Private Equity Net Asset Values and Future Cash Flows

Transcription

1 Private Equity Net Asset Values and Future Cash Flows Tim Jenkinson* Said Business School, University of Oxford Wayne R. Landsman Kenan-Flagler Business School, University of North Carolina Brian Rountree Jones Graduate School of Business, Rice University Kazbi Soonawalla Said Business School, University of Oxford Abstract This paper analyzes whether fund valuations produced by private equity managers are biased predictors of future discounted cash flows (DCF). Our research is based on an extensive set of timed cash flows and reported net asset values (NAVs) that relates to 483 funds spanning Using an ex ante lens, we find that, on average, reported NAVs converge on the future DCF early in the life of the fund. This result is particularly interesting to investors for whom unbiased asset valuations are important in keeping portfolios optimally allocated. In addition, findings indicate that although NAVs generally are more conservative in the first half of the sample period, NAVs for venture capital funds tend to overstate economic value after 1999 following the bursting of the tech bubble. We also find some evidence that private equity managers of funds that perform less well use their discretion over asset valuations to keep asset values high during fundraising periods, as well as at the end of the fund life, which can result in higher management fees. July 2015 Keywords: Private equity, asset valuation, fair value *Corresponding author: Wayne Landsman is also an expert consultant financial economist for the Securities and Exchange Commission. The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication or statement by any of its employees. The views expressed herein are those of Wayne Landsman and his coauthors and do not necessarily reflect the views of the Commission or the staff of the Commission. We thank Florin Vasvari and workshop participants at the University of Chicago, the University of North Carolina, and Washington University in St. Louis for helpful comments. We appreciate funding from the Private Equity Institute, Said Business School, and Center for Finance and Accounting Research, Kenan-Flagler Business School. We thank Burgiss Private IQ for providing data and Wendy Hu for programming assistance.

2 1. Introduction Although discounted cash flow (DCF) analysis provides the theoretical basis for the valuation of assets, it is difficult to apply in practice because of the on-going nature of most businesses. Cash flows continue at least in expectation into the future, which results in much of the value being assigned to a terminal value that is notoriously difficult to estimate. However, private equity (PE) funds have relatively short finite lives. This is because they typically are established as limited partnerships that take on limited term investments. The funds make investments into private companies, or take existing public companies private. These investments are held for a period of years during which time the managers of the fund, i.e., the general partners (GPs), seek to increase value. However, because the funds typically have ten-year lives, once they liquidate, the full set of cash flows are readily observable and there is no need to estimate a terminal value. Until all the investments are sold, the GPs provide the fund s investors, i.e., the limited partners (LPs), with reports on the valuation of the companies held by the fund. In this paper we use this unusual setting, where the cash flows into and out of the fund are completed within a designated period, to investigate the relation between the valuations reported by GPs to LPs and the fund s subsequent cash flows. To investigate this relation, we adopt an ex ante approach and compare NAVs at each valuation date to the corresponding future discounted cash flows using cross-sectional regressions. In doing so, we take the DCFs as the true economic measure of fund value, i.e., the fair value, at each valuation date. If GPs are unbiased in their valuations, then the NAVs and DCFs should essentially be the same. The valuation of their fund investments is important to LPs because they use these valuations as inputs into their asset allocation models. If, for example, an investor is aiming to have 10% of his assets in private equity, he will make inappropriate investment allocation 1

3 decisions if the valuation of his existing PE fund investments is biased. If GPs systematically under-value their investments which they might do to smooth the reported returns to investors and ensure there are no volatile swings in valuations then investors will tend to have too much invested in private equity. On the other hand, if GPs systematically over-value their investments which they might be tempted to do to increase the returns they report during the life of the fund to help raise their next fund then investors would become under-allocated to private equity. 1 In particular, because GPs typically raise funds every 3-4 years and therefore before the previous fund has been fully realized, they have incentives to inflate NAVs beginning in years 3-4 to create high reported rates of return at the time they are fundraising. Comparing current NAVs to future fund cash flows is a simple idea, but faces two main challenges. The first is data. Reliable data on private equity cash flows and reported NAVs has been elusive to academic researchers. Reliable data are now available from Burgiss, a private equity portfolio management data firm, which provides investment and data analysis to investors holding a broad spectrum of funds. Because Burgiss obtains its data entirely from investors, studies that access its database can avoid many of the sample selection issues faced by databases that rely on GPs for data. The first study to exploit the Burgiss database is Harris, Jenkinson, and Kaplan (2014), which analyzes the performance of PE funds relative to public markets over long periods of time. Ours is the first study to use both the cash-flow data and the history of reported NAVs, which allows us to compare, at each valuation date, the reported asset values to future cash flows. The second challenge relates to discount rates. Although we now have reliable and verified cash flows, what discount rate should be used when computing discounted cash 1 Even if investors apply filters based on their knowledge that NAVs can systematically deviate from fair value, their allocations to private equity can still depart from their desired levels because of the inherent difficulty of knowing which GPs are reporting biased valuations. 2

4 flows? The approach we adopt is to take an ex ante view by applying a discount rate that LP investors, on average, use when valuing their investments. Unfortunately, the rate investors use is unobservable. However, because their expected discount rates likely are influenced by realized returns that investors have received from PE funds, we use the standard practice of setting the ex ante discount rate equal to recent realized rates of return. We use 11%, which is based on the average realized internal rates of return that Kaplan and Schoar (2005) reports for its sample of funds that are fully or largely realized for a sample period that significantly overlaps with ours. To address our research question, we estimate cross-sectional regressions of DCFs, which we take as an estimate of true economic value, on NAVs at each valuation date typically quarterly over the life of the fund. Our sample, which comprises NAV and cash flow information taken from the Burgiss private equity fund database, relates to 483 funds with available information beginning in 1988 and ending in We estimate separate regressions for 327 venture capital funds and 156 buyout funds, thereby permitting coefficient differences for the two types of funds potentially arising from relative discretion accorded to GPs of venture capital funds whose investments are more difficult to value. To assess whether there are any patterns in valuations throughout the average fund s life, we estimate separate fund-year regressions in which we partition sample observations by fundyear. To assess whether there are any intertemporal patterns in valuations, we estimate separate yearly regressions in which we partition observations by calendar year, along with estimating fund-year regressions separately over the first and second halves of our sample period. The fund-year regressions permit us to assess whether there are identifiable trends or biases in the valuations during the fund life. For example, because as noted earlier, GPs typically begin to fundraise for new funds approximately midway through the typical tenyear life of the fund they manage, they face incentives to overstate NAVs during those years 3

5 and understate NAVs in the preceding years. Similarly, GPs of relatively unsuccessful funds may face incentives to overstate NAVs to obtain higher management fees. The calendar year regressions permit us to assess if GPs valuations tend to improve over calendar time because of learning or changes in valuation techniques. Findings from our primary tests indicate that the NAVs GPs provide to LPs of both venture capital and buyout funds are extremely good predictors of future economic performance, i.e., NAVs are relatively unbiased indicators of true economic value of the funds they manage. Findings from the fund-year regressions generally indicate that NAVs are somewhat conservative estimates of value early in a fund s life, which we show likely is attributable to GPs simply setting NAVs to contributions in the first few years. However, NAVs generally converge to true economic value by year three. Findings from the calendar year regressions indicate that NAVs generally are more conservative in the first half of our sample period, but a somewhat different picture obtains in the latter half of the sample. Most notably, NAVs for venture capital funds tend to overstate economic value after 1999, which suggests that venture capital fund GPs did not incorporate in a timely manner the drop in expected future cash flows associated with the bursting of the tech bubble in 2000, and failed in future years to make adjustments to correct for NAV overstatement. We also conduct cross-sectional tests that focus on whether there is evidence of managerial manipulation of NAVs in response to incentives to overstate NAVs during fundraising and in the later years of a fund. The findings indicate that GPs of relatively poor performing venture capital funds appear to overstate NAVs during fundraising periods, and that GPs of relatively poor performing buyout funds tend to overstate NAVs during a fund s latter years. We also estimate fund-year regressions using data for the subset of funds for which a breakdown of investments by private vs. public holdings is available, thereby permitting us to test whether NAV coefficients differ for funds that invest in relatively high 4

