“Private Equity Net Asset Values and Future Cash Flows”faculty.chicagobooth.edu/workshops/accounting/pdf/RountreeBrian.pdf · Private Equity Net Asset Values and Future Cash Flows

ACCOUNTING WORKSHOP

“Private Equity Net Asset Values and Future Cash Flows”

By

Tim Jenkinson University of Oxford

Wayne Landsman

University of North Carolina

Brian Rountree* Rice University

Kazbi Soonawalla

University of Oxford

Thursday, March 5, 2015 1:20 – 2:50 p.m.

Room C06 *Speaker Paper Available in Room 447

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 Management Rice University

Kazbi Soonawalla

Said Business School University of Oxford

March 2015

*Corresponding author: [email protected]. 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.

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Private Equity Net Asset Values and Future Cash Flows

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 1988-2011. 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 our 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.

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1. Introduction

The purpose of this study is to determine how net asset values (NAVs) that general

partners (GPs) of private equity funds provide to their funds’ limited partners (LPs) compare

to the subsequent net cash flows the LPs will receive. To do this, we compare NAVs at each

valuation date to the corresponding future discounted cash flows (DCFs) using cross-sectional

regressions. 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.

NAVs are generally regarded as estimates of fair value. LPs use these valuations to

assess interim fund performance and to make investment allocation decisions. As a result, the

question of whether NAVs are unbiased assessments of fair value has been a central focus of

academic and professional research examining private equity fund performance. Studies have

generally focused on how private equity funds perform relative to some benchmark such as

the S&P 500 or relative to each other (see Kaplan and Schoar, 2005; Harris, Jenkinson, and

Kaplan, 2014; among others). Others examine how short term changes in NAVs relate to

corresponding cash flows (Jenkinson, Sousa, and Stucke, 2013). However, ours is the first

study to examine whether NAVs are unbiased predictors of future discounted cash flows. In

addition, our research approach permits us to examine if there are identifiable trends or biases

in the valuations during the fund life, particularly in response to incentives GPs face over the

life of the funds that they manage.

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

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flow information taken from the Burgiss private equity fund database, relates to 483 funds

with available information beginning in 1988 and ending in 2011. We estimate separate

regressions for the 327 venture capital funds and 156 buyout funds, to permit coefficient

differences potentially arising from relative discretion accorded to GPs of venture capital

funds that 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 fund-year. 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. In

particular, because GPs typically begin to fundraise for new funds approximately midway

through the typical ten-year life of the fund they manage, they face incentives to overstate

NAVs. 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 is likely

attributable to GPs simply setting NAVs to contributions in the first few years. However,

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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 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 (buyout

funds) appear to overstate NAVs during fundraising periods (in the latter years).

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 (the General Partner, or GP, of the

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partnership) raises money from institutional investors (the Limited Partners, or 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

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 will specify 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 as and 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 are typically permitted to

raise a follow-on fund, to ensure they are always able to make investments should

opportunities arise. When the fund’s investment period is over, the GP can no longer seek

additional 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

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period. During the former, a management fee of around 1.5 – 2% is charged. Importantly,

the fee basis is committed capital, rather than invested capital. During the post-investment

period, the GP receives either a smaller percentage of committed capital (for instance, 1%, or

the fee might “step-down” 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 net asset value (NAV) of the fund. A reason for the “lower of” clause is that if

NAV is used, then the GP can, in principle, manipulate his/her compensation by manipulating

the reported NAV, but no such 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 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., excess of cash realized by the

fund in excess of committed capital. However, the GP 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, although some GPs with excellent reputations manage to avoid having to

achieve a hurdle rate. It is important to note that, 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

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than reported NAVs. This is unlike hedge funds where profits are often shared on an annual

basis using the reported NAVs each year, subject to a “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 the

jurisdiction), they typically conform to a set of industry standards.1 The interim financial

statements are not typically audited, but the annual statements are audited. In contrast to

managers of publicly traded firms, private equity fund managers have considerably more

discretion when measuring NAVs. Regressing quarterly changes in NAVs on quarterly

changes in cash flows for funds managed by CALPERS, 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.

