Open fulfillment obligation

Figure 01 / 12

Separate probability, severity, and exposure

The simplified one-year expected loss is PD × LGD × EAD = $28,314.00. PD is 8.25%, LGD is 44.00%, and EAD is $780,000. This is a teaching expected-value calculation, not an accounting allowance method or a capital standard.

Figure data and text version

Input	Value	Unit
PD	8.25	Percent over one year
LGD	44	Percent of exposure lost conditional on default
EAD	780,000	USD at default
Expected loss	28,314	USD over the stated horizon

The exposure report measures promises still open today. Current payment volume is a flow and cannot replace the stock of undelivered obligations.

Reconstruct remaining obligations by purchase cohort and remove overlap among loss estimates.

All amounts, rates, capacity limits, and outcomes in this case are synthetic. The three conditions are separate assumptions for comparison. A better result in the response condition is not measured proof that the proposed control causes that improvement. The figures expose the calculation and its limits; a real deployment needs its own evidence.

Read the result

The case has $780,000 of exposure. Its stated one-year PD and LGD imply $28,314.00 of expected loss, while the cover analysis leaves $550,000.00 of stress exposure. Monthly cash coverage is 0.81×. These are separate measures: one describes an average under probability assumptions, one describes available cover, and one describes a period’s funding capacity.

Figure 02 / 12

Probability and severity move the result together

Each cell is the same exposure multiplied by the row default probability and the column loss severity. The grid makes joint stress visible. A downturn can affect both factors; the calculation does not assume that the two causes are independent.

Figure data and text version

PD	LGD 25%	LGD 50%	LGD 75%
2%	3,900	7,800	11,700
5%	9,750	19,500	29,250
10%	19,500	39,000	58,500
20%	39,000	78,000	117,000

Figure 03 / 12

Recorded collateral and eligible cover

The collateral record is $140,000, but a 25% illustrative haircut leaves $105,000.00 eligible in this scenario. Reserve cover adds $125,000. The resulting uncovered exposure is $550,000.00. Eligibility also needs enforceability and operational access; this arithmetic does not establish either.

Figure data and text version

Measure	USD
Recorded collateral	140,000
Eligible collateral	105,000
Recorded reserve	125,000
Combined usable cover	230,000
Uncovered exposure	550,000

Figure 04 / 12

Cash available for the period’s debt service

Defined cash available is $28,200.00 against $35,000.00 of debt service, for a 0.81× ratio. The ratio uses one period and one defined cash measure. It does not establish affordability, suitability, or a required underwriting threshold.

Figure data and text version

Component	USD	Meaning
Cash available	28,200	After the expenses included in this illustration
Debt service	35,000	Principal and interest due in the same period
Cash after debt service	-6,800	Negative means a modeled shortfall

Figure 05 / 12

A constant-hazard illustration

The curve converts the stated one-year PD of 8.25% to a constant monthly hazard using h = 1 − (1 − PD)^(1/12). Survival after 12 months is therefore 1 − PD. Constant hazard is an assumption; seasonality and changing exposure are omitted. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Months since start	Survival %
M0	100
M2	98.58
M4	97.17
M6	95.79
M8	94.42
M10	93.08
M12	91.75

Figure 06 / 12

Cumulative expected loss at comparable age

This curve multiplies cumulative modeled default probability by a fixed EAD and LGD. It is useful for separating observation age from the chosen assumptions. It omits amortization, recoveries over time, prepayment, and changing utilization. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Age	Expected USD
M0	0
M2	4,889.9
M4	9,710.14
M6	14,461.69
M8	19,145.55
M10	23,762.67
M12	28,314

Figure 07 / 12

Expected loss sensitivity to PD

Exposure stays at $780,000 and LGD stays at 44.00% while PD changes. The linear relationship follows the simplified expected-loss formula. It is not evidence that real-world losses respond linearly to economic stress. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

One-year PD	Expected USD
1%	3,432
3%	10,296
5%	17,160
8%	27,456
12%	41,184
20%	68,640

Figure 08 / 12

A shared dependency can dominate exposure

The four amounts are disjoint portions of this case’s exposure. The largest bucket represents one shared supplier, funding source, or other specified dependency. Counting customers alone would not reveal this common loss driver.

Figure data and text version

Dependency bucket	Exposure USD
unfulfilled orders — primary	312,000
Independent group B	234,000
Independent group C	156,000
Independent group D	78,000

Figure 09 / 12

A weak month can disappear inside an average

The six-month path applies explicit seasonal factors to the defined monthly cash amount and compares it with fixed debt service. These are constructed cash assumptions, not a forecast. A negative month needs a funding or terms response even when the average ratio looks comfortable. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Month	Cash available	Debt service
M1	19,740	35,000
M2	23,970	35,000
M3	31,020	35,000
M4	25,380	35,000
M5	36,660	35,000
M6	32,430	35,000

Figure 10 / 12

Terms belong in the decision record

This record concerns estimate the open obligation. A binary approval omits the amount, observation horizon, cover assumptions, and review trigger. Retaining those terms makes the decision reproducible and identifies when changed facts require another assessment.

Figure data and text version

Field	Illustrative value
entity	Open fulfillment obligation
exposure_usd	780,000
horizon	One year for PD; one month for cash coverage
pd_percent	8.25
lgd_percent	44
review_trigger	Processing volume falls to zero after the merchant stops selling, while refunds remain due.

Figure 11 / 12

One cause can affect several loss components

The stress path connects unfulfilled orders to repayment cash, default probability, recovery, and funding needs. Arrows state the scenario’s assumed causal chain. They are hypotheses to test with evidence, not proof that every affected customer will default.

Figure data and text version

Stage	Mechanism
Dependency shock	Processing volume falls to zero after the merchant stops selling, while refunds remain due.
Cash pressure	Receipts fall or essential payments move earlier
Default and severity	Repayment probability and recovery can both worsen
Response	Reassess terms, usable cover, and exposure within the approved process

Figure 12 / 12

Expected loss, uncovered exposure, and cash gap

Expected loss ($28,314.00), uncovered exposure ($550,000.00), and monthly cash gap ($6,800.00) answer different questions. The bars are deliberately separated measures and must not be added. A low expected value can coexist with a large stress exposure.

Figure data and text version

Measure	USD
Expected one-year loss	28,314
Uncovered stress exposure	550,000
Monthly cash gap	6,800

Connect the result to the system

Reconstruct remaining obligations by purchase cohort and remove overlap among loss estimates.

Check the population, evidence, permitted action, and actual effect together. A balanced calculation can still use the wrong population; a successful response can still leave an unknown financial outcome. The case’s numerical result applies only to its stated assumptions.