{ "category": "Financial functions", "display_name": "DB", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.DB", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 2034, "other_mismatch": 0, "refused": 0, "rows": 2034, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 2,034 in the answer bank and 11 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 2,045 recorded answers", "workbook_corpus": { "cells": 11, "matched": 11 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/financial.rs#L289-L294", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/depreciation_family.rs#L3-L17", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/depreciation_family.rs#L98-L143", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/depreciation_family.rs#L145-L215" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "decimal::low32", "decimal::Natural::zero", "decimal::Natural::from_u64", "decimal::Natural::normalize", "decimal::Natural::is_zero", "decimal::Natural::mul_add_small", "decimal::Natural::times_pow5", "decimal::Natural::times_pow2", "decimal::ExactDecimal::read", "decimal::ExactDecimal::binary", "ported/depreciation_family::validate_finite", "ported/depreciation_family::publish_depreciation", "ported/depreciation_family::depreciation_integer_power", "ported/excel_numeric::backend::sqrt", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_pow_positive", "ported/excel_numeric::excel_pow_chain", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/financial.rs#L289-L294", "state": "matches", "suite": null, "summary": "Matches all 2,045 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.DB.json", "name": "DB", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- **[DDB](FUNC.DDB.md)** — the other declining-balance function. The contrast is sharp and worth\n learning: `DDB` takes the rate as a `factor` and derives nothing; `DB` derives the rate from\n the salvage ratio and rounds it. `DDB` clamps each charge so the book value never falls below\n `salvage`; `DB` has no clamp and relies on the rate to land near it. `DDB` has no\n first-year proration; `DB` has `month`.\n- **`VDB`** — the general declining-balance function, with a rate `factor`, a period *range*, and\n an optional switch to straight line. The most flexible member of the family.\n- **`SLN`** — straight line, `(cost − salvage)/life`, the flat comparison every declining-balance\n schedule is measured against.\n- **`SYD`** — sum-of-years-digits, an accelerated schedule that does exhaust `cost − salvage`\n exactly, unlike `DB`.\n- **[AMORDEGRC](FUNC.AMORDEGRC.md)** and **[AMORLINC](FUNC.AMORLINC.md)** — the French\n date-prorated pair. They answer the same accounting question with a date interval instead of a\n `month` count and with 0-based periods.\n- **Confused with**: `DDB` (above), and with the assumption that a `DB` schedule sums to\n `cost − salvage`. It does not.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n1. **The rounding of `rate` dominates everything.** Three decimal places is coarse: on a\n ten-period asset the difference between a rate of 0.2065 and its rounded 0.207 compounds\n through the whole schedule. Any implementation must round at exactly the same point — after\n forming `1 − ratio^(1/life)`, before the first charge — and with the same tie rule.\n2. **`ratio^(1/life)` is a general power** and is the only transcendental in the function. It\n is evaluated as `exp(ln(ratio)/life)` on most platforms, so `DB` inherits whatever `pow` the\n host provides — the same dependency the Handbook's research record traced through the bond and\n distribution families to a single shared library routine. The rounding to three decimals\n mercifully hides the last-bit differences, but only until the fourth decimal sits near a tie.\n4. **The stub-year branch is decided by `floor(life)`**, so a fractional `life` moves it. This is\n an implementation decision with no documentary support.\n\n\n", "quirks": "\n### The rounded rate\n\n\n`rate` is **rounded to three decimal places** before any charge is computed. Microsoft documents\nthis explicitly, and it is not a display convention: the rounded rate is what the schedule uses,\nso it changes every number the function returns.\n\nTwo consequences follow, and both are visible in ordinary use:\n\n1. **The schedule does not land on `salvage`.** The exact rate would; a rate rounded to three\n decimals will not. A `DB` schedule summed over its whole life leaves a residual book value\n that is above or below `salvage` depending on which way the rounding went. Anyone reconciling\n a `DB` column against `cost − salvage` will find a discrepancy, and it is by construction.\n2. **The function is a step function of its inputs.** Nudge `salvage`, `cost` or `life` slightly\n and `rate` may not change at all — or may jump by 0.001, moving every subsequent charge. `DB`\n is therefore piecewise-constant in a way none of its siblings are, and small input errors\n produce either no error or a discontinuous one.