Return metrics

MOIC (multiple on invested capital)

Total value returned and remaining, divided by capital invested at cost. It is a gross, asset-level, time-insensitive measure and is the correct metric for judging underwriting because it cannot be improved by timing.

Field	Value
Formula	MOIC = (Realised proceeds + Residual value) / Invested capital at cost
Worked	100 invested, 118 realised, 12 residual: MOIC = 130 / 100 = 1.30x
Implied annual return	IRR = MOIC^(1/n) - 1 for a single draw and single return. 1.30^(1/3) - 1 = 9.14 percent; 1.30^(1/5) - 1 = 5.39 percent.
Inverse	MOIC required for a target IRR over n years = (1 + IRR)^n. A 12.00 percent target over 3 years needs 1.4049x.

• In private credit MOIC is compressed by construction: a performing loan returns par plus coupon, so a 1.2x to 1.4x MOIC covers almost the whole distribution of good outcomes while a workout can produce 0.4x. The distribution is left-skewed, which means an average MOIC tells you almost nothing about how many loans went wrong.
• Because MOIC ignores time, it is the metric that a manager cannot flatter with a subscription line, a delayed capital call, or an early recycling. Where MOIC and IRR tell different stories, MOIC is describing the credit and IRR is describing the treasury.
• MOIC on invested capital and TVPI on paid-in capital differ by fees, expenses, and uninvested capital. They are frequently reported side by side and are not the same denominator.

DPI, RVPI, and TVPI

The three paid-in ratios. DPI is cash actually returned per unit of capital called. RVPI is the remaining mark. TVPI is their sum. The identity TVPI = DPI + RVPI holds exactly, which is what makes the split informative.

Field	Value
Formula	DPI = D / PIC; RVPI = NAV / PIC; TVPI = (D + NAV) / PIC = DPI + RVPI
Worked	PIC 100, D 118, NAV 12: DPI = 1.18x, RVPI = 0.12x, TVPI = 1.30x. Check: 1.18 + 0.12 = 1.30.
Early fund	PIC 100, D 8, NAV 105: DPI = 0.08x, RVPI = 1.05x, TVPI = 1.13x - the same TVPI as a fund at 1.13x DPI and zero RVPI, with entirely different information content

• Read the split, not the sum. A private credit fund with high DPI is a fund whose loans have repaid, which is the only unambiguous evidence of credit quality. A fund with high RVPI is a fund holding its own marks.
• DPI can be raised without a realisation, by drawing a NAV facility and distributing the proceeds. The LP's DPI rises, their RVPI falls by less than the distribution, and they are now behind a secured lender. Reconciling distributions to realisations is the check.
• In credit, RVPI should converge to zero on a schedule set by the loans' maturities. RVPI that persists past the weighted average life of the portfolio is a portfolio of amended loans, not a portfolio of unrealised gains.

Source: ILPA Reporting Template defines PIC, DPI, RVPI, and TVPI for LP reporting.

Gross versus net IRR

Gross IRR is computed on cash flows between the fund and its investments. Net IRR is computed on cash flows between the fund and its LPs, and is therefore reduced by management fees, incentive fees, fund expenses, and organisational costs, and affected by the cost and timing of any fund-level borrowing.

Field	Value
Formula	Net IRR solves 0 = sum over t of LP_CF_t / (1 + IRR)^t, where LP_CF includes capital calls (negative), distributions (positive), and the terminal NAV
Worked, the gap	Using the worked fee table: a 9.80 percent gross asset yield levered 1:1 at 6.00 percent produces 13.60 percent gross return on equity and 10.91 percent net of a 1.00 percent gross-assets management fee and a 15 percent incentive fee over a 7.00 percent hurdle. The 269 bps gap is the fee load.
Fee load framing	(2.00 + 0.69) / 19.60 = 13.7 percent of gross investment income, or 2.69 percent of equity

• A management fee quoted on gross assets is a different fee from one quoted on net assets, and the difference is exactly the leverage ratio. One percent of gross assets at 1:1 leverage is two percent of equity; at 2:1 it is three percent. Comparing headline fee rates across vehicles without normalising to the equity base is comparing nothing.
• The gross-to-net gap in private credit is proportionally larger than in private equity for the same fee schedule, because the gross return is lower. A 200 bps fee load on a 20 percent gross return is a tenth of the return; on a 10 percent gross return it is a fifth.
• Net IRR is the only number that describes what an LP received, and it is also the number most sensitive to when capital was called. Those two facts together are why gross-to-net bridges and subscription-line disclosure exist.

