FE Review Engineering Economics.pdf

Fundamentals of Engineering Exam Review
Engineering Economics
Dr. Jerome Lavelle
Associate Dean, College of Engineering
jerome_lavelle@ncsu.edu; 919-515-3263; 120 Page Hall

We are grateful to NCEES for granting us permission to copy
short sections from the FE Handbook to show students how to
use Handbook information in solving problems. This information
will normally appear in these videos as white boxes.

Engineering Economy in FE Exams:
Chemical Engineering
13. Process Design and Economics (8-12 questions)
Civil Engineering
5. Engineering Economics (4-6 questions)
Electrical and Computer Engineering
Environmental Engineering
Industrial and Systems Engineering
Mechanical Engineering
Other Disciplines

Time Value of Money = Discounted Cash Flow Analysis
Finding the equivalence between quantities of money.
These are related by:
- timing (when they occur in time)
- interest rate (the rate charged or earned)
Key Valuables Are:
P = Present single sum of money
F = Future single sum of money
A = Annuity, equivalent cash flow series
G = Gradient, increasing/decreasing cash flow series
i% = effective interest rate per period
n = number of periods, period number

Cash Flow Diagram: for an investment scenario
SINGLE CASH FLOWS
Investment scenario
0 1 2 3 t
P= INVESTMENT
F=WITHDRAWAL
i = 10%

1. How much money must be invested now at 8% to purchase a machine in 5 years
for $200,000? (Answer) $136,117

2. I put $1000 in an account from my high school graduation gifts, and $2000 into the
same account after my college graduation 4 years later. Five years after I started my
first job how much is in the account if it earns 4% per year? (Answer) $3857

ANNUITY CASH FLOW SERIES
Investment scenario
0 1 2 3 4 5 6 7 8 t
A = INVESTMENTS
F=WITHDRAWAL
i = 10%

Cash Flow Diagram: for a borrowing scenario
ANNUITY CASH FLOW SERIES
Borrowing scenario
A = PAYMENTS
P=LOAN AMT
0 1 2 3 4 5 6 7 8 t
i = 10%

3. What amount invested in a savings account that pays 8% interest annually is
worth $215,892.50 after 10 years? (Answer) $100,000

4. A company wishes to set aside budget to cover the maintenance costs of a
machine for its lifetime of 12 years. The maintenance charges are $1000 annually
and paid at the end of each year of service. How much money must be invested at
the beginning of the first year to pay for the maintenance costs if the interest rate is
4% on the set aside dollars? (Answer) $9,385

5. A computer purchased for $1200 will have a salvage value of $600 after 6 years.
Annual maintenance charges are estimated to be $100. At an interest rate of 10%,
what is the equivalent uniform annual cost (EUAC)? (Answer) $298

6. A company wishes to make 5 equal annual investments so that on the date of the
last investment, it will have $50,000 to buy a new machine. What amount must be
invested each year at an interest of 4%? (Answer) $9,230

7. A mother wishes to put enough money in a fund today for her son to attend college
starting in 10 years. How much money must she invest today at 5% interest to
provide $15,000 per year for the 4 years? (Answer) $34,284

8. A software company has a projected cash flow for a business activity as follows:
Year 0 = $ -100,000
Year 1 = $ -150,000
Year 2 = $ 150,000
Year 3 = $ 400,000
Assuming each cash flow occurs at the end of the year and an interest rate of 8%,
what is the annual worth (uniform annual income) of this activity over the 3-year
period? (Answer) $80,411

9. A company is considering buying a truck which has an initial cost of $100,000, an
expected life of 10 years, and a salvage value of $10,000. Annual operating costs for
the first 5 years are estimated to be $5,000 per year, and will be $8000 per year for
the second 5 years. If the interest rate is 8% per year, the present cost of this
investment is? (Answer) $137,074

GRADIENT CASH FLOW SERIES
Investment scenario
0 1 2 3 4 5 6 7 8 t
A=100
F=WITHDRAWAL
i = 10%
G=50
100
150
200
250
300
350 400
450

Cash Flow Diagram: for maintenance fund scenario
GRADIENT CASH FLOW SERIES
Maintenance fund scenario
0 1 2 3 4 5 6 7 8 t
A=100
P=SEED FUND
i = 10%
G=50
100
150
200
250
300
350
400 450