6 or low percentages of assets characterized as private holdings. Findings suggest that managers of funds with the greatest flexibility to measure investment values i.e., those with relatively high percentages of private holdings on average overstate NAVs in the period when fundraising for follow-on funds is most likely to occur. The remainder of the paper is organized as follows. The next section discusses the institutional background and related literature. Section 3 presents our predictions and research design, section 4 describes our sample and data, and section 5 presents our results. Section 6 provides concluding remarks. 2. Institutional Background and Related Literature 2.1 Private Equity Funds Private equity comprises equity investments that are not publicly traded or listed on an exchange. Usually private equity managers focus on either more entrepreneurial companies Venture Capital (VC) or later-stage growth companies and/or buyouts of relatively mature companies. We refer to funds that invest in VCs as VC funds, and those that invest in more mature companies as Buyout funds. Most private equity is raised using limited partnership fund structures, where a private equity manager (GP) raises money generally from institutional investors (LPs). These limited partnership funds are closed-end with a finite life, and are usually incorporated in favorable tax and legal jurisdictions. The GP receives a management fee and, if the fund s internal rate of return during its life exceeds a threshold rate, additional compensation in the form of carried interest. We explain the economics of private equity funds in more detail below in relation to the valuation of the fund s assets. Private equity funds typically have a specified contractual life of ten years, during which time they invest in, work with, and then sell their stakes in portfolio companies. The 5

7 fund life can be, and often is, extended by agreement should the fund have remaining investments that have not yet been sold by the end of the 10-year period. The terms of the partnership are governed by the Limited Partnership Agreement (LPA), which specifies the investment mandate, the governance of the partnership, and the obligations and rewards for the LPs and the GPs. The LPs commit capital to the fund, which is drawn down when the GP identifies investment opportunities. The initial years typically the first 5-6 years comprise the fund s investment period, during which time the GPs can draw down the committed capital. Towards the end of the investment period GPs typically are permitted to raise a follow-on fund; this overlap of funds enables GPs always to have capital available to make investments should opportunities arise. When the fund s investment period is over, the GP can no longer draw down any unused committed capital, and the GP has the remaining fund life to realize investment returns. As soon as investments are realized the funds are distributed to the LPs. The GP s compensation has two components. The first is an annual management fee for running the fund. Although the details vary by fund, the typical LPA specifies different arrangements for the management fee in the investment period and the post-investment period. During the former, a management fee of 1.5 2% is typically charged. Importantly, the fee basis is committed capital, rather than invested capital, and so does not depend upon reported asset values. During the post-investment period, the GP receives either a smaller percentage of committed capital (e.g., 1%, or the fee might fall by 20% per annum over the remaining life of the fund) or the GP is allowed to charge a fixed percentage of invested capital. Typically, the invested capital is defined in the LPA as the lower of (i) the original cost of the remaining investments and (ii) the reported NAV. A reason for the lower of clause is that if NAV is used as a basis for the GP s management fee, then the GP can manipulate his/her compensation by manipulating the reported NAV, but no such 6

8 manipulation is possible if original cost is used so long as NAV exceeds original cost. However, manipulation is still possible if NAV is less than original cost and the GP fails to report NAV correctly. Regardless, it is clear that the fixed compensation is structured so that the GP receives the largest proportion during the investment period, during which time he/she is actively identifying assets to be purchased by the fund. The second part of the GP s compensation is a profit share, or carried interest, which is typically 20% of the private equity fund s profit, i.e., cash received by the fund in excess of committed capital. However, the GP often does not receive carried interest unless the fund s internal rate of return (IRR) to investors exceeds a pre-determined hurdle rate established in the partnership agreement. The vast majority of private equity funds stipulate an 8% hurdle rate (Preqin, 2014), although some well-established GPs manage to avoid having to achieve a hurdle rate. In addition, although some interim payments of carried interest may be made during the life of the partnership, the final distribution of profits will be made on the basis of the cash received by the investors at the end of the fund s life, rather than reported NAVs. This is unlike typical hedge funds where profits are often shared on an annual basis using the reported NAVs each year, subject to a so-called high water mark so that if valuations fall future profits are not paid unless the fund exceeds its prior highest valuation. 2.2 Reporting and performance measurement LPs receive semi-annual or quarterly financial statements from the GP, which include the NAV of the fund, along with an income statement and a cash flow statement. Although the statements need not be prepared in accordance with US GAAP or IFRS (depending on 7

9 the jurisdiction), they typically conform to a set of industry standards. 2 Although the interim financial statements typically are not audited, the annual financial statements are. In contrast to managers of publicly traded firms, private equity fund managers have considerably more discretion when measuring NAVs, in large part because of differences in financial reporting requirements. There are incentives for GPs to take advantage of their financial reporting flexibility by inflating NAVs. First, as noted above, GPs typically raise follow-on funds during years 3 through 6 of the life of an existing fund. Potential investors in the follow-on fund will want to know the performance of the current fund, and this will depend to a considerable extent on the reported NAVs. Fund performance tends to be measured using two metrics: the internal rate of return (IRR) and the multiple of invested capital (MOIC). During the life of the fund both of these will depend upon the reported NAVs. In the case of the IRR, the NAV at the calculation date is treated as a final distribution, in addition to the cash contributions and distributions that have occurred up to that point. In the case of the MOIC, it is customary to measure this by summing the cash distributed and the remaining NAV, and comparing this to the cash contributed up to the date of measurement. For many funds, cash returns for few investments in a fund s portfolio have been realized at the time the fundraising occurs, and so these interim performance measures rely heavily upon the reported NAVs. This can create incentives to inflate NAVs to impress potential investors. Second, as noted in the previous section, in the post-investment period management fees are charged on the basis of the lower of the historic cost of the remaining investments and the NAV. This creates an incentive for the GP to avoid writing down poorly performing assets. This temptation to milk the management fees applies later in the life of the fund, 2 In many countries, the International Private Equity Valuation guidelines are adopted as the guiding principles, as specified in the LPA for the partnership. See See PWC (2013) and EY (2009) for detailed discussions of the issues faced in producing financial statements for private equity funds. 8

10 and only for the funds that are performing poorly. Of course, working against these incentives to overstate NAVs are the potential longer-term impact on the reputation of a GP whose ultimate returns of the funds he manages may be significantly smaller than those based on NAVs reported to LPs during the life of the fund, and the incentive to keep in reserve some gains to cushion future losses, which effectively smooths the reported returns to investors. 3 We test in our empirical work whether there is any evidence of GPs reporting higher NAVs either in the fundraising period or towards the end of the life of the fund. 2.3 Valuation and asset allocation decisions Although the commitment of capital that investors make to GPs extends over several years, investors want to know the amount they have invested in private equity each year. A typical pension fund, endowment, or other institutional investor will perform a portfolio optimization based on its appetite for risk, expected asset returns, and liquidity needs. This will result in a strategic asset allocation for each asset class. If, for example, the allocation to private equity is 10%, then the chief investment officer will have to work out the extent, and distribution over time, of fund commitments that will achieve this target. This is not straightforward because capital is only invested as the GPs find profitable opportunities, and the extent and timing of investments liquidation are unknown and difficult to predict. Having decided on the optimal commitment schedule, the investor will then monitor the extent of the capital invested over time, with a view to keeping close to the target allocation. For this purpose the reported NAVs are typically used, because GPs are better informed and there typically is little external information available for investors to conduct their own valuation analyses. 3 Regressing quarterly changes in NAVs on quarterly changes in cash flows for funds managed by California Public Employees Retirement System, Jenkinson, Sousa, and Stucke (2013) provides evidence that private equity fund GPs appear to understate NAVs over the life of the fund, particularly during the early years of a fund, perhaps to smooth returns and avoid having to report asset write-downs. 9

