Fund economics and the waterfall

Committed, contributed, invested and paid-in capital

Four different denominators that are routinely used interchangeably and are not the same number. Committed capital is what the LP has promised. Contributed or paid-in capital is what has actually been called and paid, including capital called to pay fees and expenses. Invested capital is the cost basis of the investments themselves. Net invested capital is invested capital less the cost basis of investments already realised.

Field	Value
Formula	PIC = I + F + X, where I is investment cost, F is management fees called and X is partnership expenses called. Every multiple must state which of C, PIC or I is its denominator
Worked, reference fund	C = 500.0; PIC = 500.0; I = 425.0; F = 66.2; X = 8.8. Check: 425.0 + 66.2 + 8.8 = 500.0
Same proceeds, three multiples	935.0/425.0 = 2.2000x on invested capital; 935.0/500.0 = 1.8700x on paid-in; 848.0/500.0 = 1.6960x net to the LP on paid-in
Spread	0.5040x of multiple between the number a deal team quotes and the number the LP receives, on one fund

• The gap between 2.2000x and 1.8700x is not fees on the way out; it is the fact that 75.0 of the 500.0 called never bought an asset. A gross MOIC quoted on invested capital is arithmetically insulated from the fee load by construction.
• PIC can exceed committed capital where the LPA permits recycling, and can fall short of it where the fund never fully deploys. Neither case is unusual, so PIC/C is a real number to ask for rather than an assumed 1.00x.
• The most common reporting error is a TVPI computed on invested capital and a DPI computed on paid-in in the same document. Check that DPI + RVPI equals TVPI before reading any of them.

Source: ILPA Reporting Template defines paid-in capital, DPI, RVPI and TVPI for LP reporting.

The management fee base during and after the investment period

During the investment period the fee is normally charged on committed capital, which pays the manager for readiness rather than for assets. After the investment period the base changes to something that shrinks as the fund harvests: invested capital, net invested capital, or net asset value. The base matters more than the rate.

Field	Value
Formula	Fee_t = rate_t * base_t. Total fee as a share of commitments = sum of Fee_t / C; as a share of capital actually deployed = sum of Fee_t / I
Worked, investment period	2.00 percent of 500.0 for five years = 50.00, against 425.0 of cost eventually deployed and only 105.0 deployed in year 1
Worked, harvest period	1.50 percent of the unrealised cost basis: 1.50 percent of 380.0, 320.0, 220.0, 120.0 and 40.0 = 5.70 + 4.80 + 3.30 + 1.80 + 0.60 = 16.20
Total	66.20 = 13.240 percent of commitments = 15.576 percent of the 425.0 invested
Fee on commitments throughout	100.00, or 20.000 percent of commitments - a 33.80 difference on identical headline terms

• A NAV base is not a step-down. On the reference fund a 1.50 percent NAV fee costs 77.780 against 66.200 on unrealised cost, because the portfolio is marked above cost through the harvest years. A NAV base also pays the manager more when it marks its own book up, which is the reason LPs resist it.
• The single most valuable disclosure here is the fee schedule in currency by year rather than as a rate. A rate hides the base; a schedule cannot.
• Ask which day the base is struck on and whether it is averaged. A base measured at period end on a fund that realises in the final month of each period is materially cheaper than one averaged daily, on identical words.

The step-down and what actually triggers it

The reduction in the management fee at the end of the commitment period. Three things can step: the rate, the base, or both. A step-down that changes only the rate while leaving the base on commitments is a much smaller concession than one that moves the base to invested capital.

Field	Value
Formula	Post-investment-period fee = rate_2 * base_2. Compare against rate_1 * C to size the concession
Base steps, rate does not	2.00 percent of unrealised cost: 71.600 total
Rate steps, base does not	Rate declining 10 percent of itself each year on commitments: 86.856 total
Worked, both step - the reference fund	1.50 percent of unrealised cost: 5.70 + 4.80 + 3.30 + 1.80 + 0.60 = 16.20 in the harvest years, so 66.200 in total
Neither steps	100.000 total

• The trigger is usually the earlier of the end of the commitment period and the first closing of a successor fund. The second limb is the one that matters, because it stops an LP paying a full fee on a harvesting fund while paying a second full fee on the successor.
• A step-down measured on invested capital keeps paying on a written-down asset unless the definition says net of write-downs. On the reference fund, investment B is worth 30.0 against a cost of 60.0 - a fee on cost charges for the full 60.0 until realisation.
• The step-down is one of very few fee terms with no offsetting argument for the manager once the successor fund has closed, which makes the successor-fund trigger the easiest of the fee points to win.

