CH0401 Process Engineering Economics. Lecture 1e. Balasubramanian S. Department of Chemical Engineering SRM University

Transcription

1 CH0401 Process Engineering Economics Lecture 1e Balasubramanian S Department of Chemical Engineering SRM University

2 Process Engineering Economics Introduction Time Value of Money Equivalence Equations for economic studies Amortization Depreciation and Depletion Balasubramanian S Department of Chemical Engineering 2

3 Process Engineering Economics Introduction Time Value of Money Equivalence Equations for economic studies Amortization Depreciation and Depletion Balasubramanian S Department of Chemical Engineering 3

4 Process Engineering Economics Introduction Time Value of Money Equivalence Equations for economic studies Amortization Depreciation and Depletion Balasubramanian S Department of Chemical Engineering 4

5 Depreciation Depreciation has many meanings, but only two are discussed in our syllabus loss of value of capital with the time when equipment wears out or becomes obsolete. the systematic allocation of costs of an asset that produces an income from operations. In short, depreciation may be considered as a cost for protection of depreciating capital without interest over a period, which the capital (asset or equipment) is used. Balasubramanian S Department of Chemical Engineering 5

6 Depreciation- Methods 1. Straight Line method 2. Fixed Percentage (or) Declining Balance 3. Sinking fund 4. Sum-of-the-years digits method Balasubramanian S Department of Chemical Engineering 6

7 1. Straight Line method Principal or original sum or investment or fixed capital cost! Annual Depreciation Depreciation up to any age(or time) n in life service of the asset or accumulated/cumulative depreciation at any age (or time) n in life service. Book value at the end of year or beginning of the year A D P! L n D n n'(p! L) n B v P! n' ( P! L ) n Salvage value or Scrap Value Total number of life service Number of years of service upto n age (or time) Salvage value or Scrap Value Total number of life service Number of years of service upto n age (or time) Salvage value or Scrap Value Total number of life service Principal or original sum or investment or fixed capital cost Balasubramanian S Department of Chemical Engineering 7

8 2. Fixed Percentage or Declining Balance Method A D Depreciation factor (f) Book value at the beginning of the year f 1 n L P Where, f depreciation rate (or) depreciation factor expressed in percentage; L salvage value or scrap value; P principal/ original sum or fixed capital investment; B v book value at the end or beginning of the year; n total number of life service Balasubramanian S Department of Chemical Engineering 8

9 3. Sinking Fund Method Salvage value or Scrap Value Annual Depreciation Principal or original sum or investment or fixed capital cost Sinking fund interest rate i' A D (P L) (1+ i') n 1 Sinking fund interest rate Total number of life service Balasubramanian S Department of Chemical Engineering 9

10 3. Sinking Fund Method Depreciation up to any age(or time) n in life service of the asset or accumulated/ cumulative depreciation at any age (or time) n in life service. Principal or original sum or investment or fixed capital cost Sinking fund interest rate D n (P L) i' (1+ i') n 1 i' (1+ i') n' 1 Salvage value or Scrap Value Sinking fund interest rate Total number of life service Sinking fund interest rate Number of years of service upto n age (or time) Balasubramanian S Department of Chemical Engineering 10

11 Process Engineering Economics Equations for economic studies 3. Sinking Fund Method Salvage value or Scrap Value Book value at the end of year or beginning of the year Principal or original sum or investment or fixed capital cost Sinking fund interest rate i' (1+ i') B v P (P L) n 1 i' (1+ i') n' 1 Sinking fund interest rate Total number of life service Sinking fund interest rate Number of years of service upto n age (or time) Balasubramanian S Department of Chemical Engineering 11

12 4. Sum the years digits method Total depreciable cost P L Depreciation factor A D (Total Depriciable cost) (Depreciation factor) decreasing order of life service of the asset sum-of-the-years digits sum-of-the-years digits n + n 2 2 B V at the end of the year (Book value at the begining of the year) ( A D ) Balasubramanian S Department of Chemical Engineering 12

13 Example problem If a heat exchanger costs $1,100 with 10 years of service life had a salvage value of $100. Estimate the annual depreciation of heat exchanger by 1. Straight-line method 2. Fixed percentage (or) declining balance method 3. Sinking fund method 4. Sum-of-the-year s digits method. Show the behavior of book value and depreciation in graph for each of the abovementioned methods. Balasubramanian S Department of Chemical Engineering 13

