3 – 1
CHAPTER
3
Depreciation Accounting Techniques
1. A contractor purchased a tractor for $180,000 and anticipates using it for nine years. The
salvage value of the tractor at the end of the nine years is estimated to be $27,000. Using the
straight-line method of depreciation accounting, determine the book value of the tractor at the
end of each of the nine years.
The annual depreciation rate can be determined with Equation 3.1 to be
The annual depreciation amount can be determined with Equation 3.2 to be
The book value for each year can be determined with Equation 3.3 as shown in the table
below.
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
N/A
N/A
$180,000
1
1/9 = 0.11
R1(P-F) = $17,000
$180,000 – $17,000 = $163,000
2
1/9 = 0.11
R1(P-F) = $17,000
$163,000 – $17,000 = $146,000
3
1/9 = 0.11
R1(P-F) = $17,000
$146,000 – $17,000 = $129,000
4
1/9 = 0.11
R1(P-F) = $17,000
$129,000 – $17,000 = $112,000
5
1/9 = 0.11
R1(P-F) = $17,000
$112,000 – $17,000 = $95,000
6
1/9 = 0.11
R1(P-F) = $17,000
$95,000 – $17,000 = $78,000
7
1/9 = 0.11
R1(P-F) = $17,000
$78,000 – $17,000 = $61,000
8
1/9 = 0.11
R1(P-F) = $17,000
$61,000 – $17,000 = $44,000
9
1/9 = 0.11
R1(P-F) = $17,000
$44,000 – $17,000 = $27,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
3 – 2
2. Determine the book value at the end of each of the nine years for the tractor described in
Problem 1, using the sum-of-the-years method of depreciation accounting.
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
N/A
N/A
$180,000
1
(9-1+1)/SOY
R1(P-F) = $30,600
$180,000 – $30,600 = $149,400
2
(9-2+1)/SOY
R1(P-F) = $27,200
$163,000 – $27,200 = $122,200
3
(9-3+1)/SOY
R1(P-F) = $23,800
$146,000 – $23,800 = $98,400
4
(9-4+1)/SOY
R1(P-F) = $20,400
$129,000 – $20,400 = $78,000
5
(9-5+1)/SOY
R1(P-F) = $17,000
$112,000 – $17,000 = $61,000
6
(9-6+1)/SOY
R1(P-F) = $13,600
$95,000 – $13,600 = $47,400
7
(9-7+1)/SOY
R1(P-F) = $10,200
$78,000 – $10,200 = $37,200
8
(9-8+1)/SOY
R1(P-F) = $6,800
$61,000 – $6,800 = $30,400
9
(9-9+1)/SOY
R1(P-F) = $3,400
$44,000 – $3,400 = $27,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
3. Determine the book value at the end of each of the nine years for the tractor described in
Problem 1, using the 1.80 declining-balance method of depreciation accounting.
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
N/A
N/A
$180,000
1
1.8/9=0.20
R1(P-F) = $36,000
$180,000 – $36,000 = $144,000
2
0.20
R1(P-F) = $28,800
$163,000 – $28,800 = $115,200
3
0.20
R1(P-F) = $23,040
$146,000 – $23,040 = $92,160
4
0.20
R1(P-F) = $18,432
$129,000 – $18,432 = $73,728
5
0.20
R1(P-F) = $14,746
$112,000 – $14,746 = $58,982
6
0.20
R1(P-F) = $11,796
$95,000 – $11,796 = $47,186
7
0.20
R1(P-F) = $9,437
$78,000 – $9,437 = $37,749
8
0.20
R1(P-F) = $7,549
$61,000 – $7,549 = $30,199
9
0.20
R1(P-F) = $3,199
$44,000 – $3,199 = $27,000
Note that the initial book value is the purchase price, but the final book value may be above the
salvage value, but never below.
3 – 3
4. An excavator has an initial cost of $150,000 and an estimated useful life of ten years. The
salvage value after ten years of use is estimated to be $40,000.
a. What is the book value at the end of the fifth year, if you use the straight-line method
of depreciation accounting?
Straight Line
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$150,000
1
0.100
$11,000
$139,000
2
0.100
$11,000
$128,000
3
0.100
$11,000
$117,000
4
0.100
$11,000
$106,000
5
0.100
$11,000
$95,000
6
0.100
$11,000
$84,000
7
0.100
$11,000
$73,000
8
0.100
$11,000
$62,000
9
0.100
$11,000
$51,000
10
0.100
$11,000
$40,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
b. What is the book value at the end of the fifth year, if you use the sum-of-the-year
method of depreciation accounting?
SOY
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$150,000
1
0.18
$20,000
$130,000
2
0.16
$18,000
$112,000
3
0.15
$16,000
$96,000
4
0.13
$14,000
$82,000
5
0.11
$12,000
$70,000
6
0.09
$10,000
$60,000
7
0.07
$8,000
$52,000
8
0.05
$6,000
$46,000
9
0.04
$4,000
$42,000
10
0.02
$2,000
$40,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
3 – 4
c. What is the book value at the end of the fifth year, if you use the double declining-
balance method of depreciation accounting?
2.0 Declining Balance
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$150,000
1
0.20
$30,000
$120,000
2
0.20
$24,000
$96,000
3
0.20
$19,200
$76,800
4
0.20
$15,360
$61,440
5
0.20
$12,288
$49,152
6
0.20
$9,152
$40,000
7
0.20
$-
$40,000
8
0.20
$-
$40,000
9
0.20
$-
$40,000
10
0.20
$-
$40,000
Note that the initial book value is the purchase price, but the final book value may be above the
salvage value, but never below.