Why IRR and MOIC disagree

IRR is a rate and MOIC is a ratio. For a single draw and a single return, they are related by IRR = MOIC^(1/n) - 1, so the same MOIC maps to a range of IRRs depending only on the holding period. For a stream of cash flows the relationship has no closed form, and IRR additionally assumes interim distributions earn the IRR itself.

Field	Value
Formula	Single-draw case: IRR = MOIC^(1/n) - 1; equivalently MOIC = (1 + IRR)^n
Worked	MOIC 1.30x: over 2 years IRR = 14.02 percent; 3 years 9.14 percent; 5 years 5.39 percent; 8 years 3.33 percent
Reverse	A 10.00 percent IRR needs 1.10x over 1 year, 1.33x over 3 years, and 1.61x over 5. Sustaining an IRR through a longer hold requires a rising multiple.

• In a credit fund the multiple is capped near par plus coupon, so a manager cannot raise MOIC to defend an IRR through a longer hold. The only levers are shortening the hold, recycling faster, or adding leverage. That constraint - not skill - explains most IRR dispersion between credit managers with similar loss experience.
• Recycling repaid principal within the investment period raises TVPI on the same paid-in capital, so it improves both the multiple and the IRR without any change to per-loan performance. The recycling provision in the LPA is therefore a return term, and it is in the legal section.
• IRR is not additive across funds or time periods and cannot be averaged. Pooling cash flows and re-solving is the only correct aggregation.

Subscription line effect on net IRR

A subscription facility secured by uncalled LP commitments lets the fund invest before calling capital. The investment's cash flows are unchanged; the LP's are shifted later. Because IRR is a function of timing, net IRR rises while MOIC and TVPI do not.

Field	Value
Formula	IRR_reported = MOIC_after_facility_cost^(1/(n - delay)) - 1, where delay is the period funded by the facility
Worked	A 1.30x MOIC realised 3 years after the investment date. Calling capital at inception: IRR = 1.30^(1/3) - 1 = 9.14 percent. Calling capital 6 months later, with facility interest reducing the multiple to 1.2985x: IRR = 1.2985^(1/2.5) - 1 = 11.01 percent.
Effect	+187 bps of net IRR, -0.0015x of multiple. The economics got very slightly worse and the headline got materially better.

• This is the clearest case in fund reporting where a metric and the underlying economics move in opposite directions. It is not improper - the facility genuinely reduces the LP's capital-at-risk period - but any comparison of net IRRs between a fund that uses a line and one that does not is meaningless without an unlevered restatement.
• The facility cost is a real drag on the multiple, borne by the LPs, in exchange for an IRR improvement that accrues to the manager's track record and, where the hurdle is IRR-based, to the manager's carry.
• Ask for net IRR computed both with and without the facility, and for the average number of days between investment and capital call. The second number tells you the size of the first adjustment before it is calculated.

Source: ILPA Subscription Lines of Credit guidance recommends disclosure of net IRR with and without the facility.

Loss-adjusted yield

The all-in yield reduced by the expected annualised credit loss, being the annual default rate multiplied by loss given default. It converts a promised yield into an expected yield and is the only basis on which two loans at different risk can be compared.

