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FE Review

FE Review. Engineering Economics. Things to Expect. Multiple Choice Test Its Long and Brutal a morning and afternoon session of 4 hours each. Don’t rely on cramming the night before Eat well the day before – get a good nights sleep Decompress Your preping for a marathon as much as a test

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FE Review

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  1. FE Review Engineering Economics

  2. Things to Expect • Multiple Choice Test • Its Long and Brutal a morning and afternoon session of 4 hours each. • Don’t rely on cramming the night before • Eat well the day before – get a good nights sleep • Decompress • Your preping for a marathon as much as a test • Bring a lunch because time between sessions is short • Its Fast Paced • Morning session is 120 questions in 4 hours • Ie – 2 minutes each including time to look things up and transcribe answers • Afternoon session is 60 questions in 4 hours • 4 minutes each

  3. Things to Expect Continued • Materials • You will have a Formula book • A test booklet for writing in • May have an index telling you where the Engineering Econ Question are but there is no indicating in the question set where one subject begins or ends • An answer sheet. • Efficient movement is important • Know the formula book but probably should not be your study guide • May write answers down and then at end of the page (not the test) transcribe them to the answer sheet • Restricted to only certain calculators • Is a financial or two available • Can’t have preprogrammed formulas • No “Class Assistant” on your laptop

  4. Strategies • Name of the Game is to get 70% of the Questions right • There is no penalty for wrong answers • Thus – leave no question unanswered even if you fill in blank circles by “the force” at the end • Nail “low hanging fruit” quick • Eliminate answers that are clearly wrong • You can get a lot of questions down to 2 or 3 answers by inspection • Mark what you could come back to and improve • Have another mark for things were you don’t have anything but “the force” to guide you

  5. Engineering Economics • About 8% of the Morning Session • Afternoon you can take specialized FE’s for engineering disciplines, but if you go the general route about 10% of afternoon • Formula Section of Your Reference book is mostly interest tables • Most formulas are for the common “magic numbers” – P/F, F/P, P/A, A/P, A/F, F/A • Are a few tables or formulas for depreciation • There are a few definitions which you should probably know already and never have to look up

  6. Approach • I’ll try to review • Then I’ll give you a problem that tests that • Well time to see who can kill it in 90 seconds • We’ll check the answer • See if anyone needs to see how we got that.

  7. The “Magic Numbers” • Two most important questions • How much do I get • When do I get it • I can add only money at the same point in time • Concept of Equivalence

  8. Looking For Easy Problems • Lots of problems on first half of FE can have one shot solutions • Take a number – multiply by a magic number • Get the Answer • Easy because have the form AXB =C

  9. Basic Magic Numbers • F/P – If you know how much you have now, how much will you have in the future • P/F – If you know how much you have in the future what is that equal to today $known $to be found 0 n $known $to be found 0 n

  10. Unit Cancelation Trick • I know Future amount but I don’t know the present amount • Similarly – I know what I have now how much will I have in the future

  11. Two Ways to Get “Magic Number” • Formula’s • These are found in your book

  12. Using Tables • Tables are designed for only one rate of interest given at the top of table

  13. Question • $500 is deposited into a bank savings account with 6% interest compounded annually. Most nearly how much will be in the account at the end of 3 years • (A) 550 • (B) $600 • (C) $650 • (D) $700 1.1910 Try this table look-up style.

  14. The Answer • How Many Picked B- $600

  15. How Did I Do That? • This is an AXB = C problem • I have $500 now - that’s A • I want to convert it to equivalent money in 3 years • Present * F/P = Future (F/P for 3 years and 6% interest is B

  16. Look Up F/P I’ve got my 6% interest Read over from N = 3 to F/P get 1.1910 Now $500 * 1.1910 = $595.50 very close to $600

  17. Another Try • If you need $800 in savings at the end of 4 years and your savings account yielded 5% interest paid annually, most nearly how much would you need to deposit today? • A- $570 • B- $600 • C- $660 • D- $770 P/F = (1+i)^-n This time we will do the formula method.

  18. Checking Answer • How Many Got C - $660?

  19. How Did I Do That? • I know I have $800 dollars in the future – I need the equivalent amount now. • Future * P/F = Present • P/F for 4 years and 5% interest • Plug in • (1+0.05)^-4 = 0.8227 • $800*0.8227 = $658.16 – close to $660

  20. Another Easy One Is the Money Doubling type • They ask you how long it takes for money to double at some interest rate • Of course to make that happen you need F/P=2 • Do a quick look up in the table for the first time F/P is about 2 • Look over to the value of n and report that as the answer

  21. Try Another • Most nearly, how long will it take a sum of money to double at a 5% annual percentage rate. • (A)- 6 years • (B)- 10 years • (C)- 11 years • (D)- 14 years 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Oh yes they would Make you interpolate Between two tables.

