1. IENG 217 Cost Estimating for Engineers Break Even & Sensitivity

2. Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. Your boss asks you to figure out if it should be done.

3. Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. 1 2 3 4 5 100,000 25,000 i = 15%

4. Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. 1 2 3 4 5 100,000 25,000 NPW = -100 + 25(P/A,15,5) = -16,196 i = 15%

5. Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. 1 2 3 4 5 100,000 25,000 NPW = -100 + 25(P/A,15,5) = -16,196 i = 15%

6. Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market. 1 2 3 4 5 100,000 40,000

7. Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market. 1 2 3 4 5 100,000 40,000 NPW = -100 + 40(P/A,15,5) = 34,086

8. Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market. 1 2 3 4 5 100,000 40,000 NPW = -100 + 40(P/A,15,5) = 34,086

9. Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate 1 2 3 4 5 100,000 32,000

10. Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate 1 2 3 4 5 100,000 32,000 NPW = -100 + 32(P/A,15,5) = 7,269

11. Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate 1 2 3 4 5 100,000 32,000 NPW = -100 + 32(P/A,15,5) = 7,269

12. Motivation Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know....

13. Motivation Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know.... I’ll do anything, just tell me what numbers you want to use!

14. Motivation 1 2 3 4 5 100,000 A NPW = -100 + A(P/A,15,5) > 0

15. Motivation 1 2 3 4 5 100,000 A NPW = -100 + A(P/A,15,5) > 0 A > 100(A/P,15,5) > 29,830

16. A < 29,830 A > 29,830 Motivation 1 2 3 4 5 100,000 A

17. Fixed vs Variable u Fixed - do not vary with production general admin., taxes, rent, depreciation u Variable - costs vary in proportion to the quantity of output material, direct labor, material handling

18. Fixed vs Variable u Fixed - do not vary with production general admin., taxes, rent, depreciation u Variable - costs vary in proportion to the quantity of output material, direct labor, material handling TC(x) = FC + VC(x)

19. Fixed vs Variable TC(x) = FC + VC(x) FC TC VC

20. Break Even Profit = R(x) - FC - VC(x) FC TC R

21. Break-Even Analysis SiteFixed Cost/YrVariable Cost A=Austin $20,000 $50 S= Sioux Falls60,000 40 D=Denver80,00030 TC = FC + VC * X

22. Break-Even (cont) Break-Even Analysis 0 50,000 100,000 150,000 200,000 250,000 05001,0001,5002,0002,5003,0003,5004,000 Volume Total Cost Austin S. Falls Denver

23. Example u Company produces crude oil from a field where the basis of decision is the number of barrels produced. Two methods for production are: u automated tank battery u manually operated tank battery

24. Example u Automated tank battery u annual depreciation = $3,200 u annual maintenance = $5,200 u Other fixed & variable costs

25. Automated Tank Battery TC(x) = (982 + 3,200 + 5,200) + 0.01136 X

26. Example u Manual Tank Battery u annual depreciation = $2,000 u annual maintenance = $7,500 u other costs

27. Manual Tank Battery TC(x) = (2,000 + 7,500 + 358) + 0.00810 X

28. BreakEven TC A (x) = TC M (x)

29. BreakEven TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x

30. BreakEven TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x 0.0033 x = 476

31. BreakEven TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x 0.0033 x = 476 x * = 145,000

32. Example

33. Average vs Marginal Cost x xTC xAC )( )(  x xTC xMC    )( )(

34. Example u Cost of running an automobile is TC(x) = $950 + 0.20 x where $950 covers annual depreciation and maintenance and x is the number of miles driven per year

35. Example 20.0 950)( )(  xx xTC xAC 20.0 ).0950()( )(        x x x xTC xMC

36. Example Average vs Marginal Cost (Automobile) 0.0 0.5 1.0 1.5 010,00020,00030,000 Miles per year cost Average Marginal

37. Marginal Returns

38. Example u Small firm sells garden chemicals. x = number of tons sold per year SP(x) = selling price per ton (to sell x tons) = $(800 - 0.8x) TR(x) = total revenue at x tons = $(800 - 0.8x) x TC(x) = total production cost for x tons = $(8,000 + 400x)

39. Example TP(x) = total profit at x tons = TR(x) - TX(x) = (800x - 0.8x 2 ) - (8,000 + 400x) = -0.8x 2 + 400x - 8,000 Compute a.x at which revenue is maximized b.marginal revenue at max revenue c.x at which profit is maximized d.average profit at max profit

40. Example TR(x) = -0.8x 2 + 800x a.max R tonsx x x xx x xTR 500 8006.1 ) 8.0( 0 )( 2       

41. Example TR(x) = -0.8x 2 + 800x b.Marginal Revenue MR(500) = -1.6(500) + 800 = $0

42. Example TP(x) = -0.8x 2 + 400x - 8,000 c.max profit 250 4006.1 )000,84008.( 0 )( 2        x x x xx x xTP

43. Example TP(x) = -0.8x 2 + 400x - 8,000 c.average profit tonAP xx x xx x /168$)250( /000,84008.0 000,84008.0 )( 2    

44. Break-Even Analysis SiteFixed Cost/YrVariable Cost A=Austin $20,000 $50 S= Sioux Falls60,000 40 D=Denver80,00030 TC = FC + VC * X