11 The answer to our central question are NAVs unbiased predictors of future cash flows? is, therefore, critical to investors. For instance, if NAVs are, on average, conservative estimates of fair value, then investors will over-allocate to private equity if relying on the reported NAVs, and vice versa. Whereas investors can use market prices for investments traded in liquid markets when making their investment allocation decisions, no such market prices exist for private equity funds. Therefore, our analysis will compare, at each NAV valuation date, the current NAV reported by the GP and the future cash flows. Such a comparison only becomes meaningful once a reasonable proportion of the committed capital has been invested, and therefore we focus on results after the first year of the fund, but we report results for all NAV dates including the initial one for each fund. A key question relates to the discount rate to use for this NPV calculation. From an ex ante perspective, investors are likely to use a discount rate that is consistent with average realized returns from historical private equity investments. We implement this approach and draw on the findings in Kaplan and Schoar (2005) as a measure of historical rates of return. Investors are also interested in the extent to which NAVs represent fair value when making investment decisions. If NAVs are biased estimators of fair value, then the interim performance numbers produced by GPs at the time of fundraising by GPs will be unreliable. The performance of the current fund is one of many factors investors should consider when making investment decisions into future funds. Despite evidence that performance persistence in private equity is weak (Harris, Jenkinson, Kaplan, and Stucke, 2014), current fund performance remains an important factor for most investors. 2.4 Related Literature The literature concerning private equity is experiencing rapid growth with the availability of several new data sources providing direct access to private equity valuations 10

12 on a quarterly basis. Previously, researchers assessing the performance of private equity were limited to using information at irregular, discrete event dates, such as those relating to initial public offerings of firms in private equity investment portfolios or those relating to acquisitions. These investments exhibit an inherent self-selection bias in that they tend to be successful ventures and thus returns to private equity based on these events are biased upwards (Cochrane, 2005). With the availability of private equity data, self-selection is less of an issue because valuations are observable even for funds not performing very well. 4 A number of studies using these databases investigate issues surrounding private equity investments including whether private equity funds provide competitive returns (Kaplan and Schoar, 2005; Phalippou and Gottschalg, 2009; among others), variation in performance including persistence in successive funds as well as networking related differences (Gompers and Lerner, 2000; Hochberg, Ljungqvist, and Lu, 2007; Barber and Yasuda, 2014), and GP compensation-related issues (e.g., Gompers and Lerner, 1999; Metrick and Yasuda, 2010). When assessing performance most studies adjust reported returns calculated from the combination of cash flows that have occurred and NAVs, which as explained above are treated as terminal period cash flows, using a benchmark such as the S&P 500 (Kaplan and Schoar, 2005), or some other risk adjusted return based on average industry unlevered betas (Phalippou and Gottschalg, 2009). Most recently, using data from a variety of data providers including Burgiss, Cambridge Associates, and Preqin spanning the 1990s and 2000s, Harris, Jenkinson, and Kaplan (2014) compares the performance of private equity to the S&P 500. The study finds 4 Self-selection is still an issue if GPs selectively report performance only for the more successful funds they manage. Databases have improved their data collection efforts over time, thereby minimizing concerns about self-selection bias because data providers, such as Burgiss, have an incentive to provide LPs, who pay for the services, with accurate information on which to base investment decisions. 11

13 that Buyout funds consistently outperforms the S&P 500 and that VC funds outperformed the S&P 500 in the 1990s but underperformed during the 2000s. In contrast to the studies that focus on whether private equity investments provide reasonable levels of returns to investors relative to other investment opportunities, our research objective is to determine how NAVs that GPs provide to their funds investors compare to the subsequent net cash flows they will receive. In doing so, we also assess whether (a) there are identifiable trends or biases in the valuations during the fund life, (b) GPs valuations tend to improve over calendar time because of learning or changes in valuation techniques, and (c) there are discernable differences in valuations between Buyout funds and VC funds. Other studies focus on whether there are specific incentives faced by GPs that may cause them to manipulate NAVs. Jenkinson, Sousa, and Stucke (2013) uses quarterly NAV and cash flow information for private equity funds investments of the California Public Employees Retirement System, the largest pension funds in the US. The study regresses quarter-by-quarter changes in NAVs on cash flows and series of controls and finds that for every dollar returned to investors the NAV falls by approximately 65 cents. The authors interpret this finding as arising from a generally conservative NAV valuation, particularly in the early years of a fund, as evidenced by higher changes in NAV during the fundraising period. The authors conjecture that perhaps GPs behave conservatively early in a fund s life in an effort to make it easier to report improved performance during periods in which the GPs are trying to raise money for a new follow on fund. Brown, Gredil, and Kaplan (2014), which also accesses the Burgiss private equity database, considers whether GPs boost reported returns by inflating NAVs during fundraising periods. The study finds some evidence of such manipulation by examining whether there is a relation between a fund s IRR during the fundraising period and its actual 12

14 realized IRR. However, the study also finds that managers who succumb to this temptation are less likely to raise a subsequent fund, which suggests that investors see through such manipulation. Barber and Yasuda (2014), which accesses the Preqin private equity database, shows that fundraising success, as reflected by the ability to raise a subsequent fund and the size of any such fund, is related to reported performance, as measured by IRRs, relative to funds of the same vintage. The study also finds that GPs time their fundraising efforts when such relative performance is at a peak, and that subsequent asset write downs after fundraising suggest that NAVs are inflated by some GPs during fundraising. Taken together, these studies tend to focus on the shorter-term behavior of IRRs, particularly around fundraising. In contrast, we examine the longer-term behavior of NAVs in terms of their relation to actual subsequent cash flows over the life of the fund. If the biases in valuations documented in prior research relating to the incentive for GPs to show high fund performance during fundraising are prevalent which we refer to as the fundraising incentive then the relation between NAVs and cash flows should show a discernable pattern during fund life. In addition, we also consider whether fund valuations exhibit biases in later years because GPs have incentives to keep NAVs high towards the end of the life of funds, especially for GPs whose funds have performed poorly and so may boost NAVs to reap greater management fees, which we refer to as the milking incentive. Our study also relates to the vast literature examining properties of fair value accounting estimates (see Landsman (2007) for a summary of the literature). Most of the literature addresses whether fair values are relevant and reliable as assessed by investors. In particular, a large number of studies examines how accounting measures of fair value or changes in those values correspond to stock prices or stock returns. Representative studies typically focus on banks because such entities have large investments in financial assets, the 13

15 book values of which either approximate fair value or explicitly are subject to fair value measurement, i.e., investment securities (Barth, Beaver, and Landsman, 1996; Eccher, Ramesh, and Thiagarajan, 1996; and Nelson, 1996). Developments in standard setting that define the fair value hierarchy, and permit firms to use fair value measurement for financial assets and liabilities for which fair value measurement is not required, have led researchers to assess whether there are differences in value relevance across asset hierarchy categories. 5 In particular, a primary focus is whether Level 1 assets, i.e., those for which market prices are readily available, are more value relevant than Level 3 assets, i.e., those for which fair values must typically be estimated using models or matrix pricing. Again in the context of banks, Song, Thomas, and Yi (2010) and Goh, Li, Ng, and Yong (2015) find evidence that the SFAS 157 fair values of Levels 1, 2, and 3 assets of large financial firms are value relevant for stock prices, with valuation coefficients being generally higher for Levels 1 and 2 relative to Level 3 amounts. A disadvantage of examining value relevance questions using banks is that banks are subject to regulatory pressures that can create incentives for managers to exercise discretion when applying fair value measurement rules. Lawrence, Siriviriyakul, and Sloan (2015) avoids this issue by examining value relevance of fair value estimates for closed-end mutual funds, which offers the additional advantage of having virtually all of their assets being subject to fair value measurement. In contrast to the banking studies, Lawrence, Siriviriyakul, and Sloan (2015) finds that Level 3 fair values have similar value relevance to Level 1 and Level 2 fair values. 5 The fair value hierarchy is defined in Statement of Financial Accounting Standards No. 157, Fair Value Measurements (Financial Accounting Standards Board, 2006), and the fair value option is described in Statement of Financial Accounting Standards No. 159, The Fair Value Option for Financial Assets and Financial Liabilities (FASB, 2007). 14