Fee offsets - transaction, monitoring and break-up fees

Fees the manager or its affiliates receive from portfolio companies or from failed transactions, credited against the management fee otherwise payable. The two variables are the offset percentage and the completeness of the definition of what counts.

Field	Value
Formula	Fee borne by LPs = gross management fee - s * O, where O is offsettable fee income and s the offset share. The GP retains (1 - s) * O
Setup	Assume 12.0 of transaction, monitoring and break-up fee income over the fund's life, chosen for legibility
Worked, 100 percent offset	Fee borne by LPs falls from 66.20 to 54.20; paid-in falls from 500.00 to 488.00; LP DPI rises from 1.6960x to 1.7328x; net IRR rises from 11.9825 percent to 12.4116 percent, a gain of 42.9 basis points
The counterintuitive part	GP carry rises from 87.0000 to 89.4000, because profit rises from 435.0 to 447.0. The offset costs the GP 12.00 of fee income and returns 2.40 of carry, a net cost of 9.60
Partial offsets	80 percent: LPs bear 56.60, GP keeps 2.40. 50 percent: LPs bear 60.20, GP keeps 6.00. 0 percent: LPs bear 66.20, GP keeps 12.00

• The percentage is negotiated and reported; the definition is not. What matters is whether the offset captures fees received by affiliates and operating-partner entities, whether it captures fees charged to a portfolio company for services rather than for the transaction, and whether unused offset credits carry forward when the fee in a period is already zero.
• An offset credit that cannot be carried forward is worth nothing in a year when the management fee is small. On the reference fund the year-10 fee is 0.60, so an offset arising in year 10 is almost entirely wasted unless it carries back or forward.
• Break-up fees are the cleanest case for a full offset, because the expenses of the failed deal were borne by the fund. Monitoring fees are the least clean, and an accelerated monitoring fee taken at exit is the item most worth reading in the fee-and-expense schedule.

Source: ILPA Private Equity Principles address fee offsets and the treatment of transaction and monitoring fees.

Carried interest

The GP's share of fund profit, expressed as a percentage of profit rather than as a fee on assets. Under a whole-fund waterfall that has cleared its catch-up, total carry is exactly the carry rate multiplied by total fund profit, and no term in the waterfall changes that total - only its timing.

Field	Value
Formula	Total carry under a whole-fund waterfall, once the catch-up has completed = k * (D_total - PIC). Total carry under a deal-by-deal waterfall = k * sum of positive per-investment profits
Worked, whole-fund	0.20 * (935.0 - 500.0) = 0.20 * 435.0 = 87.0000
Worked, deal-by-deal	0.20 * (57.0588 + 192.3529 + 107.3529 + 85.8824 + 32.9412) = 0.20 * 475.5882 = 95.1176
The difference	0.20 * 40.5882, the shortfall on investment B, which the whole-fund waterfall nets and the deal-by-deal waterfall does not
Carry as a share of gross proceeds	87.0000/935.0 = 9.305 percent whole-fund; 95.1176/935.0 = 10.173 percent deal-by-deal

• The identity is worth internalising: on a fund past its catch-up, arguing the hurdle down does not reduce total carry by a penny. The terms that change total carry are the waterfall type, the definition of profit, and whether losses net.
• Carry is charged on profit over contributed capital, which includes the 75.0 of fees and expenses. That is favourable to the LP relative to a carry charged over invested capital only, and it is worth checking which the LPA says.
• A carry rate above the market default is sometimes paired with a higher hurdle and presented as a trade. On a fund that clears its catch-up the rate is real and the hurdle is not, so the trade is not symmetric.

Preferred return, and what it accrues on

A rate of return the LP must receive before the GP participates in profit. Three variables define it: the rate, the base it accrues on, and whether it compounds. The base is almost always contributed capital reduced as capital is returned, which makes the accrual path-dependent on the distribution schedule.