Field	Value
Formula	LAY = Y - d * (1 - R), where d is the annualised default rate on par and R is the recovery on defaulted par. LGD = 1 - R.
Worked	Y = 9.80 percent, d = 2.00 percent, R = 60 percent: LGD = 40 percent, expected loss = 2.00 * 0.40 = 0.80 percent, LAY = 9.80 - 0.80 = 9.00 percent
Same loss, different mix	d = 4.00 percent with R = 80 percent gives the same 0.80 percent expected loss and the same 9.00 percent LAY, from a very different credit profile
Spread decomposition	Of a 580 bps all-in spread, 80 bps is expected loss and 500 bps is compensation for everything else - illiquidity, unexpected loss, and the manager's fee

• Default rate and recovery are not independent, and treating them as separate inputs is the standard error. Defaults cluster in the conditions that also depress recoveries, so the product d * LGD computed from independently-estimated averages understates loss in the states of the world that matter.
• The inputs above are illustrative parameters chosen to make the arithmetic legible. Any specific default or recovery figure is an estimate about a particular portfolio in a particular period, and a loss-adjusted yield is only as good as the two numbers fed into it.
• LAY is a first moment and credit returns are not symmetric. Two portfolios with identical LAY and different loss dispersion are not equivalent, and the difference is what fund-level leverage amplifies.
• Recovery must be measured on the tranche, not the credit. First-lien and second-lien recoveries on the same defaulted borrower are different numbers, and applying a blended figure to a junior position overstates it.

Breakeven default rate

The annualised default rate at which a position's loss-adjusted yield falls to a chosen threshold - zero, or a hurdle rate, or the point at which levered equity is wiped out. It restates a yield as the cushion it buys, which is a more useful comparison than the yield itself.

Field	Value
Formula	d* = (Y - h) / (1 - R), where h is the threshold return. With fund-level leverage L at cost c, equity return is zero when the asset return equals c*L/(1+L), so d*_levered = (Y - c*L/(1+L)) / (1 - R).
Worked, unlevered to zero	Y = 9.80 percent, R = 60 percent: d* = 9.80 / 0.40 = 24.5 percent annualised default rate
Worked, unlevered to a 4.00 percent hurdle	d* = (9.80 - 4.00) / 0.40 = 14.5 percent
Worked, levered 1:1 at 6.00 percent, to zero equity return	Asset return at which equity earns zero = 6.00 * 1.0 / 2.0 = 3.00 percent, so d* = (9.80 - 3.00) / 0.40 = 17.0 percent
Levered 2:1	Asset breakeven = 6.00 * 2.0 / 3.0 = 4.00 percent, so d* = (9.80 - 4.00) / 0.40 = 14.5 percent

• The comparison that matters is between the breakeven rate and the loss experience of the relevant cohort in a real downturn, not against a long-run average. Averages include the good years.
• Leverage cuts the breakeven default rate and does so non-linearly in the cost of debt. Going from unlevered to 1:1 took the cushion from 24.5 to 17.0 percent here; going to 2:1 took it to 14.5. Each incremental turn buys less return and costs more cushion.
• A high breakeven default rate on a portfolio with correlated borrowers is not the protection it appears to be, because the metric is an annualised average and correlated losses arrive together. The same expected loss delivered in one year rather than five behaves entirely differently against a leverage facility with an LTV covenant.
• Stated as a sentence, this is the most useful single output of a credit model: 'a fifth of this portfolio can default at a 40 percent loss severity before the equity earns nothing.' That is a claim an allocator can argue with.

Levered return through a fund-level facility

The return on equity produced by borrowing at the fund level and investing the proceeds alongside equity in the same asset pool. It is linear in the asset return and linear in the cost of debt, with the leverage ratio as the multiplier on both.

Field	Value
Formula	R_e = R_a * (1 + L) - c * L, where L = D/E, R_a is the asset-level return net of asset-level costs, and c is the all-in cost of the facility
Worked	R_a = 9.80 percent, L = 1.0, c = 6.00 percent: R_e = 9.80 * 2.0 - 6.00 * 1.0 = 19.60 - 6.00 = 13.60 percent
Loss-adjusted	R_a = 9.00 percent: R_e = 18.00 - 6.00 = 12.00 percent. Leverage magnified the 80 bps of expected loss into 160 bps of equity return.
Spread capture	Equivalent form: R_e = R_a + L * (R_a - c). The equity return is the asset return plus L times the spread earned on borrowed money. At R_a = 9.80 and c = 6.00 the spread is 380 bps per turn.
Breakeven	R_e = 0 when R_a = c * L / (1 + L). At L = 1.0 and c = 6.00 percent that is 3.00 percent.