45. Break-Even (cont) Break-Even Analysis 0 50,000 100,000 150,000 200,000 250,000 05001,0001,5002,0002,5003,0003,5004,000 Volume Total Cost Austin S. Falls Denver

46. Class Problem A firm is considering a new product line and the following data have been recorded: Sales price$ 15 / unit Cost of Capital$300,000 Overhead$ 50,000 / yr. Oper/maint.$ 50 / hr. Material Cost$ 5 / unit Production 50 hrs / 1,000 units Planning Horizon 5 yrs. MARR 15% Compute the break even point.

47. Class Problem

48. Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $50 / hr = $ 7.50 / unit 50 hrs 1000 units

49. Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $25 / hr = $ 7.50 / unit 50 hrs 1000 units 1 2 3 4 5 300,000 7.5X 50,000

50. Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $25 / hr = $ 7.50 / unit 50 hrs 1000 units 1 2 3 4 5 300,000 7.5X 50,000 300,000(A/P,15,5) + 50,000 = 7.5X 139,495 = 7.5X X = 18,600

51. Suppose we consider the following cash flow diagram: NPW = -100 + 35(P/A,15,5) = $ 17,325 Sensitivity 1 2 3 4 5 100,000 35,000 i = 15%

52. Suppose we don’t know A=35,000 exactly but believe we can estimate it within some percentage error of + X. Sensitivity 1 2 3 4 5 100,000 35,000(1+X) i = 15%

53. Then, EUAW = -100(A/P,15,5) + 35(1+X) > 0 35(1+X) > 100(.2983) X > -0.148 Sensitivity 1 2 3 4 5 100,000 35,000(1+X) i = 15%

54. Sensitivity (cont.) NPV vs. Errors in A (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50,000 -0.30-0.20-0.100.000.100.20 Error X NPV

55. Now suppose we believe that the initial investment might be off by some amount X. Sensitivity (A o ) 1 2 3 4 5 100,000(1+X) 35,000 i = 15%

56. Sensitivity (A o ) NPV vs Initial Cost Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50,000 -0.30-0.20-0.100.000.100.20 Error X NPV

57. Sensitivity (A & A o ) NPV vs Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50,000 -0.30-0.20-0.100.000.100.20 Error X NPV Errors in initial cost Errors in Annual receipts

58. Now suppose we believe that the planning horizon might be shorter or longer than we expected. Sensitivity (PH) 1 2 3 4 5 6 7 100,000 35,000 i = 15%

59. Sensitivity (PH) NPV vs Planning Horizon (30,000) (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50,000 01234567 NPV PH

60. Sensitivity (Ind. Changes) NPV vs Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50,000 -0.30-0.20-0.100.000.100.20 Error X NPV Errors in initial cost Errors in Annual receipts n=3 n=7 Planning Horizon MARR

61. Multivariable Sensitivity Suppose our net revenue is composed of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%). 1 2 3 4 5 100,000 50,000(1+X) 20,000(1+Y)

62. Multivariable Sensitivity Suppose our net revenue is compose of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%). 1 2 3 4 5 100,000 50,000(1+X) 20,000(1+Y) You Solve It!!!

63. Multivariable Sensitivity

64. EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > 29.83 1 2 3 4 5 100,000 50,000(1+X) 20,000(1+Y)

65. Multivariable Sensitivity EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > 29.83 50X - 20Y > -0.17 X > 0.4Y - 0.003 1 2 3 4 5 100,000 50,000(1+X) 20,000(1+Y)

66. Multivariable Sensitivity Unfavorable Favorable + 10%

67. Mutually Exclusive Alt. Suppose we work for an entity in which the MARR is not specifically stated and there is some uncertainty as to which value to use. Suppose also we have the following cash flows for 3 mutually exclusive alternatives. tA 1t A 2t A 3t 0(50,000)(75,000)(100,000) 118,000 25,000 32,000 218,000 25,000 32,000 318,000 25,000 32,000 418,000 25,000 32,000 518,000 25,000 32,000

68. Mutually Exclusive Alt. tA 1t A 2t A 3t 0(50,000)(75,000)(100,000) 118,000 25,000 32,000 218,000 25,000 32,000 318,000 25,000 32,000 418,000 25,000 32,000 518,000 25,000 32,000 MARR =NPV 1 NPV 2 NPV 3 4.0%30,133 36,296 42,458 6.0%25,823 30,309 34,796 8.0%21,869 24,818 27,767 10.0%18,234 19,770 21,305 12.0%14,886 15,119 15,353 14.0%11,795 10,827 9,859 16.0%8,937 6,857 4,777 18.0%6,289 3,179 69 20.0%3,831 (235)(4,300)

69. Mutually Exclusive Alt. NPV vs. MARR (10,000) 0 10,000 20,000 30,000 40,000 50,000 0.0%5.0%10.0%15.0%20.0% MARR NPV NPV1 NPV2 NPV3