Author: Gert-Tom Draisma / www.TristanFinance.com

First published: 24th of September 2026

Latest update: 2nd of October 2026

Status: First Draft

Part I established the basic mechanics of a waterfall without allowing time to determine the result.

It introduced the waterfall as an ordered sequence of allocation rules operating on economic events and calculation state:

Previous State + New Economic Event + Waterfall Rules = New State

That framework remains unchanged.

What changes in Part II is that time itself becomes an input to the economics.

A €100 million contribution outstanding for three months is not economically equivalent to the same €100 million contribution outstanding for three years where the waterfall contains a time-based preferred return or hurdle.

Similarly, two funds can have:

• exactly the same total contributions;
• exactly the same total distributions;
• exactly the same carry percentage; and
• exactly the same stated hurdle rate,

and nevertheless generate different carried interest because their cash flows occurred on different dates.

The calculation therefore moves from:

Amount + Classification

to:

Amount + Classification + Economic Date

This Part develops that additional dimension progressively.

It begins with simple preferred return, moves to compound preferred return, then develops IRR and MOIC hurdles, hard and soft hurdles, catch-up mechanics, multiple performance thresholds and super carry.

Particular attention is given to compound preferred return because apparently simple terminology such as:

8% preferred return, compounded annually

does not by itself provide a complete calculation specification.

Several additional questions must be answered.

For example:

• Which contributions earn preferred return?
• From what date does each contribution begin to earn it?
• When does accrual stop?
• Is preferred return accrued daily, monthly, quarterly or annually?
• Is accrued preferred return itself entitled to preferred return?
• If so, when does that compounding occur?
• Does each contribution have its own compounding anniversary?
• Or is accrued preferred return capitalised on one or more common compounding dates?
• How are contributions occurring between compounding dates treated?
• How are distributions occurring between compounding dates treated?
• Which balance does a distribution reduce first?
• What day-count convention applies?

This leads to one of the central distinctions in this Part:

Accrual Frequency ≠ Compounding Frequency ≠ Compounding Date

Every relevant cash flow may have its own economic date.

But that does not necessarily mean that every cash flow has its own compounding date.

Therefore:

Each Cash Flow Has Its Own Economic Date

but:

Each Cash Flow Having Its Own Economic Date ≠ Each Cash Flow Having Its Own Compounding Date

Two different compound preferred-return structures will consequently be developed in detail.

The first is individual-anniversary compounding, where contributions can maintain their own compounding schedules.

The second is common-date compounding, where individual cash flows accrue from their respective economic dates but accrued preferred return is capitalised on defined common dates.

Neither is inherently the correct methodology.

The governing economics determine which methodology applies.

1. Time Changes the Economics

Consider two investments.

Investment A

An investor contributes:

€100m

One year later the investor receives:

€120m

Profit:

€20m

MOIC:

1.20x

Investment B

An investor contributes:

€100m

Five years later the investor receives:

€120m

Profit:

€20m

MOIC:

1.20x

Viewed purely in absolute terms, the two investments appear identical.

Both produced:

€20m Profit

and:

1.20x MOIC

But economically they are very different.

Investment A generated €20 million profit in one year.

Investment B required five years to generate the same amount.

The annualised return on Investment A is 20%.

The annualised return on Investment B is approximately 3.7%.

Therefore:

Same Profit ≠ Same Annualised Return

and:

Same MOIC ≠ Same IRR

This difference matters immediately when the waterfall contains an 8% annual hurdle.

Investment A has comfortably exceeded an 8% annual return.

Investment B has not.

A waterfall based solely on a multiple might treat the two investments identically.

A waterfall based on annualised return would not.

The performance measure is therefore part of the economics.

2. Preferred Return

A preferred return generally gives investors a defined economic return before carried interest participates in some or all subsequent profits.

A simplified waterfall might therefore contain:

Return of Capital → Preferred Return → Carry

Assume:

• contribution = €100m;
• preferred-return rate = 8%;
• holding period = exactly one year;
• simple annual preferred return;
• no intermediate cash flows.

Preferred return:

€100m × 8% = €8m

The amount required to return capital and satisfy the preferred return is therefore:

€100m + €8m = €108m

If only €105 million is available for distribution:

• €100m returns capital;
• €5m satisfies part of the preferred return;
• €3m preferred return remains unsatisfied;
• nothing reaches the carry tier.

If €108 million is available:

• €100m returns capital;
• €8m satisfies the preferred return;
• nothing remains for carry.

If €120 million is available:

• €100m returns capital;
• €8m satisfies the preferred return;
• €12m remains available for subsequent waterfall tiers.

At this level, the calculation appears straightforward.

The complexity begins when we ask what exactly the words 8% preferred return mean.

3. A Rate Is Not a Calculation Specification

Suppose two LPAs both state an 8% preferred return.

That does not necessarily mean their preferred-return calculations are economically identical.

Consider the following possible differences.

Fund A

Preferred return:

• applies only to investment contributions;
• accrues from the investor funding date;
• uses simple interest;
• accrues daily;
• uses Actual/365.

Fund B

Preferred return:

• applies to investments, management fees and expenses;
• uses a contractually defined economic funding date;
• compounds annually;
• compounds on a common date;
• uses a different day-count convention.

Both may be described informally as having:

an 8% preferred return.

Yet the calculations can produce materially different hurdle amounts.

Therefore:

Hurdle Rate Alone ≠ Hurdle Definition

The rate is one parameter within a larger calculation specification.

4. The Preferred-Return Calculation Specification

Before calculating preferred return, at least five dimensions should be considered.

4.1 Economic base

What earns preferred return?

Potentially:

• investment contributions;
• management fees;
• fund expenses;
• organisational expenses;
• broken-deal costs;
• other contributions;
• some combination of these.

Suppose:

• €100m is contributed for investments;
• €10m for management fees;
• €5m for other fund expenses.

If all €115 million earns an 8% preferred return for one year:

€115m × 8% = €9.2m

If only the €100 million investment contribution participates:

€100m × 8% = €8m

Difference:

€1.2m

Same rate.

Different economic base.

4.2 Economic date

When does an amount begin to earn preferred return?

Possible dates include:

• date the investor funds;
• date an investment is funded;
• date a subscription facility funds the investment;
• another contractually specified date.

4.3 Accrual convention

How is preferred return earned between dates?

For example:

• daily;
• monthly;
• quarterly;
• annually.

4.4 Compounding convention

Does accrued preferred return itself earn preferred return?

If yes:

When?

This question is distinct from the accrual question.

4.5 Distribution ordering

When value is distributed, what balance does it satisfy?

For example:

Capital → Preferred Return → Catch-Up → Residual

or another contractual sequence.

All five dimensions can affect the final carry calculation.

Section A — Simple Preferred Return

5. Simple Preferred Return

We begin with the simplest time-based methodology.

Under simple preferred return, accrued preferred return does not itself generate additional preferred return.

For one contribution:

Preferred Return = Capital × Annual Rate × Time

Assume:

• contribution = €100m;
• rate = 8%;
• period = three years.

Preferred return:

€100m × 8% × 3 = €24m

At the end of three years:

Capital = €100m

Preferred Return = €24m

Total amount required before subsequent tiers:

€124m

The €24 million of accrued preferred return has not itself earned preferred return.

6. Simple Preferred Return over Multiple Years

The annual development can be shown explicitly.

