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Unformatted text preview: Homework Assignment #7 Solutions
PURDUE UNIVERSITY
IE 343: Engineering Economics
Fall 2010
Instructor: A. Capponi Homework Assignment #7
Assigned: 15 Oct 2010
Due: 22 Oct 2010 Missing name on the top of each page submitted – 2
Not stapled together – 2
Not completed on the correct template – 10 Problem 1
(15 points)
Sugar Spice, a cook factory, needs a new cookie cutter machine. They have narrowed their
choices to three different types of machines, which are presented below
A
B
C
Cost
$50,000 $22,000 $15,000
Annual Net Income $5,093 $2,077 $1,643
Each alternative has a useful life of 20 years with no salvage value. If the MARR is 6%,
which alternative should be selected, if any?
We first need to determine which of the alternative is attractive. To this purpose, we compute the
internal rate of return of each and compare it to MARR. We have $50,000 + $5,093 (PA, i, 20) = 0. Using Excel, i = 8% for Alternative A.
$22,000 + $2,077 (PA, i, 20) = 0. Using Excel, i = 7% for Alternative B.
$15,000 + $1,643 (PA, i, 20) = 0. Using Excel, i = 9% for Alternative C. Thus, all alternatives are attractive since they are all greater than 6%. As discussed in class, the
IRR cannot be used to rank investment, but an incremental analysis is needed. We first rank
alternatives based on the cost of the initial investment. This produces the ranking of C < B < A.
The alternative C is the base alternative. We compare alternative C and B.
The incremental investment leads to extra revenues The IRR of this incremental investment is the rate i such that
(
)
(
)
(
) As 2.14% < MARR, then alternative C remains the winner and the most attractive up to this
point. IE 343 – Homework Assignment #7 Solutions – Page 1 Homework Assignment #7 Solutions
We next compare alternative C and A.
The incremental investment leads to extra revenues The IRR of this incremental investment is the rate i such that
(
)
(
)
(
) As 7.56% > MARR, then the extra investment of $35,000 in alternative A is justified, as it leads
to attractive incremental revenues, yielding a rate of return of 7.56%. Thus, the winner is A.
Choose alternative A. IE 343 – Homework Assignment #7 Solutions – Page 2 Homework Assignment #7 Solutions
Problem 2
(10 points)
Textbook Problem 65
Which mutually exclusive design (if any) should be chosen from the designs listed here? A
10year study period is to be used, and the MARR is 10% per year. All market values are
negligible.
Design A Design B Design C
Capital investment $170,000 $330,000 $300,000
Annual receipts
114,000 147,000
130,000
Annual expenses
70,000
79,000
64,000
Use the FW method. Confirm your recommendation, using the PW and AW methods.
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) Therefore, all methods, FW, PW, and AW, choose Design C IE 343 – Homework Assignment #7 Solutions – Page 3 Homework Assignment #7 Solutions
Problem 3
(15 points)
Textbook Problem 618
A stem cell research project requires expensive specialized laboratory equipment. For this
purpose, three pieces of equipment and their associated cash flows (listed below) are under
consideration. One piece of equipment must be selected, and the laboratory’s MARR is
15% per year.
Equipment
EOY
A
B
C
0
$136,500 $84,000 $126,000
1 – 4 $12,500 $31,500 $15,500
5
$15,000 $31,500 $15,500
a. Use the PW method to rankorder the economic attractiveness of the three projects.
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( ( ) ) So the rankorder is C>A>B. (C is the best one.)
b. Determine the interest rate at which the laboratory would be indifferent between
Equipment B and Equipment C.
This means that the PW or AW of Equipment B and Equipment C are equivalent.
USING PRESENT WORTH
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( ( ) ) Using Excel, we get, i’=26.19%.
If the MARR > 26.19%, select Equipment B. If the MARR < 26.19%, select Equipment C. IE 343 – Homework Assignment #7 Solutions – Page 4 ) Homework Assignment #7 Solutions
Problem 4
(15 points)
Textbook Problem 624
Two mutually exclusive harvesting combines are being considered for purchase by a wheat
farmer. He must buy a new combine now. Information relevant to his comparison of the
alternatives is summarized below.
Deere
FMC
Capital investment
$240,000 $200,000
Market value at end of service life
$80,000 $20,000
Annual fuel and maintenance expenses
$5,000 $10,000
Service life
12 years 12 years
Use the IRR method to determine the better machine to purchase. The farmer’s MARR is
12% per year.
Based on the incremental analysis method, savings in annual expenses of $5,000 are achieved by
selecting the ‘Deere’ option, which comes at an additional investment cost of $40,000 and a loss
of $60,000 of market value at the end of the service life. Therefore, select Deere as the basis for
incremental IRR. The present worth of this incremental investment is given by
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) ) Using Excel, you can solve using IRR. This will result in i = 14.3%.
Since i = 14.3% > 12%. Therefore, the Deere option is better.
Additional solution – not asked for…
This can also be confirmed by simply computing the PW for both options, using the MARR =
12%.
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( ) ( ) ) IE 343 – Homework Assignment #7 Solutions – Page 5 Homework Assignment #7 Solutions
Problem 5
(15 points)
Textbook Problem 628
Consider the following EOY cash flows for two mutually exclusive alternatives (one must
be chosen):
Machine X Machine Y
Capital investment
$6,000
$14,000
Annual expenses
$2,500
$2,400
Useful life
12 years
18 years
Market value at end of useful life
$0
$2,800
The MARR is 5% per year.
a. Determine which alternative should be selected if the repeatability assumption applies.
USING ANNUAL WORTH
Machine X
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Machine Y
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Machine X
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IE 343 – Homework Assignment #7 Solutions – Page 6 ) ) (
( )
) Homework Assignment #7 Solutions
b. Determine which alternative should be selected if the analysis period is 18 years, the
repeatability assumption does not apply, and a machine can be leased for $8,000 per
year after the useful life of either machine is over.
USING ANNUAL WORTH
Machine X
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Machine X
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) ( ) ) For PW or AW, select Alternative Y IE 343 – Homework Assignment #7 Solutions – Page 7 ...
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This note was uploaded on 09/19/2011 for the course IE 343 taught by Professor Vincent,g during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Vincent,G

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