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FE about engineering economics formula sheet, Cheat Sheet of Engineering Economy

FE formula sheet in engineering economic in which include single payment compound amount, uniform series sinking fund and capital recovery, macrs factors and factors tables.From the university of MEMPHIS.

Typology: Cheat Sheet

2021/2022

Uploaded on 02/07/2022

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127 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P,i%,n) (1 + i)n
Single Payment
Present Worth to P given F (P/F,i%,n) (1 + i)n
Uniform Series
Sinking Fund to A given F (A/F,i%,n)
( )
11 +n
i
i
Capital Recovery to A given P (A/P,i%,n)
( )
( )
11
1
+
+
n
n
i
ii
Uniform Series
Compound Amount to F given A (F/A,i%,n)
( )
i
in11 +
Uniform Series
Present Worth to P given A (P/A, i%,n)
( )
( )
n
n
ii
i
+
+
1
11
Uniform Gradient
Present Worth to P given G (P/G,i%,n)
( )
( ) ( )
nn
n
ii
n
ii
i
+
+
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G,i%,n)
( )
i
n
i
in
+
2
11
Uniform Gradient
Uniform Series to A given G (A/G,i%,n)
( )
11
1
+
n
i
n
i
NOMENCLATURE AND DEFINITIONS
A .......... Uniform amount per interest period
B .......... Benefit
BV ........ Book value
C .......... Cost
d........... Inflation adjusted interest rate per interest period
Dj ......... Depreciation in year j
F .......... Future worth, value, or amount
f ........... General inflation rate per interest period
G .......... Uniform gradient amount per interest period
i ........... Interest rate per interest period
ie .......... Annual effective interest rate
m .......... Number of compounding periods per year
n........... Number of compounding periods; or the expected life
of an asset
P .......... Present worth, value, or amount
r ........... Nominal annual interest rate
Sn ......... Expected salvage value in year n
Subscripts
j ........... at time j
n........... at time n
........... F/G = (F/A n)/i = (F/A) × (A/G)
Risk
Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis.
NON-ANNUAL COMPOUNDING
im
r
11
e
m
=+ -
bl
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical. This value is the break-even point.
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will just cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment.
pf3
pf4
pf5

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ENGINEERING ECONOMICS

Factor Name Converts Symbol Formula

Single Payment

Compound Amount

to F given P ( F/P , i% , n ) (1 + i )

n

Single Payment

Present Worth

to P given F ( P/F , i% , n ) (1 + i )

  • n

Uniform Series

Sinking Fund

to A given F ( A/F , i% , n )

n

i

i

Capital Recovery to A given P ( A/P , i% , n )

n

n

i

i i

Uniform Series

Compound Amount

to F given A ( F/A , i% , n )

i

i

n

Uniform Series

Present Worth

to P given A ( P/A, i% , n )

n

n

i i

i

Uniform Gradient

Present Worth

to P given G ( P/G , i% , n )

n n

n

i i

n

i i

i

2

Uniform Gradient †

Future Worth

to F given G ( F/G , i% , n )

i

n

i

i

n

2

Uniform Gradient

Uniform Series

to A given G ( A/G , i% , n )

− n

i

n

i

NOMENCLATURE AND DEFINITIONS

A .......... Uniform amount per interest period

B .......... Benefit

BV ........ Book value

C .......... Cost

d ........... Inflation adjusted interest rate per interest period

Dj ......... Depreciation in year j

F .......... Future worth, value, or amount

f ........... General inflation rate per interest period

G .......... Uniform gradient amount per interest period

i ........... Interest rate per interest period

i e .......... Annual effective interest rate

m .......... Number of compounding periods per year

n ........... Number of compounding periods; or the expected life

of an asset

P .......... Present worth, value, or amount

r ........... Nominal annual interest rate

Sn ......... Expected salvage value in year n

Subscripts

j ........... at time j

n ........... at time n

†........... F/G = ( F/A – n ) / i = ( F/A ) × ( A/G )

Risk

Risk is the chance of an outcome other than what is planned to

occur or expected in the analysis.

NON-ANNUAL COMPOUNDING

i

m

1^ r 1

e

m

= b^ + l -

BREAK-EVEN ANALYSIS

By altering the value of any one of the variables in a situation,

holding all of the other values constant, it is possible to find a

value for that variable that makes the two alternatives equally

economical. This value is the break-even point.

Break-even analysis is used to describe the percentage of

capacity of operation for a manufacturing plant at which

income will just cover expenses.