After five years:

Capital + Preferred Return = €140m

The annual preferred-return amount remains €8 million because the €100 million capital base remains unchanged and previously accrued preferred return does not enter the accrual base.

7. Multiple Contributions

Now introduce several contributions.

Assume:

Assume:

• 8% simple preferred return;
• calculation date = 1 January 2029;
• no distributions before that date.

The total contribution is:

€100m

But the €100 million has not been outstanding for the same length of time.

Contribution 1

€50 million outstanding for three years:

€50m × 8% × 3 = €12m

Contribution 2

€30 million outstanding for two years:

€30m × 8% × 2 = €4.8m

Contribution 3

€20 million outstanding for one year:

€20m × 8% × 1 = €1.6m

Total preferred return:

€12m + €4.8m + €1.6m = €18.4m

Total capital:

€100m

Capital plus preferred return:

€118.4m

Now compare this with €100 million contributed entirely on 1 January 2026.

Preferred return:

€100m × 8% × 3 = €24m

Difference:

€24m − €18.4m = €5.6m

The total contribution is identical.

The timing is not.

Therefore:

Same Total Contributions ≠ Same Preferred Return

8. Each Cash Flow Has Its Own Economic Date

The preceding example establishes an important principle that will continue throughout this Part.

A cumulative capital balance is not necessarily sufficient to calculate a time-based return.

Consider the position at 1 January 2029:

Cumulative Contributions = €100m

If we know only that number, we cannot calculate the preferred return correctly.

We also need to know when the €100 million entered the relevant economic population.

The contribution history is:

€50m → three years

€30m → two years

€20m → one year

Therefore:

Cumulative Amount + No Timing Information ≠ Sufficient Data for Time-Based Hurdle

The individual economic dates matter.

9. Partial Return of Capital

Now assume:

• €100m contributed on 1 January 2026;
• 8% simple preferred return;
• €40m capital returned on 1 January 2027;
• remaining €60m returned on 1 January 2029.

For the first year:

€100m × 8% = €8m

After the €40 million return, only €60 million remains outstanding.

For the next two years:

€60m × 8% × 2 = €9.6m

Total preferred return:

€8m + €9.6m = €17.6m

Compare this with leaving the entire €100 million outstanding for three years:

€100m × 8% × 3 = €24m

Difference:

€6.4m

A distribution can therefore affect not only the current allocation but also future preferred-return accrual.

10. Unreturned Capital and Accrued Preferred Return

Once preferred return is introduced, the model needs at least two conceptually separate balances:

Unreturned Capital

and:

Accrued but Unpaid Preferred Return

Assume:

• €100m contributed;
• 8% simple preferred return;
• one year passes.

Immediately before a distribution:

Unreturned Capital = €100m

Accrued Preferred Return = €8m

Suppose a €50 million distribution occurs and the waterfall returns capital first.

After the distribution:

Unreturned Capital = €50m

but:

Accrued Preferred Return = €8m

The two balances have developed differently.

If another year passes, the capital may generate:

€50m × 8% = €4m

of additional simple preferred return.

The previous €8 million preferred-return balance does not itself generate return under a simple methodology.

At the end of the second year:

Unreturned Capital = €50m

Accrued Preferred Return = €12m

This separation becomes even more important when we introduce compounding.

11. Preferred Return Accrued Versus Preferred Return Paid

Suppose:

• unreturned capital has been fully returned;
• accrued preferred return = €10m;
• only €6m remains available for distribution.

The waterfall can pay:

€6m

toward the preferred-return tier.

But the accrued preferred return was:

€10m

Therefore:

Preferred Return Paid = €6m

Unpaid Preferred Return = €4m

This gives:

Preferred Return Accrued ≠ Preferred Return Paid

The distinction matters because the unpaid €4 million may remain relevant to future calculations.

Under a simple preferred-return structure, it may remain as an unpaid balance without itself earning further preferred return.

Under a compound structure, it may eventually become part of the compounding base.

That depends on the contractual mechanics.

Section B — Compound Preferred Return

12. Introducing Compounding

Under a compounded preferred return, accrued preferred return can itself generate additional preferred return.

For a single contribution with annual compounding:

Future Value = Principal × (1 + Rate)ⁿ

Assume:

• principal = €100m;
• rate = 8%;
• annual compounding;
• three years.

After Year 1:

€100m × 1.08 = €108m

After Year 2:

€108m × 1.08 = €116.64m

After Year 3:

€116.64m × 1.08 = €125.9712m

Therefore:

Total Preferred Return = €25.9712m

Compare simple preferred return:

€24m

Difference:

€1.9712m

That difference arises because previously accrued preferred return has itself generated preferred return.

13. Simple Versus Compound Preferred Return over Time

Using €100 million at 8%:

The difference grows over time.

After one year there is no difference.

After ten years, the difference is approximately:

€35.892m

Thus the distinction between simple and compound preferred return is not merely technical.

For long-duration funds it can materially affect the point at which carry becomes payable.

14. Compounding Requires More Than a Rate

The previous example contained only:

• one contribution;
• no intermediate distributions;
• exact annual periods.

Now consider:

• €50m contributed on 1 January 2026;
• €30m contributed on 1 July 2026;
• 8% preferred return;
• compounded annually.

What does:

compounded annually

mean?

There are at least two distinct possibilities.

Version 1 — Individual-anniversary compounding

Contribution A compounds on:

1 January

Contribution B compounds on:

1 July

Each contribution effectively maintains its own compounding schedule.

Version 2 — Common-date compounding

Both contributions accrue from their respective economic dates.

But accrued preferred return is capitalised on a common date, for example:

31 December

These are not the same calculation.

This distinction gives us:

Accrual Frequency ≠ Compounding Frequency ≠ Compounding Date

and:

Individual Economic Date ≠ Necessarily Individual Compounding Date

Section C — Version 1: Individual-Anniversary Compounding

15. Individual-Anniversary Method

Under an individual-anniversary methodology, each relevant contribution or tranche has its own compounding cycle.

Assume:

Rate:

8%

Annual compounding.

Tranche A compounds on each 1 January.

Tranche B compounds on each 1 July.

The cash flows therefore share the same annual rate but not the same compounding dates.

16. Tranche A

Initial contribution:

€50m

1 January 2027

Preferred return:

€50m × 8% = €4m

New compounded balance:

€54m

1 January 2028

Preferred return:

€54m × 8% = €4.32m

New balance:

€58.32m

1 January 2029

Preferred return:

€58.32m × 8% = €4.6656m

New balance:

€62.9856m

Cumulative preferred return:

€62.9856m − €50m = €12.9856m

17. Tranche B

Initial contribution:

€30m on 1 July 2026

1 July 2027

Preferred return:

€30m × 8% = €2.4m

Balance:

€32.4m

1 July 2028

Preferred return:

€32.4m × 8% = €2.592m

Balance:

€34.992m

1 July 2029

Preferred return:

€34.992m × 8% = €2.79936m

Balance:

€37.79136m

Cumulative preferred return:

€7.79136m

The important difference is temporal.

Tranche B's compounding dates are six months later than Tranche A's.

18. Adding a Third Tranche

Now add:

€20m on 1 April 2027

The compounding calendar becomes:

Tranche A

1 January each year.

Tranche C

1 April each year.

Tranche B

1 July each year.

The calculation therefore needs to preserve three independent compounding schedules.

At larger scale, a fund could have many more.

