Lowell Outland
IET 310
Engineering Economic Analysis
IET 310: 301 Engineering Economic Analysis: Fall 2011
Homework # 8 (Based on Chapter 11) (50 points)
Due date - November 20’Th (Sunday), 2011, before 11.55 PM EST
Prof. Rajeev Nair
1. Al Jafar Jewel Co. purchased a crystal extraction machine for $50,000 that has an estimated
salvage value of $10,000 at the end of its 8-year useful life. Compute the depreciation schedule
using: (10 points)
(a) MACRS depreciation – using excel spreadsheet. =VDB(cost, salvage, life, start-period, end
period, factor, no-switch)
50,000 cost
10,000 salvage
8 life
Period
1
2
3
4
5
6
7
8
Depreciation
$6,250.00
$5,468.75
$4,785.16
$4,699.22
$4,699.22
$4,699.22
$4,699.22
$4,699.22
value left
$33,750.00
$28,281.25
$23,496.09
$18,796.88
$14,097.66
$9,398.44
$4,699.22
$0.00
(b) Straight-line depreciation
dt =
𝐵−𝑆
𝑁
=
50,000−10,000
Year
1
2
3
4
5
6
7
8
8
=
40,000
8
= $5,000
Depreciation
$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
Sum of Depreciation
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$25,000
$30,000
Book value
$45,000
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
Lowell Outland
IET 310
Engineering Economic Analysis
(c) Sum-of-the-years’ digits (SOYD) depreciation
𝑑𝑡 =
𝑆𝑂𝑌𝐷 =
𝑑6 =
𝑁(𝑁+1)
8−6+1
36
2
=
8(8+1)
2
𝑁−𝑡+1
(𝐵 − 𝑆)
𝑆𝑂𝑌𝐷
= 36
𝑑1 =
8−1+1
($50,000 − $10,000) = $8,888.89
36
𝑑2 =
8−2+1
($50,000 − $10,000) = $7,777.78
36
𝑑3 =
8−3+1
($50,000 − $10,000) = $6,666.67
36
𝑑4 =
8−4+1
($50,000 − $10,000) = $5,555.56
36
𝑑5 =
8−5+1
($50,000 − $10,000) = $4,444.44
36
($50,000 − $10,000) = $3,333.33
𝑑7 =
8−7+1
($50,000 − $10,000) = $2,222.22
36
𝑑8 =
8−8+1
($50,000 − $10,000) = $1,111.11
36
(d) Double declining balance depreciation
Year
1
2
3
4
5
6
7
8
Depreciation for year
2
Using 𝑑𝑡 = 𝑁 (𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒𝑡−1 )
$12,500
$9,375
$7,031.25
$5,273.44
$3,955.08
$2,966.31
$2,274.73
$1,668.55
Sum Of
Depreciation
Book value at
end of year t
$12,500
$21,875
$28,906.25
$34,179.69
$38,134.77
$41,101.08
$43,375.81
$45,044.36
$37,500
$28,125
$21,093.75
$15,820.31
$11,865.23
$8,898.92
$6,624.19
$4,955.64
Lowell Outland
IET 310
Engineering Economic Analysis
2. The Upjohn Company purchased new packaging equipment with an estimated useful life of five
years. The cost of the equipment was $55,000, and the salvage value was estimated to be $5,000 at
the end of year 5. Compute the annual depreciation expenses over the five-year life of the equipment
under each of the following methods of book depreciation: (10 points)
(a) Straight-line method
Dt =
𝐵−𝑆
𝑁
=
55,000−5,000
Year
1
2
3
4
5
5
=
50,000
5
= $10,000
Depreciation
$10,000
$10,000
$10,000
$10,000
$10,000
Sum of Depreciation
$10,000
$20,000
$30,000
$40,000
$50,000
Book value
$45,000
$35,000
$25,000
$15,000
$5,000
(b) Double-declining balance method
Year
Depreciation for year
Using 𝑑𝑡 =
2
(𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒𝑡−1 )
𝑁
Sum Of Depreciation
Book value at end of
year t
1
2
3
4
5
$22,000
$13,200
$7,,920
$4,752
$2,851.20
$22,000
$35,200
$43,120
$47,872
$50,723.20
$33,000
$19,800
$11,880
$7,128
$4,277
3. O’Leary Engineering Corp. has been depreciating a $50,000 machine for the last three years. The
