Apple Numbers DDB: Declining-Balance Factors and Salvage Checks
Reproduce Apple’s declining-balance depreciation schedule, compare factor choices and avoid confusing a factor of one with straight-line depreciation.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =DDB(1000,100,4,1) has Apple’s documented double-declining first-year result of 500. The optional depreciation factor defaults to 2, or 200%.
Availability and version history
- Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the original release and introduction date remain unknown.
- Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition; no final supported-version endpoint is established.
- Scope: Shared iWork reference. Individual Mac, iPad, iPhone and iCloud build availability and historical behavior are not established here.
- Checked: October 14, 2026, against the official DDB reference. Documentation and independent depreciation models; no native Numbers test.
Syntax and documented arguments
=DDB(cost, salvage, life, depr-period, depr-factor)
Cost and salvage are required numbers at least zero. Life is required and greater than zero; fractional life values are allowed. Depr-period is required, must be greater than zero, and has its fractional part ignored.
Depr-factor is optional. Its default is 2; a factor of 1.5 or 150% means one and a half times the rate based on the useful life. Larger factors accelerate the ordinary declining-balance model. The short entry does not provide a complete allowed-factor or native-error matrix.
The returned value is the charge for one specified period. It is not the asset’s closing book value or cumulative depreciation. Keep life and period in the same unit when building a model.
Apple’s full four-year example
Create a Numbers table named DecliningBalance, with five columns A:E and five rows. Put Year, Depreciation, Opening book value, Closing book value and Uncapped rate check in A1:E1. Enter 1, 2, 3, 4 in A2:A5.
Enter =DDB(1000,100,4,A2,2) in B2 and fill to B5. These charges are explicitly published by Apple:
| Year | Expected B | Expected opening C | Expected closing D | Expected E |
|---|---|---|---|---|
| 1 | 500 | 1000 | 500 | 500 |
| 2 | 250 | 500 | 250 | 250 |
| 3 | 125 | 250 | 125 | 125 |
| 4 | 25 | 125 | 100 | 62.5 |
Enter 1000 in C2, =C2-B2 in D2 and =C2*2/4 in E2. In C3 enter =D2, in D3 enter =C3-B3, and in E3 enter =C3*2/4; fill C3:E3 through row 5.
For the first three years, the published charge equals half the opening value. In the last year, Apple returns 25, leaving the stated salvage of 100, rather than the uncapped 62.5 that would leave only 62.5. The example demonstrates why simply multiplying each opening balance by 50% is not a sufficient reconstruction of the entire DDB schedule.
Extend the table to seven rows. Put =500+250+125+25 in B7; the total is 900, matching cost minus salvage for this example. The four period results should be combined only once each.
Check the default and fractional period rule
Create a separate table named Controls, with three columns and four rows. Put 1, 2, 2.9 in A2:A4. In B2 enter =DDB(1000,100,4,A2) and fill to B4. Expected values are 500, 250, 250.
The omitted factor selects 2. Period 2.9 uses period 2 because Apple explicitly ignores the period’s fractional part. This does not mean the calculation measures 2.9 years of cumulative depreciation.
In C2 enter =DDB(1000,100,4,A2,200%) and fill to C4. The factor 200% is numerically 2, so these have the same expected targets. An ordinary numeric 200 would be a radically different supplied factor, not another spelling of 200%.
Advanced: compare depreciation factors
Create another table named Factors, with four columns and five rows. Put Factor, First-year DDB, Cost-times-rate model and Difference in A1:D1. Enter 1, 1.5, 2, 3 in A2:A5.
Enter B2 =DDB(1000,100,4,1,A2), C2 =1000*A2/4 and D2 =B2-C2. Fill B2:D2 through row 5. Independent first-period targets are 250, 375, 500, 750, with zero mathematical differences. Apple explicitly publishes the factor-1, factor-2 and factor-3 first-year values.
These first-period comparisons do not guarantee that the same uncapped expression remains valid through the end of the asset’s life. The earlier schedule shows the importance of the remaining depreciable amount.
A source wording trap: factor 1 is not automatically SLN
Apple’s factor-1 example returns 250 and calls it straight-line depreciation. For the same cost 1000, salvage 100 and life 4, the direct SLN formula is (1000-100)/4, which is 225. Those are different values.
On a separate table named MethodCheck, with three columns and two rows, enter =DDB(1000,100,4,1,1) in A2, =SLN(1000,100,4) in B2 and =A2-B2 in C2. Independent expected values are 250, 225 and 25.
Follow the numeric definition and the documented example, rather than treating the factor-1 wording as proof that DDB and SLN are interchangeable. This guide preserves that source discrepancy instead of assigning a native behavior change or a version when it was corrected.
Practical limits and related methods
A cost, salvage estimate, life and factor are modeling inputs. DDB does not decide which method is permitted for a particular accounting or tax purpose. Currency formatting is regional presentation, not an automatic conversion of units or currencies.
The source does not establish every blank/text coercion, factor boundary, period beyond life or exact error code. Validate those cases separately before relying on them. The formulas here use English comma separators; regional decimal settings may require semicolons.
DB is fixed-declining depreciation with a first-year month argument. VDB returns a chosen interval and can switch to straight-line depreciation. Those argument lists answer different questions from DDB’s single-period output.