16 A key limitation of the value relevance literature is that because there is no direct independent measure of economic value i.e., future cash flows are unobservable researchers have to assume that investors assessments of value are reliable proxies for economic value. Stock prices can be noisy and biased measures of economic value, making it difficult to assess whether managers fair value estimates accurately reflect a firm s economic value. A major advantage of our research setting examining valuations made by GPs of private equity funds is that the relatively short lives of such funds permit us to observe the actual cash flows associated with each fund throughout the life of the fund. Thus, we can compare directly the economic value of the funds to the accounting estimates that GPs provide without having to view accounting estimates through the filter of investors assessments of value as reflected in stock prices. 3 Predictions and Research Design 3.1 Primary Estimations Our research objective is to determine how NAVs that GPs provide to their funds LPs compare to the subsequent net cash flows they will receive. To do this, we compare NAVs to the subsequent DCFs at each valuation date. In doing so, we take the DCFs as the true economic measure of fund value at each valuation date. If GPs are unbiased in their valuations, then the NAVs and DCFs should essentially be the same. If there are identifiable trends or biases in the valuations during the fund life, particularly in response to fundraising and milking incentives, then NAVs should exceed DCFs for funds with valuations that are affected by these incentives. If GPs valuations tend to improve over calendar time because of learning or changes in valuation techniques, then NAVs should generally grow closer to DCFs during our sample period. If VC funds, which invest primarily in new startups, are inherently more difficult to value than Buyout funds, which invest in existing companies, 15

17 then VC fund valuations may be more affected by the influence of GP incentives because of greater discretion. To address our research question and to examine whether any of the biases and patterns we conjecture is present, we estimate a regression of our estimate of true economic value on net asset values. Our estimate of the true economic value of a fund is the net present value of a fund s remaining future cash flows as of each valuation date. That is, for a given net asset value at date t, NAV t, we construct a corresponding discounted cash flow, DCF t. The future cash flows can be both inflows, i.e., fund contributions, or outflows, i.e., distributions to fund investors. We set the discount rate equal to 11%, which is the average realized cash internal rate of return for funds in Kaplan and Schoar (2005). Each fund generally has four quarterly valuations per year, although valuation dates vary across funds. For example, one fund can have a quarterly valuation on May 28 and another on June 10. When estimating regressions by calendar year, we use all observations within that calendar year, y. For each fund, f, we construct the fund year, n, by subtracting the year of the fund s inception date from the calendar year in which NAV t and DCF t appear. We then estimate the number of years since inception by dividing the difference by 365 and taking the integer as the value of the fund-year. Because sample sizes are small for n >10, we only tabulate findings relating to fund years between 0 and 10. Untabulated statistics reveal NAV and DCF are highly skewed. Thus, we estimate regressions using their natural logs. The fund life regressions are given by equation (1): ln DCF fn = α 1n ln NAV fn + ε fn. (1) Equation (1) permits us to assess whether there are any patterns in valuations throughout the average fund s life. The calendar year regressions are given by equation (2): ln DCF fy = α 1 y ln NAV fy + ε fy. (2) 16

18 Equation (2) permits us to assess whether there are any intertemporal patterns in valuations that are evidence of learning or improvements in valuation techniques over time. We estimate equations (1) and (2) separately for Buyout funds and VC funds to allow for differences in risk characteristics of the types of funds as well as incentives of fund managers. 6 In the fund-year regressions, i.e., equation (1), we cluster standard errors by fund and calendar year. In calendar-year regressions, i.e., equation (2), we cluster standard errors by fund and fund-year. When estimating equations (1) and (2), we constrain the intercept to be zero. We do so to ensure that the relation between the economic value of a fund, DCF, and the GP s accounting-based value, NAV, is reflected by the slope rather than the intercept and the slope. Untabulated findings from estimations that include an intercept result in significantly positive intercepts and significantly smaller slopes than those associated with estimation of equations (1) and (2), especially in the early lives of funds. Although fitted DCF values based on the equations (1) and (2) and estimations that include intercepts are similar, the constrained regressions permit a more parsimonious and meaningful economic interpretation of how the slope coefficient varies with fund life or over calendar time. Also, unlike many research settings, theoretically the regression line should be constrained to go through the origin because when NAV is equal to zero, DCF should be equal to zero. 7 If GPs report net asset values that are unbiased, i.e., approximate the economic values of their funds, and our assumed 11% discount rate is representative of the average fund, then we expect α 1n and α 1y to equal one. If valuations under- (over-) state the economic value 6 To the extent that VC funds are riskier than Buyout funds, their α 1 coefficients will be higher than those for Buyout funds and will converge to a number in excess of one. Regarding differences in incentives, as we describe below in the data section, Buyout funds are typically orders of magnitude larger than VC funds as measured by committed capital. As a result, managers of Buyout funds have a greater incentive to obtain compensation from management fees. 7 GPs typically report NAVs that equal contributed capital in the first several valuations, which results in DCFs from these early valuations that are systematically substantially larger than their associated NAVs. As a result, estimating equations (1) and (2) permitting intercepts to differ from zero would yield a positive intercept and a biased downward slope coefficient for the NAV variable. 17

19 of the funds, then we expect α 1n and α 1y to be greater (less than) one. However, if the discount rate that investors apply to the average fund exceeds (is less than) 11%, then our average measure of DCF is overstated (understated). In this case, even if GPs report α 1n unbiased net asset values, then we expect and to exceed one (be less than one). Because there is no way for us to know what rate investors actually use, our focus is primarily on whether NAV coefficients exhibit intertemporal patterns and tend to converge over the life of the fund. For ease of exposition we will continue to use benchmark coefficient values of one when discussing our findings. Assuming expected discount rates are relatively stable over time and over a fund s life, then relative comparisons of coefficients at different points during the life of a fund are still appropriate. For example, if NAVs tend to be understated in the early years relative to the later years, then the early year coefficients will be higher than those in the later years. 8 Other things equal, we have no a priori predictions regarding potential bias in the calendar-year regression coefficients. However, if there is a bias during early sample years, then it is likely that the bias will dissipate over time as general partners learn. In other words, α 1y should converge to one (or some constant if the true expected discount rate differs from 11%) sometime during our sample period. Potential bias might also be expected to dissipate over time if valuation techniques improved, perhaps reflecting the influence of changes in accounting standards relating to fair value accounting. 9 α 1y 8 We also estimated all regressions described below computing discounted cash flows using 7% and 15% discount rates. By construction, the NAV coefficients shift up (down) when using the 7% (15%) discount rates. However, untabulated findings reveal that the same general trends across fund years and over calendar years obtain using these alternative discount rates. 9 It is unlikely that Financial Accounting Standard No. 157, Fair Value Measurements, which provides guidance for measuring fair value, has any direct influence because it became applicable in the same year that our sample NAVs end, i.e.,

20 3.2 Estimations Relating to Managerial Incentives We assess more directly whether there is evidence of incentive effects by estimating versions of equation (1), permitting the NAV coefficient to vary in particular years depending on whether a firm has achieved a benchmark level of performance. First, to assess whether there is an incentive for GPs of relatively unsuccessful funds to overstate NAVs relative to GPs of successful funds during the fundraising period, we distinguish funds that achieve a to-date (meaning from the beginning of the fund s life to the current valuation date) 8% internal rate of return the typical hurdle rate for being eligible for carried interest and have invested at least 70 percent of committed capital during years two through six from those that do not. We then estimate fund-year regressions for years three through six, permitting the NAV coefficient to differ for relatively successful and unsuccessful funds. We apply the 70 percent criterion to ensure that a sufficient amount of investment has already taken place so that the GP can be reasonably confident that the fund is, in fact, successful so that he can divert his attention to raising money for a follow-on fund. 10 We therefore estimate equation (3), which includes the interaction of an indicator variable, D_70_8 and NAV, where D_70_8 equals one if a fund has met the carried interest and committed capital thresholds, and zero otherwise. ln DCF fn = a 1n ln NAV fn + a 2n D _ 70_8 NAV fn +ε fn (3) Based on the prediction that funds that fail to meet the carried interest and committed capital thresholds by the fundraising period, we expect a 2n to be positive. That is, the total NAV coefficient for successful funds, a 1n + a 2n, will be higher than that for less successful funds, 10 For our sample, the median fund reaches the 100 percent contribution threshold somewhere between years four and five. The 70 percent threshold is reached somewhere between years two and three, providing assurance that it is a reasonable criterion to establish whether a fund is at or near a fundraising period. See figure 2, panel B. 19

