Chapter Five Appendix DEPRECIATION METHODS

DEPRECIATION METHODS Straight-Line Sum-of-the-Years’-Digits Double-Declining-Balance Modified Accelerated Cost Recovery System

EXAMPLE: For all illustrations in this appendix, we will assume that a delivery van was purchased for $40,000. It has a five year useful life and salvage value of $4,000.

STRAIGHT-LINE METHOD = = Under this method, an equal amount of depreciation will be taken each period. STEP #1: Compute the depreciable cost = COST SALVAGE VALUE DEPRECIABLE COST = $36,000 $40,000 $4,000

Depreciation Expense per year STRAIGHT-LINE METHOD STEP #2: Divide the depreciable cost by the expected life of the asset. Depreciable Cost Depreciation Expense per year = Years of Life $7,200 per year $36,000 = 5 years

20% STRAIGHT-LINE METHOD = = 100% Years of Life 100% 5 years It is often convenient to use a depreciation rate per year. 20% of the asset’s depreciable cost will be recognized as Depreciation Expense each year. 100% Depreciation rate per year = Years of Life 100% 20% = 5 years

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 Original Cost minus Salvage Value $40,000 - $4,000

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% 100% / Years of Life 100% / 5 year life

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 Depreciable Cost x Depreciation Rate $36,000 x 20%

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 Since this is the first year of the asset’s life, only this year’s depreciation has accumulated.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 Book Value is Cost minus Accumulated Depreciation. $40,000 - $7,200

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 Depreciable Cost does not change.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% Depreciation Rate does not change.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 Depreciation Expense remains the same each year.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 $14,400 Now two years of depreciation has accumulated. $7,200 + $7,200

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 $14,400 $25,600 Cost - Accumulated Depreciation $40,000 - $14,400

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 $14,400 $25,600 Book Value declines over the life of the asset.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 $14,400 $25,600 3 $36,000 20% $7,200 $21,600 $18,400 4 $36,000 20% $7,200 $28,800 $11,200 5 $36,000 20% $7,200 $36,000 The entire Depreciable Cost has now been recognized as Depreciation Expense.

STRAIGHT-LINE DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 20% $7,200 $7,200 $32,800 2 $36,000 20% $7,200 $14,400 $25,600 3 $36,000 20% $7,200 $21,600 $18,400 4 $36,000 20% $7,200 $28,800 $11,200 5 $36,000 20% $7,200 $36,000 $4,000 Book Value has fallen to the Salvage Value.

SUM-OF-THE-YEARS’-DIGITS Depreciation is determined by multiplying the depreciable cost by a schedule of fractions. The numerator (top) of the fraction for a specific year is the number of years of remaining useful life. The denominator (bottom) of the fraction is determined by adding the digits of the years of the estimated life of the asset.

SUM-OF-THE-YEARS’-DIGITS FORMULA: DEPRECIABLE COST Remember, Depreciable Cost is Original Cost minus Salvage Value.

SUM-OF-THE-YEARS’-DIGITS FORMULA: YEARS REMAINING DEPRECIABLE COST X This is measured from the beginning of the year. For example, to calculate the first year’s depreciation…. we would say there are 5 years remaining.

SUM-OF-THE-YEARS’-DIGITS FORMULA: YEARS REMAINING DEPRECIABLE COST X SUM-OF-THE-YEARS’-DIGITS 5 YEAR LIFE = 5+4+3+2+1 OR 15 10 YEAR LIFE = 10+9+8+7+6+5+4+3+2+1 OR 55

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 Original Cost minus Salvage Value $40,000 - $4,000

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 Five years remaining divided by sum-of-years’-digits of 15 (5+4+3+2+1)

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $36,000 X 5/15

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 Sum-of-the-years’-digits method recognizes large amounts of depreciation in the first year of the asset’s life and smaller amounts each subsequent year.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 Only this first year of depreciation has accumulated so far.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 Original Cost minus Accumulated Depreciation $40,000 - $12,000

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 Depreciable Cost does not change.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 Now there are 4 years remaining.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 $9,600 Since the rate (fraction) is smaller, the depreciation expense is also smaller in the 2nd year.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 $9,600 $21,600 There are now two years of depreciation accumulated. $12,000 + $9,600

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 $9,600 $21,600 $18,400 Book Value falls as the asset ages.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 $9,600 $21,600 $18,400 3 $36,000 3/15 $7,200 $28,800 $11,200 4 $36,000 2/15 $4,800 $33,600 $6,400 5 $36,000 2/15 $2,400 $36,000 The entire depreciable cost has been recognized as Depreciation Expense.

SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE Accumulated Depreciation (end of year) Depreciable Cost Depreciation Expense Book Value (end of year) x = Year Rate 1 $36,000 5/15 $12,000 $12,000 $28,000 2 $36,000 4/15 $9,600 $21,600 $18,400 3 $36,000 3/15 $7,200 $28,800 $11,200 4 $36,000 2/15 $4,800 $33,600 $6,400 5 $36,000 2/15 $2,400 $36,000 $4,000 Book value now matches the Salvage Value.

DOUBLE-DECLINING- BALANCE Book Value is multiplied by a fixed rate. often double the straight-line rate Once the book value is reduced to the expected salvage value, no more depreciation may be recognized. Similar to Sum-of-the-Years’-Digits, larger amounts of depreciation are taken in the early years of the asset’s life.

DOUBLE-DECLINING-BALANCE FORMULA: Book Value Cost minus Accumulated Depreciation equals Book Value. For an asset’s first year depreciation, Book Value equals Original Cost.

DOUBLE-DECLINING-BALANCE FORMULA: Book Value x 2 (Straight-Line Rate) 100% / Useful Life For our example…… 100%/5years = 20%

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 Original Cost minus Accumulated Depr. $40,000 - $0

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% Twice the Straight-Line Rate 2 (100%/5) or 2 x 20%

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 Book Value x twice the Straight-Line Rate $40,000 x 40%

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 First year’s depreciation is all that has accumulated.

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 Original Cost minus Accumulated Depreciation $40,000 - $16,000

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 The Book Value at the end of one year becomes the next year’s beginning Book Value.

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% Rate will be the same every year. Always twice the straight-line rate

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 Depreciation Expense will be smaller each year because the book value is declining each year.

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 $25,600 Two years’ depreciation has accumulated…. $16,000 + $9,600

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 $25,600 $14,400 Original Cost - Acc. Depreciation $40,000 - $25,600

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 $25,600 $14,400 3 $14,400 40% $5,760 $31,360 $8,640 4 $8,640 40% $3,456 $34,816 $5,184 Book Value can fall only to the amount of the Salvage Value. $5,184 - $4,000 = $1,184 to go!!

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 $25,600 $14,400 3 $14,400 40% $5,760 $31,360 $8,640 4 $8,640 40% $3,456 $34,816 $5,184 5 $5,184 $1,184 Book Value x Rate = $2,073 This would be too much depreciation. Can recognize only $1,184

Double-Declining-Balance Depreciation Schedule Book Value (Beginning of Year) Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Rate 1 $40,000 40% $16,000 $16,000 $24,000 2 $24,000 40% $9,600 $25,600 $14,400 3 $14,400 40% $5,760 $31,360 $8,640 4 $8,640 40% $3,456 $34,816 $5,184 5 $5,184 $1,184 $36,000 $4,000 Book Value has reached the Salvage Value.

MODIFIED ACCELERATED COST RECOVERY SYSTEM Used for Tax Purposes Internal Revenue Service classifies various assets according to useful life and sets depreciation rates for each year of the asset’s life. Rates are then multiplied by the cost of the asset. Abbreviated MACRS

The IRS would give this van a 6-year life and no salvage MACRS example A delivery van was purchased for $40,000. It has a five year useful life and salvage value of $4,000. The IRS would give this van a 6-year life and no salvage value.

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 IRS doesn’t allow a Salvage Value for this asset.

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% IRS sets the first year rate at 20%.

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% $8,000 Cost x Rate $40,000 x 20%

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% $8,000 $8,000 $32,000 Cost - Accumulated Depreciation $40,000 - $8,000

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% $8,000 $8,000 $32,000 2 $40,000 32% IRS has a larger 2nd year rate.

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% $8,000 $8,000 $32,000 2 $40,000 32% $12,800 $20,800 $19,200 3 $40,000 19.20% Each year has a different rate.

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate At the end of the 6 years, 100% of the asset’s cost will have been recognized as Depreciation Expense. 1 $40,000 20% $8,000 $8,000 $32,000 2 $40,000 32% $12,800 $20,800 $19,200 3 $40,000 19.20% $7,680 $28,480 $11,520 4 $40,000 11.52% $4,608 $33,088 $6,912 5 $40,000 11.52% $4,608 $37,696 $2,304 6 $40,000 5.76% 100%

MACRS Depreciation Schedule Accumulated Depreciation (end of year) Depreciation Expense Book Value (end of year) x = Year Cost Rate 1 $40,000 20% $8,000 $8,000 $32,000 2 $40,000 32% $12,800 $20,800 $19,200 3 $40,000 19.20% $7,680 $28,480 $11,520 4 $40,000 11.52% $4,608 $33,088 $6,912 5 $40,000 11.52% $4,608 $37,696 $2,304 6 $40,000 5.76% $2,304 $40,000 $0 100% $40,000