The Islamic University of Gaza
Industrial Engineering department
Engineering Economy, EIND 4303
Instructor: Dr. Mohammad Abuhaiba, P.E.
Fall 2010
Exam date: 23/01/2011
Final Exam (Open Book)
Question
Exam Duration: 2 hours
Grade
Maximum Grade
1
20
2
9
3
6
4
35
5
30
Total
100
1
Question #1 (20 points):
Your Company has purchased a large new truck-tractor for over-the-road use (asset class 00.26). It has a cost
basis of $180,000. With additional options costing $15,000, the cost basis for depreciation purposes is
$195,000. Its MV at the end of five years is estimated as $40,000. Assume it will be depreciated under the
MACRS GDS:
1. What is the cumulative depreciation through the end of year three?
2. What is the MACRS depreciation in the fourth year?
3. What is the BV at the end of year two?
Solution:
From Table 11.2, the truck has a 3-year MACRS class life. Depreciation rates are obtained from Table 11.3 and
listed in the table below.
The amounts of depreciation, cumulative depreciation, and book values are calculated as shown in the table
below.
1. cumulative depreciation through the end of year three = $180,551
2. MACRS depreciation in the fourth year = $14,450
3. BV at the end of year two = $43,329
depreciation
EOY
MV
BV
dk
dk*
rate
0
195000 195000
1
130007
0.3333
64994 64994
2
43329
0.4445
86678 151671
3
14450
0.1481
28880 180551
4
0
0.0741
14450 195000
5
0
0
5
40000
0
0
2
Question #2 (9 points):
A special purpose machine is to be depreciated as a linear function of use (units of production method). It costs
$25,000 and is expected to produce 100,000 units and then be sold for $5000. Up to the end of the third year, it
had produced 60,000 units, and during the fourth year it produced 10,000 units. What is the depreciation
deduction for the fourth year and the BV at the end of the fourth year?
Solution:
Depreciation deduction for the fourth year = (10,000/100,000)*(25,000 – 5,000) = $2000
Cumulative depreciation through the end of year four = (70,000/100,000)*(25,000 – 5,000) = $14,000
BV at the end of the fourth year = 25,000 – 14,000 = $11,000
Question #3 (6 points):
The before-tax MARR for a particular firm is 18% per year. The state income tax rate is 5%, and the federal
income tax rate is 39%. State income taxes are deductable from federal taxable income. What is this firm's
after-tax MARR?
Solution:
Effective tax rate = State tax rate + Federal tax rate * (1 - State tax rate)
= 0.05 + 0.39 (1 – 0.05) = 0.4205
After tax MARR = Before tax MARR * (1 - Effective tax rate) = 0.18*(1 – 0.4205) = 0.1043 = 10.43%
3
Question #4 (35 points):
Two alternative machines will produce the same product, but one is capable of higher-quality work, which can
be expected to return greater revenue. The following are relevant data:
Machine A Machine B
$20,000
$30,000
Capital investment
12
years
8 years
Life
$4,000
$0
Terminal BV (and MV)
$150,000
$188,000
Annual receipts
$138,000
$170,000
Annual expenses
Determine which is the better alternative, assuming repeatability and using SL depreciation, an income tax rate
of 40%, and after-tax MARR of 10%.
Solution:
Machine A:
(A/P, 10%, 12) = 0.1468
(A/F, 10%, 12) = 0.0468
Annual depreciation = (20000 – 4000) / 12 = $1333.33
BTCF = Annual Revenues – Annual expenses
Taxable income = BTCF - Annual depreciation
Annual tax amount = 0.40*Taxable income
ATCF = BTCF - Annual tax amount
After tax EUACA = -20,000 (A/P, 10%, 12) + 4000 (A/F, 10%, 12) + 7733 = $4985
Machine A
EOY
BV
0
20000
1
2
3
4
5
6
7
8
9
10
11
12
12
Revenues Expenses
150000
150000
150000
150000
150000
150000
150000
150000
150000
150000
150000
150000
0
138000
138000
138000
138000
138000
138000
138000
138000
138000
138000
138000
138000
dk
1333
1333
1333
1333
1333
1333
1333
1333
1333
1333
1333
1333
BTCF
20000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
4000
Taxable
Income
10667
10667
10667
10667
10667
10667
10667
10667
10667
10667
10667
10667
Tax
4267
4267
4267
4267
4267
4267
4267
4267
4267
4267
4267
4267
ATCF EUAC
20000
7733
7733
7733
7733
7733
7733
7733
7733
7733
7733
7733
7733
4000
-2936
7733
187
4985
4
Machine B:
(A/P, 10%, 8) = 0.18740
Annual depreciation = (30000) / 12 = $3750
BTCF = Annual Revenues – Annual expenses
Taxable income = BTCF - Annual depreciation
Annual tax amount = 0.40*Taxable income
ATCF = BTCF - Annual tax amount
After tax EUACB = -30,000 (A/P, 10%, 8) + 12300 = $6678
Machine B
EOY
BV
0
30000
1
2
3
4
5
6
7
8
8
Revenues Expenses
188000
188000
188000
188000
188000
188000
188000
188000
170000
170000
170000
170000
170000
170000
170000
170000
dk
3750
3750
3750
3750
3750
3750
3750
3750
0
BTCF
30000
18000
18000
18000
18000
18000
18000
18000
18000
0
Taxable
Income
14250
14250
14250
14250
14250
14250
14250
14250
Tax
5700
5700
5700
5700
5700
5700
5700
5700
ATCF EUAC
30000
12300
12300
12300
12300
12300
12300
12300
12300
0
-5622
12300
0
6678
EUACB > EUACA
Therefore, machine B is a better alternative
5
Question #5 (30 points):
A truck was purchased four years ago for $65,000 to move raw materials and finished goods between a
production facility and four remote warehouses. This truck (the defender) can be sold at the present time for
$40,000 and replaced by a new tuck (the challenger) with a purchase price of $70,000. Given the MVs and
operating and maintenance costs that follow and if MARR = 10%:
Defender
Challenger
EOY
Market Value
O&M Costs
EOY
Market Value
O&M Costs
1
2
3
4
$30,000
20,000
12,000
4,000
$8,500
10,500
14,000
16,000
1
2
3
4
$56,000
44,000
34,000
22,000
$5,500
6,800
7,400
9,700
1. What is the total marginal cost of the defender if MARR = 10%?
2. What is the economic life of the challenger if MARR = 10%?
3. When the defender should be replaced.
Solution:
Defender
EOY
MV
1
2
3
4
40000
30000
20000
12000
4000
O&M
Costs
Loss in
MV
Forgone Interest
Marginal Cost
8500
10500
14000
16000
10000
10000
8000
8000
4000
3000
2000
1200
22500
23500
24000
25200
Challenger
EOY
MV
1
2
3
4
70000
56000
44000
34000
22000
O&M
Costs
P/F
A/P
EUAC
5500
6800
7400
9700
0.9091
0.8264
0.7513
0.6830
1.1000
0.5762
0.4021
0.3155
26500
25500
24381
24539
The defender should be kept for three years, then replaced by the challenger.
6