund expense.

Our example gives us the cash flow schedule below:

Let’s analyze years two and six. Notice how each year starts with the prior year’s ending NAV. In year two’s called capital, we are multiplying $300,000 by 20% to get 60,000, while in year six the investment rate is zero so there is no additional called capital. Management fees are 2% * $31,185 + $60,000 * 2% * .5 in year two and $359,207.92 * 2% in year 6 resulting in $1,223.7 and $7,184.16 respectively. The fund expenses are calculated at $31,185 * .1% + $60,000 * .1% * .5 for year two and $359,207.92 * .1% which equals $61.19, and $359.21 respectively. Next, we have market returns which for year two is calculated at $31,185 * 10% + $60,000 * 10% * .5 = $6,118.5. Market returns for year six = $359,207.92 * 10% = $35,920.79. This leaves us a pre-distribution total of $96,018.62 in year two ($31,185 + $60,000 – $1,223.7 – $61.19 + $6,118.5) and pre-distribution total of $387,585.35 in year six ($359,207.92 – $7,184.16 – $359.21 + $35,920.79). We then multiply each of these pre-distribution totals by each year’s divestment rate which gets us 0 (0% * $96,018.62) and $19,379.27 (5% * $387,585.35) for years two and six respectively. This distribution figure reflects the distributable cash flows in any given year, which is what we are primarily interested in. Last, we take the starting period NAV + the called capital – management fees – fund expense + market returns – distributions to get ending NAV. This is $96,018.62 ($31,185 + $60,000 – $1,223.7 – $61.19 + $6,118.5 – 0) for year two and $368,206.08 ($359,207.92 -$7,184.16 – $359.21 + $35,920.79 – $19,379.27) for year six respectively.

Now that we have mapped out the flow of funds throughout the fund’s life we can identify our allocable cash distribution schedule. This equals the distributions for each year of the fund as noted in the graphic above:

Cash available for allocation for each year of the forecast is: 0, 0, 0, 0, 0, 19,379.3, 19,864.7, 81,449.3, 14,0614.1, 227.583.9

This is what we will be allocating to the GP vs LP interests in the following section.


Background Information to Distribute Cash Flows

The intro referenced how the GP interest scales at a non-linear rate. Each LP agreement specifies the payouts attributable to each partner based on certain metrics being hit. For our example we are assuming a standard distribution agreement as follows:

  1. Before any distributions to the GP (general partner) the LPs (limited partners) receive an amount equal to their capital investment + a 5% compounded return.
  2. After condition 1 has been satisfied, the GP is entitled to 80% of the remaining distributions until it has received 20% of the LP return on capital.
  3. After condition 2 has been satisfied, the remaining funds will be distributed with 90% going to the LPs and 10% to the GP.



We start our allocation schedule with three priorities. Each priority will have the following:

  • Cash Available for Allocation: Represents the total cash available for distribution, or the cash available for other priorities if it’s not the first priority.
  • LP Participation: Indicates the percentage of cash allocated to Limited Partners (LPs) for each priority. For priority 1, it’s 100%; for priority 2, it’s 20%; and for priority 3, it’s 90%.
  • Beginning Period Target Allocation: The amount of cash needed in the current period to meet the priority’s requirements. For priority 1, LPs need a 5% compounded return; for priority 2, the GP gets 20% of LPs’ returns from priority 1.
  • Ending Period Target Allocation: Calculated by subtracting the cash distributed from the beginning period target allocation to determine if the priority’s condition is met.
  • GP Participation: Shows the percentage of cash allocated to the General Partner (GP) for each priority. For priority 1, it’s 0%; for priority 2, it’s 80%; and for priority 3, it’s 10%.
  • Allocated Cash: The total amount of cash assigned to both GP and LP participation.
  • Cash Available for Other Priorities: The remaining cash after subtracting the allocated cash from the total cash available for allocation.

