Calculate Net Returns from the Gross MOIC and Gross IRR and estimates for Management Fee, Fund Expense, and Carried Interest.

Module Category: Fees, Expenses, Carry, and FX

Value Drivers: Carry, Fees & Expenses

Key Concept: You can efficiently calculate Net MOICs and Net IRRs for individual deals and groups of investments by converting the GP or Fund’s Management Fees and Fund Expenses (F&E) into a relative fee load (%F) that can be systematically applied to every dollar of gross invested capital (GIC).

Jump to: Overview (90 sec) | Net Multiples (3 min) | Net IRRs (2.5 min)

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Net Return Overview

Calculating hypothetical Net MOICs and Net IRRs for individual portfolio companies or groups of deals can be messy. Conventional net return models are highly sensitive to subjective decisions about the magnitude and timing of hypothetical management fee, fund expense, and carried interest deductions. Analysts must frequently revisit these assumptions and often rebuild models from scratch following routine events, like portfolio company acquisitions or exits. Traditional net return models do not scale.

The ValueBridge.net framework can solve this problem by treating management fees, fund expenses, and carried interest as value drivers that “bridge the gap” between the general partner’s Gross Return and the limited partner’s Net Return. Systematic application of a “fee load” (%F) removes subjective decisions about the magnitude and timing of deductions and can also incorporate carried interest on either a pooled or deal-by-deal basis. From values generally available in Fund reporting and GP marketing materials, the approach can provide very good Net IRR estimates for deals and portfolios, without needing time series cashflow data.

Return Measurements and Variables

Net MOIC and Net IRR calculations rely on the following:

Gross Invested Capital: GIC
Gross Return: GR
Gross Multiple of Invested Capital: Gross MOIC = GR/GIC
Gross Internal Rate of Return: Gross IRR

Management Fees and Fund Expenses: F&E
Carried Interest: Carry = %C ∙ (GR – GIC – F&E)
F&E Rate: %F = F&E / GIC
Carry Rate: %C (usually 20%)

Net Invested Capital: NIC = GIC + F&E
Net Return: NR = GR – Carry
Net Multiple of Invested Capital: Net MOIC = NR / NIC
Net Internal Rate of Return: Net IRR

Holding Period (years): Δt
Effective Holding Period (years): Δt’

Net Return Mathematics

The Net MOIC is related to the gross return (GR), gross invested capital (GIC), management fees and fund expenses (F&E), and carried interest (Carry), as follows:

$Net\,MOIC = \frac{NR}{NIC} = \frac{GR-Carry}{GIC+F\&E}$

First determine the portfolio’s %F and χ_F&E from the absolute ($) value of F&E and GIC.

$\chi_{F\&E} = 1 + \%F = 1 + \frac{F\&E}{GIC}$

The Carry Multiplier is calculated from the Carry Rate (%C, usually 20%), %F, and the Gross MOIC.

$\chi_{Carry} = MAX \left[ 1, 1 / \left( 1- \%C + \%C \cdot \frac{1+ \%F}{Gross\,MOIC} \right) \right]$

Net Returns can be calculated either on a pooled or deal-by-deal basis. To measure Carry on a pooled-basis, the entire portfolio’s Gross MOIC should be used to calculate χ_Carry. To measure Carry on a deal-by-deal basis, an individual deal’s Gross MOIC should be used to calculate χ_Carry.

$Net\,MOIC = \frac{GR-Carry}{GIC+F\&E} = \frac{GR / \chi_{Carry}}{GIC \cdot \chi_{F\&E}} = \frac{Gross\,MOIC}{\chi_{F\&E} \cdot \chi_{Carry}}$

Calculating Net IRR requires the effective holding period (Δt’, not Δt), which is discussed in further detail below.

$\Delta t = \frac{Exit\,Date-Entry\,Date}{365}$

$\Delta t' = \frac{\ln{\left( Gross\,MOIC \right)}}{ \ln{\left( 1+Gross\,IRR \right)}}$

The Net IRR is a function of the Net MOIC and Δt’.