21 a 1n. If there is a general tendency for GPs of both successful and unsuccessful funds to overstate NAVs, then a 1n + a 2n and a 1n will both be less than one. Second, to assess whether there is an incentive for GPs of relatively unsuccessful funds to overstate NAVs relative to GPs of successful funds during the later fund years, we distinguish funds that achieve an 8% internal rate of return from those that have not. We then estimate fund-year regressions for years seven through ten, permitting the NAV coefficient to differ for relatively successful and unsuccessful funds. The estimating equation (4) includes the interaction of NAV and an indicator variable, D_MILK, which equals one if a fund has failed to meet the 8% carried interest threshold, and zero otherwise. ln DCF fn = a 1n ln NAV fn + a 2n D _ MILK NAV fn +ε fn (4) Based on the prediction that GPs of less successful funds have a greater incentive to milk the management fees than managers of successful funds, then we expect a 2n to be negative. If there is general tendency for GPs to milk the management fees, then a 1n + a 2n and a 1n will both be less than one. As with equations (1) and (2), we estimate equations (3) and (4) separately for Buyout and VC funds Does Percentage of Private Holdings Affect Valuation? The final question we turn to is whether differences in the measurement attributes of funds investments affect the ability of reported NAVs to reflect more appropriately the realized value of the funds. In particular, do NAVs of funds with investments whose measurement attribute that can be characterized as based on market prices better reflect 11 One caveat regarding our partitioning on performance to assess whether there are systematic differences in NAV coefficients that we would like to attribute to differences in managerial incentives is that such differences could arise mechanically. In particular, funds that fall below (exceed) an 8% threshold as of any valuation date are more likely to fall below (exceed) the 11% expected discount rate we impose on the discounted cash flows. In the regression framework we use, this means the NAV coefficient for relatively poor performing funds will likely be less than that for funds that have met the 8% IRR threshold. 20

22 realized fund value than NAVs of funds with investments that do not have available market prices? As noted above, prior banking research finds investments with readily available market prices generally are more value relevant than those investments without market prices. In contrast, for closed-end mutual funds, there is no distinction in the value relevance of investments with and without readily available market prices. For a subset of funds after 2009, Burgiss has recorded the percentage of NAV relating to Levels 1, 2, and 3 fair value determinations based on the SFAS 157 hierarchy. 12 Because, as described below in section 4, our NAVs end in 2007, the Burgiss Levels data are not directly useful to us. However, the data permit us to develop proxies for the Level 3 vs. Level 1 and 2 investment percentages throughout our sample period by accessing data contained in the Burgiss dataset that identifies for a sample of funds the proportion of investments representing private and public holdings. 13 Using the post-2009 subsample, we correlated the percentage of private holdings and percentage of Level 3 investments separately for Buyout and VC funds. Untabulated findings indicate that Pearson (Spearman) correlations for the 4,204 Buyout and 3,762 VC fund valuations are 0.83 and 0.43 (0.81 and 0.86), and suggest that private holdings are a reasonable proxy for Level 3 investments. Based on these findings, we use the private holdings percentages to estimate a proxy Level 3 amount for the subset of 5,174 observations for which we have reported public vs. private holding percentages. This permits us to address the final research question regarding whether differences in the measurement attributes of funds investments affects their ability 12 As defined in SFAS 157, a fair value estimate based on a quoted price in an active market without adjustment is a Level 1 measurement. A fair value estimate based on a quoted market price that must be adjusted, but there are no significant unobservable inputs, is a Level 2 measurement. A fair value estimate based on a significant number of unobservable inputs is a Level 3 measurement. Thus, Level 1 (3) fair value measurement affords the least (most) discretion when estimating fair value. 13 PE funds mostly invest in private companies. However, they may hold their investments for some time after initial public offerings (IPOs) because of lock up periods and other considerations. Lock up periods are usually between 90 and 180 days but in some situations the fund might hold the IPO stock beyond this period; Fürth and Rauch (2014) finds buyout funds hold onto the post-ipo stock for an average of 2.8 years. Burgiss classifies a holding as public if there is ticker, cusip, and exchange information. 21

23 to reflect more appropriately the realized value of the funds by estimating the following equation: ln DCF fn = a 1n ln NAV fn + a 2 n D _Tercile1 NAV fn + a 3n D _Tercile3 NAV fn + ε fn. (5) D_Tercile1 and D_Tercile3 are indicator variables for whether fund f in fund-year n is in the top or bottom tercile of funds ranked by the percentage of private holdings. The funds in tercile 3 can be thought of as those funds whose NAVs are most affected by Level 3 value estimates in that their NAVs are measured with the greatest proportion of non-public holdings. If fund managers systematically over-estimate NAVs when there is greater latitude, i.e., those funds in tercile 3, then we expect to see a 3n < Data and Sample We obtain all data for estimation of equations (1) through (5) from Burgiss, which provides portfolio management software and data and analytics to asset owners investing in private equity capital. 14 Recently, Burgiss has begun to make available archival data to academic researchers. Because of confidentiality agreements between Burgiss and its customers, we and other academic researchers are unable to access the data directly. As a result, we indicate to Burgiss the data items we wish to access and they provide programming assistance that enables us to compute sample summary statistics and to conduct regression analyses. This protocol involves our submitting programs to them and their providing output and a log of each program s execution. 15 As noted in Harris, Jenkinson, and Kaplan (2014), [a]ccording to Burgiss, the dataset is sourced exclusively from LPs [i.e., the primary investors] and includes their complete transactional and valuation history between themselves and their primary fund 14 See Harris, Jenkinson, and Kaplan (2014) for a description of the Burgiss database. 15 We reviewed each log file together with the related output to assess whether the output and program appeared to be internally consistent. For example, when imposing particular data screens, we examined output with and without the screens and the log files to determine that the screens were properly implemented. 22

24 investments. Although the data LPs can access includes detailed information about individual investments held by each fund in which they invest, Burgiss currently only makes available to academics fund-level information. We construct our dataset by using all available net asset values and cash flow histories relating to North American buyout funds and venture capital funds beginning in January 1988 and ending in December Because there are few funds with available data before 1988, we start our sample period then. In addition, to ensure that all cash distributions are complete, we end our sample period in That is, we do not include net asset values beyond 2007, but use the cash flow data necessary to compute discounted cash flows through We also exclude NAVs beyond year ten of the fund life to minimize the impact of inactive funds on reported NAVs (Phalippou and Gottschalg, 2009). 17 We delete outlier observations based on the ratio of discounted cash flow to net asset value, i.e., DCF/NAV. In particular, using the full sample, we exclude those observations that are in the top or bottom 2.5%. This ensures that we have net asset values that appropriately correspond to the remaining cash flows. For example, some general partners update the net asset values in anticipation of the final cash distribution, which yields an extreme value of DCF/NAV. Our trimming procedure effectively eliminates such observations that tend to occur at the beginning or end of a fund s life. Table 1 presents descriptive statistics showing the number of fund and valuation observations per year separately for Buyout and VC funds and for the total. The number of funds and valuations are highest in the middle sample years, with the distributions exhibiting 16 The version of the Burgiss dataset we accessed extends through June Because Burgiss does not indicate when a fund closes, we impose the restriction that there are no distributions between December 2011 and June 2013 for a fund to be included in our sample. In addition, although there are some funds with net asset values beyond 2007 that also end by 2011, there are not enough of them to make reliable inferences. 17 We also eliminate observations for which NAV is zero within two years of the end of the fund and a handful of observations with negative NAVs or negative DCFs. 23