The payback period is the period of time required for the profit

or other benefits of an investment to equal the cost of the

investment.

INFLATION

To account for inflation, the dollars are deflated by the general

inflation rate per interest period f , and then they are shifted

over the time scale using the interest rate per interest period i.

Use an inflation adjusted interest rate per interest period d for

computing present worth values P.

The formula for d is d = i + f + ( i × f )

DEPRECIATION

Straight Line

D

n

C S

j

= - n

Modified Accelerated Cost Recovery System (MACRS)

Dj = (factor) C

A table of MACRS factors is provided below.

BOOK VALUE

BV = initial cost – Σ Dj

TAXATION

Income taxes are paid at a specific rate on taxable income.

Taxable income is total income less depreciation and

ordinary expenses. Expenses do not include capital items,

which should be depreciated.

CAPITALIZED COSTS

Capitalized costs are present worth values using an assumed

perpetual period of time.

Capitalized Costs = P

i

A

BONDS

Bond value equals the present worth of the payments the

purchaser (or holder of the bond) receives during the life of

the bond at some interest rate i.

Bond yield equals the computed interest rate of the bond value

when compared with the bond cost.

RATE-OF-RETURN

The minimum acceptable rate-of-return (MARR) is that

interest rate that one is willing to accept, or the rate one

desires to earn on investments. The rate-of-return on an

investment is the interest rate that makes the benefits and costs

equal.

BENEFIT-COST ANALYSIS

In a benefit-cost analysis, the benefits B of a project should

exceed the estimated costs C.

B – C ≥ 0, or B/C ≥ 1

MACRS FACTORS

Recovery Period (Years)

Year 3 5 7 10

Recovery Rate (Percent)