Let’s walk through each of the priorities starting with priority 1:

  • Cash available for allocation is linked directly to the distributions row from our cash flow distribution schedule for each year.
  • The LP participation percentage is 100% because the LPs get 100% of the cash flows until the first priority is satisfied per the LP agreement described.
  • The LP participation formula for each year is the minimum of the beginning period target allocation and the cash available for allocation * the LP participation % of 100%.
  • The beginning period target allocation is the previous period’s ending period target allocation * (1+the LP return of 5%) +the called capital * .5 * the LP return of 5% + the called capital.
  • For year 2 it would be $30,750 * 1.05 + $60,000 * .5 * 5% + $60,000 = $93,787.5
  • Ending period target allocation is the beginning period target allocation minus the LP participation.
  • GP participation is the LP participation/the LP participation % * the GP participation %
  • Allocated cash is the GP participation + LP participation.
  • Cash available for other priorities is cash available for allocation – allocated cash.

After we have satisfied priority 1, we can start distributing the remaining cash flows in each year based on priority 2:

  • Cash available for allocation = the remaining cash available for other priorities in each year of the prior priority (priority 1).
  • LP participation = GP participation/GP participation rate * LP participation rate. The LP participation rate is 1 minus the GP participation rate.
  • The beginning period target allocation is the (sum of the LP participation across priority 1 minus the total called capital) * 20%. This is based on the LP agreement.
  • The ending period target allocation is the beginning period target allocation minus the GP participation.
  • The GP participation is the minimum of the beginning period target allocation and the cash available for allocation * the GP participation rate of 80%.
  • The allocated cash = the LP participation + the GP participation.
  • Cash available for other priorities is the cash available for allocation minus the allocated cash.

The last priority covers the residual unallocated cash, so we don’t need to worry about beginning or ending period target allocations since there is no threshold that needs to be hit.

  • For this one, cash available for allocation = priority 2s cash available for other priorities.
  • LP participation = cash available for allocation * LP participation rate of 90%.
  • GP participation = cash available for allocation * GP participation rate of 10%.
  • Allocated cash = LP participation + GP participation.
  • Cash available for other priorities = cash available for allocation – allocated cash (this should = 0 in the final year).

Now that we have successfully allocated the cash between GPs and LPs the last task is to discount the cash flows back to today. For this exercise we chose to use a discount rate of 7%. To arrive at the present value of the investment for both the GP and LPs we must do the following steps:

  • Identify the total LP cash flows in each year – this is done by summing the LP participation in each year across all priorities.
  • Identify the total GP cash flows in each year – this is done by summing the GP participation in each year across all priorities.
  • Identify the number of periods – We are using the mid-year convention so it’s just the year – .5.
  • Present value each year’s cash flow at the 7% discount rate.
  • Sum the present value of the cash flows associated with the interested partnership type across all years.

As shown below for this project we arrived at a PV of LP and GP interests of $259,842.12 and $14,136.46 respectively. Additionally, if one was assessing a fund, they could present value the called capital and when they would need to provide it to assess how much value the fund was adding to them. In this scenario, the present value of the LP stake was $259,842.12 whereas if they hadn’t invested in the fund, the present value would be $250,806.09. The fund added a little over 9 thousand dollars’ worth of value to the LPs. Similarly, if the GP was debating if managing the fund is worthwhile, they can see the present value of the carry component is $14,136.46.




Conclusion

Valuing GP and LP stakes involves a detailed and nuanced approach, with significant attention required to the specifics of the partnership agreement and distribution mechanics. The process encompasses identifying the timing and amount of distributions, accurately allocating these to the relevant shareholders, and discounting future cash flows to determine present value. Common pitfalls include misinterpreting the partnership agreement, making oversimplified assumptions, and neglecting to track changes in NAV over time. Avoiding these mistakes demands both meticulous attention to detail and a thorough understanding of the underlying assumptions and the LP agreement.

If you find yourself needing expert assistance or a second opinion on your valuation work, the Business Valuation team at Frank, Rimerman + Co. is here to help. Feel free to reach out to us with any questions or for professional support.

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