TM 661 Engineering Economics for Managers

1. TM 661Engineering Economics forManagers 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. 25,000 1 2 3 4 5 100,000 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. i = 15%

4. 25,000 1 2 3 4 5 100,000 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. i = 15% NPW = -100 + 25(P/A,15,5) = -16,196

5. 25,000 1 2 3 4 5 100,000 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. i = 15% NPW = -100 + 25(P/A,15,5) = -16,196

6. 40,000 1 2 3 4 5 100,000 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.

7. 40,000 1 2 3 4 5 100,000 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. NPW = -100 + 40(P/A,15,5) = 34,086

8. 40,000 1 2 3 4 5 100,000 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. NPW = -100 + 40(P/A,15,5) = 34,086

9. 32,000 1 2 3 4 5 100,000 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

10. 32,000 1 2 3 4 5 100,000 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 NPW = -100 + 32(P/A,15,5) = 7,269

11. 32,000 1 2 3 4 5 100,000 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 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. A 1 2 3 4 5 100,000 Motivation NPW = -100 + A(P/A,15,5) > 0

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

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

17. Break-Even Analysis Site Fixed Cost/Yr Variable Cost A=Austin $ 20,000 $ 50 S= Sioux Falls 60,000 40 D=Denver 80,000 30 TC = FC + VC * X

18. Break-Even Analysis 250,000 200,000 Austin 150,000 S. Falls Total Cost Denver 100,000 50,000 0 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 Volume Break-Even (cont)

19. 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.

20. 50 hrs 1000 units Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $50 / hr = $ 7.50 / unit

21. 50 hrs 1000 units 7.5X 1 2 3 4 5 50,000 300,000 Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $25 / hr = $ 7.50 / unit

22. 50 hrs 1000 units 7.5X 1 2 3 4 5 50,000 300,000 Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $15 - 5 - $25 / hr = $ 7.50 / unit 300,000(A/P,15,5) + 50,000 = 7.5X 139,495 = 7.5X X = 18,600

23. 35,000 1 2 3 4 5 100,000 Sensitivity Suppose we consider the following cash flow diagram: NPW = -100 + 35(P/A,15,5) = $ 17,325 i = 15%

24. 35,000(1+X) 1 2 3 4 5 100,000 Sensitivity Suppose we don’t know A=35,000 exactly but believe we can estimate it within some percentage error of + X. i = 15%

25. 35,000(1+X) 1 2 3 4 5 100,000 Sensitivity Then, EUAW = -100(A/P,15,5) + 35(1+X) > 0 35(1+X) > 100(.2983) X > -0.148 i = 15%

26. NPV vs. Errors in A 50,000 40,000 30,000 20,000 NPV 10,000 0 -0.30 -0.20 -0.10 0.00 0.10 0.20 (10,000) (20,000) Error X Sensitivity (cont.)

27. 35,000 1 2 3 4 5 100,000(1+X) Sensitivity (Ao) Now suppose we believe that the initial investment might be off by some amount X. i = 15%

28. NPV vs Initial Cost Errors 50,000 40,000 30,000 20,000 NPV 10,000 0 -0.30 -0.20 -0.10 0.00 0.10 0.20 (10,000) (20,000) Error X Sensitivity (Ao)

29. NPV vs Errors 50,000 40,000 30,000 20,000 NPV 10,000 0 -0.30 -0.20 -0.10 0.00 0.10 0.20 (10,000) (20,000) Error X Sensitivity (A & Ao) Errors in initial cost Errors in Annual receipts

30. 35,000 i = 15% 1 2 3 4 5 6 7 100,000 Sensitivity (PH) Now suppose we believe that the planning horizon might be shorter or longer than we expected.

31. NPV vs Planning Horizon 50,000 40,000 30,000 20,000 10,000 PH 0 0 1 2 3 4 5 6 7 (10,000) (20,000) (30,000) NPV Sensitivity (PH)

32. NPV vs Errors 50,000 40,000 30,000 20,000 NPV 10,000 0 -0.30 -0.20 -0.10 0.00 0.10 0.20 (10,000) (20,000) Error X Sensitivity (Ind. Changes) n=7 n=3 Planning Horizon Errors in initial cost Errors in Annual receipts MARR

33. 50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 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%).

34. 50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 You Solve It!!! 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%).

35. 50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 Multivariable Sensitivity EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > 29.83

36. 50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 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

37. Unfavorable + 10% Favorable Multivariable Sensitivity

38. 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. t A1t A2t A3t 0 (50,000) (75,000) (100,000) 1 18,000 25,000 32,000 2 18,000 25,000 32,000 3 18,000 25,000 32,000 4 18,000 25,000 32,000 5 18,000 25,000 32,000

39. t A1t A2t A3t 0 (50,000) (75,000) (100,000) 1 18,000 25,000 32,000 2 18,000 25,000 32,000 3 18,000 25,000 32,000 4 18,000 25,000 32,000 5 18,000 25,000 32,000 MARR = NPV1 NPV2 NPV3 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) Mutually Exclusive Alt.

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