asset was just sold for 60% of its first cost. What is the size of the recaptured depreciation or loss at
disposal using the following depreciation methods? (10 points)
(a) Sum-of-years’-digits with N = 8 and S = 2000
𝑑𝑡 =
𝑆𝑂𝑌𝐷 =
𝑁−𝑡+1
(𝐵 − 𝑆)
𝑆𝑂𝑌𝐷
𝑁(𝑁 + 1)
8(8 + 1)
=
= 36
2
2
Lowell Outland
IET 310
Engineering Economic Analysis
𝑑1 =
8−1+1
𝑑2 =
8−2+1
36
36
($50,000 − $2,000) = $12,000
($50,000 − $2,000) = $10,666.67
8−3+1
𝑑3 = 36 ($50,000 − $2,000) = $9,333.33
Total Depreciation = $32,000
Book value at the end of year 3 = $50,000-$32,000 = $18,000
The Item sold for $30,000 ($50,000x60%)
$30,000(sale price) - $18,000(book value) = $12,000 recaptured depreciation
(c) Straight line depreciation with N = 8 and S = 2000
dt =
𝐵−𝑆
𝑁
=
Year
1
2
3
50,000−2,000
8
=
48,000
8
= $6,000
Depreciation
$6,000
$6,000
$6,000
Sum of Depreciation
$6,000
$12,000
$18,000
Book value
$44,000
$38,000
$32,000
Total Depreciation = $18,000
Book value at the end of year 3 = $50,000-$18,000 = $32,000
The Item sold for $30,000 ($50,000x60%)
$30,000(sale price) - $32,000(book value) = -$2,000 = a net loss of $2,000 depreciation
(d) MACRS GDS depreciation, classified as a 7-year property
Year
1
2
3
MACRS,rt * Cost
Basis
14.29%*$50,000
24.49%*$50,000
17.49%*$50,000
dt
Cum dt
Book Value
$7,145
$12,245
$8,745
$7,145
$19,390
$28,135
$42,855
$30,610
$21,865
Total Depreciation = $28,135
Book value at the end of year 3 = $50,000-$18,000 = $21,865
The Item sold for $30,000 ($50,000x60%)
$30,000(sale price) - $21,865(book value) = $8,135 recaptured depreciation
4. The ABC Corporation placed an asset in service three years ago. The company uses the MACRS
method (seven-year life) for tax purposes and the straight-line method (seven-year useful life) for
financial reporting purposes. The cost of the asset is $100,000, and the salvage value used for
depreciating purposes is $20,000. What is the difference in the current book value obtained using
both methods?
Lowell Outland
IET 310
Engineering Economic Analysis
MACRS GDS depreciation, classified as a 7-year property
Year
MACRS,rt * Cost
Basis
1
14.29%*$100,000
2
24.49%*$100,000
3
17.49%*$100,000
Current book value = $43,730
dt =
𝐵−𝑆
𝑁
=
100,000−20,000
7
=
80,000
7
dt
Cum dt
Book Value
$14,290
$24,490
$17,490
$14,290
$38,780
$56,270
$85,710
$61,220
$43,730
= $11,428.57
Year
Depreciation
1
$11,428.57
2
$11,428.57
3
$11,428.57
Current book value = $65,714.29
Sum of Depreciation
$11,428.57
$22,857.14
$34,285.71
Book value
$88,571.43
$77,142.86
$65,714.29
$65714.29-$43,730 = $21,984.29
There is a difference of $21,984.29
5. A coal mine expected to contain 6.5 million tons of coal was purchased at a cost of $30 million.
One million tons of coal for steel-making is produced this year. The gross income for this coal is
$150,000,000 and operating costs (excluding depletion expenses) are $1,850,000. If you know that
coal has a 10% depletion allowance, what will be the depletion allowance?
(a) Cost depletion
$30,000,000
= $4.61538462 𝑝𝑒𝑟 𝑡𝑜𝑛
$6,500,000
$4.61538462 ∗ 1,000,000 𝑡𝑜𝑛𝑠 = $4,615,384.62
Cost depletion = $4,615,384.62
(b) Percentage depletion
Lowell Outland
IET 310
Engineering Economic Analysis
Computed Percentage depletion
Gross Income from mine
$150,000,000
Depletion percentage
x
10%
Computed percentage depletion $15,000,000