IRR, MOIC, DPI and TVPI explained with worked examples

A private equity fund reports its performance in a handful of initials, and the same fund can look good on one and ordinary on another. This page defines each metric, shows how they connect with labelled worked examples, and says where the standard-setters draw the lines. It is part of the fundamentals section.

The metrics in one table

Wellington Management lists IRR, the multiple (called MOIC or TVPI) and DPI as the standard return metrics in private equity⁶. The GIPS Standards for Firms add two more ratios, RVPI and PIC¹. The table lines them up.

The IRR is time sensitive while the multiple and DPI are not, and the IRR and multiple each account for unrealised value while the DPI does not⁶. Reading all three together gives a fuller indication of performance than any one alone⁶.

IRR: how fast money grew

IRR is the discount rate that makes the net present value of all cash flows equal to zero⁶. The calculation accounts not only for the magnitude of the returns but also their timing, so returns in a short period of time have a larger impact on IRR than those over a longer period⁶. Under the GIPS Standards, a composite report must present the annualised since-inception money-weighted return, the IRR family, through the most recent annual period end¹, calculated using daily external cash flows¹.

IRR dominates how managers talk about their own work. In a survey of 79 private equity investors⁸, the firms rely primarily on IRR and multiples to evaluate investments⁸, rather than present-value techniques⁸, and typically target an internal rate of return of 22% on their investments on average, with the vast majority of targets between 20 and 25%⁸. Those are targets that managers say they use, not results that anyone has achieved.

Worked example: same multiple, different IRR

Take two imaginary investments. Each returns twice the money put in. Only the timing differs. All inputs are invented (our numbers).

With a single outflow and a single inflow, the IRR is the multiple raised to one over the number of years, minus one: 2 to the power of one third gives 26.0%, and 2 to the power of one sixth gives 12.2% (our arithmetic). Both cases return 2.0 times the money, and the faster one has about double the IRR (our arithmetic)⁶. This is why a multiple and an IRR are quoted together. A short, early profit raises IRR sharply, and a long hold lowers it even when the multiple is unchanged.

IRR is also fragile in the early years of a fund. Interim IRRs computed before a fund reaches maturity are not very informative⁹, and writing up a portfolio investment long before any actual cash distribution to investors flatters the time profile of returns and thus increases the accounting IRR⁹. The J-curve page shows the pattern across a fund’s life.

TVPI, DPI and RVPI: the multiples family

Each of these three divides by the same denominator, the capital investors have paid in¹. They differ in what goes on top. DPI uses distributions, which are cash that has been paid out⁶. RVPI uses the residual value of what the fund still holds¹. TVPI uses total value, so RVPI equals TVPI minus DPI⁷. The multiples carry no time dimension⁶.

Two further points matter when reading them.

• Net or gross. TVPI is quoted net of carried interest: net value is gross value minus realised and accrued carried interest⁷. Fee and carry treatment is covered on the fees and carry page.
• DPI is the cautious one. Realised returns can be spent or reinvested, while unrealised returns are illiquid, so in volatile environments many investors place a premium on DPI⁶. The higher the RVPI, the more speculative the performance, because much of it is based on unsold companies⁷.

Worked example: one fund, two dates

An imaginary fund has commitments of 100. It calls 30 at the end of year 0, 30 at the end of year 1 and 20 at the end of year 2 (assumed), so paid-in capital is 80 and PIC is 0.8 (our arithmetic)¹. The table gives two snapshots, with cash flows assumed at each year end.

At the end of year 3 almost all of the 1.25 times is unrealised: DPI is 0.125 and RVPI is 1.125 (our arithmetic)⁷. By year 6 the position has reversed, with DPI 2.125 and RVPI 0.25 (our arithmetic)⁷. TVPI roughly doubled, and the IRR with it. The IRR figures come from the spreadsheet IRR function on the annual cash flows (our arithmetic)⁶. Any year-3 number depends on how the manager valued the 90 still held, which is the subject of the valuation section below.

MOIC versus TVPI: a naming problem

The labels are not used the same way everywhere. Wellington treats the multiple as the same idea under two names, MOIC and TVPI⁶. The ILPA Performance Template separates them by cash-flow level. Its fund-level table is based on the cash flows between the fund and its investors and displays net IRR and TVPI⁴. Its gross portfolio-level table is based on cash flows between the fund and its investments and displays gross IRR and MOIC for the realised portfolio, the unrealised portfolio and the total portfolio⁴. So in ILPA’s usage TVPI is mainly a fund-to-investor, net measure, and MOIC a fund-to-investment, deal-level measure⁴.