$Net\,IRR = Net\,MOIC^{1/\Delta t'} -1$

$Net\,IRR = \left( \frac{Gross\,MOIC}{\chi_{F\&E} \cdot \chi_{Carry}} \right)^{1/\Delta t'} -1$

$Net\,IRR = \left( \frac{Gross\,MOIC}{\left( 1+\%F \right) \cdot MAX \left[ 1,1 / \left( 1- \%C + \%C \cdot \frac{1+ \%F}{Gross\,MOIC} \right) \right]} \right)^{1/\Delta t'} -1$

Sources of F&E

Required F&E values are typically available in Fund reporting materials. They may also be estimated from size and age of the portfolio (e.g., $X of GIC would require a Fund size of $Y, which would be charged a Management Fee of 2.0% per year in each of the first four years and…). Actual Fund F&E values already include adjustments for activities like recycling and management fee offsets, so are generally preferred.

Range of χ_F&E and χ_Carry

Both the multipliers have a minimum of 1.00x and can generally range up to a maximum of about 1.25x. The minimum is governed by the fact that there is generally no such thing as negative Management Fees, Fund Expenses, or Carried Interest.

A χ_F&E value of 1.25x would mean that the GP charges $0.25 of Management Fees and Fund Expenses for every dollar of Gross Invested Capital. This would be high, even by the standards of private equity. Features like recycling and management fee offsets tend to drive %F lower than 25%. Generally, %F values are in the mid-single digits during the first few years of an investment period, when Funds deploy most of their capital. The %F value often increases to the mid-teens toward the end of a fund’s lifecycle.

The χ_Carry value has a mathematical limit. As a deal or portfolios Gross MOIC goes to infinity, χ_Carry becomes 1/(1-%C). This means a deal with the traditional 20% Carry rate has a maximum of 1.25x, and a deal with a 10% Carry rate has a maximum of 1.11x. However, deals generally don’t approach these maximums until they hit Gross MOICs of 10x, 20x, or 50x. Expect χ_Carry values to be about halfway to the maximum for private equity deals with Gross MOICs around 3.00x.

Pooled Carry-based Net Return Example

Pooled Net Return models calculate each deal’s Carry with consideration to the gains and losses of the other portfolio investments. They use a Carry Multiplier based on the entire portfolio’s Gross MOIC. The Gross MOIC of 1.722x below provides a χ_Carry value of 1.073x that is applied to every deal in the table.

$\chi_{Carry} = MAX \left[ 1, 1/ \left( 1 - 20\% + 20\% \cdot \frac{1 + 13.9\%}{1.722x} \right) \right] = 1.073x$

Port Co	Cap Invst	Cap Rlzd	Unrlzd Val	Tot Val	Gross MOIC	Gross IRR	Eff Hold	F&E Mult	Carry Mult	Net MOIC	Net IRR

Echo	$20	$60	–	$60	3.00x	55.2%	2.50	1.14x	1.07x	2.46x	43.3%
Alpha	$20	$45	–	$45	2.25x	32.2%	2.91	1.14x	1.07x	1.84x	23.4%
Golf	$25	$50	–	$50	2.00x	58.8%	1.50	1.14x	1.07x	1.64x	38.9%
Bravo	$25	$15	–	$15	0.60x	-18.5%	2.50	1.14x	1.07x	0.49x	-24.7%
Sub-tot	$90	$170	–	$170	1.89x	27.3%	2.63	1.14x	1.07x	1.55x	18.0%

Charl.	$25	–	$75	$75	3.00x	24.6%	5.00	1.14x	1.07x	2.46x	19.7%
Foxtr.	$15	$15	$15	$30	2.00x	29.5%	2.68	1.14x	1.07x	1.64x	20.2%
Hotel	$20	–	$15	$15	0.75x	-10.9%	2.50	1.14x	1.07x	0.61x	-17.7%
Delta	$30	–	$20	$20	0.67x	-10.7%	3.59	1.14x	1.07x	0.55x	-15.5%
Sub-tot	$90	$15	$125	$140	1.56x	12.9%	3.65	1.14x	1.07x	1.27x	6.8%

Total	$180	$185	$125	$310	1.72x	19.9%	2.99	1.14x	1.07x	1.41x	12.2%

Deal-by-Deal Carry-based Net Return Example

Deal-by-deal Net Return models calculate Carry for each deal individually, without consideration to the gains and losses of other portfolio investments. They use a Carry Multiplier based on each deal’s individual Gross MOIC. Thus, every deal has a different χ_Carry value. For example, Echo Co’s Gross MOIC of 3.00x provides an χ_Carry value of 1.142x.

