Declining-Balance Depreciation (Book Value)
Also known as accelerated depreciation · reducing balance
Worked example: $20,000 at 20% declining, 3 years → $10,240 book value — press Try an example to run it live, then adjust anything.
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Decay and depreciation →
Grade 11Grade 11 Math — Functions & Applications
Wearing out on paper →
UniversityApplied Field Engineering
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Declining-Balance Depreciation (Book Value) explained
Declining balance takes the same fraction off whatever is left each year, so the write-down is large at first and shrinks steadily after. A $20,000 asset at 20% a year goes 20,000, then 16,000, then 12,800, then 10,240, which the closed form reproduces as . This matches how equipment actually loses value far better than a straight line does, which is why most tax authorities use it. Canada's Capital Cost Allowance system is declining balance throughout.
There is a curiosity built into the mathematics: multiplying by a fraction repeatedly never reaches zero. In theory the asset is worth something forever. Accounting rules paper over this by switching to straight line near the end, or by writing off the remainder once it drops below a threshold. It also means you cannot solve for the rate from a book value of exactly zero, and the solver will tell you so.
The rate is often set from the life rather than measured. "Double declining balance" uses , so a ten-year asset is written down 20% a year, which is where the figure in the example above comes from.
Declining-Balance Depreciation (Book Value) formula
- = Book value after k years ($)
- = Initial cost ($)
- = Depreciation rate per year (/yr)
- = Years elapsed
Missing one of these? Work it out first, then come back
- Book value after k years — Currency Exchange Conversion, Gross Pay from an Hourly Wage
- Initial cost — Straight-Line Depreciation, Net Present Value of a Uniform Annual Cash Flow
- Depreciation rate per year — Solow Steady-State Capital per Effective Worker
- Years elapsed — Straight-Line Depreciation, Net Present Value of a Uniform Annual Cash Flow