Fund-level net returns cannot be read straight off the deals. Net portfolio-level IRRs may be calculated by applying the ratio or spread of the fund-level net IRR to gross IRR to the portfolio-level gross IRR⁴, and the portfolio-level net MOIC is a synthetic calculation using the ratio of net to gross TVPI⁴. When a manager quotes a MOIC, ask whether it is gross, per deal or for the fund, and whether realised and unrealised are separated: ILPA gives no definition of realised or unrealised and asks funds to be clear and consistent and to disclose their methodology⁴.

Cross-check against a CFA Institute sample report

The GIPS Standards include a sample report for a closed-end composite. Its figures let us test the definitions. The row, in euro millions, reads: paid-in capital 200, cumulative committed capital 300, distributions 20, TVPI 1.2, DPI 0.1, RVPI 1.1, PIC 0.7¹.

Worked example: checking the sample (our arithmetic)

The sample is internally consistent: the realisation and unrealised multiples add up to the investment multiple, and PIC is rounded to one decimal¹. Note how little of the 1.2 times is cash. Only 20 of 240 of total value has been distributed (our arithmetic)¹.

Gross or net, fund or deal

• Gross returns come before fees and carry, and net after them. The GIPS Standards say a firm should present both annualised gross-of-fees and net-of-fees since-inception money-weighted returns¹. Net IRR is the annualised return after fees and carried interest, counting both realised and unrealised companies⁷.
• Fund-level measures use the cash flows between the fund and its investors; portfolio-level measures use the cash flows between the fund and its investments⁴.
• Benchmarks. A public market equivalent assumes buying and selling an index on the same dates and amounts as the fund’s limited partner capital calls and distributions⁶, so private and public returns can be compared on the same timing.

Subscription lines: how borrowing flatters IRR

A subscription line of credit is a loan against investors’ unfunded commitments that lets a fund make an investment now and call investors’ money later. Because IRR counts when cash left the investor’s account, delaying the call raises IRR without changing the multiple.

Worked example: delaying the call (simplified, our arithmetic)

A fund invests 100 and sells for 150 at the end of year 4 (assumed)⁶. Interest on the credit line and fees are ignored (assumed).

The multiple is identical, and the IRR is nearly four points higher only because investors’ money was outstanding for three years and not four (our arithmetic)⁶. In a real fund the line costs interest, which lowers the net figures, and the line is repaid with a later capital call.

Both standard-setters respond by asking for two numbers. Under GIPS, if a subscription line of credit is used, the firm must present the since-inception money-weighted return both with and without the line¹. The exception: it need not show the without-line figure where the line was repaid within 120 days using committed capital drawn down through a capital call and was not used to fund distributions². ILPA’s fund-level table shows net IRR and TVPI both with and without the impact of fund-level subscription facilities⁴.

What the standards require reporting

ILPA publishes two versions of the Performance Template, and both display the same fund- and portfolio-level performance metrics and cash flow data³. The table sets out what each document asks for, not what any fund does.

Valuation sits under TVPI and RVPI

DPI is cash. TVPI and RVPI are not: they include residual value, which is the manager’s estimate of what unsold companies are worth¹. For the same reason accounting valuations are not bankable and may never be followed by commensurate cash distributions⁹. Two safeguards are worth knowing.

• IPEV Valuation Guidelines. The IPEV Board’s mission is to provide high quality, uniform, globally acceptable, best practice guidance for private capital valuation purposes⁵. The Board published its latest Valuation Guidelines on 14 December 2022⁵.
• GIPS disclosure. A firm must present the percentage of the total fair value of composite assets valued using subjective, unobservable inputs, if such investments represent a material amount of composite assets¹.

Which metric answers which question

Limits of this page

The worked examples use invented figures and annual cash flows to show how the arithmetic works. They are not forecasts of any fund and are not a benchmark. Definitions follow the CFA Institute and ILPA documents cited, and a manager’s own report may differ in detail, so read the notes to any performance table. Education only: nothing here is an offer or advice, and no fund or manager is recommended.