Conceptually:

Contribution → Tranche → Accrual → Individual Anniversary → Compounding → Updated Tranche Balance

19. Calculation Between Anniversaries

Suppose the calculation date is:

1 April 2028

Tranche A has completed two annual compounding periods:

€50m × 1.08² = €58.32m

Tranche B has completed one:

€30m × 1.08 = €32.4m

But A has also been outstanding for three months since its most recent anniversary, while B has been outstanding for nine months since its most recent anniversary.

The model now needs another rule:

How is preferred return accrued between annual compounding dates?

One possible methodology is simple accrual between anniversaries.

If that is the contractual method:

Tranche A

Three-month accrual:

€58.32m × 8% × 3/12 = €1.1664m

Balance including accrued but not yet compounded return:

€59.4864m

Tranche B

Nine-month accrual:

€32.4m × 8% × 9/12 = €1.944m

Balance:

€34.344m

This demonstrates that even after defining individual-anniversary compounding, the calculation specification is still incomplete unless treatment between anniversaries is defined.

20. Compounded Balance Versus Accrued Balance

At an interim calculation date, it can therefore be useful to distinguish:

Compounded Base

from:

Accrued but Not Yet Compounded Preferred Return

Suppose Tranche A has:

• compounded base = €58.32m;
• accrued since last anniversary = €1.1664m.

Then:

Current Economic Balance = €59.4864m

But the amount currently generating preferred return may still be:

€58.32m

until the next compounding date, depending on the contractual methodology.

This is an important modelling distinction.

Accrued Preferred Return ≠ Necessarily Compounding Base

21. Distribution Against Individual Tranches

Now introduce a distribution.

Suppose:

• Tranche A principal = €50m;
• Tranche B principal = €30m;
• €20m of capital is returned.

Which contribution is reduced?

If the waterfall specifies oldest capital first:

Tranche A becomes:

€30m

Tranche B remains:

€30m

If instead capital is reduced proportionally:

A reduction:

€20m × 50/80 = €12.5m

B reduction:

€20m × 30/80 = €7.5m

Remaining:

A:

€37.5m

B:

€22.5m

Total remaining capital is €60 million under either method.

But the tranches have different economic dates.

Consequently, future preferred return may differ.

Therefore:

Same Closing Capital ≠ Necessarily Same Future Preferred Return

The allocation of capital reductions between dated tranches can itself be economically relevant.

Section D — Version 2: Common-Date Compounding

22. Common-Date Method

Under common-date compounding:

• each contribution begins accruing preferred return from its own economic date;
• accrued preferred return is capitalised on a defined common date.

Assume:

Common Annual Compounding Date = 31 December

and:

• €50m contribution on 1 January;
• €30m contribution on 1 July;
• rate = 8%.

For simplicity, initially use a half-year fraction for the July contribution.

Contribution A

Accrual:

€50m × 8% = €4m

Contribution B

Accrual:

€30m × 8% × 0.5 = €1.2m

Total accrued preferred return:

€5.2m

At 31 December, that amount is capitalised.

Principal:

€80m

Accrued preferred return:

€5.2m

New compounding base:

€85.2m

The two contributions had different accrual periods.

They nevertheless enter a common compounded balance at the specified common date.

23. Second Year under Common-Date Compounding

Assume no cash flows during the following year.

Opening compounded base:

€85.2m

Preferred return:

€85.2m × 8% = €6.816m

Closing compounded balance:

€92.016m

Original contributions:

€80m

Cumulative preferred return:

€92.016m − €80m = €12.016m

At this point, the €5.2 million preferred return accrued in the first period has itself earned preferred return during the second period.

24. A Contribution Shortly Before the Common Date

Now change the second contribution.

Assume:

• €50m contributed 1 January;
• €30m contributed 1 December;
• common compounding date = 31 December;
• 8% annual rate.

The €30 million contribution has only been outstanding for approximately one month before the first common compounding date.

Using a simplified 1/12 fraction:

Contribution A:

€50m × 8% = €4m

Contribution B:

€30m × 8% × 1/12 = €0.2m

Total accrued preferred return:

€4.2m

New compounded balance:

€84.2m

It would generally be incorrect under this assumed methodology to give the December contribution a full year's 8% merely because it exists on the 31 December compounding date.

A common compounding date does not eliminate the individual economic dates.

Therefore:

Common Compounding Date ≠ Common Accrual Start Date

25. Accrual Versus Compounding

The distinction can now be stated precisely.

Accrual

Determines the preferred return earned between economic dates.

Compounding

Determines when previously accrued preferred return itself becomes part of the base generating future preferred return.

Therefore:

Accrual Determines How Much Return Has Been Earned

while:

Compounding Determines When Earned Return Begins Earning Return

This distinction is essential to implementing compound preferred return correctly.

26. Comparing the Two Versions

Assume again:

• €50m contributed 1 January 2026;
• €30m contributed 1 July 2026;
• 8% annual rate.

Under individual-anniversary compounding, the first preferred return on the €30 million contribution becomes compounded on:

1 July 2027

Under common-date compounding, the return accrued from 1 July to 31 December 2026 may become compounded on:

31 December 2026

Thus part of the preferred return on the July contribution begins generating additional preferred return approximately six months earlier under the common-date method.

Over a short period the difference may be small.

Over a long period, or across large contributions, the difference can become significant.

Therefore:

Same Rate + Same Cash Flows + Different Compounding Convention = Potentially Different Hurdle

and consequently:

Potentially Different Carry

27. Neither Version Is Automatically Correct

The purpose of comparing the two methodologies is not to choose one as superior.

The purpose is to show why the contractual rule must precede the calculation.

The correct sequence is:

Governing Economics

↓

Accrual Convention

↓

Compounding Convention

↓

Calculation Method

A model should not impose its preferred methodology on the fund.

A system default is merely a system default.

It does not determine the economics.

Section E — Contributions and Distributions Between Compounding Dates

28. Contributions Between Common Compounding Dates

Assume:

• opening compounded balance on 1 January = €100m;
• rate = 8%;
• common compounding date = 31 December;
• additional contribution of €40m on 1 July.

Using simplified half-year accrual:

Opening balance accrual:

€100m × 8% = €8m

July contribution accrual:

€40m × 8% × 0.5 = €1.6m

Total accrual:

€9.6m

Closing compounded balance:

€100m + €40m + €9.6m = €149.6m

It would be incorrect to calculate:

€140m × 8% = €11.2m

because the additional €40 million was not outstanding for the entire year.

29. Distribution Between Common Compounding Dates

Assume:

• €100m outstanding on 1 January;
• rate = 8%;
• €40m capital returned on 1 July;
• common compounding date = 31 December.

Simplified accrual:

First half:

€100m × 8% × 0.5 = €4m

Second half:

€60m × 8% × 0.5 = €2.4m

Total:

€6.4m

If the model instead calculated:

€100m × 8% = €8m

it would overstate preferred return by:

€1.6m

because it would ignore the mid-year capital reduction.

30. Multiple Events within One Period

Now assume:

The capital base changes several times.

A robust calculation divides the period into intervals.

Conceptually:

1 Jan–1 Apr: €100m

1 Apr–1 Jul: €120m

1 Jul–1 Oct: €90m

1 Oct–31 Dec: €100m

Preferred return is accrued over each interval according to the applicable time convention.

