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FE Review

FE Review. Engineering Economics. Things to Expect. Multiple Choice Test Need to Pick off Answers fast Narrowing field by knowing what to expect will help Don’t have to get it right, just close enough to pick. Restricted to only certain calculators Is a financial or two available

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FE Review

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  1. FE Review Engineering Economics

  2. Things to Expect • Multiple Choice Test • Need to Pick off Answers fast • Narrowing field by knowing what to expect will help • Don’t have to get it right, just close enough to pick. • Restricted to only certain calculators • Is a financial or two available • Can’t have preprogrammed formulas • No “Class Assistant” on your laptop

  3. Resources • You will have a list of Formulas including for 6 magic numbers (F/P, P/F, A/P, P/A, A/F, F/A) • Few other Formulas • Interest Tables, Modified ACRS factors • Problems are designed for fast solution • If you know what to do a few quick multiplications of divisions will “take out” the problem

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

  5. 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 3 minutes • We’ll check the answer • See if anyone needs to see how they got that.

  6. 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

  7. 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

  8. 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%

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

  10. How Did I Do That • Ie= ( 1 + (0.05/4))^4 = 1.050495 • The 1 preserves my original investment • -1 • 0.0509495 • Convert back to % • 5.09495 – very close to 5.1%

  11. 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%

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

  13. 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%

  14. 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

  15. 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

  16. 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

  17. Finish Up • $5700 * 4.212 = $2408.4

  18. 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

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

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

  21. 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

  22. 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

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

  24. 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

  25. Now Convert to An Annuity Over the Service Life Get the Cost Per Year for 12 years NPV * A/P(6%,12)

  26. Ok You Couldn’t Read it Get A/P(6%,12)

  27. Now Get the Total Life Cycle Cost • NPV * A/P(6%,12) =

  28. Now Try This • Warehouse A cost $100,000 now and has a salvage value of $10,000 after 10 years. • Warehouse B costs $70,000 now, needs $18,000 of service every 3 years and is salvaged after 12 years for $5,000 • Warehousing is needed forever. Which warehouse is the better deal • (A)A by $140 per year • (B) A by $190 per year • (C) B by $190 per year • (D) A by $880 per year

  29. The Answer • How Many Got (D) A by $880/per year

  30. Can Have Limiting Cases To • What if the annuity goes forever?

  31. Annuity Issues • An annuity has to be a repeating payment that occurs at the compounding interval • Suppose I have an event that occurs every 5 years • I can convert that to an annual equivilent • 5 year amount * A/P for 5 years = annual amount • Now I have made an infrequently occurring event equal to a regularly occurring one

  32. Try This • A Tractor Manufacture signs a long term contract with a farm consortium to provide a new tractor for $24,000 every 5 years indefinitely. At a 6% interest rate what is the capitalized cost (present value of the contract) (A)- $950 (B)- $5700 (C)- $80,000 (D)- $95,000

  33. The Answer • How Many Got (D)- $95,000

  34. How Did I Do That? • Convert 24,000 to an annual annuity • 24,000 * A/P(5,6%) • $24,000 * 0.2374 = $5698 • Now just plug into the forever annuity formula • NPV = $5,698 / 0.06 = $94,967 • About equal $95,000

  35. Depreciation • Things wear out with time or use • In taxes or book keeping we spread the cost of a long lived asset over its useful life • There are different ways of doing that but the simplest is straight line depreciation • I have an asset that cost $700,000 • It lasts 7 years • Each Year I use up $700,000/7 = $100,000

  36. Book Values with Depreciation • Book Value is Original Value – Depreciation taken to date • My $700,000 truck has a book value of $200,000 after 5 years of depreciation • $700,000 – 5*100,000 = $200,000

  37. Salvage Value • Not Everything depreciates to zero value • Suppose my truck cost $710,000. • When its all worn out I can still get $10,000 out of scrap metal or salvage • My Annual Depreciation is • (Cost – Salvage)/years of life • (710,000 – 10,000)/ 7 = 100,000

  38. Book Value with Salvage • Original Cost – Depreciation to Date = Book Value • My Truck after 5 years • $710,000 – 5*100,000 = $210,000

  39. Now You Try It • A $100,000 Asset • It lasts 7 years • It has a salvage value of $15,000 • What is its book value after 3 years of depreciation • (A) 12,100 • (B) 36,400 • (C) 57,100 • (D) 63,100

  40. What Answer Did You Get • (D) 63,100

  41. How Did I Do That? • Get Annual Depreciation • (100,000 – 15,000)/ 7 = $12,173 • Get Book Value • $100,000 – 3*$12,173 = $63,571 • Close to $63,600 which is answer D

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