25 an inverted U-shape. For example, the number of buyout funds is lowest in 1988, 31, rises monotonically through 1999, 115, and falls monotonically to 48 in Note that by construction, the number of observations trails off beginning in 2003 because of our requirement that all sample funds must have cash distributions that end in Table 2 presents mean, median, and standard deviations for the ratio of discounted cash flow to net asset value, DCF/NAV, separately for Buyout funds and VC funds. Panel A (B) presents statistics by fund year (calendar year). Because the ratio can be dominated by extreme values, we limit our discussion here to medians. 18 Panel A reveals that for both Buyout and VC funds, median values start high and generally monotonically decline during fund life. For example, for buyout funds, the median ratio at beginning of fund life is 2.29, and it declines to a minimum of 0.99 in year 10. Assuming the 11% discount rate we apply is appropriate, this pattern reveals that GPs, on average, tend to understate NAVs throughout the fund life, but the NAVs converge to the true economic value of the fund throughout the fund life. Panel B reveals that for both Buyout and VC funds, median values of DCF/NAV are generally higher in the first half of the sample period, i.e., through , than in the second half, i.e., For example, for Buyout funds, median DCF/NAV reaches a maximum of 1.59 in 1994, but is never less than 1.14 before 1998, and reaches a minimum of 0.74 in 2000 but is never higher than 1.10 after However, the medians for the two types of funds display some differences. In particular, although both types of funds seem to be affected by the bursting of the tech bubble in , the median DCF/NAV for VC funds is more greatly affected, falling nearly 50 percent to 0.57 in 2000, and it never 18 The effects of extreme values are mitigated when estimating equations (1) through (5), in which natural logs of NAV and DCF are used. 24

26 recovers back to In contrast, median DCF/NAV for Buyout funds is at least 1.00 from 2002 to Figure 1, panels A and B, plots the median DCF/NAV values taken from table 2, panels A and B. Panel A illustrates clearly that the trend in median DCF/NAV starts well in excess of 1.0, gradually falling to near 1.0 by year 2 for Buyout funds and year 4 for VC funds. This pattern suggests that GPs are conservative, i.e., bias downward NAVs in the early life of a fund. This could be attributable to what Jenkinson, Sousa, and Stucke (2013) suggests is the use of discretion on the part of GPs to understate NAVs in the years immediately preceding marketing follow-on funds so that implied rates of return are high. Alternatively, the fund managers may simply be setting NAVs to contributed capital in the early years before they have a better idea of the ultimate potential for success of their funds investments. 19 The fact that the medians level off by year 4 for both types of funds suggests that GPs generally have a good handle on their funds values by then. The fact that the medians level off at 1.0 indicates that our use of the 11% discount rate based on the average implied internal rate of return in Kaplan and Schoar (2005) yields sensible values of discounted cash flows. Figure 1, panel B, which plots median DCF/NAV values over calendar time, indicates that valuations become increasingly conservative between 1988 and 1994, when median DCF/NAV peaks for both types of funds, and is increasingly less conservative between 1994 and The extreme fall of the median DCF/NAV in 2000 to below 0.8 for Buyout funds and 0.6 for VC funds suggests that fund managers were surprised by the bursting of the tech 19 Figure 2, panel A, plots the median ratio of cumulative contributions to NAV by fund year, which indicates that the median is essentially one for both buyout and venture capital funds through year 3. This is consistent with the second reason for the apparent conservative bias in a fund s early years, but it does not rule out the incentive-based reason. 25

27 bubble. The fact that the medians remain below 1.0 for VC funds suggests that their fund managers never fully adjusted NAVs for the long-term systemic drop in future cash flows Results 5.1 Primary Estimations Table 3, panels A and B, presents regression summary statistics relating to estimation of equations (1) and (2), which relate to fund life and calendar year. We present separate findings for Buyout funds and VC funds. Figure 3, panels A and B, plots the corresponding fund life and calendar year coefficients, α 1n and α 1y. Untabulated findings reveal all α 1n and α 1y coefficients are significantly greater than zero. However, because our focus is on the extent to which α 1n and α 1y differ from one, we tabulate t-statistics corresponding to tests for differences from one rather than zero. 21 The findings in Table 3, panel A, indicate that for both types of funds, with the exception of years 0 and 1 (and year 2 for VC funds), all α 1n coefficients are insignificantly different from one. These findings provide statistical support for the inference we draw from the median plots in figure 1 and the coefficient plots in figure 3, panel A, that fund managers, on average, do a remarkably good job in estimating the economic value of their funds, particularly after the first few fund years. Finding the α 1n coefficients are significantly greater than one in years 0 and 1, as well as for year 2 for VC funds, is consistent with fund managers conservatively setting NAVs to contributed capital in the early years until GPs can determine the actual value of the investments. The plots in figure 2 20 To the extent that VC funds became more risky in the years leading up to the tech bubble and therefore a higher discount rate would have been more appropriate for calculating DCFs, the tabulated median DCF/NAV ratios after 2000 are biased upward towards one. 21 Significance levels for α 1 coefficients are based on a two-sided alternative. We refer to a coefficient as being significantly different from one (marginally significant) if it meets the 0.05 (0.10) significance level. 26

28 of cumulative contributions to NAVs are consistent with this explanation. In particular, for the first several years of the fund, contributions are effectively equal to NAVs, i.e., the ratio is very close to one. Later in the fund life, contributions exceed NAVs as GPs make distributions to LPs and they begin the process of winding down the fund. The findings in table 3, panel B, which correspond to calendar year regression results, indicate that the magnitude of the coefficients are remarkably close to one, although several coefficients are significantly different from one. They range from 1.03 for Buyout funds in 1994 to 0.97 for VC funds in 2000 and The only discernable pattern is that VC funds exhibit coefficients that are significantly lower than one beginning in 2000, with the exception of 2003 (coefficient = 0.99, p-value = 0.14). This finding suggests that VC fund managers did not incorporate in a timely manner the drop in expected future cash flows associated with the bursting of the tech bubble. In addition, it appears VC fund managers failed to make adjustments in the future to correct for the NAV overstatement. This could also reflect their inability to incorporate the effects of the financial crisis on future cash flows when reporting NAVs in the years preceding the crisis. The findings in table 3 suggest the possibility that fund life coefficients could be higher in the years preceding the bursting of the tech bubble. To assess whether this is the case, we re-estimate equation (1) for Buyout and VC funds, partitioning the sample into two subperiods. The first (second) includes observations whose NAVs are between 1988 and 1997 (1998 and 2007). Table 4, panels A and B, presents regression summary statistics corresponding to the earlier and later time periods. The findings in panel A indicate that as with the full sample findings in table 3, panel A, fund-year coefficients,, in the first few years are the largest in magnitude and are significantly greater than one. However, in contrast to the full sample, the coefficients in the remaining fund years also are generally α 1n 27

29 significantly greater than one, suggesting that fund managers tend to understate NAVs throughout the fund life for NAVs between 1988 and The findings in panel B, which relate to NAVs in the subperiod, reveal a different picture from that in panel A. First, the majority of coefficient estimates generally are less than one whereas in the prior period all estimates are above one (ignoring statistical significance). Buyout funds in years 2 through 4 and year 0 have coefficients that are significantly less than one, whereas VC funds have coefficients significantly less than one more towards the latter half of their fund lives (years 5 through 8), which indicates that VC fund managers tend to overstate NAVs in the latter half of the life of their funds in the subperiod. It is difficult to determine from the data whether this is a purposeful manipulation of NAVs or simply the general inability to anticipate economic shocks. However, even if the latter explanation is true, we expect that NAVs should at some point reflect updated expectations of future cash flows and thus should not exhibit systematic overvaluations such as those observed in table 4, panel B. Collectively, the findings in tables 3 and 4 indicate that combining all sample years as is done in table 3, panel A masks significant differences over the full sample period that are apparent from the table 4 findings. 5.2 Effects of Managerial Incentives We extend the previous analyses that focus on the general relation between the NAVs that GPs report and future cash flows by examining specific periods in which incentives may be higher to manipulate reported NAVs. As previously noted, the prior literature has findings that are consistent with GPs increasing NAVs during periods in which they are attempting to raise money for new follow on funds to show better performance (Brown, Gredil, and Kaplan, 2013; Jenkinson, Sousa, and Stucke, 2013; Barber and Yasuda, 2014). 28