\n\n\n### Result and edge cases\n\n\nReturns a `Number`: the charge for the requested period, in the units of `cost`.\n\n- **`salvage` = 0.** The ratio is 0, `0^(1/life)` is 0, and the rate is exactly 1 — so the first\n period writes off the entire asset (prorated by `month`) and later periods charge nothing. The\n formula is doing what it says; the method simply has no meaning when the target salvage is\n zero. Microsoft's page does not flag this. If Excel special-cases it, that is a divergence\n worth recording.\n- **`salvage` close to `cost`** gives a rate near 0, which rounds to 0.000 and produces a\n schedule of zeros. Again the rounding, not the mathematics.\n- **`period` = `life` + 1 with `month` < 12** is the stub year and uses the last-period formula.\n- **Fractional `life`** is accepted; the \"last full regular period\" is taken as its floor, which\n moves where the stub-year formula applies.\n- Empty, missing and error arguments follow the shared call model; see\n [The value universe](../model/01-value-universe.md).\n\n\n\n### Errors\n\n\n**Microsoft's Learn page documents no error conditions for this function** — it carries the\nparameter table and the three formulas, and stops. There is no published statement of what\nhappens with a negative `cost`, a `month` of 13, or a `period` beyond the schedule.\n\nNote that `salvage` > `cost` is **not** rejected: the ratio exceeds 1, the power is above 1, and\nthe rate goes negative — producing negative depreciation, that is, appreciation. Whether Excel\nadmits that is unverified, and the documentation is silent.\n\n\n", "sources": "- Microsoft Learn, **WorksheetFunction.Db method (Excel)** —\n . Source of the\n parameter table with its quoted descriptions, the `month` default, the ordinary-period formula\n with the rate derivation and its three-decimal rounding, and the first-period and last-period\n formulas. This page documents no error conditions.\n- Microsoft Learn, **WorksheetFunction.Ddb method (Excel)** —\n . Cited for the\n sibling's formula and defaults in the comparison above.\n- Microsoft 365 support, **DB function** —\n .\n The worksheet-surface page; **not retrieved** for this entry (the host returned HTTP 403), so\n nothing here is quoted from it.\n- Handbook, `content/lastbit/MATERIAL_W109_PRIMITIVES.md` §19 — the recorded identification of a\n single shared host `pow` routine underneath several unrelated Excel function families.\n- Handbook chapters [01 the value universe](../model/01-value-universe.md),\n [02 coercion and lifting](../model/02-coercion-and-lifting.md),\n [06 claim language](../model/06-claim-language.md).\n- `data/functions/FUNC.DB.json`, `data/presence/FUNC.DB.json`, `data/battery/FUNC.DB.json`.\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 20430 | Windows, 64-bit, CPU not recorded | 129,326 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.DB.json).", "what-it-does": "\n`DB(cost, salvage, life, period, [month])` returns the depreciation charge for **one period**\nunder the fixed-declining-balance method.\n\n\"Fixed\" means the *rate* is fixed, not the charge: a constant fraction of the remaining book\nvalue is written off each period, so charges fall geometrically. Microsoft's Learn page states\nthe whole schedule in three formulas.\n\nThe ordinary period:\n\n> charge = (cost − total depreciation from prior periods) × rate\n> where rate = 1 − (salvage / cost) ^ (1 / life), rounded to three decimal places\n\nThe first period, prorated by the number of months the asset was held in the first year:\n\n> charge = cost × rate × month / 12\n\nAnd the last period — the extra stub period that exists only when `month` < 12:\n\n> charge = ((cost − total depreciation from prior periods) × rate × (12 − month)) / 12\n\nThose three formulas are quoted from Microsoft. Together they define a schedule of `life`\nperiods when `month` is 12, and `life + 1` periods otherwise: the first and last are partial\nyears that sum to one full year of depreciation.\n\nThe **derivation of `rate`** is the idea worth pausing on. Solving\n`salvage = cost × (1 − rate)^life` for `rate` gives exactly the formula above: it is the constant\nrate that would depreciate the asset from `cost` down to precisely `salvage` over `life` periods.\n`DB` is therefore the declining-balance method that *targets* the salvage value, rather than one\nthat stops when it reaches it.\n\nExcept that it does not quite reach it, because of the rounding.\n\n\n\n### Arguments\n\n\n`DB(cost, salvage, life, period, [month])`\n\n| Argument | Meaning (Microsoft's wording) | Required? |\n|---|---|---|\n| `cost` | \"The initial cost of the asset.\" | Required |\n| `salvage` | \"The value at the end of the depreciation (sometimes called the salvage value of the asset).\" | Required |\n| `life` | \"The number of periods over which the asset is being depreciated (sometimes called the useful life of the asset).