However, there are also incentives to inflate 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 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

1 In many countries, the International Private Equity Valuation (IPEV) guidelines are adopted as the guiding principles, as specified of the LPA for the partnership. See www.privateequityvaluation.com .

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“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,

and only for the funds that are performing poorly. 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

While the commitment of capital that investors make to GPs extends over several

years, investors need to know the amount actually invested each year. A typical pension fund,

endowment or other institutional investor will perform a portfolio optimization based on their

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 as capital is

only invested as the GPs find profitable opportunities, and the extent and timing of

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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, as investors seldom “second guess” the GPs regarding valuation

issues since little information is available for the investors to conduct their own valuation

analyses.

The answer to our central question – are NAVs unbiased predictors of future cash

flows? – is, therefore, critical to investors. For instance, if NAVs were, on average,

conservative estimates of fair value, then investors’ would over-allocate to private equity if

relying on the reported NAVs, and vice versa. In the case of other assets there are market

prices that should discount the expected future cash flows accruing to that asset using the

(unobserved) cost of capital. No such market prices exist for private equity funds. Therefore,

our analysis will compare, at each point in time, the current NAV produced by the fund

(and/or its auditors) and the unknown future cash flows. Such a comparison clearly only

becomes meaningful once a reasonable proportion of the committed capital has been invested,

and so we will 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, it seems reasonable for investors

to use a discount rate that is consistent with average realized returns, and this is the approach

we adopt drawing on the findings of Harris, Jenkinson, and Kaplan (2014).

Investors are clearly also interested in the extent to which NAVs represent fair value

when making investment decisions. If NAVs are systematically biased estimators of fair

value, then the interim performance numbers produced by GPs at the time of fundraising by

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GPs will be unreliable. Clearly, the performance of the current fund should be only one

consideration when making investment decisions into future funds, as the evidence of

performance persistence in private equity is weak, but it remains nonetheless 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 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 since

valuations are observable even for funds not performing very well.2 A number of studies

using these databases have investigated 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).

2 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.

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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).

Phalippou and Gottschalg (2009) addresses the question of how private equity

performs relative to the S&P 500 stock index. Using the Thomson Venture Economics

database that includes quarterly NAV and cash flow information for a sample of private

equity funds from 1980-2003, the study finds that private equity fund performance reported in

prior research is biased upward because performance was based on reported NAVs. In

particular, many funds in their sample have no reported cash flows for extended periods of

time at the end of the fund life (i.e., the last five years), yet the fund maintains an NAV. As

discussed above in the calculation of IRRs, this NAV is assumed to be the final distribution of

cash flows. Phalippou and Gottschalg (2009) documents that this standard method of

calculating performance can bias estimates upwards making it more likely for private equity

investments to appear to be attractive.

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) finds that whereas private equity that invested in buyout funds consistently

outperforms the S&P 500, private equity that invested in venture capital outperformed the

S&P 500 in the 1990s but underperformed during the 2000s. The study also points out that

the performance bias documented in Phalippou and Gottschalg (2009) is largely a reflection

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of the Venture Economics database that study used, which failed to record cash flows after

2001 relating to many funds.

In contrast to these 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 for funds that

invest in existing companies—buyout funds—or those that invest in new startups—venture

capital 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) extracts 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. This study 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

fund raising 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.

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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 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.

Finally, Barber and Yasuda (2014), which accesses the Preqin private equity database,

shows that fundraising success – in terms of the ability to raise a subsequent fund, and the size

of any such fund – is related to reported performance – 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 (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

who have performed poorly and so may be boosting NAVs to reap greater management fees

(the “milking” incentive).

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Our study also relates to the vast literature examining properties of fair value

accounting estimates (see Landsman (2007) for a summary of the literature). As Landsman

(2007) points out, most of the literature addresses whether fair values are relevant and reliable

as assessed by investors. In particular, a large number of studies examine how accounting

measures of fair value or changes in those values correspond to stock prices or stock returns.

A key limitation of such studies is that there generally is no direct independent measure of

economic value—i.e., future cash flows are unobservable— thus, researchers have to assume

that investors’ assessments of value are reliable proxies for 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 permits us to observe the actual cash flows

associated with each fund throughout the life of the fund. This permits us to directly compare

the economic value of the funds to the accounting estimates that GPs provide.

