FE Review Engineering Economics.pdf

econ

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

2. Fundamentals of Engineering Exam Review
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shortsectionsfromtheFEHandbooktoshowstudentshowto
useHandbookinformationinsolvingproblems.Thisinformation
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3. Fundamentals of Engineering Exam Review
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
4. Engineering Economics (3-5 questions)
Environmental Engineering
4. Engineering Economics (4-6 questions)
Industrial and Systems Engineering
4. Engineering Economics (10-12 questions)
Mechanical Engineering
5. Engineering Economics (3-5 questions)
Other Disciplines
7. Engineering Economics (7-11 questions)

4. Fundamentals of Engineering Exam Review

5. Fundamentals of Engineering Exam Review
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

6. Fundamentals of Engineering Exam Review

7. Fundamentals of Engineering Exam Review
Cash Flow Diagram:for an investment scenario
SINGLE CASH FLOWS
Investment scenario
0 1 2 3 t
P= INVESTMENT
F=WITHDRAWAL
i= 10%

8. Fundamentals of Engineering Exam Review
1.Howmuchmoneymustbeinvestednowat8%topurchaseamachinein5years
for$200,000? (Answer)$136,117

9. Fundamentals of Engineering Exam Review

10. Fundamentals of Engineering Exam Review
2.Iput$1000inanaccountfrommyhighschoolgraduationgifts,and$2000intothe
sameaccountaftermycollegegraduation4yearslater.FiveyearsafterIstartedmy
firstjobhowmuchisintheaccountifitearns4%peryear? (Answer)$3857

11. Fundamentals of Engineering Exam Review
Cash Flow Diagram:for an investment scenario
ANNUITY CASH FLOW SERIES
Investment scenario
0 1 2 3 4 5 6 7 8 t
A = INVESTMENTS
F=WITHDRAWAL
i= 10%

12. Fundamentals of Engineering Exam Review
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%

13. Fundamentals of Engineering Exam Review
3.Whatamountinvestedinasavingsaccountthatpays8%interestannuallyis
worth$215,892.50after10years? (Answer)$100,000

14. Fundamentals of Engineering Exam Review
4.Acompanywishestosetasidebudgettocoverthemaintenancecostsofa
machineforitslifetimeof12years.Themaintenancechargesare$1000annually
andpaidattheendofeachyearofservice.Howmuchmoneymustbeinvestedat
thebeginningofthefirstyeartopayforthemaintenancecostsiftheinterestrateis
4%onthesetasidedollars? (Answer)$9,385

15. Fundamentals of Engineering Exam Review
5.Acomputerpurchasedfor$1200willhaveasalvagevalueof$600after6years.
Annualmaintenancechargesareestimatedtobe$100.Ataninterestrateof10%,
whatistheequivalentuniformannualcost(EUAC)? (Answer)$298

16. Fundamentals of Engineering Exam Review

17. Fundamentals of Engineering Exam Review
6.Acompanywishestomake5equalannualinvestmentssothatonthedateofthe
lastinvestment,itwillhave$50,000tobuyanewmachine.Whatamountmustbe
investedeachyearataninterestof4%? (Answer)$9,230

18. Fundamentals of Engineering Exam Review
7.Amotherwishestoputenoughmoneyinafundtodayforhersontoattendcollege
startingin10years.Howmuchmoneymustsheinvesttodayat5%interestto
provide$15,000peryearforthe4years? (Answer)$34,284

19. Fundamentals of Engineering Exam Review
8.Asoftwarecompanyhasaprojectedcashflowforabusinessactivityasfollows:
Year 0 = $ -100,000
Year 1= $ -150,000
Year 2= $ 150,000
Year 3= $ 400,000
Assumingeachcashflowoccursattheendoftheyearandaninterestrateof8%,
whatistheannualworth(uniformannualincome)ofthisactivityoverthe3-year
period? (Answer)$80,411

20. Fundamentals of Engineering Exam Review
9.Acompanyisconsideringbuyingatruckwhichhasaninitialcostof$100,000,an
expectedlifeof10years,andasalvagevalueof$10,000.Annualoperatingcostsfor
thefirst5yearsareestimatedtobe$5,000peryear,andwillbe$8000peryearfor
thesecond5years.Iftheinterestrateis8%peryear,thepresentcostofthis
investmentis? (Answer)$137,074

21. Fundamentals of Engineering Exam Review
Cash Flow Diagram:for an investment scenario
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

22. Fundamentals of Engineering Exam Review
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

23. Fundamentals of Engineering Exam Review

24. Fundamentals of Engineering Exam Review
10.Acompanywishestoestablishafundtocoverthemaintenanceofamachinefor
itslifetimeof12years.Themaintenancechargesarepaidattheendofeachyearof
serviceandareestimatedtobe$1000thefirstyearandincreaseby$100ineach
subsequentyear.Howmuchmoneymustbeinvestedatthebeginningofthefirst
yeartopayforthemaintenancecostsiftheinterestrateis4%peryear?
(Answer) $14,110

25. Fundamentals of Engineering Exam Review

26. 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 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!

