Homework 2
docx
keyboard_arrow_up
School
Stevens Institute Of Technology *
*We aren’t endorsed by this school
Course
622
Subject
English
Date
Dec 6, 2023
Type
docx
Pages
8
Uploaded by JudgeBraveryTiger5
EM-600
ASSIGNMENT – 2
ENGINEERING ECONOMICS AND COST ANALYSIS
Question 1 (30 points):
The New England Soap Company is considering adding some processing equipment to the plant to aid in the removal of impurities from some raw materials. By adding the processing equipment, the firm can purchase lower-
grade raw material at reduced cost and upgrade it for use in its products. Two types of equipment are being considered and their costs/revenues are shown below:
The process equipment will run for 3 years. With a MARR of 8%, calculate the following:
1. a) Calculate the Future Value at end of year (EOY) 3 for each option. DO NOT CALCULATE USING THE FINANCIAL FUNCTIONS IN EXCEL.
(Week 4 slides have an example for calculating the future-worth)
2. b) Use try-and-error with linear interpolation to calculate IRR for each option.
i. Determine whether IRR is greater or less than 30% for each project. (5 + 5 points)
ii. Change the interest rate by 5% and calculate PW. Specifically, if IRR > 30%, then try 35%; if IRR < 30%, then try 25%. Repeat thisprocedure until a sign change of PW. (5 + 5 points)
iii. Find out IRR by linear interpolation. (5 + 5 points)
Question 2 (30 points):
AT&T considers rebuilding a central cell tower, which was destroyed by hurricane Sandy. The contractor showed some possible plans and the company narrowed it down to 2 alternatives with the following given data:
Cash Flow
Alternative 1
Alternative 2
Investment
$4,500,000
$3,500,000
Annual O&M cost
$200,000
(start from EOY 1)
$250,000
(start from EOY 1)
Annual revenue
$1,300,000
(start from EOY 2)
$1,400,000
(start from EOY2)
At a MARR of 18% and program life of 20 years, calculate the following:
Calculate the BCR for each program option. (15 + 15 points) USE PRESENT WORTH ANALYSIS
Answer :
Evaluate alternatives based on the benefit cost analysis
Alternative 1
PV
costs1
= $4,500,000 + $200,000 * (P/A, 18%, 20)
Compute (P/A, i%, n) using [(1 + i)
n
- 1] / [i * (1 + i)
n
]
(P/A, 18%, 20) = [(1 + 0.18)
20
- 1] / [0.18 * (1 + 0.18)
20
] = [(1.18)
20
- 1] / [0.18 * (1.18)
20
]
= [27.3930 - 1] / [0.18 * 27.3930] = 5.3527
PV
costs1
= $4,500,000 + ($200,000 * 5.3527) = $4,500,000 + $1,070,540 = $5,570,540
PV
benefits1
= $1,300,000 * (P/A, 18%, 19) * (P/F, 18%, 1)
Compute (P/A, i%, n) using [(1 + i)
n
- 1] / [i * (1 + i)
n
]
(P/A, 18%, 19) = [(1 + 0.18)
19
- 1] / [0.18 * (1 + 0.18)
19
] = [(1.18)
19
- 1] / [0.18 * (1.18)
19
]
= [23.2144 - 1] / [0.18 * 23.2144] = 5.3162
Compute (P/F, i%, n) using (1 + i)
(-n)
(P/F, 18%, 1) = (1 + 0.18)
(-1)
= (1.18)
(-1)
= 0.8475
PV
benefits1
= $1,300,000 * 5.3162 * 0.8475 = $5,857,123
Benefit Cost ratio 1
(B/C)
1
= PV
benefits1
/ PV
costs1
= $5,857,123 / $5,570,540 = 1.05
Benefit Cost Ratio of alternative 1 is 1.05
Alternative 2
PV
costs2
= $3,500,000 + $250,000 * (P/A, 18%, 20)
= $3,500,000 + ($250,000 * 5.3527) = $3,500,000 + $1,338,175 = $4,838,175
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
PV
benefits2
= $1,400,000 * (P/A, 18%, 19) * (P/F, 18%, 1)
= $1,400,000 * 5.3162 * 0.8475 = $6,307,671
Benefit Cost ratio 2
(B/C)
2
= PV
benefits2
/ PV
costs2
= $6,307,671 / $4,838,175 = 1.30
Benefit Cost Ratio of alternative 2 is 1.30
Question 3 (40 points):
Fred's Fabrication, Inc. bought a 50-kilowatt gas turbine that costs $40,000. It is estimated that the machine will have a depreciated salvage value of $5,000 at the end of its 3 - year useful life. Use the double-declining balance method:
1. Calculate the annual depreciation allowances. (Please ignore the depreciation adjustment at this time) (17 points)
2. Calculate the annual book values. (Please ignore the depreciation adjustment
at this time) (17 points)
3. What do you notice about the book value at the end of year 3? What does this mean? (3 + 3 points)
Answer :
a)
First year Depreciation according to double declining balance method=2*$40000/3=2*$13333.33=$26666.67.