The annual preferred return is therefore not:

Year-End Capital × 8%

nor:

Maximum Capital × 8%

nor:

Average Capital × 8%

unless the contract specifically defines such an approach.

It is derived from the economic history.

31. Event-by-Event Accrual

The previous example illustrates a general calculation method.

At each economic event:

1. determine the time since the previous event;
2. accrue preferred return on the applicable base for that interval;
3. process the new economic event;
4. update the relevant balances;
5. continue to the next event;
6. compound accrued preferred return when a contractual compounding date is reached.

Conceptually:

Opening State

↓

Accrue to Next Event

↓

Process Event

↓

Update State

↓

Accrue to Next Event

↓

Process Event

↓

Compound When Required

This event-driven approach will become increasingly important as the calculations become more complex.

32. Distribution Ordering within the Preferred-Return Waterfall

Suppose:

• capital = €100m;
• accrued preferred return = €8m;
• distribution = €40m.

If the contractual waterfall returns capital first:

Capital after distribution = €60m

Accrued preferred return = €8m

If instead the distribution satisfies preferred return first:

Preferred return paid:

€8m

Remaining distribution:

€32m

Capital after distribution:

€68m

The closing economic states are different.

This matters because the capital and preferred-return balances may accrue differently in the future.

Thus:

Same Distribution + Different Allocation Order = Different Future State

33. A Distribution Immediately Before Compounding

Suppose:

• common compounding date = 31 December;
• accrued but uncapitalised preferred return = €8m on 30 December;
• a €20m distribution occurs on 30 December.

If the distribution satisfies the €8 million accrued preferred return first:

Only:

€12m

remains to reduce capital.

If the distribution reduces capital first:

Capital falls by:

€20m

and the €8 million accrued preferred return may remain available for capitalisation on 31 December.

Those two treatments can produce different opening balances for the following year.

Therefore:

Event Ordering Around a Compounding Date Can Affect Future Preferred Return

Section F — Day-Count Conventions

34. Irregular Dates

Real cash flows do not normally occur on convenient annual boundaries.

Suppose:

• €100m contributed 17 March;
• distributed 8 November;
• rate = 8%.

The calculation requires a measure of elapsed time.

That measure must be specified.

A simple educational calculation might use months.

A production calculation normally requires a defined day-count convention.

35. Actual/365 Example

Assume the capital is outstanding for 183 days.

Using Actual/365:

Preferred Return = €100m × 8% × 183/365

Approximately:

€4.011m

Using a 180/360 convention:

€100m × 8% × 180/360 = €4m

The difference is approximately:

€11,000

on €100 million for this short period.

Small differences can become material when applied to:

• larger funds;
• longer periods;
• repeated cash flows; and
• multiple investors.

36. Leap Years

Suppose a contribution is outstanding for 183 days during a leap year.

Should the denominator be:

365

or:

366

or should an Actual/Actual methodology divide the period according to the relevant calendar years?

The answer is not a matter of mathematical preference.

It is a calculation convention.

Therefore:

Rate + Dates ≠ Fully Defined Accrual

A day-count rule is also required.

37. Inclusive and Exclusive Dates

Even after selecting a day-count convention, another question can arise:

Does accrual include:

• the contribution date;
• the distribution date;
• both;
• neither?

A one-day difference on one €1 million cash flow is usually immaterial.

A one-day difference across billions of euros and many years may not be.

More importantly, a reproducible calculation should not depend on which spreadsheet formula a particular modeller happened to use.

The convention should be explicit.

Section G — IRR-Based Hurdles

38. Preferred-Return Balance Versus IRR

A preferred-return balance and an IRR test are related concepts but are not automatically identical.

Consider:

The annual IRR is:

8%

An 8% annually compounded preferred-return calculation also produces:

€108m

In this simple case, the two methods appear identical.

Now introduce intermediate cash flows.

The equivalence can disappear.

Therefore:

Preferred-Return Balance ≠ Automatically IRR

The precise waterfall methodology matters.

39. IRR Uses the Complete Dated Cash-Flow Series

Consider:

Total distributions:

€104m

Profit:

€4m

But the investor received €50 million after only six months.

The economic return cannot be understood simply as:

€4m / €100m = 4%

The timing of the €50 million interim distribution affects the annualised return.

IRR therefore evaluates the complete dated cash-flow history.

40. The Waterfall Often Needs to Solve for the Hurdle

In a waterfall, we frequently know:

• historical cash flows;
• current distribution available;
• target IRR.

What we do not initially know is:

How much of the current distribution must be allocated to the LP to bring the LP exactly to the hurdle?

Let:

H = Current Distribution Amount Required to Satisfy Hurdle

Then:

IRR(Historical Cash Flows + H) = Target IRR

The waterfall solves for H.

Any distribution remaining after H can then enter the next tier.

This is different from allocating the entire distribution first and calculating the resulting IRR afterwards.

41. Simple Hurdle Solution

Assume:

• contribution = €100m on 1 January 2026;
• target IRR = 8%;
• current distribution date = 1 January 2027.

The amount required is:

€108m

If €150 million is available:

Hurdle allocation:

€108m

Remaining for subsequent tiers:

€42m

This is straightforward because there is only one contribution and one year.

42. Multiple Contributions

Now assume:

Total contributions:

€100m

The final distribution required for an 8% IRR is not the same as if €100 million had been contributed on 1 January 2026.

Each contribution has been outstanding for a different period.

Thus:

IRR Hurdle = Function of Amounts and Dates

not merely:

Total Contributions × Hurdle Percentage

43. Intermediate Distributions

Now assume:

The final amount required to achieve 8% must reflect the fact that €70 million has already been distributed before the final date.

Again, the relevant question is:

What final distribution causes the complete cash-flow series to produce exactly 8%?

This is why an IRR hurdle should be treated as a performance equation rather than a simple accumulated balance unless the governing methodology explicitly defines an equivalent balance approach.

44. Exact Hurdle Solving

A robust model should be capable of solving the hurdle to an appropriate precision.

Suppose the target is:

8.000000%

If the model allocates an amount producing:

8.250000%

too much value may have been allocated to the hurdle tier.

If it produces:

7.750000%

too little may have been allocated.

The hurdle solution should satisfy:

Calculated IRR ≈ Contractual Hurdle

within the defined numerical tolerance.

This becomes a useful control.

45. IRR and Multiple Solutions

IRR calculations can become more complicated when cash flows change sign more than once.

A conventional private equity pattern often resembles:

Contributions → Distributions

but real economic histories can include:

Contribution → Distribution → Recall → Distribution

or other combinations.

Certain cash-flow patterns can mathematically produce:

• more than one IRR;
• no economically meaningful IRR; or
• results sensitive to the solving method.

This does not mean that IRR cannot be used in a waterfall.

It means the calculation specification needs to address the cash-flow patterns that can actually arise.

A waterfall engine should not assume that every possible cash-flow series has one unique, obvious IRR solution.

Section H — Economic Dates and Subscription Facilities

46. One Transaction Can Have Several Dates

Consider an investment acquired using a subscription facility.

The transaction might have:

• investment completion date: 1 January;
• facility draw date: 1 January;
• capital-call notice: 1 March;
• LP funding date: 1 April;
• accounting posting date: another date.

Which date starts the preferred return?

The bank statement cannot answer that question.

The governing economics must.