27. Fundamentals of Engineering Exam Review
11.TheThumbscrewsCreditCardhasanadvertisedandchargesarateof10%per
monthonanyunpaidbalanceofaloan.Expressthisvalueasaneffectiveannual
interestrate. (Answer)214%

28. Fundamentals of Engineering Exam Review
12.Howmuchmoneymustbeinvestedinaretirementplaneachmonthto
accumulate$500,000in5years?Assumeanannualinterestrateof6%
compoundedmonthly. (Answer)$7,150

29. Fundamentals of Engineering Exam Review

30. Fundamentals of Engineering Exam Review
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

31. Fundamentals of Engineering Exam Review
14.Afirmhasestimatedthatthefixedcostsofoperationsforanewproductat$4.5M
peryear.Variablecostswilldependonthevolumeofproduction,andhasbeen
quantifiedat$250perunit.Ifthefirmplanstoselltheproductfor$1000.Whatvolume
ofsalesisneededforthisproducttobreak-even? (Answer)6,000units

32. Fundamentals of Engineering Exam Review
15.Ifaccumulatedtuition,feesandinterestonyourundergraduateengineering
educationloanis$37,500whenyougraduate,andyoucanuse20%ofyourstarting
annualsalaryof$75,000eachyeartopayofftheloan,whatisthepaybackperiodof
thisinvestment?(ignorediscounting) (Answer)2.5years

33. Fundamentals of Engineering Exam Review

34. Fundamentals of Engineering Exam Review
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%

35. Fundamentals of Engineering Exam Review
17.Iftheinflationadjustedinterestratefromagovernmentstudywasgivenas7.00%,
andinflationforthestatedperiodwas2.5%,whatwastherealinterestrateper
period? (Answer)4.4%

36. Fundamentals of Engineering Exam Review

37. Fundamentals of Engineering Exam Review
Problems18-21refertoacertainmachinewhichhasafirstcostof$30,000,annual
costsof$6,000,asalvagevalueof$4,000andalifeof10years.Assumeaninterest
rateof8%.
18.Whatisthedepreciationallowanceinyears1-10forthisassetusingstraightline
depreciation? (Answer)$2,600

38. Fundamentals of Engineering Exam Review
19.Whatisthebookvalueofthismachineattheendofthethirdyearusingstraight
linedepreciation? (Answer)$22,200

39. Fundamentals of Engineering Exam Review
20.UsingMACRSdepreciationmethod,whatisthedepreciationallowanceforthis
assetinthe6
th
yearofitslife? (Answer)$2,211

40. Fundamentals of Engineering Exam Review
21.WhatisthebookvalueofthismachineattheendofthethirdyearusingModified
ACRSdepreciation? (Answer)$17,280

41. Fundamentals of Engineering Exam Review

42. Fundamentals of Engineering Exam Review
22.Anindividualwishestoestablishanendowmentforascholarshipfundthat
generates$9000everyyear.Ataninterestrateof3%,theamountthatmustbe
providedfortheendowmentisclosestto: (Answer)$300,000

43. Fundamentals of Engineering Exam Review

44. Fundamentals of Engineering Exam Review
23.Abondpaysinterest$25twiceayear.Itwillberedeemedfor$1000in5years.At
aninterestrateof4%peryearsemi-annualcompounding,whatisthepresentvalue
ofthebond? (Answer)$1,045

45. Fundamentals of Engineering Exam Review

46. Fundamentals of Engineering Exam Review
24.Ifyoudeposit$1000inanaccountandthenwithdraw$200010yearlaterwhat
rateofreturndoyouearnonyourinvestment? (Answer)7.2%peryear

47. Fundamentals of Engineering Exam Review
25.Youdeposit$1000eachyearinanaccountfor5years.Atthetimeofthelast
depositthebanktellsyoutheaccountisworth$6,500.Whatrateofreturndidyou
earnonyourinvestment? (Answer)13.1%peryear

48. Fundamentals of Engineering Exam Review
26.Howmanyyearswillittakeforaninitialinvestmentof$10,000todoubleatan
annualinterestrateof4%? (Answer)17.7years

49. Fundamentals of Engineering Exam Review

50. Fundamentals of Engineering Exam Review
27.WhatistheB/CRatioforafirmconsideringaninvestmentinanewmanufacturing
technology:
Investment=$2,500,000 Netannualsaving:$600,000
Salvagevalue:$150,000 Projectlife=10years
MARR (i%) = 15% (Answer) 1.22

51. Fundamentals of Engineering Exam Review
28.Ifinterestis0%(ignoringtimevalueofmoney)whataretheannualcostsofa12
yearprojectthatsavesacompany$600,000overthetermoftheprojectandhasa
B/CRatioof1.0? (Answer)$50,000

52. Fundamentals of Engineering Exam Review

53. Fundamentals of Engineering Exam Review

54. Fundamentals of Engineering Exam Review
Good Luck
on the
FE Exam!!
Jerome Lavelle