Introduction

The measured performance of a fund's investments is crucial information for both the fund's managers as well as the fund's investors.

The fund manager's priority is to focus invested capital on those investments that provide the highest realized cash yield, and the performance measurement is a critical tool to determine the effectiveness of investment strategies across industries, sectors, geographies and investment types.

Fund investors, on the other hand, require accurate reporting of a fund’s performance in order to evaluate the overall effectiveness of the private equity fund investment and for benchmarking against the return of other private equity funds, different asset classes and the overall market.

When calculating performance of a private equity investment, there are a number of tools available, which may yield varying results depending on the calculation methodology used. We’ll explore the strengths and weaknesses of each methodology, as well as tools available to calculate each type of measure.

This discussion is broken up into 3 parts:

• Part 1 - IRR and related methodologies for closed-end funds (current part)

• Part 2 - Return methodologies for open-end funds (TWRR, Simple and Modified Dietz)

• Part 3 - Fund multiples (DPI, RVPI, TVPI, and PIC) (coming March 27)

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Table of Contents - Part 1

1. Introduction
2. Calculation Methodologies
• IRR
• MIRR
• PME
• PME+
• Direct Alpha
3. What does ILPA say?
4. Summary
5. References
6. Comments

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Calculation Methodologies

Internal Rate of Return (IRR)

Internal Rate of Return (also referred to as the dollar weighted return), attempts to measure a fund’s or investment's performance between two dates. The definition of the Internal Rate of Return as most often used for private equity investments is:

The discount rate that equates the present value of an investment’s cash outflows with the sum of the present value of the investment’s cash inflows and the present value of the unrealized value of that investment, if it is still held ¹.

The IRR factors in cash flows in its calculation, including net investment outflows (initial investment purchase and follow-on investments), capital gain distributions received, periodic interest and dividend payments, and any final realization proceeds if the investment has been fully realized. From the investor's viewpoint, the effect of this methodology is that the IRR is affected by both the size and the timing of investor cash contributions and distributions made by the fund.

Represented as a formula, the IRR calculation can thus be described as:

$$NPV = CF_1 - \sum_{n=1}^{p} {CF_n \over (1 + r)^n} = 0.$$

Where,

NPV represents the net present value,

CF ₁ is the initial cash flow, representing the initial investment cash outflow,

CF _n represents the stream of subsequent cash inflows (and outflows, e.g., for subsequent investment rounds), and

p are the number of cash flow periods during the life of the investment (or fund).

With the inclusion of p, the number of cash flow periods, in the calculation, the calculated IRR becomes time based, and will vary based on the length of the holding period of the investment. All else being constant, the longer the holding period, the less the calculated IRR will be.

Calculation

Since a manual calculation of the IRR involves iteratively solving a polynomial equation, the use of Excel or a dedicated software product would be a smart starting point.

To calculate the IRR using Excel, first determine all the cash flows related to the fund, including the precise cash flow dates and amounts. Note the $0 cash flow periods included for illustration of the periods where the fund is holding its portfolio investments and not throwing off distributions to the investors.

Date	Description	Cash In (Out) Flow
December 31, 2007	Initial contribution	($10,000,000)
December 31, 2008	Additional contribution	($1,000,000)
2009 - 2013	No cash flow activity (fund investment period)	$0
December 31, 2014	Fund distribution	$1,000,000
December 31, 2015	Fund distribution	$1,500,000
December 31, 2016	Final fund distribution	$15,000,000

Calculated IRR: 6.62%

When calculating the IRR of the above cash flows in Excel, either the IRR or XIRR formulas can be used. The XIRR formula includes the period dates, and unlike the IRR formula does not require the $0 cash flow periods to be included.

Gross versus Net IRR

An important distinction must be made between the concepts of gross and net IRR:

Gross IRR represents the return the fund manager realizes from an investment, factoring in the cash outflows and inflows over the life of the investment. Gross IRRs can be calculated on an investment-by-investment basis, in order to compare the effectiveness of individual investments, or on a more aggregated industry, sector, geography, or whole fund level. Sufficiently advanced software platforms should be able to group investment cash flows based on portfolio attributes in order to facilitate this type of analysis.