30 5.2.1 Fund Raising Period Table 5, panel A, presents regression summary statistics relating to estimation of equation (3). We tabulate the total NAV coefficient corresponding to those funds for which D_70_8 is zero and one, i.e., the relatively low and high performing funds, as well as p- values corresponding to the test for coefficient differences between the two sets of funds. Findings indicate there is no difference in coefficients for Buyout funds in any of the four fund-years where fundraising is most likely to occur. In contrast, in three of the four fundyears, years 4 through 6, the NAV coefficient for VC funds is significantly larger for relatively high performing funds, i.e., those for which D_70_8 is one. In fact, for these three fund-years, whereas each of the NAV coefficients for relatively low performing funds are less than one, 0.995, 0.993, and 0.996, those for relatively high performing funds are greater than one, 1.012, 1.017, and Taken together, these findings are consistent with our prediction that GPs of relatively poor performing VC funds having an incentive to overstate NAVs during the fundraising period. One possible explanation for there being a difference in coefficients only for VC funds is that VC funds are inherently more difficult to value and therefore afford their GPs greater discretion in reporting NAVs to limited partners Late Fund Life Management Fees Table 5, panel B, presents regression summary statistics relating to estimation of equation (4). We tabulate the total NAV coefficient corresponding to those funds for which D_MILK is zero and one, i.e., the relatively high and low performing funds, as well as p- values corresponding to the test for coefficient differences between the two sets of funds. In contrast to panel A, findings indicate there is no difference in coefficients for VC funds in any of the four late-stage years, and in three of the four fund-years for Buyout funds, years 8 through 10, the NAV coefficient is significantly larger for relatively high performing funds, 29

31 i.e., those for which D_MILK is zero. In fact, for these three fund-years, whereas each of the NAV coefficients for relatively low performing funds is less than one, 0.993, 0.996, and 0.993, those for relatively high performing funds are greater than one, 1.007, 1.006, and Taken together, these findings are consistent with the prediction that GPs of relatively poor performing Buyout funds having an incentive to generate larger management fees during the later stages of the funds they manage. One possible explanation why there is a difference of coefficients only for Buyout funds is that management fees comprise a substantially larger component of GPs compensation because Buyout funds typically are substantially larger than VC funds. 5.3 Percentage of Private Holdings and Valuation Table 6 presents coefficient values and related p-values for the incremental coefficient for D _Tercile3, a 3n, from estimation of equation (5). 22 The findings relating to Buyout funds reveal that a 3n is significantly negative in fund years 2, 3, and 4 (coefficients = 0.019, 0.019, and 0.013; p-values = 0.08, 0.05, and 0.08). 23 The findings relating to VC funds reveal that a 3n is negative in those same fund years, but insignificantly so (coefficients = 0.015, 0.013, and 0.006; p-values = 0.20, 0.22, and 0.33). Taken at face value, these findings suggest that managers, particularly of Buyout funds, with the greatest flexibility to measure investment values on average overstate NAVs in the period when fundraising for follow-on funds is most likely to occur. 22 P-values in table 6 are based on the empirical distribution of coefficients obtained using random assignment of observations into terciles for each fund year, and estimating equation (5) 5,000 times. Basing significance on the empirical distribution enables us to avoid assuming normality when conducting significance tests. Untabulated findings indicate that a 3n is insignificantly different from zero for Buyout funds in years 2 and 4 when t-statistics are based on clustered standard errors. This is consistent with the reduction of sample sizes by roughly two-thirds in table 6 relative to table 3 affecting our ability to detect significant a 3n coefficients when using clustered standard errors. 23 Untabulated findings reveal the coefficient for tercile 2, i.e., a 1n, is generally insignificantly different from one. 30

32 6. Summary and Concluding Remarks The purpose of this study is to determine how NAVs that GPs of private equity funds provide to their funds LPs compare to the subsequent net cash flows the LPs will receive. This study is the first to capitalize on the unique self-liquidating nature of private equity funds, thereby permitting us to compute net present values without making assumptions about terminal values. To address our research question, we estimate cross-sectional regressions of DCFs, which we take as an estimate of true economic value, on NAVs at each date for which NAVs are provided. This research approach provides a direct means to assess the relative accuracy of net asset valuations that general partners provide to investors. Our sample, which comprises NAV and cash flow information taken from the Burgiss private equity fund database, relates to 483 funds with available information beginning in 1988 and ending in Findings from our primary tests indicate that the NAVs of both venture capital and buyout funds are, on average, good predictors of future DCFs using a discount rate based on average realized internal rates of return. Findings from the fund year regressions generally indicate that NAVs are somewhat conservative estimates of value early in a fund s life, which we show is likely attributable to GPs simply setting NAVs to contributions in the first few years. However, NAVs generally converge to discounted cash flows as early as year three. Findings from the calendar year regressions indicate that although NAVs generally are more conservative in the first half of our sample period, NAVs for venture capital funds tend to overstate economic value after This latter finding suggests that venture capital fund GPs did not incorporate in a timely manner the drop in expected future cash flows associated with the bursting of the tech bubble in 2000, and failed in future years to make adjustments to correct for NAV overstatement. 31

33 Finally, we analyze whether the relation between NAVs that GPs report and cash flows is affected by fundraising incentives, the relative proportion of private holdings, and fund performance. For Buyout funds, we find evidence that funds with greater discretion over valuation, i.e. those with a higher proportion of private holdings, report NAVs that are biased upwards during the usual fundraising period. We also find evidence that poorly performing buyout funds maintain higher NAVs toward the end of the fund life, which is consistent with their incentive to maintain management fee income. For VC funds we find no evidence that this management fee incentive biases NAVs, and only weak evidence of the proportion of private holdings biasing valuations. However, we do find that NAVs are, on average, biased upward for poorly performing venture capital funds in the middle of their fund lives, when fundraising typically occurs. Taken together, these temporal and crosssectional findings are consistent with valuations being affected by the incentives faced by fund managers. 32

34 References Barber, B. M, Yasuda, A., Interim fund performance and fundraising in private equity. Working Paper. Barth, M. E., Beaver, W. H., Landsman, W. R., Value-Relevance of Banks Fair Value Disclosures under SFAS 107. The Accounting Review 71, Brown, G. W., Gredil, O. R., Kaplan, S. N., Do private equity funds game returns? Working Paper. Cochrane, J. H., The risk and return of venture capital. Journal of Financial Economics 75, Eccher, A., Ramesh, K., Thiagarajan, S. R., Fair Value Disclosures by Bank Holding Companies. Journal of Accounting and Economics 22, EY, 2009, Fair Value Measurements Private Equity. Available at Financial Accounting Standards Board, Statement of Financial Accounting Standards No. 157, Fair Value Measurements. FASB: Norwalk, Connecticut. Financial Accounting Standards Board, Statement of Financial Accounting Standards No. 159, The Fair Value Option for Financial Assets and Financial Liabilities. FASB: Norwalk, Connecticut. Fürth, S., Rauch, C., Fare Thee Well? An Analysis of Buyout Funds Exit Strategies, Financial Management, forthcoming. Goh, B.W., Li, D., Ng, J., Yong, K.O., Market Pricing of Banks Fair Value Assets Reported under SFAS 157 Since the 2008 Economic Crisis. Journal of Accounting and Public Policy 34, Gompers, P., Lerner, J., The Venture Capital Cycle. Cambridge, MA: MIT Press. Harris, R. S., Jenkinson, T., Kaplan, S. N., Private equity performance: What do we know? Journal of Finance 69, Harris, R. S., Jenkinson, T., Kaplan, S. N., Stucke, R., Has Persistence Persisted in Private Equity? Evidence From Buyout and Venture Capital Funds. Working paper. Harris, R. S., Jenkinson, T., Stucke, R., A white paper on private equity data and research. Working paper. Hochberg, Y., Ljungqvist, A., Lu, Y., Venture capital networks and investment performance. Journal of Finance 60,