Therefore:

Cash Date ≠ Automatically Economic Date

47. Subscription Facility Example

Assume:

• investment = €100m;
• facility funds investment on 1 January;
• LP capital called on 1 April;
• investment realised on 31 December;
• hurdle = 8%.

Method A — 1 January economic start date

Simplified one-year preferred return:

approximately:

€8m

Method B — 1 April economic start date

Simplified nine-month preferred return:

€100m × 8% × 9/12 = €6m

Difference:

€2m

That difference can move directly into subsequent waterfall tiers.

If the fund has a 100% catch-up, it can also affect the catch-up calculation.

The subscription facility has therefore potentially changed the timing of carry even though it has not changed the investment's purchase price or ultimate proceeds.

48. Investment Performance Versus Investor Cash-Flow Performance

A subscription facility can create two different performance perspectives.

Investment perspective

Capital was economically deployed on:

1 January

Investor cash-flow perspective

LP cash left the investor on:

1 April

Those two perspectives can generate different annualised returns.

Therefore:

Investment Performance ≠ Investor Cash-Flow IRR

A waterfall must use the perspective specified by its governing economics.

49. The Economic-Date Principle

The calculation sequence should therefore be:

Identify Economic Event

↓

Determine Contractual Economic Date

↓

Accrue or Test Performance from That Date

rather than:

Observe Accounting Cash Date

↓

Assume It Is the Waterfall Date

This distinction becomes particularly important when technology systems obtain cash-flow data from accounting records.

The accounting date may be a source field.

It is not necessarily the economic answer.

Section I — Hard Hurdles

50. Hard-Hurdle Mechanics

Assume:

• capital = €100m;
• preferred return = €20m;
• distribution = €150m;
• carry = 20%;
• hard hurdle;
• no catch-up.

Tier 1 — Return capital

LP:

€100m

Remaining:

€50m

Tier 2 — Preferred return

LP:

€20m

Remaining:

€30m

Tier 3 — Residual split

LP:

€30m × 80% = €24m

GP:

€30m × 20% = €6m

Total LP:

€144m

Total GP:

€6m

Total profit:

€50m

GP share of total profit:

€6m / €50m = 12%

Although the residual carry percentage is 20%, the GP receives only 12% of total profit.

The hurdle amount remains entirely with the LP.

51. Hard Hurdle at Different Performance Levels

Using the same €20 million hard hurdle:

As performance increases, the GP's effective percentage of total profit approaches 20%, but under this simplified hard-hurdle structure it remains below 20% because the first €20 million of profit is permanently excluded from carry.

Section J — Soft Hurdles and Catch-Up

52. Soft-Hurdle Mechanics

Now use the same economics but add a 100% GP catch-up.

Assume:

• capital = €100m;
• preferred return = €20m;
• target carry = 20%;
• GP catch-up = 100%;
• residual split = 80:20;
• distribution = €150m.

Tier 1

Return capital:

€100m

Remaining:

€50m

Tier 2

Preferred return:

€20m

Remaining:

€30m

Tier 3

GP catch-up:

€5m

Remaining:

€25m

Tier 4

Residual:

GP:

€25m × 20% = €5m

LP:

€20m

Total GP:

€10m

Total LP:

€140m

Total profit:

€50m

GP share:

€10m / €50m = 20%

The catch-up has brought the GP to its target share of cumulative profit.

53. Why the Catch-Up Is €5 Million

Suppose the LP has already received:

€20m

of preferred profit.

The GP needs an amount C such that:

C / (€20m + C) = 20%

Solve:

C = 20% × (€20m + C)

C = €4m + 0.20C

0.80C = €4m

C = €5m

Therefore:

Required Full Catch-Up = €5m

54. Why 20% of Preferred Return Is Wrong

A tempting shortcut is:

€20m × 20% = €4m

But then:

LP profit:

€20m

GP profit:

€4m

Total:

€24m

GP percentage:

€4m / €24m = 16.67%

The GP has not reached 20%.

With €5 million:

€5m / €25m = 20%

This illustrates why catch-up mathematics should be derived rather than guessed from the carry percentage.

55. General Full Catch-Up Formula

Let:

• P = preferred profit allocated to LP;
• c = target carry percentage;
• C = GP catch-up.

Then:

C / (P + C) = c

Solving:

C = c(P + C)

C = cP + cC

C − cC = cP

C(1 − c) = cP

Therefore:

C = [c / (1 − c)] × P

For 20% carry:

C = 20% / 80% × P

C = 25% × P

If preferred profit is:

€8m

catch-up:

€2m

If preferred profit is:

€20m

catch-up:

€5m

If preferred profit is:

€40m

catch-up:

€10m

56. Incomplete Catch-Up

Assume:

• capital = €100m;
• preferred return = €20m;
• full catch-up requirement = €5m;
• total distribution = €123m.

After capital:

€23m remains

After preferred return:

€3m remains

The GP receives:

€3m

The distribution is exhausted.

GP share of total €23 million profit:

€3m / €23m = 13.04%

The GP has entered the catch-up tier but has not reached the target 20%.

Therefore:

Being in Catch-Up ≠ Having Completed Catch-Up

57. Carry Sensitivity Through the Catch-Up Tier

Using the same structure:

Within this range, the marginal GP allocation is:

100%

Yet the cumulative effective carry percentage rises gradually:

Therefore:

Marginal Carry Percentage ≠ Cumulative Effective Carry Percentage

58. Partial Catch-Up

A catch-up tier does not necessarily allocate 100% to the GP.

Assume:

• preferred profit = €20m;
• target carry = 20%;
• catch-up allocation = 50% GP / 50% LP.

Let:

X = Total Value Passing Through Catch-Up

GP receives:

0.5X

The GP must reach 20% of:

€20m + X

Therefore:

0.5X / (€20m + X) = 20%

Solve:

0.5X = €4m + 0.2X

0.3X = €4m

X = €13.3333m

GP receives:

€6.6667m

LP receives during catch-up:

€6.6667m

Total relevant profit:

€20m + €13.3333m = €33.3333m

GP:

€6.6667m

Check:

€6.6667m / €33.3333m = 20%

59. General Partial Catch-Up Formula

Let:

• P = preferred profit previously allocated to LP;
• c = target carry percentage;
• k = GP percentage of the catch-up tier;
• X = total value passing through catch-up.

Then:

kX / (P + X) = c

Solving:

kX = cP + cX

X(k − c) = cP

Therefore:

X = cP / (k − c)

The GP's catch-up allocation is:

kX

This formula requires:

k > c

If:

k ≤ c

the GP cannot catch up from zero participation in the preferred amount to the target percentage through that tier.

That condition is itself a useful model validation.

Section K — Complete Soft-Hurdle Waterfall

60. Worked Example

Assume:

• capital = €100m;
• preferred return = €20m;
• target carry = 20%;
• 100% catch-up;
• residual split = 80:20;
• total distribution = €180m.

Tier 1 — Capital

LP:

€100m

Remaining:

€80m

Tier 2 — Preferred return

LP:

€20m

Remaining:

€60m

Tier 3 — Catch-up

GP:

€5m

Remaining:

€55m

Tier 4 — Residual

LP:

€44m

GP:

€11m

Total

LP:

€100m + €20m + €44m = €164m

GP:

€5m + €11m = €16m

Total:

€180m

Profit:

€80m

GP share:

€16m / €80m = 20%

Reconciled.

61. Performance Sensitivity

Run the same waterfall at different distribution levels.