3 Predictions and Research Design

3.1 Primary Estimations

Our research objective is to determine how NAVs that GPs provide to their funds’

limited partners compare to the subsequent net cash flows they will receive. To do this, we

compare NAVs to the subsequent discounted cash flows (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

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NAVs should generally grow closer to DCFs during our sample period. If venture capital

funds, which invest primarily in new startups, are inherently more difficult to value than

buyout funds, which invest in existing companies, then venture capital fund valuations may be

more affected by the influence of GP incentives because of greater discretion.

To address our research objective and to examine whether any of the biases and

patterns we conjecture are 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, NAVt , we construct a corresponding discounted cash flow, DCFt .

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 Jenkinson et al. (2013).3

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 NAVt and DCFt 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.

3 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.

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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 DCFfn=α

1nln 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 DCFfy=α

1 yln NAV

fy+ ε

fy. (2)

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.4 In the fund-year regressions, i.e., equation (1), standard errors are clustered by

fund and calendar year. In calendar-year regressions, i.e., equation (2) standard errors are

clustered 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. Economic

interpretations of DCF values based on the equations (1) and (2) and estimations that include

intercepts are equivalent. The constrained regressions permit a more parsimonious and

meaningful economic interpretation of how the slope coefficient varies with fund life or over

4 For example, as we describe below in the data section, buyout funds are typically orders of magnitude larger than venture capital funds as measured by committed capital. As a result, managers of buyout funds have a greater incentive to obtain compensation from management fees.

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calendar time.5 Also, unlike many research settings, theoretically the intercept should be

constrained to go through the origin because when NAV is equal to zero, DCF should be equal

to zero.

If general partners 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 α1n and α1y to equal one. However, if their valuations under-

(over-) state the economic value of their funds, then we expect α1n and α1y to be greater (less

than) one. If the inferences based on Jenkinson et al. (2013) hold, on average, using our

measure of economic value, then we expect to see α1n exceed one in early fund years. This

bias can stem from incentives for general partners to understate net asset values early in a

fund’s life so as to show high accounting-based internal rates of return during the marketing

period for follow-on funds, which typically occur during years three through six in a current

fund. The bias can also reflect the possibility that general partners simply set net asset values

to contributed capital in a fund’s early years before they learn whether the fund’s investments

will be successful. Because funds, on average, are successful, setting net asset values to

contributed capital results in understated net asset values in a fund’s early years. We examine

the empirical validity of this source of bias below in section 4.6

5 We are currently in the process of estimating versions of equations (1) and (2) that do not restrict intercepts to be zero. Such regressions have the benefit of permitting us to include year fixed effects when estimating equation (1) and fund-year fixed effects when estimating equation (2). Although estimating such regressions no longer permits us to benchmark the NAV slope coefficient against one, we still should be able to use them to assess relative differences in slope coefficients over fund life and calendar time. 6 To the extent that the true discount rate is greater than (less than) 11%, the appropriate benchmark prediction for !!! and !!! is no longer one. However, 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.

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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,

α1y should converge to one (or some constant if the true expected discount rate differs from

11%) sometime during our sample period. Even if there is no bias, valuations might improve

over time if valuation techniques improved, perhaps reflecting the influence of changes in

accounting standards relating to fair value accounting.7

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

received at least 70 percent of committed capital during years two through six from those that

do not. We then estimate fund-year regressions permitting the NAV coefficient to differ

during years three through six. 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-

7 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., 2007.

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on fund.8 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.

lnDCFfn = a1n lnNAVfn + a2nD_70_8× NAVfn +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 a2n to be positive. That is, the total NAV

coefficient for successful funds, a1n + a2n , will be higher than that for less successful funds,

a1n . If there is a general tendency for GPs of both successful and unsuccessful funds to

overstate NAVs, then a1n + a2n and a1n 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 permitting the NAV coefficient to differ during years seven

through ten. The estimating equation (4) includes the interaction of an indicator variable,

D_MILK and NAV, where D_MILK equals one if a fund has failed to meet the 8% carried

interest threshold.

lnDCFfn = a1n lnNAVfn + a2nD_MILK × NAVfn +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 a2n to be negative. If

8 Figure 2, Panel B, plots the median percentage of total contributions received by fund year. 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.