14 Solution: Given: Principal (or) Original sum (or) Initial Investment (or) Fixed capital cost $1,100 Service life of the heat exchanger 10 years Salvage value of the heat exchanger at the end of 10 th year is $100 Required: Annual depreciation by 1. Straight-line method 2. Fixed percentage (or) Declining Balance Method 3. Sinking fund method 4. Sum of the years digits method and show all the methods behavior in a graph. Balasubramanian S Department of Chemical Engineering 14

15 1. Straight Line method Principal or original sum or investment or fixed capital cost! Annual Depreciation Depreciation up to any age(or time) n in life service of the asset or accumulated/cumulative depreciation at any age (or time) n in life service. Book value at the end of year or beginning of the year A D P! L n D n n'(p! L) n B v P! n' ( P! L ) n Salvage value or Scrap Value Total number of life service Number of years of service upto n age (or time) Salvage value or Scrap Value Total number of life service Number of years of service upto n age (or time) Salvage value or Scrap Value Total number of life service Principal or original sum or investment or fixed capital cost Balasubramanian S Department of Chemical Engineering 15

16 1. Straight Line method A D A D A D 100 P L n Note: Annual depreciation in straight line method is constant for the entire service life of the equipment Balasubramanian S Department of Chemical Engineering 16

17 1. Straight Line method D n n'(p L) n B v P n' ( P L) n " 1(1100!100)% D 1 # $ 10 & ' 100 " D 2 # $ " D 3 # $ " D 4 # $ " D 5 # $ " D 6 # $ " D 7 # $ " D 8 # $ " D 9 # $ " D 10 # $ 2(1100!100) 10 3(1100!100) 10 4(1100!100) 10 5(1100!100) 10 6(1100!100) 10 7(1100!100) 10 8(1100!100) 10 9(1100!100) 10 0(1100!100) 10 " D 0 # $ % & ' 200 % & ' 300 % & ' 400 % & ' 500 % & ' 600 % & ' 700 % & ' 800 % & ' 900 % & ' (1100!100) 10! % & ' 0 B V (0) B V B V1 B V (100) 1000 Similarly for other years as follows, B V2 900 B V B V4 700 B V5 600 B V6 500 B V7 400 B V8 300 B V9 200 B V Balasubramanian S Department of Chemical Engineering 17

18 1. Straight Line method A D P L n A D 10 A D 100 Sum of D n and B v at the end of service life will be the original sum invested i.e $1100 Years (n)! Book value at the beginning of the year (B v ), $ Annual Depreciation (A D ), $ Depreciation upto any age (or time) (D n ) or Cumulative depreciation (C D ), $ Book value at the end of the year (B v ), $ n'(p L) D n n 0( ) D B v P n' ( P L) n B v ( ) B v ( ) B v ( ) 10 Balasubramanian S Department of Chemical Engineering 18

19 1. Straight line method Depreciation by straight line method Book Value, $ Years, n Depreciation, $ Book Value, $ Depreciation, $! Accumulated depreciation Book value at the Years (or) end of the year (n) Cumulative depreciation (B v ), $ (C D ), $ Balasubramanian S Department of Chemical Engineering 19

20 2. Fixed Percentage or Declining Balance Method A D Depreciation factor (f) Book value at the beginning of the year f 1 n L P D n n'(p L) n Where, f depreciation rate (or) depreciation factor expressed in percentage; L salvage value or scrap value; P principal/ original sum or fixed capital investment; B v book value at the end or beginning of the year; n total number of life service; D n Depreciation up to any age(or time) n in life service of the asset or accumulated/ cumulative depreciation at any age (or time) n in life service. n Number of years of service upto n age (or time) Balasubramanian S Department of Chemical Engineering 20

21 2. Fixed Percentage or Declining Balance Method B V B V B V B V B V B V B V B V B V B V f 1 f A D Depreciation rate (f) Book value at the beginning of the year n L P A D A D A D Note: Depreciation rate f in fixed percentage or declining balance method is constant for the entire service life of the equipment Balasubramanian S Department of Chemical Engineering 21