The carry function changes character twice:

• at €120 million;
• at €125 million.

This is a piecewise function.

62. Piecewise Representation

Let:

D = Total Distribution

Then:

D ≤ €120m

Carry = €0

€120m < D ≤ €125m

Carry = D − €120m

D > €125m

Carry = €5m + 20% × (D − €125m)

This representation is extremely useful because more complicated waterfalls simply add more conditions and more pieces.

Section L — MOIC Hurdles

63. Time Is Not Required for Every Hurdle

Not all performance thresholds are annualised.

A waterfall can instead use a multiple.

For a simple investment:

MOIC = Value Returned / Capital Invested

Assume:

• capital = €100m;
• value returned = €150m.

MOIC:

1.50x

The calculation does not inherently care whether €150 million was returned after:

• two years;
• five years;
• ten years.

This makes MOIC economically different from IRR.

64. Same MOIC, Different IRR

Invest:

€100m

Receive:

€200m

After two years

MOIC:

2.00x

Annualised return:

approximately 41.4%

After five years

MOIC:

2.00x

Annualised return:

approximately 14.9%

After ten years

MOIC:

2.00x

Annualised return:

approximately 7.2%

Thus:

Same MOIC ≠ Same IRR

A 2.0x return can represent exceptional annualised performance or relatively modest annualised performance depending on time.

65. Same IRR, Different MOIC

Assume annualised return:

20%

After one year:

€100m → €120m

MOIC:

1.20x

After five years:

€100m × 1.20⁵ ≈ €248.832m

MOIC:

approximately 2.49x

Therefore:

Same IRR ≠ Same MOIC

The two measures answer different economic questions.

66. A Hard 1.5x Hurdle

Assume:

• capital = €100m;
• hard hurdle = 1.5x;
• carry above hurdle = 20%.

Threshold:

€100m × 1.5 = €150m

At €140 million:

No carry.

At €150 million:

Hurdle exactly reached.

No excess.

At €170 million:

Excess:

€20m

Carry:

€4m

At €200 million:

Excess:

€50m

Carry:

€10m

The elapsed time does not change this simplified MOIC calculation.

Section M — Combined IRR and MOIC Tests

67. Multiple Conditions

A waterfall may require:

8% IRR AND 1.5x MOIC

This prevents a high annualised return over a short period from satisfying the hurdle if the absolute multiple remains below the required threshold.

Alternatively, a waterfall might use:

8% IRR OR 1.5x MOIC

The logic is fundamentally different.

68. AND Logic

Condition:

IRR ≥ 8% AND MOIC ≥ 1.5x

Both tests must be satisfied.

69. OR Logic

Condition:

IRR ≥ 8% OR MOIC ≥ 1.5x

Only one test needs to be satisfied.

Therefore:

AND ≠ OR

A single word in the economic rule can materially alter the carry result.

Section N — Multiple Hurdles and Super Carry

70. Multiple Carry Rates

Now consider:

• base carry = 20%;
• higher carry = 25%;
• super carry = 30%.

The first question is not how to calculate 25% or 30%.

The first question is:

To what profit does each percentage apply?

There are at least two fundamentally different structures:

Marginal structure

The higher rate applies only to incremental profits above its threshold.

Equalised structure

Crossing the higher threshold causes the GP to become entitled to the higher percentage of a broader cumulative profit base, usually requiring another catch-up or equalisation mechanism.

These structures should not be confused.

71. Marginal Super Carry

Assume:

• first €50m profit: 20% carry;
• next €50m: 25%;
• profit above €100m: 30%.

At €150 million total profit:

First €50m:

€10m carry

Second €50m:

€12.5m carry

Final €50m:

€15m carry

Total:

€37.5m

Effective carry percentage:

€37.5m / €150m = 25%

The marginal rate on the final €50 million is 30%.

The cumulative effective rate is 25%.

Therefore:

Marginal Carry Rate ≠ Overall Carry Rate

72. Equalised Super Carry

Now assume that once a second threshold is reached, the GP should ultimately receive 25% of a defined cumulative profit base.

Suppose:

• relevant cumulative profit = €100m;
• carry previously generated at 20% = €20m;
• target cumulative carry = 25%.

Target:

€100m × 25% = €25m

Additional carry required:

€5m

The waterfall therefore needs an equalisation mechanism.

It cannot simply apply 25% to the next euro and assume the GP has reached 25% cumulatively.

This creates another catch-up tier.

73. Equalisation Is Another Piecewise Transition

Conceptually:

20% Carry Tier

↓

Higher Performance Threshold

↓

Equalisation / Catch-Up

↓

25% Carry Tier

↓

Further Performance Threshold

↓

Further Equalisation

↓

30% Carry Tier

The waterfall has become a sequence of piecewise allocation functions.

The headline statement:

20% carry increasing to 25% and 30%

is therefore insufficient to calculate anything reliably.

74. Super-Carry Specification

For every higher carry tier, the model should identify:

1. the performance threshold;
2. the performance measure;
3. the economic population;
4. the applicable profit base;
5. whether the higher rate is marginal or cumulative;
6. whether catch-up or equalisation applies;
7. the catch-up percentage;
8. the residual split after equalisation;
9. interaction with earlier tiers.

Therefore:

Super-Carry Percentage Alone ≠ Super-Carry Calculation

Section O — Boundary Testing

75. Why Thresholds Need Explicit Testing

Performance waterfalls contain numerous boundaries.

Examples:

• preferred return becomes satisfied;
• catch-up begins;
• catch-up ends;
• MOIC threshold is reached;
• second carry tier begins;
• super-carry threshold is reached.

Every boundary should be tested:

Immediately Below

Exactly At

Immediately Above

76. Preferred-Return Boundary

Suppose:

• capital = €100m;
• preferred amount = €20m.

Test:

€119.999999m

€120.000000m

€120.000001m

At the first value, preferred return is not quite fully satisfied.

At the second, it is exactly satisfied.

At the third, the next tier receives a tiny amount.

The transition should occur without unexplained jumps.

77. Catch-Up Boundary

Full catch-up ends at:

€125m

Test:

€124.999999m

€125.000000m

€125.000001m

Immediately before the boundary, marginal GP allocation is 100%.

Immediately after it, marginal GP allocation becomes 20%.

The cumulative entitlement should nevertheless remain continuous.

78. MOIC Boundary

For a 1.50x threshold:

Test:

1.499999x

1.500000x

1.500001x

The exact treatment at the threshold itself depends on the governing language.

The model should implement that language explicitly rather than rely on an arbitrary greater-than or greater-than-or-equal programming choice.

79. Combined-Hurdle Boundaries

For:

8% IRR AND 1.5x MOIC

testing only the case where both are comfortably exceeded is insufficient.

The model should also test:

• IRR above, MOIC below;
• IRR below, MOIC above;
• both immediately below;
• one exactly at threshold;
• both exactly at threshold;
• both immediately above.

Boundary testing is therefore an economic control, not merely a software test.

Section P — Common Calculation Errors

80. Compounding Cumulative Contributions from Fund Inception

Suppose:

• €50m contributed in Year 1;
• €50m contributed in Year 4;
• calculation date = Year 5.

Incorrect:

€100m × 1.08⁵

This treats the Year 4 contribution as if it had existed since Year 1.

The calculation must preserve the economic dates of the underlying cash flows.