Field	Value
Formula	PA_t = PA_(t-1) + h * UC_(t-1), where UC is unreturned contributed capital. Distributions reduce UC first and then PA
Worked, accrual	Year 2: 8.00 percent of the 119.300 opening balance = 9.544. Year 5: 8.00 percent of 430.800 = 34.464. Cumulative unpaid pref peaks at 147.120 at the end of year 7
Worked, total paid	150.544 over the fund's life, being 30.109 percent of commitments and 34.610 percent of the 435.0 of profit
Effect of the rate	6.00 percent accrues 112.908; 10.00 percent accrues 188.180. The pref is close to linear in the rate here because the capital path is fixed
Counterintuitive	A higher gross MOIC produces a smaller pref. At 2.6400x the pref paid is 143.120 against 150.544 at 2.2000x, because capital comes back sooner and stops accruing

• Whether the pref accrues on all contributed capital or only on capital used to fund investments is a real distinction worth 75.0 of base on the reference fund. Accrual on all contributions is the LP-favourable formulation and the common one.
• The order of tiers 1 and 2 is not universal. Paying the pref before returning capital produces the same totals in the end but a different interim path, and a materially different answer if the fund is terminated early.
• A pref that compounds quarterly rather than annually at the same nominal rate is a higher pref. On the reference fund an 8.00 percent rate compounded quarterly is an effective 8.243 percent, which raises the accrual accordingly. Ask for the compounding convention, not just the rate.

On a successful fund the hurdle is a timing term, not an economic one

With a full catch-up, once cumulative profit distributed exceeds the catch-up boundary, the LP has received exactly (1 - k) of profit and the GP exactly k, whatever the hurdle rate was. The hurdle changes total carry only if the fund never reaches that boundary.

Field	Value
Formula	The hurdle affects total carry only while cumulative profit P < Pref * c/(c - k). With c = 1 and k = 0.20 that boundary is 1.25 * Pref
Worked, seven hurdles	At 0, 6, 7, 8, 9, 10 and 12 percent the total GP carry on the reference fund is 87.0000 in every case, and LP DPI is 1.6960x in every case
What does move	LP net IRR ranges from 11.9605 percent at a 0.00 percent hurdle to 12.0611 percent at 10.00 percent - about 10 basis points across the whole range
The boundary	At an 8.00 percent hurdle the pref is 150.544 and the boundary profit is 188.180, reached when gross proceeds exceed 705.37, a gross MOIC of 1.6597x
Below the boundary	At a gross MOIC of 1.5400x the hurdle removes 30.9000 of carry entirely; at 1.6425x it removes 6.2776; at 1.7600x it removes nothing

• This is the reason a GP concedes a higher hurdle readily and resists a lower catch-up share fiercely. The hurdle is a deferral in the outcomes the GP is underwriting to; the catch-up share is a permanent transfer in the outcomes it is not.
• The result reverses for a mediocre fund. Between roughly 1.32x and 1.66x gross MOIC on the reference fund the hurdle is the single most valuable LP term in the waterfall, worth up to 30.9 of carry. An LP negotiating the hurdle is buying protection precisely in the outcome band where funds most often land.
• The corollary for a hard hurdle - one with no catch-up, so the GP takes k only of profit above the pref - is that it does change the total. A hard 8.00 percent hurdle on the reference fund would give the GP 0.20 * (435.0 - 150.544) = 56.891 rather than 87.0000.

Catch-up, and the algebra of its boundary

The tier that restores the GP to its target share of total profit after the preferred return has been paid to the LP. Inside the catch-up band the GP receives share c of each distribution until its cumulative receipts equal k of cumulative profit distributed. c is the negotiated term and it decides how fast, not how much.

Field	Value
Formula	G = k*Pref/(c - k). GP receives c*G = c*k*Pref/(c - k). Cumulative profit when the catch-up completes = Pref * c/(c - k). The catch-up never completes if c <= k
Worked, 100 percent catch-up	G = 0.20 * 150.544/0.80 = 37.6360, all to the GP. Profit at completion = 150.544 * 1/0.80 = 188.1800
Worked, 80/20 catch-up	G = 0.20 * 150.544/0.60 = 50.1813; GP receives 0.80 * 50.1813 = 40.1451 and the LP 10.0363. Profit at completion = 150.544 * 0.80/0.60 = 200.7253
Worked, 50/50 catch-up	G = 0.20 * 150.544/0.30 = 100.3627; GP receives 50.1813. Profit at completion = 150.544 * 0.50/0.30 = 250.9067
Check on the reference fund	37.6360 = 0.25 * 150.544, and the GP's cumulative carry at completion is 37.6360 = 0.20 * 188.1800

