Private Equity: formula sheet

Key formulas

Management fee

Annual fee = fee rate × fee base (committed or invested capital)

The fee base depends on the fund terms. Read the question to see which base applies.

Carried interest (simple, no hurdle or catch-up)

Carry = carry rate × profit (state whether before or after fees, as the question specifies)

Use only when the question gives no hurdle. If a hurdle exists, carry applies only as the terms specify. Check whether the profit base is before or after fees. The first worked example uses profit after fees.

Net profit to LPs

LP profit = total profit − management fees − carried interest

Fees reduce LP returns. Check the order the question gives.

Unfunded commitment

Unfunded commitment = total commitment − capital drawn down

The LP must still be ready to fund this amount on request.

Liability in a limited partnership

LP: limited to commitment. GP: unlimited

Use this to explain why the GP bears more risk.

Equity value from enterprise value

Equity value = Enterprise value − Net debt

Net debt = debt − cash. Use it at entry and at exit to see how debt paydown adds to equity.

Money multiple (MOIC)

MOIC = Exit equity proceeds ÷ Equity invested

Ignores timing. Use IRR when time matters.

Enterprise value from multiple

EV = EBITDA × EV/EBITDA multiple

Use the entry multiple at purchase and the exit multiple at sale.

Value creation drivers in an LBO

Change in equity value = EBITDA growth effect + Multiple change effect + Net debt reduction

EBITDA growth effect = (Exit EBITDA − Entry EBITDA) × Entry multiple. Multiple effect = (Exit multiple − Entry multiple) × Exit EBITDA. Debt effect = Entry net debt − Exit net debt. These add up exactly to the change in equity value.

Approximate IRR from a multiple

IRR ≈ MOIC^(1 ÷ years) − 1

Valid when there is one investment and one exit, with no interim cash flows.

Post-money value

Post-money = Pre-money + Investment

Pre-money is the value before the new money goes in.

Investor ownership share

Ownership = Investment ÷ Post-money value

Use the post-money value, not the pre-money value.

VC method: post-money today

Post-money today = Exit value ÷ (1 + r)^N

r is the target rate of return. N is years to exit. Exit value is the expected value at exit before any dilution adjustment.

VC method: pre-money

Pre-money = Post-money − Investment

Do this after discounting the exit value.

Required ownership at exit

Required final ownership = Investment × (1 + r)^N ÷ Exit value

This is the same as Investment ÷ Post-money today.

Retention with later dilution

Current ownership = Required final ownership ÷ Retention ratio

Retention ratio = 1 − expected dilution from later rounds. Current ownership is the share needed today to end with the required final share.

Enterprise value to equity value

Equity value = Enterprise value − Net debt

Net debt = debt − cash. Adjust for other claims such as preferred stock if present.

Multiple-based value

Enterprise value = Multiple × Metric

For example EV/EBITDA × EBITDA. Match the multiple and metric.

Marketability adjustment

Adjusted value = Value × (1 − DLOM)

Apply to the right base. Do not stack it with a control adjustment without thinking about the basis.

Management fee

Fee = fee rate × fee base (committed capital, invested capital or NAV, per the terms)

Read which base applies in each period. Fee is paid regardless of performance.

Carried interest, no hurdle or catch-up

Carry = carry rate × total profit

Profit = distributions − contributed capital (after fees if the terms say so).

Hurdle (compound)

Preferred return = capital × [(1 + h)^t − 1]

Use simple interest only if the question says so. Hurdle is on LP contributed capital.

Full catch-up size

Catch-up amount = carry rate ÷ (1 − carry rate) × preferred return (for a 100% GP catch-up)

E.g. 20% carry: catch-up = 0.25 × preferred return. Then GP has 20% of profit so far.

Standard tier order

1) Return of contributed capital → 2) Preferred return → 3) GP catch-up (if any) → 4) Split, e.g. 80/20

Whole-fund applies this on the whole fund. Deal-by-deal applies it deal by deal.

Clawback

Clawback = carry paid − (carry rate × cumulative fund profit), if positive

Often limited to after-tax carry or a set cap. Follow the stated terms.

DPI (distributed to paid-in)

DPI = cumulative distributions ÷ paid-in capital

Realized return. It does not depend on GP valuations. It starts at zero and rises as exits happen.

RVPI (residual value to paid-in)

RVPI = NAV (residual value) ÷ paid-in capital

Unrealized portion. It relies on the GP's valuation, so treat it with caution early in the fund's life.

TVPI (total value to paid-in)

TVPI = (cumulative distributions + NAV) ÷ paid-in capital = DPI + RVPI

Also called the investment multiple. Usually net of fees and carried interest when measured at LP level. Ignores timing.