$\chi_{Carry} = MAX \left[ 1, 1/ \left( 1 - 20\% + 20\% \cdot \frac{1 + 13.9\%}{3.000x} \right) \right] = 1.142x$

Port Co	Cap Invst	Cap Rlzd	Unrlzd Val	Tot Val	Gross MOIC	Gross IRR	Eff Hold	F&E Mult	Carry Mult	Net MOIC	Net IRR

Echo	$20	$60	–	$60	3.00x	55.2%	2.50	1.14x	1.14x	2.31x	39.7%
Alpha	$20	$45	–	$45	2.25x	32.2%	2.91	1.14x	1.11x	1.78x	21.9%
Golf	$25	$50	–	$50	2.00x	58.8%	1.50	1.14x	1.09x	1.60x	37.1%
Bravo	$25	$15	–	$15	0.60x	-18.5%	2.50	1.14x	1.00x	0.53x	-22.6%
Sub-tot	$90	$170	–	$170	1.89x	27.3%	2.63	1.14x	1.09x	1.53x	17.4%

Charl.	$25	–	$75	$75	3.00x	24.6%	5.00	1.14x	1.14x	2.31x	18.2%
Foxtr.	$15	$15	$15	$30	2.00x	29.5%	2.68	1.14x	1.09x	1.60x	19.3%
Hotel	$20	–	$15	$15	0.75x	-10.9%	2.50	1.14x	1.00x	0.66x	-15.4%
Delta	$30	–	$20	$20	0.67x	-10.7%	3.59	1.14x	1.00x	0.59x	-13.9%
Sub-tot	$90	$15	$125	$140	1.56x	12.9%	3.65	1.14x	1.06x	1.29x	7.3%

Total	$180	$185	$125	$310	1.72x	19.9%	2.99	1.14x	1.07x	1.41x	12.2%

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The Effective Holding Period

The Effective Holding period is a dollar weighted duration that accounts for all the inflows and outflows that occur during an ownership period.

$\Delta t' = \frac{\ln{\left( Gross\,MOIC \right)}}{\ln{\left( 1+Gross\,IRR \right)}}$

This formula reduces all the portfolio capital investments, realizations, and fair market values to a single investment (contribution) and a single realization (distribution), separated by a number of years, months, days, hours, minutes, seconds, etc. By reducing a problem with many cashflows into one with only two cashflow, we can calculate an IRR with the standard Compounded Annual Growth Rate (CAGR) formula.

$IRR \approx CAGR = MOIC^{1/\Delta t'}=MOIC^{\ln{\left( 1+Gross\,IRR \right)} / \ln{\left( Gross\,MOIC \right)}}$

For investments that have only one inflow and one outflow, the Effective Hold (Δt’) formula will simply provide the Actual Hold (Δt) in years. For investments with more cashflows, such as follow-on investments or distributions prior to the final exit, Δt’ will always be smaller than Δt because there is less capital “at risk” or “in play” during the period.

Note that LOG(1) is equal to 0, so the Δt’ formula can break for investments with Gross MOICs of 1.00x and Gross IRRs of 0.00%. In such cases, either substitute Δt for Δt’ or take the limit as the return approaches 1.00x or 0.00% (achieved by nudging the investment’s FMV up or down slightly).

References and Further Reading

Private equity net return models are covered extensively in the book, on the AUXILIA Mathematica website, and on the YouTube channel. The following resources provide more detail (and much longer explanations) about the underlying mathematics and additional applications.

Private Equity Value Creation Analysis: Volume I: Theory

Reinard, M. 2021. Private Equity Value Creation Analysis: Volume I: Theory: A Technical Handbook for the Analysis of Private Companies and Portfolios. AUXILIA Press.

See Chapter 14: Gross Returns and Net Returns.

Available at Amazon.com.

AUXILIA Press Whitepaper

Reinard, M., A Better Net Return Model, April 30, 2021. (Download)

Articles on AUXILIA Mathematica

Private Equity Net Return video series

NR100: Introduction (Video | Episode Page)
NR101: New SEC Marketing Rule (Video | Episode Page)
NR102: Conventional Net Return Model (Video | Episode Page)
NR103: A Better Net Return Model (Video | Episode Page)
NR104: The Effective Net IRR (Video | Episode Page)

01. Net MOIC and Net IRR

Net Return Overview

Return Measurements and Variables