81. Giving Every Contribution a Full Year's Return at a Common Compounding Date

Suppose €30 million is contributed one month before the annual common compounding date.

Applying:

€30m × 8%

would give the contribution a full year's return.

Under a methodology that accrues from the actual economic date, that is wrong.

The compounding date determines when accrued return is capitalised.

It does not automatically determine the length of the accrual period.

82. Assuming Every Contribution Has Its Own Anniversary

The reverse error is equally possible.

A model may automatically create an annual anniversary for every contribution.

That is wrong if the governing economics require common-date compounding.

Therefore:

Individual Cash-Flow Accrual ≠ Automatically Individual-Anniversary Compounding

83. Treating Accrued Return as Immediately Compounded

Suppose preferred return accrues daily but compounds annually.

A model might incorrectly add each day's accrual immediately to the next day's preferred-return base.

That would effectively create daily compounding.

But:

Daily Accrual + Annual Compounding ≠ Daily Compounding

This is exactly why accrual frequency and compounding frequency must be separated.

84. Treating a Preferred-Return Balance as an IRR Without Testing Equivalence

A balance-based preferred-return calculation can resemble an IRR hurdle in simple cases.

That does not mean the two remain equivalent when there are:

• multiple contributions;
• intermediate distributions;
• recalls;
• irregular dates;
• different compounding rules.

The governing economics determine which method applies.

85. Applying 20% Carry Immediately After Crossing a Soft Hurdle

At €22 million profit in our earlier example:

Correct carry:

€2m

Shortcut:

€22m × 20% = €4.4m

The shortcut ignores the fact that the waterfall is still inside the catch-up tier.

86. Confusing 100% Catch-Up with 100% Carry

A 100% catch-up means that during a particular tier:

100% of the relevant incremental amount is allocated to the GP

until the defined catch-up condition is satisfied.

It does not mean that the GP receives 100% of total profits.

Therefore:

Catch-Up Percentage ≠ Carry Percentage

87. Treating Super Carry as Automatically Retrospective

A 30% carry tier above a threshold may mean:

• 30% only on incremental profit above that threshold;

or:

• an equalisation mechanism eventually gives the GP 30% of a broader cumulative profit base.

Those are economically different.

The calculation must not choose between them without a rule.

Section Q — Reconciliation and Controls

88. Preferred-Return Roll-Forward

A balance-based preferred-return calculation should be capable of reconciliation.

Conceptually:

Opening Accrued Preferred Return

+ New Accrual

+ Compounding Effect

− Preferred Return Paid

= Closing Accrued Preferred Return

The precise form depends on the methodology.

But the movement should be explainable.

89. Capital Roll-Forward

Similarly:

Opening Unreturned Capital

+ New Relevant Contributions

− Capital Returned

= Closing Unreturned Capital

The capital balance and preferred-return balance should not be conflated.

90. Compounding Control

For common-date compounding, the model should be able to show:

1. opening compounded base;
2. contributions during the period;
3. distributions during the period;
4. accrual by interval;
5. accrued preferred return at compounding date;
6. amount capitalised;
7. new compounded base.

This provides a transparent bridge from one compounding date to the next.

91. IRR Hurdle Control

If the model solves for a distribution amount that should produce exactly an 8% hurdle:

Recalculate the IRR after allocation.

Expected:

IRR ≈ 8%

within the specified precision.

The calculation therefore validates its own hurdle solution.

92. Catch-Up Control

After a full catch-up, test:

GP Cumulative Relevant Profit / Total Cumulative Relevant Profit = Target Carry Percentage

For:

• LP preferred profit = €20m;
• GP catch-up = €5m:

€5m / €25m = 20%

The control confirms the catch-up.

93. Super-Carry Control

After an equalised 25% tier, if the economics require the GP to have 25% of the defined cumulative profit base:

Cumulative GP Carry / Defined Cumulative Profit Base = 25%

If the model instead produces:

22.3%

then either:

• equalisation is incomplete;
• the wrong base was used;
• or the structure is actually marginal rather than equalised.

Controls should test the economic objective of the tier, not merely its arithmetic.

Section R — A Complete Comparative Example

94. The Investment

Assume:

• contribution = €100m;
• final distribution = €180m;
• total profit = €80m.

We will compare several waterfalls.

Waterfall A

20% carry after return of capital.

Waterfall B

€20m hard hurdle, then 20%.

Waterfall C

€20m soft hurdle, full catch-up, then 20%.

Waterfall D

1.5x hard MOIC hurdle, then 20%.

95. Waterfall A

Capital:

€100m

Profit:

€80m

Carry:

€16m

LP:

€164m

96. Waterfall B

Capital:

€100m

Hard hurdle:

€20m

Remaining:

€60m

Carry:

€12m

LP:

€168m

97. Waterfall C

Capital:

€100m

Preferred:

€20m

Catch-up:

€5m

Residual:

€55m

Residual carry:

€11m

Total carry:

€16m

LP:

€164m

98. Waterfall D

1.5x threshold:

€150m

Distribution:

€180m

Excess:

€30m

Carry:

€6m

LP:

€174m

99. Comparison

Everything about the investment is identical.

Only the waterfall changed.

Therefore:

Same Investment Performance + Different Waterfall Architecture = Different Carry

Section S — A Complete Compounding Specification

100. Why "8% Compounded Annually" Is Not Enough

Consider:

The waterfall states:

8% preferred return, compounded annually.

Before calculating, we still need to know:

1. What is the economic date of each contribution?
2. Does each contribution have its own anniversary?
3. Or is there a common compounding date?
4. How is return accrued between compounding dates?
5. What day-count convention applies?
6. How does the €40 million distribution affect capital?
7. Does it first satisfy preferred return or capital?
8. If accrued preferred return is unpaid, does it continue accruing?
9. If so, from when does it enter the compounding base?
10. How is the final distribution date treated?

Until those questions are answered, there is no unique calculation.

101. Version 1 Specification

An individual-anniversary specification might state:

• each relevant contribution begins accruing on its economic date;
• accrual occurs according to the specified day-count convention;
• each contribution's accrued preferred return is capitalised on each anniversary of that contribution;
• accrued preferred return between anniversaries does not itself earn preferred return until capitalised;
• distributions reduce balances according to the contractual waterfall;
• reductions are allocated to contribution tranches according to a defined rule.

The model can now calculate.

102. Version 2 Specification

A common-date specification might state:

• each relevant contribution begins accruing on its individual economic date;
• accrual occurs according to the specified day-count convention;
• all accrued preferred return is capitalised on 31 December;
• accrued preferred return before 31 December does not itself earn preferred return;
• contributions and distributions occurring during the year alter the relevant base from their economic dates;
• distributions are applied according to the contractual allocation sequence.

Again, the model can now calculate.

The two specifications both describe:

8% preferred return compounded annually.

But they are not the same economics.

Section T — From Performance Mechanics to Fund Architecture

103. What Part II Has Established

Part II introduced the time and performance dimensions of the waterfall.

The first principle is:

Each Cash Flow Has Its Own Economic Date

A cumulative cash-flow total cannot by itself describe a time-based hurdle.

But individual economic dates do not automatically imply individual compounding dates.

