TM 661
Chapter 6
Solutions 1
The manager of a canned-food processing plant is trying to decide between two labeling
machines. Their respective costs are as follows:
Initial Cost
Annual Operating Cost
Salvage Value
Life (in years)
Machine A
$15,000
1,600
3,000
7
Machine B
$25,000
400
6,000
10
The minimum attractive rate of return (MARR) is 10%.
Soln: Since a planning horizon is not specified, I will use LCM and the easiest method for
LCM is to use Equivalent Uniform Annual Worth.
Alternative A
EUAW =-15,000(A/P,10,7) - 1,600 + 3,000(A/F,10,7)
= -15,000(.2054) - 1,600 + 3,000(.1054)
= - 4,365
Alternative B
EUAW = -25,000(A/P,10,10) - 400 + 6,000(A/F,10,10)
= -25,000(.1627) - 400 + 6,000(.0627)
= -4,091
EUAWB < EUAWA
Choose B
TM 661
Chapter 6
Solutions 2
A $250,000 piece of machinery is installed and is to be depreciated over 5
years. You may assume that the salvage value at the end of 5 years is $ 0. The
method of depreciation is to be 200% declining balance with conversion to
straight line using the half-year convention (you may only deduct 1/2 year of
depreciation in year 1). Establish a table showing the depreciation and the end
of year book value for each year.
Soln:
DDB for year 1 = 250,000 x 0.4 = 100,000 x 1/2
= 50,000
DSl for year 1 = 250,000/5 = 50,000 x 1/2
= 25,000
DSL for year 2 = 200,000/4.5 = 44,444
t
0
1
2
3
4
5
6
D200
DSL
50,000
80,000
48,000
28,800
25,000
44,444
34,286
28,800
28,840
14,400
Bt
250,000
200,000
120,000
72,000
43,200
14,400
0
TM 661
Chapter 6
Solutions 3
A company is thinking of investing in a new filter for a smokestack. The project
will cost $750,000 which will be capitalized by investing $500,000 internally and
borrowing the remaining $250,000. The loan is to be repaid over a 3 year period
at 10% interest. Annual returns are expected to be $200,000 per year with a
$100,000 salvage value at the end of year 5. The table below shows the project
cash flow and loan repayment schedule. Complete the partial table below.
MACRS deductions are based on a 3 year property class life. If the MARR is
20%, compute the Net Present Worth on an after tax cash flow basis.
Amt. Financed
Interest
Period of Loan
Payment
Tax rate
34%
MARR
20%
t
0
1
2
3
4
5
6
7
Project
Cash Flow
(750,000)
200,000
200,000
200,000
200,000
200,000
200,000
300,000
$250,000
10%
3
-100,529
Loan
Principle
250,000
75,529
83,082
91,390
Year
0
1
2
3
Principle
75,529
83,082
91,390
Loan Before Tax MACRS
Interest Cash Flow
%
(500,000)
25,000
99,471
33.3%
17,447
99,471
44.5%
9,139
99,471
14.8%
200,000
7.4%
200,000
200,000
300,000
Interest Total Pmt. Loan Bal.
$250,000
25,000
100,529 $174,471
17,447
100,529 $91,390
9,139
100,529
$0
MACRS
deduct
249,975
333,375
111,075
55,575
Taxable
Income
Tax
34%
After Tax
Cash Flow
(500,000)
(74,975) (25,492) 124,963
(150,822) (51,280) 150,751
79,786
27,127
72,344
144,425
49,105
150,896
200,000
68,000
132,000
200,000
68,000
132,000
300,000 102,000 198,000
NPW = $475,972