21

there is general tendency for GPs to milk the management fees, then a1n + a2n and a1n will

both be less than one. As with equations (1) and (2), we estimate equations (3) and (4)

separately for Buyout and VC funds.9

4. Data and Sample

We obtain all data for estimation of equations (1) and (2) from Burgiss, which,

according to their website, provides portfolio management software and data and analytics to

asset owners investing in private equity capital.10 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.11

As noted in Harris et al. (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 investments.’ ” We

9 One concern with 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. There is no easy solution to this mechanically induced spread between the NAV coefficients for relatively high and low performing funds. However, because we can think of no a priori reason why this mechanical effect should change over fund life, we are in the process of re-estimating equations (3) and (4) partitioning funds based on the realized IRR, i.e., ultimate actual fund performance, to determine if the coefficient spreads are larger during the fundraising and milking periods relative to other fund years, when GPs of relatively poor performing funds have an incentive to overstate NAVs. 10 See Harris et al. (2014) for a description of the Burgiss database. 11 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

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 2011. 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 2007. That is, we do not include net asset values beyond 2007, but

use the cash flow data necessary to compute discounted cash flows through 2011.12 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).13

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

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 2007. Note that by

12 The version of the Burgiss dataset we accessed extends through June 2013. 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. 13 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

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 2011.

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 venture capital

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.14 Panel A reveals that

for both buyout and venture capital funds, median values start high and generally

monotonically decline during fund life. For example, for buyout funds, the median at

beginning of fund life is 2.29, and it declines to a minimum of 0.99 in year 10. This pattern

reveals that GPs, on average, 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, medianDCF / NAV are generally

higher in the first half of the sample period, i.e., through 1998-99, than in the second half, i.e.,

1999-2007. For example, for Buyout funds, medianDCF / 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 1997. However, the medians for the two types of funds display

some differences. In particular, although both types of funds seemed to be affected by the

bursting of the tech bubble in 1999-2000, the median DCF / NAV for VC funds was more

greatly affected, falling nearly 50 percent to 0.57 in 2000, and it never recovered back to 1.00.

In contrast, median DCF / NAV for Buyout funds is at least 1.00 from 2002 to 2004.

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

14 The effects of extreme values are mitigated when estimating equations (1) and (2), in which natural logs of NAV and DCF are used.

24

excess of 1, gradually falling to near 1 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 et al. (2013) believe 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.15 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 1.00

indicates that our use of the 11% discount rate based on the average implied internal rate of

return in Jenkinson et. (2013) yields sensible values of discounted cash flows.

Figure 1, panel B, which plots medianDCF / 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 2000. 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

bubble. The fact that the medians remain below 1 for VC funds suggests that their fund

managers never fully adjusted NAVs for the long-term systemic drop in future cash flows.

15 Figure 2, Panel A, plots the median ratio of cumulative contributions to NAV by fund year, which indicate 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

5. 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, plot the corresponding

fund life and calendar year coefficients, and . Untabulated findings reveal all and

coefficients are significantly greater than zero. However, because our focus is on the

extent to which α1n and α1y differ from one, we tabulate t-statistics corresponding to tests for

differences from one rather than zero.16

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 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 on average in estimating the economic value

of their funds, particularly after the first few fund years. Finding the 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 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

16 Significance levels for α1 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.

α1n α1y α1n

α1y

α1n

α1n

26

one. Later in the fund life, contributions exceed NAVs as GPs make distributions to LPs as

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 2001. The only discernable pattern is that venture

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 venture

capital 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 venture capital

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 venture capital 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 are generally significantly

α1n

27

greater than one suggesting that fund managers generally understate NAVs throughout the

fund life for NAVs between 1988 and 1997.

