Declining balance depreciation

Declining balance depreciation assumes the asset loses a constant percentage of its current book value each year. The dollar amount falls each year (the base, book value, is shrinking) while the percentage rate $d$ stays constant.

The annual depreciation in year $n$:

$D_{DB}(n)=B{V}_{DB}(n-1)\cdot d,$

so the book value at the end of year $n$ is

$B{V}_{DB}(n)=P(1-d{)}^n.$

Year-by-year for P = \50,000$and$d = 30%$:

Year	Start BV	Depreciation	End BV
1	50,000	15,000	35,000
2	35,000	10,500	24,500
3	24,500	7,350	17,150
4	17,150	5,145	12,005
5	12,005	3,602	8,404

Depreciation expense drops each year because each year’s base is smaller than the previous.

This matches real value loss better than straight-line does. A car loses 20-30% in its first year and much less in year 5. Industrial equipment usually shows similar accelerated loss early in life.

Finding $d$ if not given. Sometimes you know $P$, $S$ (salvage value), and $N$ (useful life), and need to derive the rate that makes the asset depreciate from $P$ to $S$ in $N$ years. Set $B{V}_{DB}(N)=S$:

$P(1-d{)}^N=S⟹d=1-\sqrt[N]{\frac{S}{P}}.$

For $50,000 → $5,000 over 10 years: $d=1-(0.1{)}^{0.1}=1-0.7943=0.2057$, about 20.6%.

Book value asymptotes toward zero but never quite hits it. For accounting and tax purposes the residual is either written off fully when the asset is disposed, or the asset switches to straight-line depreciation in the last few years to reach zero on schedule (the “DB with crossover” method common in financial accounting).

Tax use: CCA

DB is the mandated depreciation model for Canadian tax purposes, via the CCA system. Each asset class has a maximum CCA rate (the maximum $d$ allowed), and corporations claim up to that rate each year. Common classes:

• Class 8 (general equipment): 20%
• Class 10 (vehicles, automobile equipment): 30%
• Class 53 (manufacturing/processing equipment): 50% for assets acquired 2016 through end of 2025; new acquisitions from 2026 onward fall to Class 43 at 30% instead.
• Class 1 (buildings): 4-10% depending on type

Class rates and rules shift with each federal budget, so verify against CRA guidance for current-year work. The post-2018 Accelerated Investment Incentive also modifies the Half-year rule for many assets, which covers the year of acquisition.