n P/F P/A P/G F/P F/A A/P A/F A/G

Factor Table - i = 2.00%

n P/F P/A P/G F/P F/A A/P A/F A/G

n P/F P/A P/G F/P F/A A/P A/F A/G

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 50 60

Factor Table - i = 6.00%

n P/F P/A P/G F/P F/A A/P A/F A/G

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 50 60

n P/F P/A P/G F/P F/A A/P A/F A/G

Factor Table - i = 18.00%

n P/F P/A P/G F/P F/A A/P A/F A/G

      1.  - 0. - 0. - 2. - 5. - 9. - 14. - 20. - 27. - 34. - 43. - 52. - 63. - 74. - 86. - 99. 
        • 1,035.
        • 1,448.
        • 3,562. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. - 9. - 10. - 11. - 12. - 13. - 14. - 15. - 16. - 17. - 18. - 19. - 20. - 22. - 23. - 24. - 25. - 26. - 32. - 44. - 56. - 69. - 129. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 7. - 8. - 8. - 9. - 9. - 10. - 10. - 11. - 11. - 14. - 18. - 23. - 28. - 45.
      1.  - 0. - 0. - 2. - 5. - 9. - 14. - 19. - 26. - 33. - 41. - 50. - 60. - 71. - 82. - 94. 
        • 1,192.
        • 2,605. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. - 9. - 10. - 11. - 12. - 13. - 14. - 16. - 17. - 18. - 19. - 20. - 22. - 23. - 24. - 25. - 26. - 28. - 34. - 48. - 64. - 81. - 170. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 7. - 8. - 8. - 9. - 9. - 10. - 10. - 11. - 11. - 13. - 18. - 22. - 26. - 41.
      1.  - 0. - 0. - 2. - 5. - 9. - 13. - 19. - 26. - 32. - 40. - 48. - 58. - 67. - 78. - 89. 
        • 1,937. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 4. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. - 9. - 10. - 11. - 13. - 14. - 15. - 16. - 17. - 19. - 20. - 21. - 23. - 24. - 25. - 27. - 28. - 30. - 37. - 54. - 73. - 96. - 228. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 7. - 8. - 8. - 9. - 9. - 9. - 10. - 10. - 11. - 13. - 17. - 21. - 25. - 37.
      1.  - 0. - 0. - 2. - 5. - 9. - 13. - 18. - 24. - 31. - 38. - 46. - 55. - 64. - 74. - 85. - 96. 
        • 1,464. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 3. - 7. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. - 9. - 10. - 12. - 13. - 14. - 15. - 17. - 18. - 20. - 21. - 22. - 24. - 25. - 27. - 28. - 30. - 32. - 40. - 60. - 84. - 114. - 312. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 7. - 7. - 8. - 8. - 9. - 9. - 10. - 10. - 10. - 13. - 16. - 20. - 23. - 33.
      1.  - 0. - 0. - 2. - 5. - 8. 
          1.  - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 3. - 4. - 7. - 10. - 50. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 9. - 10. - 12. - 13. - 15. - 16. - 18. - 20. - 21. - 23. - 25. - 27. - 29. - 31. - 34. - 36. - 39. - 41. - 56. - 95. - 152. - 237. - 1,237. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 7. - 7. - 7. - 8. - 8. - 8. - 9. - 9. - 9. - 11. - 14. - 16. - 18. - 22. 
      1.  - 0. - 0. - 2. - 4. - 7. 
          1.  - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 3. - 3. - 4. - 4. - 5. - 10. - 18. - 32. 
              1.  - 1. - 2. - 3. - 4. - 5. - 6. - 8. - 9. - 11. - 13. - 14. - 16. - 18. - 21. - 23. - 25. - 28. - 30. - 33. - 36. - 39. - 43. - 46. - 50. - 54. - 79. - 154. - 290. - 533. 
                • 5,638. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 6. - 7. - 7. - 7. - 8. - 8. - 8. - 9. - 10. - 12. - 13. - 14. - 16.
      1.  - 0. - 0. - 2. - 4. - 7. 
          1.  - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 3. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 10. - 21. - 46. - 101. - 2,199. - 1. - 2. - 3. - 4. - 5. - 7. - 8. - 10. - 12. - 14. - 16. - 18. - 21. - 24. - 27. - 30. - 33. - 37. - 41. - 45. - 50. - 55. - 60. - 66. - 73. - 113. - 259. - 573. - 1,253. - 27,484. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 3. - 4. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 6. - 7. - 7. - 7. - 7. - 8. - 8. - 9. - 10. - 11. - 11. - 12. 
        1. - 0. - 0. - 2. - 4. - 6. - 9. 
            1.  - 1. - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 4. - 4. - 5. - 5. - 6. - 6. - 7. - 8. - 8. - 9. - 10. - 17. - 45. - 117. - 304. 
              • 13,780. - 1. - 2. - 3. - 4. - 6. - 7. - 9. - 11. - 13. - 15. - 18. - 21. - 24. - 27. - 31. - 35. - 40. - 45. - 51. - 57. - 64. - 71. - 79. - 88. - 98. - 164. - 442. - 1,163. - 3,034. - 137,796. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 3. - 3. - 3. - 4. - 4. - 4. - 4. - 5. - 5. - 5. - 6. - 6. - 6. - 6. - 6. - 7. - 7. - 7. - 8. - 9. - 9. - 9. - 9.
        1.  - 1. - 1. - 1. - 1. - 1. - 1. - 2. - 2. - 2. - 3. - 3. - 3. - 4. - 4. - 5. - 6. - 6. - 7. - 8. - 9. - 10. - 12. - 13. - 15. - 17. - 29. - 93. - 289. - 897. 
          • 83,522. - 1. - 2. - 3. - 4. - 6. - 8. - 10. - 12. - 14. - 17. - 20. - 24. - 28. - 32. - 37. - 42. - 48. - 55. - 63. - 72. - 81. - 92. - 104. - 118. - 133. - 241. - 767. - 2,400. - 7,471. - 696,010. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 2. - 3. - 3. - 3. - 4. - 4. - 4. - 4. - 5. - 5. - 5. - 5. - 6. - 6. - 6. - 6. - 6. - 6. - 7. - 7. - 8. - 8. - 8.
        1.  - 1. - 1. - 1. - 1. - 2. - 2. - 3. - 3. - 4. - 5. - 6. - 7. - 8. - 10. - 11. - 14. - 16. - 19. - 23. - 27. - 32. - 38. - 45. - 53. - 62. - 143. - 750. - 3,927. 
          • 20,555.
          • 15,424,131. - 1. - 2. - 3. - 5. - 7. - 9. - 12. - 15. - 19. - 23. - 28. - 34. - 42. - 50. - 60. - 72. - 87. - 103. - 123. - 146. - 174. - 206. - 244. - 289. - 342. - 790. - 4,163. - 21,813. - 114,189. - 85,689,616. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1. - 1. - 2. - 2. - 2. - 2. - 3. - 3. - 3. - 3. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 4. - 5. - 5. - 5. - 5. - 5. - 5. - 5. - 5.