Since-inception IRR

0 = Σ [CFt ÷ (1 + IRR)^t], with contributions negative, distributions positive, and the final NAV as a terminal inflow

Money-weighted. Solved by calculator or trial and error. Sensitive to the timing of cash flows.

Kaplan-Schoar PME

KS-PME = FV of distributions + NAV (at index returns) ÷ FV of contributions (at index returns)

Above 1 means the fund outperformed the index. Below 1 means it underperformed. Equal to 1 means it matched the index.

Long-Nickels PME

PME IRR = IRR of the index-based cash flows, with the ending value being the index-equivalent value

Contributions and distributions are applied to the index. Compare this IRR with the fund IRR.

Unsmoothing appraisal returns

r(true,t) ≈ [r(obs,t) − φ × r(obs,t−1)] ÷ (1 − φ)

A common adjustment for appraisal smoothing, where φ is the first-order autocorrelation of reported returns. Unsmoothing raises measured volatility.

Unfunded commitment

Unfunded commitment = Total commitment − Capital called to date

Still a liability the investor must meet when the GP calls capital.

Net asset value after a period

Ending NAV = Beginning NAV + Contributions − Distributions + Gain (or − Loss)

Use to roll fund value forward and check reported figures.

Due diligence areas

Strategy, Team, Track record, Terms and alignment, Operations and governance

Use as a checklist to structure any recommendation.

Quick revision

• Private equity is usually held through a limited partnership: the general partner manages, limited partners supply most of the capital.
• Venture capital funds early-stage companies and carries high failure risk; buyouts use leverage on mature companies.
• Valuation of private holdings relies on estimates, so conflicts of interest and stale values are real risks.
• Management fees are charged on committed or invested capital as set by the fund terms; check which base the question uses.
• Carried interest is the general partner's share of profits, subject to terms such as a hurdle rate.
• Clawback provisions let limited partners recover excess carried interest paid earlier.
• In a waterfall, work in tier order and confirm distributions add up to total proceeds.
• Gross returns exceed net returns because of fees, carry and expenses.
• IRR depends on timing of cash flows; multiples ignore timing. Use both when judging performance.
• Illiquidity and the J-curve mean early reported returns are often negative.
• Tie every recommendation to the client's return goal, liquidity needs, horizon and risk tolerance.
• Due diligence covers the manager, strategy, track record, terms, alignment of interests and operations.

Common mistakes

• Saying LPs manage the fund and the GP supplies most of the capital. Fix: LPs provide most of the capital but stay passive. The GP manages and usually invests a small share.
• Stating that the GP has limited liability. Fix: Only LPs are limited to their commitment. The GP has unlimited liability.
• Treating growth equity as if it uses heavy leverage like an LBO. Fix: Remember that growth equity is usually a minority stake with little or no debt, while an LBO takes control and uses substantial debt.
• Calling any early funding round 'seed' stage. Fix: Link each stage to its milestone: seed is product development, early stage is first commercial production and sales, later stage is expansion of a revenue-generating firm.
• Using pre-money value to compute the investor's ownership share. Fix: Ownership = Investment ÷ Post-money. Add the investment to the pre-money first.
• Forgetting to subtract net debt when moving from a multiple-based value to equity value. Fix: Check what the multiple measures. EV multiples give enterprise value. Subtract debt and add cash to reach equity value.
• Applying the carry rate to total distributions instead of profit. Fix: Always subtract contributed capital before any carry split.
• Confusing which waterfall is LP-friendly. Fix: Link European to whole fund: LPs get capital and hurdle back across the fund first, so carry is later and safer for LPs.
• Dividing by committed capital instead of paid-in capital when computing TVPI, DPI or RVPI. Fix: Remember that the P in each ratio is paid-in. Check the data table and use only the capital actually called.
• Treating TVPI as if it shows how fast the fund made money. Fix: TVPI ignores time. Use IRR or PME when the question involves timing or comparison with an index.

Exam tips

• Link every PE answer to the client's liquidity, horizon and risk tolerance, because that is where the points are.
• Use the command word: identify needs only a name, while justify needs a reason tied to the vignette.
• In calculations, show each step and check the fee base before computing.
• Compare VC and buyouts on company stage, financing, leverage and return profile.
• Give exactly the number of responses requested.
• Always tie your strategy choice to a fact in the vignette: stage, cash flow stability, or control.
• In numerical LBO questions show each driver calculation, and then check that the three add to the total change.
• For multiple-choice items, eliminate options that mismatch the leverage level: venture and growth equity rarely use heavy debt.