Source: https://guthlabs.ai/docs/instruments/declining-balance-double-declining-depreciation/
instrument / verified-with-binding-errata
# Declining Balance / Double-Declining Depreciation
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Finance, Economics & Business (educational only — never individualized investment, tax, or legal advice)
**Tranche**: tranche-5
**Evidence ID**: t5-138
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The educational-only label is appropriate, but the formula specification needs explicit period units, beginning-book-value indexing, salvage-floor handling, straight-line comparison, input constraints, and rounding rules before implementation can be verified as unambiguous.
### Formula and scope findings
- dep_t=book_value_t*rate is ambiguous: standard declining-balance depreciation uses the beginning book value of period t, not the ending book value.
- The formula omits the salvage-value floor. Depreciation must not reduce book value below salvage value, and the final period may require an adjustment.
- The straight-line switch rule is underspecified. Standard practice compares declining-balance depreciation with remaining-book-value straight-line depreciation: (beginning book value - salvage value) / remaining periods, then selects the larger amount without exceeding the depreciable base.
- The formula does not define whether t is zero-based or one-based, nor whether book_value_t means beginning or ending book value.
- No rounding policy or final-period rounding adjustment is specified.
### Unit assumptions
- Useful life and depreciation periods are assumed to use the same unit; the vectors below use annual periods unless otherwise stated.
- cost, salvage, and book values are monetary amounts in the same currency.
- The multiplier is dimensionless; rate = multiplier / useful life.
- The standard interpretation is beginning-book-value declining balance, with a switch to remaining-life straight line when straight line is greater than declining balance, subject to the salvage floor.
- A positive integer useful life is required; multiplier is assumed to be 1.5 or 2.0.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
A useful_life input of zero causes division by zero in rate = multiplier/useful_life, producing an undefined rate and invalid schedule. The instrument should reject the input rather than emit numeric results.
## Errata and corrections
### Tranche errata
**depreciation[2:] / ending_book_value[2:]** · vector 1,2
v1 866.67×3, v2 1343.75×2
v1 1440/864/296, v2 1757.81/929.69 (greater-of rule as stated in inputs)
switched to straight-line while DB was still GREATER, violating the switch rule stated in her own inputs
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"cost": 10000,
"salvage": 1000,
"useful_life": 5,
"multiplier": 2,
"period_unit": "years",
"switch_rule": "use the greater of declining-balance and remaining-life straight-line depreciation, capped at salvage"
},
"expected_outputs": {
"rate": 0.4,
"depreciation": [
4000,
2400,
866.6666666667,
866.6666666667,
866.6666666666
],
"ending_book_value": [
6000,
3600,
2733.3333333333,
1866.6666666666,
1000
]
},
"working": "Rate = 2 / 5 = 0.4. Year 1: DB depreciation = 10000 x 0.4 = 4000; ending book value = 10000 - 4000 = 6000. Year 2: DB depreciation = 6000 x 0.4 = 2400; ending book value = 6000 - 2400 = 3600. At the start of Year 3, DB = 3600 x 0.4 = 1440. Remaining-life SL = (3600 - 1000) / 3 = 2600 / 3 = 866.6666666667, so switch to SL. Year 3 ending book value = 3600 - 866.6666666667 = 2733.3333333333. Year 4 depreciation = (2733.3333333333 - 1000) / 2 = 866.6666666667; ending book value = 1866.6666666666. Year 5 depreciation = (1866.6666666666 - 1000) / 1 = 866.6666666666; ending book value = 1000."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`