• The catch-up share is where the argument about the hurdle is actually settled. A GP that concedes a higher hurdle and holds a 100 percent catch-up has conceded timing. A GP that concedes a 50/50 catch-up has conceded a slice of every outcome between the pref and 1.667 times the pref.
• A catch-up share equal to or below the carry rate never completes, so the GP never reaches its target share. That is the mathematical description of a hard hurdle expressed in catch-up language, and it is why the two terms are alternatives rather than complements.
• The catch-up band on the reference fund runs from 150.544 to 188.180 of cumulative profit against a total of 435.0. It looks small stated that way and it is the entire difference between the GP receiving 87.0 and receiving 56.9.

Deal-by-deal against whole-fund on identical cash flows

The two waterfalls differ in what they net. A whole-fund waterfall returns all contributed capital and pays the preferred return on all of it before any carry. A deal-by-deal waterfall tests each realisation on its own, so carry is paid on winners before losers are known.

Field	Value
Formula	Whole-fund carry = k * (D_total - PIC). Deal-by-deal carry = k * sum of max(0, R_j - A_j) where A_j is attributable capital. The difference is k * sum of max(0, A_j - R_j), the losses that never net
Worked, the difference	95.1176 - 87.0000 = 8.1176 = 0.20 * 40.5882, the shortfall on investment B
Timing	Deal-by-deal pays the first carry in year 5 and 49.8824 by the end of year 7. Whole-fund pays nothing until year 8
Cost to the LP	56.8 basis points of net IRR before any clawback; 39.8 basis points even if the full 8.1176 clawback is paid in year 10
Attributable capital convention	Each investment's cost is grossed up by 500.0/425.0 = 1.1764706 so fees and expenses are allocated across the six investments and the six amounts sum to 500.0 exactly

• The residual 39.8 basis points after a full clawback is the honest measure of what deal-by-deal costs an LP on a fund with one loss: it is the time value of carry paid early and returned late, and no clawback recovers it.
• The gross-up convention is the whole argument in practice. An LPA that returns only the realised investment's own cost, with no allocation of fees and expenses, produces a materially lower hurdle per deal and therefore more carry sooner. Read the definition of the capital to be returned before modelling anything.
• Deal-by-deal is far more valuable to a GP with dispersed outcomes than to one with uniform outcomes. If every investment returned exactly 2.2000x, the two waterfalls would produce the same total carry and differ only in timing. It is the loss on B that creates the 8.1176.

GP clawback

An obligation on the GP to return carry it has already received where cumulative carry exceeds its entitlement measured across the whole fund at termination. It exists because a deal-by-deal waterfall pays carry on early winners before later losses are known.

Field	Value
Formula	Clawback = max(0, carry actually distributed - k * (D_total - PIC)). Usually capped at the carry received net of taxes paid on it
Worked, gross	95.1176 - 87.0000 = 8.1176, being 8.534 percent of the carry the GP received
After tax	If the obligation is capped at carry net of taxes at an assumed 40.00 percent combined rate, the recoverable amount falls to 4.8706 and the LP bears a 3.2471 shortfall
Interest	A clawback returned without interest hands the GP the time value of 8.1176 for five years. At the 8.00 percent pref rate that is 8.1176 * (1.08^5 - 1) = 3.8094
Net of the clawback	LP net IRR is 11.5841 percent against 11.9825 percent under a whole-fund waterfall, a 39.8 basis point residual gap

• A clawback is only as good as the balance sheet behind it. The obligation usually sits with the carry vehicle and its individual members, several years after the individuals concerned have paid tax on the money and may have left the firm. Joint and several liability among the carry recipients is the term that converts a paper obligation into a collectible one.
• An after-tax cap is standard and is also the single largest leak: it converts a full clawback into a partial one at exactly the rate of tax. An LP that accepts the cap should ask that the assumed rate be the highest marginal rate actually applicable rather than a blended one.
• Interim clawback testing - a mandatory calculation at fixed dates during the fund's life rather than only at termination - is worth more than any drafting improvement to the obligation itself, because it catches the exposure while the carry vehicle still holds cash.

Escrow securing the clawback

A portion of each carry distribution held back in an account rather than paid to the carry recipients, released only when a clawback test is satisfied. It converts an unsecured contractual obligation into cash on hand.