3 – 5
5. A contractor purchased a crane for $460,000 and plans to use the crane for eight years, at
which time she plans to sell the crane for 10% of its acquisition cost. The contractor is
considering using either the sum-of-the-years method of depreciation accounting or the
double declining-balance method of depreciation accounting.
a. If the contractor uses the sum-of-the-years method of depreciation accounting, what
will be the book value of the crane after two years of use?
SOY
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$460,000
1
0.22
$92,000
$368,000
2
0.19
$80,500
$287,500
3
0.17
$69,000
$218,500
4
0.14
$57,500
$161,000
5
0.11
$46,000
$115,000
6
0.08
$34,500
$80,500
7
0.06
$23,000
$57,500
8
0.03
$11,500
$46,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
b. If the contractor uses the double declining-balance method of depreciation
accounting, what will be the book value of the crane after two years of use?
2.0 Declining Balance
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$460,000
1
0.25
$115,000
$345,000
2
0.25
$86,250
$258,750
3
0.25
$64,687
$194,063
4
0.25
$48,516
$145,547
5
0.25
$36,387
$109,160
6
0.25
$27,290
$81,870
7
0.25
$20,467
$61,403
8
0.25
$15,351
$46,052
Note that the initial book value is the purchase price, but the final book value may be above the
salvage value, but never below.
3 – 6
6. A grader has an initial cost of $220,000 and an estimated useful life of 12 years. The salvage
value after 12 years of use is estimated to be $25,000.
a. What is the annual depreciation amount, if the straight-line method of depreciation
accounting is used?
b. What is the book value after ten years, if the straight-line method of depreciation
accounting is used?
Straight Line
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$220,000
1
0.083
$16,250
$203,750
2
0.083
$16,250
$187,500
3
0.083
$16,250
$171,250
4
0.083
$16,250
$155,000
5
0.083
$16,250
$138,750
6
0.083
$16,250
$122,500
7
0.083
$16,250
$106,250
8
0.083
$16,250
$90,000
9
0.083
$16,250
$73,750
10
0.083
$16,250
$57,500
11
0.083
$16,250
$41,250
12
0.083
$16,250
$25,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
c. What is the annual depreciation amount in the ninth year, if the sum-of-the-years
method of depreciation accounting is used?
d. What is the book value at the end of the sixth year, if the sum-of-the-years method of
depreciation accounting is used?
SOY
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$220,000
1
0.15
$30,000
$190,000
2
0.14
$27,500
$162,500
3
0.13
$25,000
$137,500
4
0.12
$22,500
$115,000
5
0.10
$20,000
$95,000
6
0.09
$17,500
$77,500
7
0.08
$15,000
$62,500
8
0.06
$12,500
$50,000
9
0.05
$10,000
$40,000
10
0.04
$7,500
$32,500
11
0.03
$5,000
$27,500
12
0.01
$2,500
$25,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
3 – 7
e. What is the annual depreciation amount in the fourth year, if the 1.5 declining-
balance method of depreciation accounting is used?
f. What is the book value at the end of the fifth year, if the 1.5 declining-balance
method of depreciation accounting is used?
1.5 Declining Balance
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$220,000
1
0.13
$27,500
$192,500
2
0.13
$24,063
$168,438
3
0.13
$21,055
$147,383
4
0.13
$18,423
$128,960
5
0.13
$16,120
$112,840
6
0.13
$14,105
$98,735
7
0.13
$12,342
$86,393
8
0.13
$10,799
$75,594
9
0.13
$9,449
$66,145
10
0.13
$9,449
$56,695
11
0.13
$9,449
$47,246
12
0.13
$8,268
$38,978
Note that the initial book value is the purchase price, but the final book value may be above the
salvage value, but never below.
3 – 8
7. A loader has an initial cost of $154,000 and an estimated useful life of eight years. The
salvage value after eight years of use is estimated to be $10,000.
a. What is the annual depreciation amount, if the straight-line method of depreciation
accounting is used?
b. What is the book value after six years, if the straight-line method of depreciation
accounting is used?
Straight Line
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$154,000
1
0.125
$18,000
$136,000
2
0.125
$18,000
$118,000
3
0.125
$18,000
$100,000
4
0.125
$18,000
$82,000
5
0.125
$18,000
$64,000
6
0.125
$18,000
$46,000
7
0.125
$18,000
$28,000
8
0.125
$18,000
$10,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
c. What is the annual depreciation amount in the fifth year, if the sum-of-the-years
method of depreciation accounting is used?
d. What is the book value at the end of the sixth year, if the sum-of-the-years method of
depreciation accounting is used?
SOY
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$154,000
1
0.22
$32,000
$122,000
2
0.19
$28,000
$94,000
3
0.17
$24,000
$70,000
4
0.14
$20,000
$50,000
5
0.11
$16,000
$34,000
6
0.08
$12,000
$22,000
7
0.06
$8,000
$14,000
8
0.03
$4,000
$10,000
Note that the initial book value is the purchase price, and the final book value is the salvage value.
3 – 9
e. What is the annual depreciation amount in the fourth year if the double declining-
balance method of depreciation accounting is used?
f. What is the book value at the end of the fifth year if the double declining-balance
method of depreciation accounting is used?
1.5 Declining Balance
After
Year
(m)
Annual Depreciation
Rate
(Rm)
Annual Depreciation
Amount
(Dm)
Book Value
(BVm)
0
$154,000
1
0.25
$38,500
$115,500
2
0.25
$28,875
$86,625
3
0.25
$21,656
$64,969
4
0.25
$16,242
$48,727
5
0.25
$12,182
$36,545
6
0.25
$9,136
$27,409
7
0.25
$6,852
$20,557
8
0.25
$5,139
$15,417
Note that the initial book value is the purchase price, but the final book value may be above the
salvage value, but never below.