• The second form, R_e = R_a + L * (R_a - c), is the one to reason with: leverage adds nothing except L copies of the spread between the asset yield and the cost of debt. When that spread compresses, additional turns add risk and almost no return.
• Both R_a and c are floating in most private credit vehicles, so a rate move largely cancels in the spread - which is the real argument for the structure. It does not cancel where the assets have base rate floors that are in the money and the facility does not, in which case falling rates compress the spread from both ends.
• Leverage is symmetric in the arithmetic and asymmetric in practice, because the facility carries an LTV or borrowing base covenant that forces deleveraging at the worst point. The formula has no term for a margin call.
• Asset-level leverage at a portfolio company and fund-level leverage compound. A 5.5x levered borrower held in a 1:1 levered fund is not a 5.5x exposure to the LP.

Cash yield versus total return

Cash yield counts only interest actually received in cash. Total return additionally includes OID accretion, PIK accrual, fee amortisation, and unrealised mark changes. The gap between them is the portion of reported income that has not been collected.

Field	Value
Formula	Cash yield = cash interest received / average cost basis. Non-cash income share = (Total investment income - cash interest received) / Total investment income.
Worked	Average cost basis 1,000. Cash interest 85. OID and fee accretion 6. PIK accrual 14. Total investment income 105. Cash yield = 8.50 percent; total yield = 10.50 percent; non-cash share = 20 / 105 = 19.0 percent.
Coverage test	If distributions to investors were 100, cash interest of 85 covers 85.0 percent of them and the remainder is funded from capital, borrowings, or realisations

• The non-cash income share is the closest thing private credit has to a single early-warning statistic. It rises when borrowers toggle to PIK, when amendments capitalise interest, and when new loans are issued at wider discounts - which are the three things that happen before a default rate moves.
• A vehicle with a distribution requirement and a rising non-cash income share is distributing cash it did not receive. That is a solvable problem for one period and a structural one across several.
• Cash yield on average cost basis and cash yield on fair value differ once marks move away from cost, and a discounted book shows a higher yield on fair value. Both are reported; only cost basis is stable across periods.

Hurdle, catch-up, and the incentive fee on income

An incentive fee on net investment income is typically payable only above a stated hurdle on equity, with a catch-up band over which the manager takes a high or full share of income until the target split is reached, after which the ordinary split applies.

Field	Value
Formula	Full catch-up boundary = hurdle / (1 - incentive rate). Between the hurdle and that boundary the manager takes 100 percent of the excess; above it, the incentive rate applies to all income.
Worked, no catch-up	Pre-incentive NII 11.60 percent, hurdle 7.00 percent, rate 15 percent: fee = 0.15 * 4.60 = 0.69 percent; net = 10.91 percent
Worked, full catch-up	Same terms: boundary = 7.00 / 0.85 = 8.235 percent. Manager takes 100 percent of income from 7.000 to 8.235, being 1.235, then 15 percent of the 3.365 above it, being 0.505. Total fee = 1.740 percent; net = 9.86 percent.
Cost of the catch-up	1.740 versus 0.690 - the catch-up more than doubles the fee at this income level, and the difference is 105 bps of net return

• The catch-up is the least-read and most expensive term in an income incentive fee. It exists so that the manager reaches its target share of total income rather than only its share of income above the hurdle, which means the hurdle is a deferral rather than a genuine preference.
• At income levels just above the hurdle the marginal fee rate inside the catch-up band is 100 percent, so the manager captures the entire benefit of the first increment of outperformance. Netting a small beat against the hurdle produces no LP benefit at all.
• An income incentive fee and a capital-gains incentive fee are separate calculations in most vehicles, with separate hurdles and separate lookbacks. Realised credit losses may reduce the second without reducing the first, so a manager can earn income fees through a period in which the LP lost principal. Whether a total-return hurdle or a loss carryforward applies is the term that closes that gap.