engineering economics review... · 2019-10-02 · fundamentals of engineering exam review...

Fundamentals of Engineering Exam Review

Engineering Economics

Dr. Jerome Lavelle

Associate Dean, College of Engineering

[email protected]; 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 moneyF = Future single sum of moneyA = Annuity, equivalent cash flow seriesG = Gradient, increasing/decreasing cash flow seriesi% = effective interest rate per periodn = number of periods, period number


Cash Flow Diagram: for an investment scenario

SINGLE CASH FLOWSInvestment 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 SERIESInvestment 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 SERIESBorrowing 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 SERIESInvestment scenario

0 1 2 3 4 5 6 7 8 t A=100

F=WITHDRAWAL

i = 10%

G=50100

150200

250300

350 400450


Cash Flow Diagram: for maintenance fund scenario

GRADIENT CASH FLOW SERIESMaintenance fund scenario

0 1 2 3 4 5 6 7 8 t

A=100

P=SEED FUND

i = 10%

G=50100

150200

250300

350400 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

engineering economics review... · 2019-10-02 · fundamentals of engineering exam review...

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