22 2. Fixed Percentage or Declining Balance Method! Depreciation Book value expense at the Depreciation Years (or) beginning rate n Annual of the year f Depreciation B v (A D ), $ Cumulative Book depreciation value at (C D ), $ the end of (or) the year D n (B v ), $ Balasubramanian S Department of Chemical Engineering 22

23 2. Fixed Percentage or Declining Balance Method Book Value, $ Depreciation by fixed percentage method Years, n Deprecia(on, $ Book Value Depreciation! Cumulative depreciation Book value at Years (C D ), $ the end of the n (or) year D n (B v ), $ Balasubramanian S Department of Chemical Engineering 23

24 3. Sinking Fund Method i' A D (P L) (1+ i') n 1 D n (P L) i' (1+ i') n 1 i' (1+ i') n' A D ( ) ( ) i' (1+ i') B v P (P L) n 1 i' (1+ i') n' 1 B V 1100 ( ) D 1 ( ) 0.06 ( ) ( ) ( ) ( ) In the same manner up to the end of tenth year A D and D n is calculated and tabulated Note: Annual depreciation in sinking fund method is constant for the entire service life of the equipment Balasubramanian S Department of Chemical Engineering 24

25 3. Sinking Fund Method i' (1+ i') B v P (P L) n 1 i' (1+ i') n' 1 B ( ) 0.06 ( ) ( ) B ( ) 0.06 ( ) ( ) In the same manner up to the end of tenth year book value is calculated and tabulated Balasubramanian S Department of Chemical Engineering 25

26 3. Sinking Fund Method! Depreciation Book value expense at the Interest Years (or) beginning of rate n Annual the year i Depreciation B v (A D ), $ Cumulative Book depreciation value at (C D ), $ the end of (or) the year D n (B v ), $ Balasubramanian S Department of Chemical Engineering 26

27 3. Sinking Fund Method Book Value, $ Depreciation by sinking fund method Years, n Book Value Deprecia1on! Depreciation, $ Book value at Years the end of the n year (B v ), $ Cumulative depreciation (C D ), $ (or) D n Balasubramanian S Department of Chemical Engineering 27

28 4. Sum the years digits method n + n Sum-of-the-years digits (or) 55! 2 2 Note: Total depreciable cost in sum-of-the years digit s method is constant for the entire service life of the equipment Book value at the end of the year Book value at the beginning of the year - Annual Depreciation i.e $ $ $609 Balasubramanian S Department of Chemical Engineering 28

29 4. Sum the years digits method Cumulative 1200 Depreciation by sum-of-the -years' method 1200 Years n Book value at the end of the year (B v ), $ depreciation (C D ),$ (or) Book Value, $ Years, n Book value Depreciation! Depreciation, $ D n Balasubramanian S Department of Chemical Engineering 29

30 4. Sum the years digits method When all the data s of four different methods are combined together Years Straight - Line Fixed percentage Sinking fund Sum-of-the-years B v C D B v C D B v C D B v C D C D represents cumulative depreciation B V represents book value at the end of the year Balasubramanian S Department of Chemical Engineering 30

31 4. Sum the years digits method When all the data s of four different methods are combined together Book value, $ Depreciation, $ Years, n Book value by straight-line method Depreciation by fixed percentage method Depreciation by sinking fund method Depreciation by sum-of-the-years' method Book value by fixed percentage method Book value by sinking fund method Book value by sum-of-the-years' method Depreciation by straight-line method Balasubramanian S Department of Chemical Engineering 31

32 Process Engineering Economics References Herbert E. Schweyer. (1955) Process Engineering Economics, Mc Graw Hill Max S. Peters, Kaus D. Timmerhaus, Ronald E. West. (2004) Plant Design and Economics for Chemical Engineers, 5 th Ed., Mc Graw Hill Max Kurtz. (1920) Engineering Economics for Professional Engineers Examinations, 3 rd Ed., Mc Graw Hill Frederic C. Jelen, James H. Black. (1985) Cost and Optimization Engineering, International Student edition, Mc Graw Hill Grant L. E, Grant Ireson. W, Leavenworth S. R. (1982) Principles of Engineering Economy, 7 th Ed., John Wiley and Sons. Balasubramanian S Department of Chemical Engineering 32