CFA Level I Exam · Investments in Private Capital: Equity and Debt

Private Equity Performance: IRR, DPI, RVPI and TVPI

Updated 7 October 2026 · Fact-checked

Private equity performance is measured with IRR, which is the discount rate that sets the present value of paid-in capital and distributions to zero, and with multiples: DPI = distributions ÷ paid-in capital, RVPI = residual value ÷ paid-in capital, and TVPI = DPI + RVPI. Compute each from paid-in capital, not committed capital.

Understand Private Equity Performance and Returns Metrics

A private equity fund does not take all your money on day one. You commit a total amount, and the general partner (GP) calls it in stages when it finds deals. The part actually called so far is paid-in capital. The part not yet called is uncalled (undrawn) commitment. Committed capital is the promise; paid-in capital is the cash that has left your pocket.

Because cash goes in and out at irregular times, a simple return does not work. The main measure is the IRR, here a since-inception IRR on the fund's cash flows. Cash flows are your capital calls (outflows), distributions (inflows), and the remaining value of unsold holdings treated as a final inflow. IRR is money-weighted, so it depends on the timing of the cash flows, which the GP largely controls.

Multiples ignore timing and show how many times you got your money back. DPI (distributed to paid-in) is cash actually returned. RVPI (residual value to paid-in) is the value still held, usually the NAV. TVPI (total value to paid-in) is the sum of the two. Some sources call TVPI the MOIC (multiple of invested capital) at fund level. DPI is realized and cash-based. RVPI depends on the GP's valuation estimates.

The J-curve describes the typical shape of cumulative returns over a fund's life. Early on, returns are negative because management fees and costs are charged on committed capital while investments are held at cost and have not yet grown. Later, as companies mature and are exited, returns rise and turn positive. Plotted, the line dips and then climbs, like a J.

Reporting issues matter. Valuations of unlisted companies are subjective, so interim IRR and RVPI can be misleading. Early IRR is very sensitive to timing. Fees and carried interest reduce net returns, so gross and net figures differ. Comparing a fund with a public index also needs care because the timing of cash flows differs.

Key formulas to remember

Paid-in capital (PIC): PIC = cumulative capital called from investors to date; Not the same as committed capital. Uncalled commitment = committed capital − paid-in capital.
DPI: DPI = cumulative distributions ÷ paid-in capital; Realized return only. Uses cash already paid out to investors.
RVPI: RVPI = residual value (NAV of remaining holdings) ÷ paid-in capital; Unrealized and dependent on GP valuation.
TVPI: TVPI = DPI + RVPI = (distributions + residual value) ÷ paid-in capital; Total value created per unit of paid-in capital. Often called MOIC for a fund. Usually stated net of fees.
IRR: 0 = Σ CFt ÷ (1 + IRR)^t, with calls as negative flows and distributions and residual value as positive flows; Solved with a financial calculator. Use the cash flow worksheet.
Fully realized fund: RVPI = 0, so TVPI = DPI; Once all holdings are sold, only distributions remain.

How to solve Private Equity Performance and Returns Metrics questions

Use this method for any question on private equity returns, multiples or the J-curve.

1Identify the data given: committed capital, capital called (paid-in), distributions and residual value (NAV).
2Check which base the question uses. DPI, RVPI and TVPI divide by paid-in capital, not committed capital.
3Compute DPI = distributions ÷ paid-in, RVPI = NAV ÷ paid-in, then TVPI = DPI + RVPI.
4If IRR is asked, list the dated cash flows: calls negative, distributions positive, and add residual value as a final positive flow.
5Enter the flows in the calculator CF worksheet and compute IRR. Check the sign and the period length (annual or quarterly).
6For concept questions, link the answer to the cause: fees on committed capital and cost-based valuation explain the J-curve; subjective NAV explains reporting risk.
7Sanity check: TVPI of 1.0 means you have your money back with no gain. DPI can never exceed TVPI.

Quickest way: Multiples first, then eliminate

When to use it: Use when the question gives dollar amounts and asks for DPI, RVPI or TVPI, or a statement about them.

Write down paid-in capital first. Ignore committed capital unless asked about uncalled amounts.
Divide distributions by paid-in for DPI and NAV by paid-in for RVPI. Add them for TVPI.
Remember the order: DPI ≤ TVPI, and TVPI − DPI = RVPI.
Options are listed smallest to largest, so check where your answer sits. If it falls between two options, you used the wrong denominator.
For IRR, if the question needs a full calculation, enter the cash flows once and read the IRR rather than guessing.