  22. Check Answer • How Many Got (D) 14 years

  23. How Did I Do That? First 2 at 18 years First 2 at 12 years

  24. Picking My Answer • Answer is about half way between 12 and 18 • Choices are • A- 6 year • B- 10 years • C- 11 years • D- 14 years So which one is between 12 and 18?

  25. The Annuity How much is that equal to right now if interest is 6% $5,700 per year for 5 years 0 1 5 I can’t just add up $5,700 * 5 because the money is at different Points in time

  26. My Magic Number Friend • P/A • Present Value = P/A*amount of one annuity payment • P/A is a function of interest rate and number of payments (6% interest, 5 payments) 4.212

  27. Finish Up • $5700 * 4.212 = $24008.4

  28. Can Do That in Reverse Have $24,000 right now Want to know an annuity of 5 equal annual payments Present Amount * A/P = Annuity (This one will be your turn)

  29. Try It You’ll Like It. Do $24,000 * A/P (for 6% interest and 5 payments)

  30. The Answer • Did you get A/P = 0.2374 • And the Annuity is $5,698 per year

  31. The Perpetual Annuity • What happens if the annuity goes on forever • Can look at the value of A/P or P/A in the table for the biggest value of n • Or can use formula for infinite annuity

  32. Try • A company will sell $100 worth of merchandise every year in perpetuity. How much are those sales worth today if the interest rate is 10%? • A- $1000 • B- $1100 • C-$1200 • D-$2,700

  33. Check the Answer • How many of you got A- $1000

  34. How Did I Do That? • $100/0.1 = $1,000

  35. The Annuity • Payments are the same repeating amount • Payments start 1 compounding period in the future • Payments occur at the end of each compounding period

  36. $1000 0 1 2 3 4 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,13 Suppose the Annuity Starts at the Wrong Time? Whats it worth now?

  37. $1000 0 1 2 3 4 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,13 Try This P/F P/A*$1,000

  38. Interest Rates • Interest is reported annually but often compounds more often • Result is that money sitting for a year will accumulate more interest than indicated by the annual rate • To Find a Yield • Caution – Interest rates are in % orally and decimals in calculations • Step 1 – get a period interest rate Annual Rate # of Compounding Periods in a Year

  39. To Get A Yield • Use the F/P formula (1+i)^n • Where n is number of compounding periods • Can substitute period interest rate into F/P formula Let r be the annual interest Rate m is the number of Compounding periods in a year Note yield is always higher than annual rate but usually not by a large amount Remember the 1 is there to preserve principle so its you’ll get 1+interest in Decimal form

  40. Your Turn • What is the effective annual rate of interest (yield) for money invested at 5% interest compounded quarterly • A 1.3% • B 5.0% • C 5.1% • D 20%

  41. The Answer • How Many had C - 5.1%

  42. How Did I Do That • Ie= ( 1 + (0.05/4))^4 -1 = 0.0509495 • The 1 preserves my original investment • 0.0509495 • Convert back to % • 5.09495 – very close to 5.1%

  43. Another Interest Application • Test writers like continuous compounding • Have all sorts of functions in books that no one uses • You can use same old formula and just make m something big A Bank advertises 4.6% Interest with continuous Compounding – What is the Effective rate of interest (A) – 4.62% (B) – 4.71% (C) – 4.89% (D) - 4.94%

  44. The Answer • How Many Picked (B) – 4.71%

  45. How Did I Do That? • Make m some big number – say 1000 • =(1+ (0.046/1000))^1000 = 1.047073 • Get rid of the 1 • 0.047073 • Convert back to % • 4.7073% which is about 4.71%

  46. The Total Life Cycle Cost • Often want to know what is most cost effective • A cheaper short lived good • Or a longer lived but more expensive good

  47. To Get a Total Life Cycle Cost • Discount all money to the time the unit enters service (almost always 0 on FE exam) • Now use A/P to spread cost over life of item

  48. Move All the Money to Time Zero- Ie Get an NPV Recover $5,000 0 3 6 9 12 Spend $18,000 NPV = $70,000 + P/F(6%,3)*$18,000 +P/F(6%,6)*$18,000 +P/F(6%,9)*$18,000 +P/F(6%,12)*$13,000 Spend $70,000

  49. Get the P/F Values from the Table • You need for 3, 6, 9, and 12 years

  50. Move All the Money to Time Zero- Ie Get an NPV Recover $5,000 0 3 6 9 12 Spend $18,000 NPV = $70,000 + P/F(6%,3)*$18,000 +P/F(6%,6)*$18,000 +P/F(6%,9)*$18,000 +P/F(6%,12)*$13,000 Spend $70,000 (-$114,917)

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