Net IRR represents the return realized by the fund investors after all fund management fees and expenses are subtracted from the gross investment cash flows. These fees and expenses include management fees charged by the fund, carried interest (or promote in case of real estate funds) allocated to the General Partner, cash management costs on contributed funds not yet invested, and other operational and deal fees not included in the above.

Advantages

There are several benefits of using this methodology as a measure of fund and investment performance:¹

1. Using built in Excel tools, IRR is fairly easy to calculate, and is often included in accounting systems by default.

2. The IRR calculation includes a time factor, which provides a more accurate representation of the periodic return as compared to a straight cash multiple, which only looks at the total cash in- and outflows of the investment, regardless of timing.

3. IRR provides a means to account for irregular cash-flows, as is often a factor in private equity investments with infrequent investment purchases up-front with cash distributions achieved much later in the investment life.

4. IRR has become somewhat of an industry standard, with large institutional investors publishing the returns on their fund investments to their respective investors, making it easier for LPs to compare the relative performance of funds. ²

Disadvantages

1. The calculated IRR can be manipulated based on the timing of the cash flows. Given a set of equal cash flows, depending on how early in the investment’s life the cash flows occur, the IRR can be boosted when compared to an investment with positive cash flows much later in its life.

2. Excess cash distributed by the investment during its life is assumed reinvested at the generated IRR, when in reality, from an LP’s perspective, this excess cash may not be able to generate the same rate of return as the investment that yielded the initial cash return.

3. Private equity funds may distribute shares (in-kind distributions) to their investors in lieu of cash, which can affect the calculated IRR from an LP's perspective depending on when they are able to ultimately realize the distributed securities due to lock-up provisions in place when the in-kind distribution was made.

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Modified IRR

The next methodology addresses the inherent challenge with the IRR of how to account for the implied rate to assign to cash distributions that occur during the life of the fund (or investment). The standard IRR calculation assumes that any cash distributed earns the same rate as the rate of return calculated for the overall fund. This may be far from the truth, as the cash yield on distributed monies may be far less than the return earned by the fund’s investment portfolio.

To mitigate this, the Modified IRR (MIRR) provides a way to specify the re-investment rate for cash distributions occurring during the life of the fund. Often, this rate will be the fund’s specified hurdle (or preferred) rate of return to limited partners.

When compared to the IRR, the MIRR may provide a more realistic picture of the actual return provided to investors, specifically when the overall final IRR is greater than the true re-investment rate achievable for distributions made during the life of the investment.

The formula to calculate the MIRR is:

$$MIRR = \sqrt[n]{FV of CF_p \over PV of CF_i } - 1.$$

where,

FV of CF_p is the future value of cash flows at the reinvestment rate,

PV of CF_i is the present value of the initial cash out flow at the intial financing rate, and

n equals the number of cash flow periods.

To calculate the MIRR of a fund investment using Excel, use the included MIRR formula, which includes variables for the initial financing rate and the re-investment rate.

The following example illustrates how the MIRR can differ from the IRR calculated for a hypothetical two year cash flow:

Date	Description	Cash In (Out) Flow
December 31, 2014	Initial investment (or contribution)	($1,000,000)
December 31, 2015	Cash flow distribution	$200,000
December 31, 2016	Final distribution	$2,000,000

Re-investment rate: 8.00%

Calculated IRR: 15.36%
Calculated MIRR: 14.72%

In this case, since the re-investment rate of 8% is lower than the actual IRR of 15.36%, using the modified IRR methodology to factor in the re-investment rate leads to a lower overall return of the investment.

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Public Market Equivalent (PME)

Another methodology that has been developed aims to make it possible to calculate a rate of return of a private equity investment that is more directly comparable to a public market investment (or reference index).

The Public Market Equivalent (PME) methodology (and direct descendants PME+ and Direct Alpha) attempt to measure the private equity investment’s actual alpha above that of the reference index.

To accomplish this, the PME method calculates the IRR of the reference investment (or index) by applying identical (in value) cash in- and outflows as those of the contributions and distributions of the private equity investment. The differential alpha between the private equity investment and the public market reference will then be determined by the ending net asset value at end of the private equity investment’s life.