35 Jenkinson, T., Sousa, M., Stucke, R., How fair are the valuations of private equity funds? Working paper. Kaplan, S., Schoar, A., Private equity returns: persistence and capital flows. Journal of Finance 60, Landsman, W. R., Is fair value accounting information relevant and reliable? Evidence from capital market research. Accounting and Business Research 37, Lawrence, A., Siriviriyakul, S., Sloan, R. G., Who s the Fairest of Them All? Evidence from Closed-End Funds. The Accounting Review, Forthcoming. Nelson, K., Fair Value Accounting for Commercial Banks: An Empirical Analysis of SFAS No The Accounting Review 71, Phalippou, L., Gottschalg, O., The performance of private equity funds. The Review of Financial Studies 22 (4), Preqin Private Equity Fund Terms Advisor PWC, 2013, Illustrative IFRS Financial Statements 2013: Private Equity Funds. Available at Song, C. J., Thomas, W. B., Yi, H., Value Relevance of FAS No. 157 Fair Value Heirarchy Information and the Impact of Corporate Governance Mechanisms. The Accounting Review 85,

36 Figure 1 Ratio of DCF to NAV This figure presents medians of the ratio of discounted cash flows (DCF) over reported net asset values (NAV) for Buyout and Venture Capital (VC) funds. For each fund valuation date, we sum all future discounted cash flows (discount rate is 11%) and then calculate the ratio. In panel A (panel B) we sort firms based on fund life (calendar year). Fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date. Panel A: Median Ratio of DCF to NAV over Fund Life Buyout VC Fund Life Panel B: Median Ratio of DCF to NAV by Calendar Year Buyout VC Calendar Year 35

37 Figure 2 Contributions Panel A plots the median ratio of cumulative contributions to net asset value, NAV, over fund life. Panel B plots the median percentage of total contributions over fund life. Fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date. Panel A: Median Ratio of Cumulative Contributions to NAV Buyout VC Fund Life Panel B: Percentage of Total Contributions over Fund Life Buyout VC Fund Life 36

38 Figure 3 Regression Coefficients This figure plots the coefficients of the natural log of NAV from regressions of the natural logarithm of future discounted cash flows, DCF, on the natural logarithm of reported net asset value, NAV, on each valuation date for Buyout and Venture Capital (VC) funds. For each fund valuation date, we calculate DCF by summing all future discounted cash flows using an 11% discount rate. All regressions exclude intercepts; reported p-values are based on differences relative to an expected coefficient estimate of Panel A (panel B) plots coefficients from fund life (calendar year) regressions. Fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date. Panel A: NAV coefficients over Fund Life Fund Life Buyout VC Panel B: NAV coefficients by Calendar Year Buyout VC 37

39 Table 1 Observations This table presents the number of funds and valuations by calendar year for Buyout and Venture Capital (VC) funds. Because funds typically report valuations on a quarterly basis (some report semi-annually), the number of valuations per calendar year exceeds the number of funds. The number of funds in the sample and the corresponding valuations begin to decrease towards the end of the sample period because of our requirement that funds not report any cash flows after 2011 to ensure we observe the entire cash flow series for all funds. Panel A: Fund Life Funds Valuations Fund Life Buyout VC Total Funds Buyout VC Total Observations , , , ,012 1, ,085 1, ,115 1, ,172 1, ,156 1, ,083 1, ,363 Total ,356 10,215 15,571 Panel B: Calendar Year Funds Valuations Year Buyout VC Total Funds Buyout VC Total Observations Total ,356 10,215 15,571 38

40 Table 2 Descriptive Statistics for Ratio of DCF to NAV This table presents descriptive statistics of the ratio of discounted cash flows (DCF) over reported net asset values (NAV) for Buyout and Venture Capital (VC) funds. For each fund valuation date, we calculate DCF by summing all future discounted cash flows using an 11% discount rate. The ρ column represents the correlation between the natural logarithm of DCF and the natural logarithm of NAV. In panel A (panel B) we sort firms based on fund life (calendar year). Fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date. See table 1, panel A (panel B), for number of observations by fund-life (calendar year). Panel A: Fund Life Fund Life Buyout Funds VC Funds Mean Median Std Dev ρ Mean Median Std Dev ρ Panel B: Calendar Year Year Buyout Funds VC Funds Mean Median Std Dev ρ Mean Median Std Dev ρ

41 Table 3 Regression Coefficients: DCF on NAV This table presents the results of regressions of the natural logarithm of future discounted cash flows, DCF, on the natural logarithm of reported net asset value, NAV, on each valuation date for Buyout and Venture Capital (VC) funds. For each fund valuation date, we calculate DCF by summing all future discounted cash flows using an 11% discount rate. All regressions exclude intercepts; reported p-values are based on differences relative to an expected coefficient estimate of Panel A (panel B) presents regression summary statistics based on fund life (calendar year); standard errors are clustered by fund and calendar year (fund and fund life). Fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date. See table 1, panel A (panel B), for number of observations by fund-life (calendar year). Panel A: By Fund Life Buyout Funds VC Funds Fund Life Coef p-value Coef p-value Panel B: By Calendar Year Buyout Funds VC Funds Year Coef p-value Coef p-value

42 Table 4 Regression Coefficients by Sub-period This table presents the results of regressions of the natural logarithm of future discounted cash flows, DCF, on the natural logarithm of reported net asset value, NAV, on each valuation date for Buyout and Venture Capital (VC) funds. For each fund valuation date, we calculate DCF by summing all future discounted cash flows using an 11% discount rate. All regressions are estimated based on fund life, which is calculated as the integer of the year difference between the inception date of the fund and each valuation date, and exclude intercepts; reported p-values are based on differences relative to an expected coefficient estimate of 1.00 and using standard errors clustered by fund and calendar year. In panel A (panel B) we use observations from ( ). See table 1, panel A, for number of observations by fund-life. Panel A: Buyout Funds VC Funds Fund Life Coef p-value Coef p-value Panel B: Buyout Funds VC Funds Fund Life Coef p-value Coef p-value

43 Table 5 Incentive Effects Panel A (panel B) presents summary statistics for the regression of the natural logarithm of future discounted cash flows, DCF, on the natural logarithm of reported net asset value, NAV, and the interaction of NAV with D_70_8 (D_MILK) on each valuation date for Buyout and Venture Capital (VC) funds. D_70_8 (D_MILK) equals one if a fund has met carried interest and committed capital thresholds, i.e., achieved an 8% internal rate of return and received 70% of committed capital (equals one if a fund has failed to meet the 8% carried interest threshold) and zero otherwise. The table presents to total ln NAV coefficient for funds that meet or fail to meet the applicable thresholds. Each Difference corresponds to differences in applicable ln NAV coefficients. All regressions exclude intercepts and are estimated by fund life, where fund life is calculated as the integer of the year difference between the inception date of the fund and each valuation date; reported p-values are based on differences relative to expected coefficient differences of zero. Standard errors are clustered by fund and calendar year. See table 1, panel A, for number of observations by fund-life. Panel A: Fundraising Incentives ln DCF fn = a 1n ln NAV fn + a 2n D _ 70_8 NAV fn +ε fn Fund Life D_70_8=0 Coef Buyout Funds D_70_8=1 Coef Difference p-value D_70_8=0 Coef VC Funds D_70_8=1 Coef Difference p-value Panel B: Late Stage Management Fee Incentives ln DCF fn = a 1n ln NAV fn + a 2n D _ MILK NAV fn +ε fn Fund Life Buyout Funds D_ MILK D_MILK=0 =1 Coef Coef Difference p-value D_ MILK =0 Coef VC Funds D_ MILK =1 Coef Difference p-value

44 Table 6 Effect of Non-public holdings on the relation between NAVs and Future Cash Flows This table presents the incremental ln NAV coefficients for funds with percentage holdings of non-public investments (i.e., market prices are not readily available) that are in the top third for a given fund life. D_Tercile1 and D_Tercile3 are indicator variables for whether a fund in a given fund-life is in the top or bottom tercile of funds ranked by the percentage of private holdings. The coefficients are relative to funds in the middle tercile of percentage holdings of non-public investments. The p-values are derived from the empirical distribution of coefficient estimates from 5,000 estimations of random draws with replacement by fund life and randomly assigning funds into terciles of private holdings. ln DCF fn = a 1n ln NAV fn + a 2 n D _Tercile1 NAV fn + a 3n D _Tercile3 NAV fn + ε fn (5) Buyout Funds VC Funds Fund Life Coef p-value N Coef p-value N