Carried Interest Valuation Techniques: Part 1 of 2

Valuation Focus

By: Phillip Zhou, CFA cogent SeniorVice President Steven Kam, ASA valuation Managing Director San Francisco Oﬃce Carried Interest Valuation Techniques: The First in a Two Part Series

Carried interest is a right that allows the general partner (”GP”) of a private investment fund to receive a share of the fund’s profits in excess of the percentage of total capital that the GP contributed to the fund. The valuation of carried interest presents unique challenges due to the complexity of its structure and the multitude of factors that drive its value. The professionals at Cogent Valuation (“Cogent”) have extensive experience in the valuation of carried interest, having performed over a hundred valuations of GP interests in private equity funds, venture capital funds, and hedge funds during the past eighteen years. This article, the first in a two-part series on carried interest, advances an overview of the two approaches used today to value carried interest, the benefits and shortcomings of each approach, and the primary factors that impact the fair market value.

In the early stage of a fund’s life, calculated, the required rate of estimate the same preferred return carried interest holders contribute return of a carried interest investor hurdles. capital to the fund that will be (discount rate) is developed starting The DCF benefits from being more deployed for investments. The with the limited partner (“LP”) return intuitive than the option model capital requirements are satisfied benchmarks of similar funds as the through either cash or non-cash fee analysis. Whereas the option base discount rate. Additional risk waivers. The carried interest holder model is perceived as a “black premiums are added to quantify the will be entitled to a future stream of box”, the inputs and outputs of the increased level of risk of carried cash flows once the fund achieves DCF analysis can be more easily interest cash flows compared to LP certain return hurdles that are set in observed and explained to parties cash flows. the fund agreement. These cash of interest and in challenges from flows will continue, as long as the Advantages of the DCF Analysis third parties. The DCF is modified fund satisfies its return hurdles, until readily to account for all of the the fund has completed its The strength of the DCF analysis lies factors that impact carried interest investment cycle and liquidated all of in its flexibility and ability to include value, including fund size, amount its investments. Any valuation major elements of the funds’ inflows analysis of carried interest must and outflows of cash and distri- of capital to be invested, invest- account for all the cash flows butions to investor classes. The DCF ment holding period, management associated with this interest. can be adapted to express the fees, other fund expenses, fund Currently, there are two primary specific characteristics of complex return expectations, and recycling. methodologies used in the valuation fund structures, various waterfalls, When there is a range of outcome of carried interest: 1) the discounted return scenarios, and a degree of scenarios for individual cash flow analysis (“DCF”) and 2) a granularity in connection with each investments, a Monte Carlo call option based model. interest holder’s capital and carried simulation can be utilized to Discounted Cash Flow Analysis accounts. This granularity cannot be account for expected investment The DCF involves projecting cash quantified through option pricing returns, and the timing of holding flows associated with the carried methodology. The DCF can be and liquidation periods. interest and discounting these cash adjusted to incorporate a wider The Option Model flows with the appropriate risk range of fund structures, relative to adjusted discount rate. Typically, The carried interest can be viewed an option model. For example, for carried interest cash flows are as a derivative that provides a derived from perceived risk, funds that have an LP preferred return to the holder when the expected return, and timing return hurdle for individual fund’s investments appreciate over assumptions of the underlying fund, investments, the DCF analysis can a certain hurdle amount. In the which are based on industry data, take into consideration the timing option model, the returns of the past fund performance and and cash flows required for the LP to GP and LPs can be replicated discussions with the fund’s man- achieve the preferred hurdle rate. using a portfolio of call options. agement. Once the cash flows to An option model requires several Typically, the Black-Scholes- the carried interest have been broad simplifying assumptions to Merton (“BSM”) model is the

About Cogent Cogent Valuation, with offices in San Francisco, Woodland Hills, and Costa Mesa, is a nationally recognized firm that has provided independent valuation and financial advisory opinions in thousands of situations since 1991. Cogent utilizes proprietary research, intensive due diligence, and the experience and insights of its seasoned valuation professionals to produce thoroughly supported, well-documented analyses that adhere to the best practices for enterprise, IP, and securities valuations and financial opinions. preferred option model for the pricing along with future cash flows. The practiced using the DCF analysis for estimate of carried interest. First, current value of an investment is purposes of determining the fair breakpoints are determined based on considered in the DCF to the extent it market value of carried interest. This the fund’s assumptions, structure and can be used to predict the future method of vigorous analysis using the distribution waterfall. Next, inputs for liquidation value, whereas the option most fundamental concept of financial the BSM model, including asset price, model will use the investment’s current analysis and market value can be exercise price, risk-free rate, volatility, value as a discrete input. constructed to consider all of the and time to expiration are estimated. Issues with the Option Model relevant variables that impact the fair If the fund has not made any While fewer assumptions are required market value of carried interest. investments, the asset price input is for the construction of the option While the option model can be a equal to the amount of capital model, the model’s simplicity is also useful tool for purposes of testing the expected to be invested over the life one of its deficiencies. One such reasonableness of the DCF value, the of the fund. If the fund has existing shortcoming is the model’s dispro- utility of the model is restricted to investments, the asset price is equal portionate reliance on the volatility funds with expected returns that to the value of the fund’s underlying assumption. The value of the carried follow a normal distribution. investments plus the amount of interest is extremely sensitive to this Moreover, the option model’s capital expected to be invested in the one input, which means that selecting construct limitations cannot future. The exercise price assump- the correct volatility is essential to incorporate critical considerations tions are variable and dependent performing a meaningful calculation. that a knowledgeable investor would upon the capital structure of the fund. The overall volatility of a fund evaluate prior to making an informed The volatility input is the average fluctuates over time depending upon investment in carried interest, such as expected volatility of the fund’s the phase of the fund (fund volatility is performance of prior funds, underlying investments over the life of usually lower at the beginning when performance of similar funds, industry the fund, and time input is equal to the fund has fewer investments, and macroeconomic outlook, and the the expected life of the fund. The increases as the fund reaches experience and track record of the product of the option model is the investment capacity, and decreases fund’s current managers and “option value” of the LP interests and again as the fund begins liquidating investment professionals. Given the carried interest. investments), increasing the difficulty in limitations of the option model, the estimating the single appropriate fair market value of carried interest is Advantages of the Option Model volatility factor. Further, the inherent better derived through the specific An advantage of the option model is assumption built into the BSM that fund’s DCF analysis. its ease of construction. Once the asset returns will be normally COGENTVALUATION.COM fund’s distribution waterfall is distributed and prices will follow a ascertained, the option model can be lognormal distribution does not apply created quickly. There is no need to to most funds. For many funds, this make assumptions for future fund assumption fails as fund returns will be returns, timing of investments, or more positively skewed, with a few Contact discount rates. Instead, the only investments having outsized returns assumptions required are the volatility and the remaining investments of the fund’s future investments and 714.668.0272 v providing average, little, or no returns. 714.668.0137 f the expected duration of the fund. The option model is capable of Conclusion factoring in the value of existing Both the DCF and option model have investments. In a DCF, only the unique inherent advantages. Since cogent investment’s future liquidation value is 1995, the professionals at Cogent valuation factored in the valuation analysis Valuation have recommended and