Common mistakes in Private Equity Performance and Returns Metrics

Dividing by committed capital instead of paid-in capital.
Committed capital is the larger, more visible number in the problem.
Fix: Use paid-in capital as the denominator for DPI, RVPI and TVPI. Committed capital only matters for uncalled amounts.
Treating DPI as the total return.
DPI sounds like overall performance.
Fix: DPI counts only cash already returned. Add RVPI to get TVPI.
Leaving residual value out of the IRR cash flows.
Students include only calls and distributions that have actually happened.
Fix: For an unliquidated fund, add the NAV as a final inflow at the measurement date.
Explaining the J-curve as the result of poor investments.
Negative early returns look like losses from bad deals.
Fix: The cause is fees and costs charged early while holdings are carried at cost and have not yet matured. A healthy fund still shows it.
Reading a high early IRR or high RVPI as proof of skill.
Both are reported figures and look precise.
Fix: Early IRR is sensitive to timing and RVPI relies on subjective valuations. DPI is the most reliable because it is realized cash.
Mixing quarterly cash flows with an annual IRR.
The calculator returns the IRR per period.
Fix: If flows are quarterly, annualize the periodic IRR, for example (1 + IRR)^4 − 1.

Worked examples

Example 1

A private equity fund has committed capital of $200 million. Investors have paid in $120 million. The fund has distributed $60 million and holds investments with a NAV of $108 million. What is the fund's TVPI?

Show the solution

Paid-in capital = $120 million (committed capital of $200 million is not used).
DPI = 60 ÷ 120 = 0.50.
RVPI = 108 ÷ 120 = 0.90.
TVPI = DPI + RVPI = 0.50 + 0.90 = 1.40.
Check: (60 + 108) ÷ 120 = 168 ÷ 120 = 1.40.

Answer: TVPI = 1.40. Using committed capital would give 0.84, which is the trap.

Example 2

An investor commits €10 million to a fund. At time 0 the fund calls €4 million. At the end of year 1 it calls €2 million. At the end of year 2 it distributes €1 million, and the remaining holdings have a NAV of €7 million at that date. Calculate the since-inception IRR, assuming the NAV is realized at the end of year 2.

Show the solution

Cash flows: t0 = −4, t1 = −2, t2 = +1 + 7 = +8 (in € millions).
Set NPV = 0: −4 − 2 ÷ (1 + r) + 8 ÷ (1 + r)^2 = 0.
Let x = 1 + r. Multiply by x²: −4x² − 2x + 8 = 0, so 2x² + x − 4 = 0.
x = [−1 + √(1 + 32)] ÷ 4 = (−1 + 5.7446) ÷ 4 = 1.1861.
IRR = 1.1861 − 1 = 18.61%.
Calculator: CF, CF0 = −4, C01 = −2, F01 = 1, C02 = 8, F02 = 1, IRR, CPT gives about 18.61.

Answer: IRR ≈ 18.6% per year. Note that paid-in capital is €6 million, so TVPI = 8 ÷ 6 = 1.33, and DPI = 1 ÷ 6 = 0.17.

Exam tips

Always find paid-in capital first. Most wrong answers come from using committed capital.
Memorize TVPI = DPI + RVPI and the reasoning behind it: realized plus unrealized.
For concept questions, link each measure to its weakness: IRR to timing, RVPI to valuation, multiples to ignoring time value.
Expect J-curve questions to ask why early returns are negative. The answer is fees and costs on committed capital with investments held at cost.
With three options and no penalty, always answer. Eliminate any option that uses committed capital or excludes residual value.

Practice questions from Investments in Private Capital: Equity and Debt

Private Equity Performance and Returns Metrics in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Private Equity Performance and Returns Metrics: frequently asked questions

What is the difference between paid-in capital and committed capital?

Committed capital is the total amount an investor agrees to provide to the fund. Paid-in capital is the portion the GP has actually called so far. The remaining part is uncalled commitment.

How do you calculate DPI, RVPI and TVPI?

DPI is cumulative distributions divided by paid-in capital. RVPI is the NAV of remaining holdings divided by paid-in capital. TVPI is DPI plus RVPI.

How do you calculate IRR for a private equity fund?

Treat capital calls as negative cash flows and distributions as positive ones. If the fund still holds assets, add the NAV as a final inflow. Then solve for the rate that makes the net present value zero, using the CF worksheet on your calculator.

Why does a private equity fund show a J-curve?

Early in the fund's life, fees and expenses are charged while investments are carried near cost and have not yet grown. Returns are therefore negative at first. They rise as portfolio companies mature and are sold.