Depreciation: Straight-Line vs. Double-Declining Balance

What is depreciation?

Depreciation allocates the cost of a long-lived asset across its useful life, reflecting wear, obsolescence, or consumption. Two common methods:

• Straight-line: equal charge each year.
• Double-declining balance (DDB): front-loaded — more depreciation early, less later. Used when an asset loses value fastest when new (vehicles, electronics, machinery).

Straight-line formula

$\text{Annual depreciation} = \dfrac{\text{Cost} - \text{Salvage}}{\text{Life}}$

Step-by-step: straight-line

$\dfrac{50{,}000 - 5{,}000}{10} = \dfrac{45{,}000}{10} = \boxed{4{,}500/\text{year}}$

Each year, book value drops by $4,500 until it hits the $5,000 salvage value at year 10.

Double-declining balance formula

$\text{Depreciation}_{\text{year } k} = \text{Book value}_{k-1} \cdot \dfrac{2}{\text{Life}}$

The rate is double the straight-line percentage, applied to the remaining book value each year. You stop depreciating once book value hits the salvage floor.

Step-by-step: DDB

Setup: DDB rate = $2/10 = 20\%$.

• Year 1: $50{,}000 \cdot 0.20 = 10{,}000$. Book value = $40{,}000$.
• Year 2: $40{,}000 \cdot 0.20 = 8{,}000$. Book value = $32{,}000$.
• Year 3: $32{,}000 \cdot 0.20 = 6{,}400$. Book value = $25{,}600$.
• Year 4: $25{,}600 \cdot 0.20 = 5{,}120$. Book value = $20{,}480$.
• Year 5: $20{,}480 \cdot 0.20 = 4{,}096$. Book value = $16{,}384$.
• Year 6: $16{,}384 \cdot 0.20 = 3{,}276.80$. Book value = $13{,}107.20$.
• Year 7: $13{,}107.20 \cdot 0.20 = 2{,}621.44$. Book value = $10{,}485.76$.
• Year 8: $10{,}485.76 \cdot 0.20 = 2{,}097.15$. Book value = $8{,}388.61$.
• Year 9: $8{,}388.61 \cdot 0.20 = 1{,}677.72$. Book value = $6{,}710.89$.
• Year 10: Salvage floor: depreciate to $5{,}000$, i.e. $1{,}710.89$.

Total DDB depreciation = $45,000 (matches straight-line total; it's just distributed differently).

Comparison at a glance

• After 3 years: SL removed $13{,}500; DDB removed$24{,}400$.
• After 5 years: SL removed $22{,}500; DDB removed$33{,}616$.
• Crossover occurs around year 5–6 where DDB drops below SL.

Why choose one over the other?

• Straight-line: simple, predictable. Favored by many accounting policies and for stable assets (buildings).
• Double-declining balance: matches reality for rapidly-depreciating assets; front-loads tax deductions.

Other methods mentioned in practice

• Sum-of-the-years'-digits (SYD): in-between approach.
• Units-of-production: depreciate per unit produced, not per time.
• MACRS (US tax): prescribed schedules by asset class.

Common mistakes

• Forgetting the salvage floor in DDB. You never depreciate below salvage value.
• Applying DDB rate to cost each year (instead of current book value). That's what SL does.
• Miscomputing the DDB rate. It's $2/n$, not $1/(n/2)$ — though these are the same; the mistake is using $1/n$ (straight-line rate).

Try it in the visualization

Year-by-year bar chart: each bar split into (depreciation taken this year) and (book value remaining). Side-by-side columns for SL vs. DDB reveal the front-loading.