Therefore:

Each Cash Flow Having Its Own Economic Date ≠ Each Cash Flow Having Its Own Compounding Date

Compound preferred return requires separate consideration of:

Accrual

and:

Compounding

because:

Accrual Determines How Much Return Has Been Earned

while:

Compounding Determines When Earned Return Begins Earning Return

Thus:

Accrual Frequency ≠ Compounding Frequency ≠ Compounding Date

Part II developed two distinct structures:

Individual Cash-Flow Accrual → Individual Anniversary Compounding

and:

Individual Cash-Flow Accrual → Common-Date Compounding

Neither should be assumed.

The governing economics determine the methodology.

Part II also established:

Unreturned Capital ≠ Accrued Preferred Return

and:

Preferred Return Accrued ≠ Preferred Return Paid

Once IRR is introduced:

Amount + Economic Date → Performance

and:

Preferred-Return Balance ≠ Automatically IRR

MOIC introduces a different performance dimension:

Same MOIC ≠ Same IRR

and:

Same IRR ≠ Same MOIC

Where several tests interact:

AND ≠ OR

Where catch-up applies:

Catch-Up Percentage ≠ Carry Percentage

and:

Being in Catch-Up ≠ Completing Catch-Up

Where multiple performance tiers exist:

Marginal Carry Rate ≠ Cumulative Effective Carry Rate

and:

Higher Carry Percentage ≠ Complete Super-Carry Definition

The broader lesson is that apparently simple headline terms are insufficient to reproduce a waterfall.

8% Hurdle + 20% Carry

is not a calculation specification.

A complete calculation requires the economics to be translated into rules governing:

• economic population;
• cash-flow classification;
• economic dates;
• accrual;
• compounding;
• performance measurement;
• hurdle conditions;
• catch-up;
• allocation order;
• higher performance tiers; and
• calculation precision.

Only then can the waterfall be executed deterministically.

Economic Terms → Calculation Specification → Economic Events → Performance State → Tier Allocation → Carry Result → Reconciliation

Part III now changes the question.

Part II asked:

How do the hurdle and performance tiers work?

Part III asks:

Over which investments, expenses, cash flows and economic streams do those rules operate?

The same 8% hurdle, 100% catch-up and 20% carry can produce very different results depending on whether it operates:

• across the whole fund;
• investment by investment;
• across a hybrid economic perimeter;
• gross or net of fees and expenses;
• across one or several carry pockets; or
• separately across different economic streams.

The next fundamental principle is therefore:

Correct Hurdle Calculation + Wrong Economic Perimeter = Wrong Carry

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References and Further Reading

Carried Interest and Waterfall Mechanics

• Stefanova, Mariya (ed.). The Definitive Guide to Carried Interest. Private Equity International, 2017. See in particular the chapters addressing waterfall calculations, modelling carried interest and the implementation of waterfall mechanics.
• Draisma, Gert-Tom. “Using Technology to Calculate and Recognise Carried Interest on the GP Side.” In Mariya Stefanova (ed.), The Definitive Guide to Carried Interest. Private Equity International, 2017, Chapter 11.

Preferred Return, Hurdles and Catch-Up

• Institutional Limited Partners Association (ILPA). ILPA Principles 3.0: Fostering Transparency, Governance and Alignment of Interests for General and Limited Partners. 2019. See in particular the principles concerning carried interest, preferred returns, calculation methodologies, waterfall structures and alignment between GPs and LPs.
• Institutional Limited Partners Association (ILPA). Private Equity Principles. Earlier ILPA guidance concerning preferred returns, carried interest, waterfall structures, calculation of carried interest, clawback and alignment of interests.
• Invest Europe. Professional Standards Handbook. See in particular the sections concerning fund terms, carried interest, hurdle rates, catch-up provisions, distributions and fund economics.
• Invest Europe. Professional Standards Handbook — Terms in the Fund Documents. See in particular the guidance concerning carried interest rates and bases of calculation, preferred returns, hurdle rates, catch-up provisions, escrow, clawback and distribution waterfalls.

IRR, MOIC and Performance Measurement

• CFA Institute. Global Investment Performance Standards (GIPS®) for Firms. See in particular the provisions and guidance concerning money-weighted returns, external cash flows and performance measurement for private-market investments.
• CFA Institute. GIPS Standards Handbook for Firms. See the discussion and examples concerning money-weighted rates of return, timing of external cash flows and private-market performance calculations.
• CFA Institute. CFA Program Curriculum — Alternative Investments. See the treatment of private equity performance measurement, internal rate of return (IRR), multiples of invested capital and the effect of cash-flow timing on investment performance.
• Kaplan, Steven N. and Antoinette Schoar. “Private Equity Performance: Returns, Persistence, and Capital Flows.” The Journal of Finance, Vol. 60, No. 4, 2005, pp. 1791–1823. See particularly the discussion of private equity performance measurement and the use of IRR and investment multiples.

IRR Mathematics and Multiple Solutions

• Lorie, James H. and Leonard J. Savage. “Three Problems in Rationing Capital.” The Journal of Business, Vol. 28, No. 4, 1955, pp. 229–239. Classic discussion of limitations in internal-rate-of-return analysis, including problems arising from non-conventional cash-flow patterns.
• Teichroew, Daniel, Alexander A. Robichek and Michael Montalbano. “Mathematical Analysis of Rates of Return Under Certainty.” Management Science, Vol. 11, No. 3, 1965, pp. 395–403. Mathematical treatment of rates of return and the problems that can arise when cash-flow patterns permit multiple rate-of-return solutions.

Subscription Facilities and Economic Dates

• Institutional Limited Partners Association (ILPA). Subscription Lines of Credit and Alignment of Interests: Considerations and Best Practices for Limited and General Partners. June 2017. See particularly the guidance concerning the effect of subscription facilities on IRR, preferred-return calculations and the appropriate date from which preferred-return hurdles should be calculated.
• Institutional Limited Partners Association (ILPA). ILPA Principles 3.0. 2019. See particularly the guidance concerning subscription facilities, transparency of their effect on reported performance and alignment of interests.

Fund Documentation and Calculation Conventions

• Invest Europe. Professional Standards Handbook — Forming and Raising a Fund. See the discussion of economic terms, carried interest, preferred returns, catch-up mechanisms, subsequent closings and equalisation.
• Invest Europe. Professional Standards Handbook — Managing Your Relationship with LPs. See particularly the guidance concerning distributions, carried-interest calculations, classification of distributions, recallability, taxation and clawback.
• Institutional Limited Partners Association (ILPA). ILPA Reporting Template and Reporting Guidance. See the reporting framework for contributions, distributions, fees, expenses, carried interest and other information required to understand and reconcile private fund economics.

Mathematical and Financial Conventions

• International Capital Market Association (ICMA). ICMA Primary Market Handbook. Reference material for commonly used interest accrual and day-count conventions in financial calculations.
• International Swaps and Derivatives Association (ISDA). 2006 ISDA Definitions. Reference source for established financial-market definitions of day-count fractions, business-day conventions and interest-calculation methodologies.

Further Reading

• Phalippou, Ludovic. Private Equity Laid Bare. Routledge. See particularly the discussion of private equity cash flows, performance measurement, IRR, investment multiples, fees and carried interest.
• Metrick, Andrew and Ayako Yasuda. Venture Capital and the Finance of Innovation. Wiley. See the treatment of private fund economics, carried interest, preferred returns and the relationship between fund performance and GP compensation.
• Gompers, Paul A. and Josh Lerner. The Venture Capital Cycle. MIT Press. See the discussion of limited partnership economics, compensation structures, carried interest and the contractual relationship between general and limited partners.

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