8.3 Declining-Balance & Sum-of-the-Years’-Digits

Why accelerated methods exist on the books

Some assets deliver more service — or lose more resale value — in the early years: vehicles, computers, certain production equipment. U.S. GAAP allows accelerated book methods when they better match cost to benefits. AIPB tests two families: declining-balance (including double-declining-balance) and sum-of-the-years’-digits (SYD). Both still stop at salvage. Both still credit Accumulated Depreciation. Neither is MACRS; tax percentages stay in Chapter 9.

Accelerated book expense raises early-year operating costs and lowers early-year book income versus straight-line. Total depreciation over the life is still cost minus salvage (assuming the asset is held for the full estimate). Only the pattern changes.

Declining-balance: rate × book value

Declining-balance (DB) applies a constant percentage of beginning book value. The most common exam version is double-declining-balance (DDB): twice the straight-line rate.

Straight-line rate = 1 ÷ useful life
DDB rate = 2 ÷ useful life
150% DB rate = 1.5 ÷ useful life
DB depreciation for the year = Rate × Beginning book value

Do not subtract salvage before multiplying. Salvage is a floor, not an input to the rate formula.

Northline Packaging buys a CNC router:

• Cost $40,000
• Salvage $4,000
• Life 5 years
• DDB rate 2 ÷ 5 = 40%
• Straight-line on the same data would be ($40,000 − $4,000) ÷ 5 = $7,200 per year — useful as a comparison, not as the DDB amount.

Year-by-year DDB (full years, salvage floor in Year 5)

Year 5 arithmetic: remaining room above salvage is $5,184 − $4,000 = $1,184. Recording $2,073.60 would drop book value to about $3,110, below salvage. The floor wins.

150% declining-balance on the same router: rate 1.5 ÷ 5 = 30%. Year 1 = 30% × $40,000 = $12,000 (between SL $7,200 and DDB $16,000). Later years still apply 30% to falling book value and still stop at $4,000.

Journal entry Year 1 DDB (nonmanufacturer):

Dr Depreciation Expense 16,000
Cr Accumulated Depreciation—Equipment 16,000

A factory router hits Manufacturing Overhead, same as SL.

Optional switch to straight-line: some policies switch from DDB to SL on remaining book value when SL would produce a higher remaining-life charge. That is a company policy, not an automatic IRS table. If the problem is silent, stay on DDB and apply the salvage floor.

DDB errors

• Year 1 = 40% × ($40,000 − $4,000) = $14,400 — salvage was subtracted too early.
• Year 1 = $7,200 because the candidate defaulted to SL.
• Year 1 = 20% × $40,000 = $8,000 — single declining-balance (1 ÷ life), not double.
• Year 5 = $2,073.60 with no floor.

Sum-of-the-years’-digits: shrinking fraction of depreciable base

SYD uses depreciable base (cost minus salvage) times a fraction that starts large and shrinks.

SYD denominator = n(n + 1) / 2 where n is useful life in years.
Year t numerator = remaining life at the beginning of the year (n in Year 1, n−1 in Year 2, …, 1 in the last year).
Year t SYD depreciation = (numerator / denominator) × (Cost − Salvage)

Denominators you should compute without a table: 3-year → 6; 4-year → 10; 5-year → 15; 6-year → 21; 8-year → 36; 10-year → 55.

Redwood Cabinet Co. buys a finishing booth:

• Cost $30,000
• Salvage $3,000
• Life 4 years
• Base $27,000
• Denominator 4 × 5 / 2 = 10

Checks: fractions sum to 1. Total expense equals base. Book value ends on salvage. Year 2 is not $10,800 again.

If you need SYD and DDB on the same $40,000 / $4,000 / 5-year router: SYD denominator 15, Year 1 = 5/15 × $36,000 = $12,000; Year 2 = 4/15 × $36,000 = $9,600; Year 3 = $7,200; Year 4 = $4,800; Year 5 = $2,400.

Pattern comparison on one asset

Same CNC router: cost $40,000, salvage $4,000, 5-year life. Total book depreciation is $36,000 under all three methods if the asset is held five years.

DDB is the most front-loaded. SYD is accelerated but smoother. SL is flat. The line chart below plots that pattern. Partial-year conventions (section 8.4) scale the first calendar year of whichever method you chose; they do not turn DDB into MACRS.

Traps

• Treating DDB as “double the SL dollar amount every year” ($14,400 forever) instead of double the rate on falling book value
• Using SYD fractions on cost instead of cost minus salvage ($12,000 in Year 1 of the booth instead of $10,800)
• Using the wrong SYD year in the numerator (Year 2 still using 4/10)
• Importing a tax 200% declining-balance table percentage into a GAAP DDB problem
• Forgetting that accelerated methods still credit Accumulated Depreciation, not the asset