10. A company wishes to establish a fund to cover the maintenance of a machine for
its lifetime of 12 years. The maintenance charges are paid at the end of each year of
service and are estimated to be $1000 the first year and increase by $100 in each
subsequent year. How much money must be invested at the beginning of the first
year to pay for the maintenance costs if the interest rate is 4% per year?
(Answer) $14,110

Non-Annual Compounding
When the interest rate is expressed on an effective timing different than
ANNUAL COMPOUNDING.
Examples:
2% per month; 5% per quarter; 7.5% semi-annually
We can use these effective rates if what we are calling a period matches to
these compounding periods.
To convert to an effective annual interest rate use the given equations.
We CAN NOT use nominal interest rates in equations or factors!

11. The Thumbscrews Credit Card has an advertised and charges a rate of 10% per
month on any unpaid balance of a loan. Express this value as an effective annual
interest rate. (Answer) 214%

12. How much money must be invested in a retirement plan each month to
accumulate $500,000 in 5 years? Assume an annual interest rate of 6%
compounded monthly. (Answer) $7,150

13. A company has two alternatives for manufacturing a certain device:
Plan A: Buy a machine for $2000 which would permit the device to be
manufactured for $3.00 per unit.
Plan B: Buy a machine for $20,000 which would permit the device to be
manufactured for $1 per unit.
Assuming a volume of 3000 devices per year, what is the break even year for these
two plans? Ignore discounting. (Answer) 3 years

14. A firm has estimated that the fixed costs of operations for a new product at $4.5M
per year. Variable costs will depend on the volume of production, and has been
quantified at $250 per unit. If the firm plans to sell the product for $1000. What volume
of sales is needed for this product to break-even? (Answer) 6,000 units

15. If accumulated tuition, fees and interest on your undergraduate engineering
education loan is $37,500 when you graduate, and you can use 20% of your starting
annual salary of $75,000 each year to pay off the loan, what is the payback period of
this investment? (ignore discounting) (Answer) 2.5 years

16. Calculate the annual inflation-adjusted interest rate, if the general inflation rate is
2% per year, and the interest rate is 3.5% per year ? (Answer) 5.6%

17. If the inflation adjusted interest rate from a government study was given as 7.00%,
and inflation for the stated period was 2.5%, what was the real interest rate per
period? (Answer) 4.4%

Problems 18-21 refer to a certain machine which has a first cost of $30,000, annual
costs of $6,000, a salvage value of $4,000 and a life of 10 years. Assume an interest
rate of 8%.
18. What is the depreciation allowance in years 1-10 for this asset using straight line
depreciation? (Answer) $2,600

19. What is the book value of this machine at the end of the third year using straight
line depreciation? (Answer) $22,200

20. Using MACRS depreciation method, what is the depreciation allowance for this
asset in the 6th year of its life? (Answer) $2,211

21. What is the book value of this machine at the end of the third year using Modified
ACRS depreciation? (Answer) $17,280

22. An individual wishes to establish an endowment for a scholarship fund that
generates $9000 every year. At an interest rate of 3%, the amount that must be
provided for the endowment is closest to: (Answer) $300,000

23. A bond pays interest $25 twice a year. It will be redeemed for $1000 in 5 years. At
an interest rate of 4% per year semi-annual compounding, what is the present value
of the bond? (Answer) $1,045

24. If you deposit $1000 in an account and then withdraw $2000 10 year later what
rate of return do you earn on your investment? (Answer) 7.2% per year

25. You deposit $1000 each year in an account for 5 years. At the time of the last
deposit the bank tells you the account is worth $6,500. What rate of return did you
earn on your investment? (Answer) 13.1% per year

26. How many years will it take for an initial investment of $10,000 to double at an
annual interest rate of 4%? (Answer) 17.7 years

27. What is the B/C Ratio for a firm considering an investment in a new manufacturing
technology:
Investment = $2,500,000 Net annual saving: $600,000
Salvage value: $150,000 Project life = 10 years
MARR (i%) = 15% (Answer) 1.22

28. If interest is 0% (ignoring time value of money) what are the annual costs of a 12
year project that saves a company $600,000 over the term of the project and has a
B/C Ratio of 1.0? (Answer) $50,000

Good Luck
on the
FE Exam!!
Jerome Lavelle

FE Review Engineering Economics.pdf

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