CFA Level IFinancial Statement AnalysisHard
A machine costs $120,000, has an estimated salvage value of $20,000, and a 4-year useful life. The company uses the sum-of-the-years'-digits (SYD) depreciation method. What is the depreciation expense recognized in Year 2?
- A$30,000
- B$20,000
- C$25,000
- D$40,000
Show answer & explanationAnswer & explanation
Correct answer: A. $30,000
The depreciable base is $120,000 − $20,000 = $100,000. The sum of the years' digits for a 4-year life is 4+3+2+1=10. Year 1 factor = 4/10, Year 2 factor = 3/10. Year 2 depreciation = $100,000 × (3/10) = $30,000.
Why the other options are wrong
- B. This is the Year 3 SYD depreciation amount ($100,000 × 2/10), not Year 2.
- C. Reflects straight-line depreciation ($100,000/4), not the SYD method.
- D. This is the Year 1 depreciation amount ($100,000 × 4/10), not Year 2.
Sum-of-the-Years'-Digits (SYD) Depreciation
SYD is an accelerated depreciation method that allocates a decreasing fraction of the depreciable base to each year, based on the sum of the years' digits of the asset's useful life.
- SYD denominator = n(n+1)/2, e.g., for 4 years = 4+3+2+1=10
- Numerator decreases each year (4,3,2,1 for a 4-year life)
- Front-loads depreciation expense more than straight-line but less abruptly than double-declining balance
Memory trick: Add the years, then count them down for each year's crown.