Field	Value
Formula	Escrow held = e * carry distributed. Uncovered exposure = max(0, clawback - escrow held)
Worked, exposure	Carry distributed 95.1176; clawback 8.1176. The escrow that exactly covers it is 8.534 percent of carry distributions
At a 30 percent escrow	28.5353 held against an 8.1176 exposure - covered 3.5 times over
At no escrow	The full 8.1176 is an unsecured claim on the carry vehicle, and 3.2471 of it is unrecoverable if the obligation is capped after tax
Cost to the GP	A 30 percent escrow defers 28.5353 of carry. Deferred from year 5 to year 10 at the 8.00 percent pref rate, the time value is 28.5353 * (1.08^5 - 1) = 13.3920

• The escrow percentage looks like the negotiation and the release condition is the negotiation. An escrow released annually on a rolling test is nearly worthless; one released only at termination or on a test that assumes remaining investments are written to a stated discount is the version that holds.
• Sizing is not arbitrary. The maximum possible clawback is k multiplied by the largest plausible aggregate shortfall on the unrealised portfolio. On the reference fund at year 7 the unrealised cost basis is 220.0, so a total loss of it would create a clawback of up to 44.0 - which is what an escrow should be sized against, not against the realised exposure.
• An escrow and a whole-fund waterfall are substitutes for the same risk. A GP offered the choice will normally prefer the escrow, which tells you which is cheaper for it.

The GP commitment

Capital the GP and its principals commit to the fund alongside the LPs, normally free of management fee and carried interest. It is the alignment term most often quoted and least often sized against the carry it sits beside.

Field	Value
Formula	Alignment ratio = expected carry / GP commitment. A total loss of the GP commitment is offset by carry arising on gross profit of GP_commitment / k
Worked, reference fund	GP commitment 10.0, being 2.00 percent of the 500.0 of LP commitments. Total fund 510.0
Alignment ratio	87.0000 of carry against 10.0 of own capital = 8.7000x. At a 1.00 percent commitment it is 17.4000x; at 5.00 percent it is 3.4800x
Symmetry	Losing the entire 10.0 commitment is offset by 10.0 of carry, which arises on 50.0 of gross fund profit - 11.5 percent of the reference fund's actual profit
Return on the GP's own capital	Free of fee and carry, 10.0 deployed into investments at the fund's 2.2000x gross MOIC returns 22.0, against 16.960 for 10.0 of LP capital at the LP's 1.6960x net

• The question that matters is not the percentage but whether it is cash from the individuals or funded out of fee income and waived management fee. A commitment funded by a fee waiver is not capital at risk in the sense the term implies; it is deferred compensation with a different tax profile.
• Alignment scales with the ratio, not the percentage. A large fund with a 2.00 percent GP commitment has a much larger absolute commitment and exactly the same alignment ratio, because carry scales too.
• The GP's capital being exempt from fee and carry is the reason a GP's own reported return on the fund is not comparable to any LP's. The two numbers differ by the entire fee and carry load - 0.5040x of multiple on the reference fund.

Hard hurdle against soft hurdle

A soft hurdle, the standard formulation, gives the GP carry on all profit once the hurdle is cleared, using the catch-up to get there. A hard hurdle gives the GP carry only on profit above the hurdle amount, which is permanently excluded from the carry base.

Field	Value
Formula	Soft hurdle carry, past the catch-up = k * P. Hard hurdle carry = k * max(0, P - Pref)
Worked, soft	0.20 * 435.0 = 87.0000
Worked, hard	0.20 * (435.0 - 150.544) = 0.20 * 284.456 = 56.8912
Difference	30.1088 of carry, being 6.022 percent of committed capital and 34.6 percent of the GP's carry
Effect on the LP	LP distributions rise from 848.0000 to 878.1088, a DPI of 1.7562x rather than 1.6960x

• A hard hurdle is the only version in which the hurdle rate itself changes total economics on a successful fund. That is why arguments about the rate and arguments about hardness are not the same argument, and the second one is worth far more.
• Hard hurdles are common in credit and real assets and uncommon in buyout. The structural reason is that a hard hurdle on a strategy with a low expected multiple removes most of the carry, while on a high-multiple strategy it removes a smaller proportion - so the term migrates to where it costs the manager least.
• A soft hurdle with a 100 percent catch-up and no hurdle at all are the same instrument above a gross MOIC of 1.6597x on the reference fund. If an LP wants the hurdle to mean something in good outcomes, hardness is the term to ask for, not the rate.