The findings in panel B, which relate to NAVs in the 1998-2007 subperiod, reveal a

very different picture from that in panel A. First, the majority of coefficient estimates are

generally less than one whereas in the prior period all estimates were above one (ignoring

statistical significance). Buyout funds in years 2 through 4 and year 0 have coefficients that

are statistically lower than one, whereas VC funds have coefficients statistically less than one

more towards the later half of their fund lives (years 5 through 8) indicating that VC fund

managers tend to overstate NAVs in the latter half of the life of their funds in the 1998-2007

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 like

that 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 accuracy of GPs in

reporting NAVs 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 in order to show better performance (Brown et al. 2013;

Jenkinson et al. 2014, Barber and Yasuda, 2014).

28

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 fund-years, years

four through six, 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 1.013. 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.

5.2.2 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 eight

29

through ten, the NAV coefficient is significantly larger for relatively high performing funds,

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 are 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

1.005. Taken together, these findings are consistent with our 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.

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. 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. 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 2011.

Findings from our primary tests indicate that the NAVs of both venture capital and

buyout funds are extremely good predictors of future DCFs. 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

30

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 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 1999. 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. Findings from 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 indicate that GPs of relatively poor

performing venture capital funds (buyout funds) appear to overstate NAVs during fundraising

(in the latter years).

31

References

Barber, B. M, Yasuda, A., 2014. Interim fund performance and fundraising in private equity. Working Paper.

Brown, G. W., Gredil, O. R., Kaplan, S. N., 2014. Do private equity funds game returns?

Working Paper. Cochrane, J. H., 2005. The risk and return of venture capital. Journal of Financial

Economics 75, 3-52. Harris, R. S., Jenkinson, T., Kaplan, S. N., 2014. Private equity performance: What do we

know? Journal of Finance 69, 1851-1882. Harris, R., Jenkinson, T., Stucke, R., 2010. A white paper on private equity data and research.

Working paper. Hochberg, Y., Ljungqvist, A., Lu, Y., 2007. Venture capital networks and investment

performance. Journal of Finance 60, 1791-1823. Jenkinson, T., Sousa, M., Stucke, R., 2013. How fair are the valuations of private equity

funds? Working paper. Kaplan, S., Schoar, A., 2005. Private equity returns: persistence and capital flows. Journal of

Finance 60, 1791-1823. Landsman, W. R., 2007. Is fair value accounting information relevant and reliable? Evidence

from capital market research. Accounting and Business Research 37, 19-30. Phalippou, L., Gottschalg, O., 2009. The performance of private equity funds. The Review of

Financial Studies 22 (4), 1748-1776.

32

Figure 1 DCF to NAV

Panel A: Median Ratio of DCF to NAV over Fund Life

Panel B: Median Ratio of DCF to NAV by Calendar Year

!"!!!!

!0.50!!

!1.00!!

!1.50!!

!2.00!!

!2.50!!

!3.00!!

0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!Fund%Life%

Buyout!VC!

!"!!!!!0.20!!!0.40!!!0.60!!!0.80!!!1.00!!!1.20!!!1.40!!!1.60!!!1.80!!

1988!

1989!

1990!

1991!

1992!

1993!

1994!

1995!

1996!

1997!

1998!

1999!

2000!

2001!

2002!

2003!

2004!

2005!

2006!

2007!

Calendar%Year%

Buyout!VC!

33

Figure 2 Contributions

Panel A: Median Ratio of Cumulative Contributions to NAV

Panel B: Percentage of Total Contributions over Fund Life

0!

1!

2!

3!

4!

5!

6!

0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!Fund%Life%

Buyout!VC!

0!

0.2!

0.4!

0.6!

0.8!

1!

1.2!

0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!Fund%Life%

Buyout!VC!

34

Figure 3 Regression Coefficients

Panel A: NAV coefficients over Fund Life

Panel B: NAV coefficients by Calendar Year

!0.970!!

!0.980!!

!0.990!!

!1.000!!

!1.010!!

!1.020!!

!1.030!!

!1.040!!

!1.050!!

!1.060!!

0! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!Fund%Life%

Buyout!VC!

!0.930!!!0.940!!!0.950!!!0.960!!!0.970!!!0.980!!!0.990!!!1.000!!!1.010!!!1.020!!!1.030!!!1.040!!

1988!

1989!

1990!