Second year Depreciation according to double declining balance method(ignoring depreciation adjustment at this time)=$40000-$26666.67-$5000(Salvage value)=$8333.33.
Third year depreciation=$0
b)
Annual Book value at the end of year 1=$40000-$26666.67=$13333.33.
Annual Book value at the end of year 2=$40000-$26666.67-$8333.33=$5000.
Annual book value at the end of year 3= $5000-0=$5000.
c)
Book value at the end of year 3 is equal to the salvage value. It means that in the double declining balance method the Book value at the end of the service life of the asset cannot be less than the salvage value of the asset.
Question 4 (30 points):
Automobiles of the future will most likely be manufactured largely with carbon fibers made from recycled plastics, wood pulp, and cellulose. Last year (year 0), Carbon Manufacturing Company purchased a piece of equipment with $50,000 for research on this. The useful life of the machine is 12 years, at the end of which,
the machine is estimated to have a $10,000 salvage value. The new machine generates annual revenues of $9,500. The annual operating and maintenance expenses are estimated to be $2,500. If the organization's MARR is 6%, calculate the following:
1. a) Draw the cash flow diagram for the project. (6 points)
2. b) Calculate the present worth of the project. (8 points)
3. c) Calculate the annual worth of the project. (8 points)
4. d) Calculate the future worth of the project. (8 points)
Answer :
Initial cost of the machine = $50,000
Useful life of the machine = 12 years
Salvage value of the machine at the end of its useful life = $10,000
Annual revenue generated by the new machine = $9,500
Annual operating and maintenance expenses = $2,500
MARR = 6%
We first need to calculate the total cash inflows and outflows over the 12-year period:
Total Cash Inflows: Annual revenue generated by the new machine = $9,500 Number of years = 12 Total cash inflows = $9,500 x 12 = $114,000
Total Cash Outflows: Initial cost of the machine = $50,000 Salvage value at the end
of 12 years = $10,000
Annual operating and maintenance expenses = $2,500 Number of years = 12
Total cash outflows = $50,000 + $2,500 x 12 - $10,000 Total cash outflows = $80,000
Next, we can use the formula for future worth to calculate the equivalent value of these cash flows at the end of the 12-year period:
F = P(F/P, i%, n) + A(F/A, i%, n)
Where: P = Present worth = -$50,000 (negative because it's a cash outflow) F/P = Future worth factor for a single payment (12 years, 6%) = 0.5080
A = Annual worth = -$5,500 (negative because it's a cash outflow) F/A = Future worth factor for an annual series (12 years, 6%) = 9.5629
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
i% = Interest rate = 6% n = Number of years = 12
F = -$50,000(0.5080) + (-$5,500)(9.5629) F = -$25,400 + (-$52,597.95) F = -$77,997.95
Therefore, the future worth of the project at the end of the 12-year period is -
$77,997.95. This means that if the organization decides to go ahead with the project, it can expect to have a negative cash flow of $77,997.95 at the end of the 12-year period. This indicates that the project is not expected to generate a positive return on investment, and the organization should consider alternative investment opportunities or ways to improve the profitability of the project.
Question 5 (20 points):
After the financial crisis in 2008, PNC bank decided to change their charging policy
for customers who take loans. Their first choice is to charge interest on the unpaid
balance at the end of every quarter with an annual interest rate of 12% compounded quarterly. The second choice is to charge interest on the unpaid
balance every six months at an annual rate of 14%. PNC want to maximize profit, help them calculate the effective interest rates in both cases.
Answer : Compound interest annual formula = P(1+r)
n
where P is the unpaid amount
r is rate of interest
n is number of years.
In case of x number of compounding every year, we divide the r by x and multiply n by x.
12% compounded quarterly means:
[1 + 12/(100*4)]
4
= 12.55% annually
14% compounded semi annually means:
[1 + 14/(100*2)]
2
= 14.49% annually