sign in sign up
<<
Home , Economics, Engineering economics, Time value of money

Fundamentals of Exam Review

Engineering

Dr. Jerome Lavelle Associate Dean, College of Engineering [email protected]; 919-515-3263; 120 Page Hall Fundamentals of Engineering Exam Review

We are grateful to NCEES for granting us permission to copy short sections from the FE Handbook to show students how to use Handbook in solving problems. This information will normally appear in these videos as white boxes. Fundamentals of Engineering Exam Review Engineering in FE Exams: Chemical Engineering 13. Process Design and Economics (8-12 questions) Civil Engineering 5. (4-6 questions) Electrical and Computer Engineering 4. Engineering Economics (3-5 questions) Environmental Engineering 4. Engineering Economics (4-6 questions) Industrial and Engineering 4. Engineering Economics (10-12 questions) Mechanical Engineering 5. Engineering Economics (3-5 questions) Other Disciplines 7. Engineering Economics (7-11 questions) Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review

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

Cash Flow Diagram: for an scenario

SINGLE CASH FLOWS

Investment scenario F=WITHDRAWAL

i = 10%

0 1 2 3 t

P= INVESTMENT Fundamentals of Engineering Exam Review

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

2. I put $1000 in an account from my high school graduation , 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 ? (Answer) $3857 Fundamentals of Engineering Exam Review

Cash Flow Diagram: for an investment scenario

ANNUITY CASH FLOW SERIES Investment scenario F=WITHDRAWAL

i = 10% 0 1 2 3 4 5 6 7 8 t

A = Fundamentals of Engineering Exam Review

Cash Flow Diagram: for a borrowing scenario

ANNUITY CASH FLOW SERIES Borrowing scenario

P=LOAN AMT

i = 10% A = PAYMENTS 0 1 2 3 4 5 6 7 8 t Fundamentals of Engineering Exam Review

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

4. A company wishes to aside to cover the maintenance of a machine for its lifetime of 12 years. The maintenance charges are $1000 annually and paid at the end of each year of . 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 Fundamentals of Engineering Exam Review

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 (EUAC)? (Answer) $298 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review

6. A company wishes to make 5 equal annual investments so that on the 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 Fundamentals of Engineering Exam Review

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 Fundamentals of Engineering Exam Review 8. A software company has a projected cash flow for a 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 ) of this activity over the 3-year period? (Answer) $80,411 Fundamentals of Engineering Exam Review 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 5 years. If the interest rate is 8% per year, the present cost of this investment is? (Answer) $137,074 Fundamentals of Engineering Exam Review

Cash Flow Diagram: for an investment scenario

GRADIENT CASH FLOW SERIES F=WITHDRAWAL Investment scenario i = 10%

0 1 2 3 4 5 6 7 8 t A=100 100 150 200 G=50 250 300 350 400 450 Fundamentals of Engineering Exam Review

Cash Flow Diagram: for maintenance fund scenario

GRADIENT CASH FLOW SERIES Maintenance fund scenario 400 450 350 300 250 200 G=50 150 100 A=100 0 1 2 3 4 5 6 7 8 t

i = 10% P=SEED FUND Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 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 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review Non-Annual Compounding When the interest rate is expressed on an effective timing different than ANNUAL COMPOUNDING. Examples: 2% per ; 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! Fundamentals of Engineering Exam Review

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% Fundamentals of Engineering Exam Review

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 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 13. A company has two alternatives for 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 Fundamentals of Engineering Exam Review

14. A firm has estimated that the fixed costs of operations for a new at $4.5M per year. Variable costs will depend on the volume of , 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 Fundamentals of Engineering Exam Review

15. If accumulated tuition, fees and interest on your undergraduate engineering 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 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review

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

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% Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 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 allowance in years 1-10 for this using straight line depreciation? (Answer) $2,600 Fundamentals of Engineering Exam Review 19. What is the book value of this machine at the end of the third year using straight line depreciation? (Answer) $22,200 Fundamentals of Engineering Exam Review

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

21. What is the book value of this machine at the end of the third year using Modified ACRS depreciation? (Answer) $17,280 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 22. An 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 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 23. A 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 of the bond? (Answer) $1,045 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 24. If you deposit $1000 in an account and then withdraw $2000 10 year later what do you earn on your investment? (Answer) 7.2% per year Fundamentals of Engineering Exam Review 25. You deposit $1000 each year in an account for 5 years. At the time of the last deposit the tells you the account is worth $6,500. What rate of return did you earn on your investment? (Answer) 13.1% per year Fundamentals of Engineering Exam Review 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 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review 27. What is the B/C Ratio for a firm considering an investment in a new manufacturing : Investment = $2,500,000 annual : $600,000 Salvage value: $150,000 Project life = 10 years MARR (i%) = 15% (Answer) 1.22 Fundamentals of Engineering Exam Review

28. If interest is 0% (ignoring ) what are the annual costs of a 12 year project that saves a company $600,000 over the of the project and has a B/C Ratio of 1.0? (Answer) $50,000 Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review Fundamentals of Engineering Exam Review Good Luck on the FE Exam!!

Jerome Lavelle