1991!

1992!

1993!

1994!

1995!

1996!

1997!

1998!

1999!

2000!

2001!

2002!

2003!

2004!

2005!

2006!

2007!

Buyout!VC!

35

Table 1 Observations

Funds Valuations

Year Buyout

VC Total Funds

Buyout

VC Total

Observations 1988 31 137 168 94 435 529 1989 43 159 202 135 492 627 1990 44 172 216 155 551 706 1991 49 187 236 171 642 813 1992 53 187 240 179 661 840 1993 60 192 252 211 683 894 1994 69 198 267 239 709 948 1995 78 195 273 273 687 960 1996 90 189 279 310 675 985 1997 98 179 277 345 642 987 1998 103 173 276 360 626 986 1999 115 165 280 396 578 974 2000 110 144 254 401 499 900 2001 104 128 232 394 446 840 2002 99 121 220 383 440 823 2003 98 113 211 366 406 772 2004 89 101 190 332 351 683 2005 73 77 150 255 288 543 2006 61 69 130 205 232 437 2007 48 51 99 152 172 324 Total 156 327 483 5,356 10,215 15,571

36

Table 2 Descriptive Statistics for Ratio of DCF to NAV

Panel A: Fund Life Fund Life Buyout Funds VC Funds Mean Median Std Dev ρ Mean Median Std Dev ρ

0 3.08 2.29 2.49 0.73 3.41 2.67 2.76 0.72 1 2.06 1.38 1.90 0.77 2.52 1.73 2.28 0.76 2 1.57 1.15 1.37 0.81 1.93 1.40 1.76 0.82 3 1.33 1.11 1.12 0.83 1.61 1.18 1.45 0.82 4 1.25 1.12 0.91 0.85 1.36 1.04 1.13 0.83 5 1.25 1.06 0.87 0.86 1.22 1.03 0.87 0.84 6 1.25 1.08 0.89 0.88 1.18 1.02 0.75 0.85 7 1.26 1.04 0.93 0.89 1.17 1.01 0.81 0.86 8 1.33 1.00 1.23 0.91 1.15 1.00 0.76 0.88 9 1.35 1.00 1.31 0.92 1.20 1.01 0.80 0.88

10 1.42 0.99 1.54 0.91 1.24 1.03 0.99 0.90 Panel B: Calendar Year Year Buyout Funds VC Funds Mean Median Std Dev ρ Mean Median Std Dev ρ 1988 1.79 1.14 1.64 0.82 1.35 0.97 1.23 0.78 1989 2.35 1.21 2.27 0.79 1.46 1.06 1.26 0.80 1990 2.15 1.30 2.03 0.83 1.63 1.20 1.40 0.83 1991 1.93 1.34 1.72 0.89 1.77 1.25 1.68 0.83 1992 2.00 1.48 1.68 0.89 1.73 1.30 1.41 0.87 1993 2.02 1.50 1.61 0.88 1.71 1.30 1.43 0.87 1994 2.25 1.59 1.83 0.89 1.79 1.37 1.47 0.86 1995 1.93 1.44 1.47 0.89 1.72 1.29 1.43 0.88 1996 1.73 1.32 1.37 0.89 1.67 1.15 1.55 0.88 1997 1.49 1.14 1.19 0.89 1.63 1.24 1.43 0.88 1998 1.33 1.02 1.06 0.88 1.75 1.25 1.64 0.89 1999 1.12 0.86 1.10 0.85 1.39 1.09 1.18 0.91 2000 1.08 0.74 1.25 0.85 0.65 0.57 0.37 0.92 2001 1.06 0.89 0.94 0.88 0.75 0.61 0.55 0.84 2002 1.10 1.01 0.61 0.92 0.97 0.80 0.86 0.84 2003 1.30 1.10 0.84 0.93 1.13 0.91 0.95 0.88 2004 1.32 1.08 1.12 0.91 1.15 0.87 1.03 0.84 2005 1.13 0.96 0.86 0.92 1.04 0.83 0.80 0.84 2006 0.99 0.86 0.98 0.91 1.02 0.79 0.93 0.89 2007 1.00 0.77 1.04 0.91 0.92 0.76 0.85 0.94