Reference Index Criteria

To be an effective comparison, the benchmark index should exhibit a number of quality characteristics to be a suitable alternative to the PE investment. Such traits include: ²

• The benchmark investment should be widely known and readily available for investment during the PE investment period,

• It should be liquid enough in order to absorb the comparative PE fund investment,

• It should be measurable in terms of determining the periodic returns,

• The benchmark should be a viable alternative in terms of style and liquidity,

• It should reflect a passive investment strategy with low turnover during the evaluation period, and

• It should exhibit a similar risk profile as the comparative PE investment

Disadvantage

The main issue with the PME calculation is that based on the amounts of the distributions during the life of the investment, the calculated NAV of the benchmark index may flip to a negative value. Once that happens, the benchmark PME IRR may become distorted from subsequent periodic returns.

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PME+

To mitigate the issue of dealing with a potential negative residual NAV, the PME+ methodology was introduced, which applies a weighting to the benchmark investment's cash outflows to ‘force’ the benchmark investment’s final residual value to equal the private equity investment’s final cash flow.

By doing so, it is impossible for the benchmark investment’s NAV to become negative during the life of the investment.

Disadvantage

Although this methodology improves the original PME calculation for those cash flow scenarios that yield negative residual NAVs for the benchmark, the weighing factor can only be know ‘after the fact’, and so in a real-life scenario, two investments could not be executed side-by-side.

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Direct Alpha

The third public market comparison approach we’ll talk about here is the Direct Alpha methodology.

The Direct Alpha approach uses the reference benchmark to compound the contributions and distributions to their respective future values as of the end of the investment’s life. This approach doesn’t consider periodic fluctuations of the index benchmark during the life of the investment, but only considers the final index value, and applies that to each periodic cash flow.

This measure then aims to create a direct opportunity cost comparison of the private equity cash flows when compared to a similar holding of the benchmark investment until the final realization date.

Calculation Examples

The following examples illustrate the calculation of the PME, PME+ and Direct Alpha methodologies of a sample private equity investment when benchmarked against a hypothetical market index, over a 9 year fund duration:

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What does ILPA say?

The Institutional Limited Partners Association (ILPA) publishes a set of principles which aim to strengthen the “alignment of interests” value proposition in private equity between the fund managers (GPs) and investors (LPs).

As part of these principles, ILPA recommends fund managers to disclose the fund's IRR as part of the Annual Report package prepared for the fund’s limited partners. In addition, the fund manager should disclose the methodology used in calculating the IRR.

Furthermore, ILPA recommends that any fund marketing materials include the following with respect to publishing performance figures for prior funds:³

• Performance information for prior funds using both IRR calculation and multiple of invested capital model,

• IRR information for prior funds on both a gross and net basis;

• An explanation of the derivation of IRR;

• Whether the general partner provides performance information to be included in any standard private equity benchmarks

Based on these principles, the methodology used is up to the fund manager’s discretion, however, the methodology used should be disclosed to achieve the desired level of transparency to investors.

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Summary

So, which rate of return methodology should be used when measuring and benchmarking fund performances? The obvious answer is to first be consistent. From the point of view of an LP investor, the most important criteria is being able to apply a consistent measure to portfolio investments across differing vehicles, both close-end and open-end.

With that in mind, fund managers of close-end private equity funds are competing for LP’s capital allocations across many available types investment products, and should be able to provide their track record in such a way that it properly compares to other investment classes.

Most importantly, being aware of the calculation methodologies, how they compare, and their advantages and challenges is a starting point for both investors and fund managers to be able to communicate effectively about the relative strengths of private equity as a contributing part of an LP's investment portfolio.

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References

1. Private Equity Accounting, Investor Reporting, and Beyond. Mariya Stefanova. April 2, 2015. ↩︎
2. A Private Investment Benchmark. Austin M. Long III, Craig J. Nickels. February 13, 1996. ↩︎
3. Quarterly Reporting Standards. Institutional Limited Partners Association. Version 1.1. Revised in September 2016. ↩︎