\" | Required |\n| `period` | \"The period for which you want to calculate the depreciation. Period must use the same units as life.\" | Required |\n| `month` | \"The number of months in the first year. If month is omitted, it is assumed to be 12.\" | Optional, defaults to 12 |\n\n**`period` is 1-based.** Period 1 is the first (possibly prorated) year. This is the opposite of\n[AMORLINC](FUNC.AMORLINC.md) and [AMORDEGRC](FUNC.AMORDEGRC.md), which number depreciation\nperiods from 0, and mixing the two conventions in one model is a reliable way to produce a\nplausible wrong schedule.\n\n**`month` is not a date.** It is a count of months in the first *year*, so it prorates by\ntwelfths regardless of the calendar. `DB` therefore needs no day-count `basis` and has none —\nwhich is exactly why it is not interchangeable with the French depreciation pair, which prorate\nby an actual date interval.\n\n**`month` < 12 adds a period.** The schedule then runs to `life + 1`, with the last period\ntaking the complementary `(12 − month)/12` fraction. Asking for `period` = `life + 1` with\n`month` = 12 is out of range; asking for it with `month` = 11 is the stub year.\n\n`salvage` and `cost` enter only through their **ratio**, so scaling both by the same factor\nleaves `rate` unchanged and scales every charge linearly.\n\nNumeric slots follow the shared model; see\n[Coercion and lifting](../model/02-coercion-and-lifting.md).\n\n\n" }, "signature": { "display": "DB(cost, salvage, life, period, [month])", "parameters": [ { "description": null, "name": "cost", "optional": false, "repeats": false }, { "description": null, "name": "salvage", "optional": false, "repeats": false }, { "description": null, "name": "life", "optional": false, "repeats": false }, { "description": null, "name": "period", "optional": false, "repeats": false }, { "description": null, "name": "month", "optional": true, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 5, "min": 4 }, "category": "Financial functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Fixed-declining-balance depreciation of an asset for one period", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the depreciation of an asset for a specified period by using the fixed-declining balance method", "microsoft_url": "https://support.microsoft.com/en-us/office/db-function-354e7d28-5f93-4ff1-8a52-eb4ee549d9d7" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "قاعدة بيانات" }, { "locale": "bg-BG", "name": "DB" }, { "locale": "cs-CZ", "name": "DB" }, { "locale": "da-DK", "name": "DB" }, { "locale": "de-DE", "name": "DB" }, { "locale": "el-GR", "name": "DB" }, { "locale": "en-AU", "name": "DB" }, { "locale": "en-GB", "name": "DB" }, { "locale": "en-US", "name": "DB" }, { "locale": "es-ES", "name": "NOSQL" }, { "locale": "et-EE", "name": "DB" }, { "locale": "fi-FI", "name": "DB" }, { "locale": "fr-FR", "name": "Base de données" }, { "locale": "he-IL", "name": "DB" }, { "locale": "hr-HR", "name": "DB" }, { "locale": "hu-HU", "name": "KCS2" }, { "locale": "id-ID", "name": "DB" }, { "locale": "it-IT", "name": "DB" }, { "locale": "ja-JP", "name": "DB" }, { "locale": "ko-KR", "name": "DB" }, { "locale": "lt-LT", "name": "DB" }, { "locale": "lv-LV", "name": "DB" }, { "locale": "nb-NO", "name": "DB" }, { "locale": "nl-NL", "name": "DB" }, { "locale": "pl-PL", "name": "DB" }, { "locale": "pt-BR", "name": "NoSQL" }, { "locale": "pt-PT", "name": "DB" }, { "locale": "ro-RO", "name": "DB" }, { "locale": "ru-RU", "name": "ФУО" }, { "locale": "sk-SK", "name": "DB" }, { "locale": "sl-SI", "name": "DB" }, { "locale": "sr-Latn-RS", "name": "DB" }, { "locale": "sv-SE", "name": "DB" }, { "locale": "th-TH", "name": "DB" }, { "locale": "tr-TR", "name": "DB" }, { "locale": "uk-UA", "name": "DB" }, { "locale": "vi-VN", "name": "DB" }, { "locale": "zh-CN", "name": "DB" }, { "locale": "zh-HK", "name": "DB" }, { "locale": "zh-TW", "name": "DB" } ], "signature": { "display": "DB(cost, salvage, life, period, [month])", "parameters": [ { "description": null, "name": "cost", "optional": false, "repeats": false }, { "description": null, "name": "salvage", "optional": false, "repeats": false }, { "description": null, "name": "life", "optional": false, "repeats": false }, { "description": null, "name": "period", "optional": false, "repeats": false }, { "description": null, "name": "month", "optional": true, "repeats": false } ], "trailing_repeats": false }, "surface_name": "DB", "version_marker": null, "xlcall": { "code": "247", "symbol": "xlfDb" } }, "microsoft": "https://support.microsoft.com/en-us/office/db-function-354e7d28-5f93-4ff1-8a52-eb4ee549d9d7" }, "try_it": { "formula": "=DB(1000,100,5,1)" }, "url": "https://handbook.dnacalc.com/functions/DB.html", "variants": [], "versions": [ { "behaviour": "129,326 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.DB.json" ] } ] }