37

Table 3 Regression Coefficients

Panel A: By Fund Life

Buyout Funds VC Funds Fund Life Coef p-value Coef p-value

0 1.040 0.00 1.047 0.00 1 1.017 0.03 1.028 0.00 2 1.007 0.31 1.016 0.04 3 1.000 0.99 1.008 0.28 4 1.000 0.97 1.001 0.85 5 1.001 0.89 0.999 0.81 6 1.001 0.86 0.999 0.75 7 1.001 0.80 0.998 0.53 8 1.001 0.69 0.998 0.40 9 1.003 0.32 1.000 0.97 10 1.001 0.81 1.000 0.95

Panel B: By Calendar Year

Buyout Funds VC Funds Year Coef p-value Coef p-value

1988 1.013 0.12 1.002 0.69 1989 1.021 0.09 1.008 0.20 1990 1.021 0.03 1.015 0.02 1991 1.019 0.01 1.017 0.01 1992 1.023 0.00 1.019 0.00 1993 1.023 0.00 1.017 0.00 1994 1.030 0.00 1.019 0.00 1995 1.023 0.00 1.017 0.00 1996 1.016 0.00 1.013 0.03 1997 1.008 0.04 1.012 0.04 1998 1.001 0.80 1.014 0.01 1999 0.989 0.01 1.004 0.16 2000 0.985 0.00 0.967 0.00 2001 0.990 0.01 0.969 0.00 2002 0.997 0.22 0.982 0.02 2003 1.005 0.04 0.992 0.14 2004 1.003 0.29 0.990 0.08 2005 0.996 0.28 0.988 0.04 2006 0.986 0.03 0.986 0.01 2007 0.985 0.08 0.984 0.00

ln DCFfn=α

1nln NAV

fn+ ε

fn

38

Table 4 Regression Coefficients by Sub-period

Panel A: 1988-1997

Buyout Funds VC Funds Fund Life Coef p-value Coef p-value

0 1.044 0.00 1.053 0.00 1 1.029 0.00 1.035 0.00 2 1.020 0.01 1.026 0.00 3 1.016 0.01 1.019 0.00 4 1.017 0.00 1.011 0.04 5 1.018 0.00 1.010 0.03 6 1.014 0.03 1.009 0.02 7 1.011 0.06 1.005 0.07 8 1.010 0.06 1.004 0.10 9 1.011 0.13 1.005 0.02 10 1.013 0.09 1.009 0.00

Panel B: 1998-2007

Buyout Funds VC Funds Fund Life Coef p-value Coef p-value

0 1.024 0.04 1.002 0.94 1 0.993 0.40 1.005 0.83 2 0.989 0.07 0.991 0.64 3 0.986 0.03 0.985 0.32 4 0.990 0.06 0.985 0.27 5 0.992 0.14 0.983 0.03 6 0.994 0.17 0.985 0.00 7 0.996 0.31 0.987 0.01 8 0.998 0.65 0.991 0.03 9 1.000 0.96 0.995 0.22 10 0.998 0.72 0.993 0.19

39

Table 5 Incentive Effects

Panel A: Fundraising Incentives

Buyout Funds VC Funds Fund Life

D_70_8=0 Coef

D_70_8=1 Coef

Difference p-value

D_70_8=0 Coef

D_70_8=1 Coef

Difference p-value

3 1.004 0.994 0.18 1.009 1.006 0.72 4 1.000 1.000 0.91 0.995 1.012 0.00 5 0.999 1.005 0.26 0.993 1.017 0.00 6 0.998 1.011 0.11 0.996 1.013 0.01

Panel B: Late Stage Management Fee Incentives

Buyout Funds VC Funds

Fund Life

D_MILK=0 Coef

D_ MILK =1

Coef Difference

p-value

D_ MILK =0

Coef

D_ MILK =1

Coef Difference

p-value

7 1.005 0.995 0.13 1.000 0.995 0.31 8 1.007 0.993 0.04 1.000 0.995 0.23 9 1.006 0.996 0.01 1.001 0.999 0.73 10 1.005 0.993 0.05 1.001 1.000 0.86