The design of a system is to be chosen from two design alternatives. The system
ID: 2814141 • Letter: T
Question
The design of a system is to be chosen from two design alternatives. The system will have a life of 12 years. Each design alternative has a life-cycle cost associated with an expected future. The tables below give the life-cycle cost (in millions of dollars) for Design 1 for the 3 possible futures F1, F2, and F3; and the life-cycle cost (in illions of dollars) for Design 2 for the 3 possible futures F1, F2, and F3. The probability of occurrence for F1-30%; the probability of occurrence for F2-50%; and the probability of occurrence for F3- 20%. Use an interest rate of 10% Design Year 1 Year 2 Year 3 Year4 Year 5 Year 6 Year7 Year8 Year 9Year 10 Year 11 Year 12 Cost tCost Cost Cost Cost 0.4 0.6 0.8 CostCostCost 0.8 Cost Cost Cost 0.8 Cost 0.8 0.6 0.8 0.9 0.8 0.8 0.8 0.8 0.8 F2 F3 1.2 1.2 1.2 1.2 1.2 Design Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year7 Year8 Year 9Year 10 Year 11 Year 12 Cost Cost 0.4 0.8 0.8 Cost Cost F1 F2 F3 Cost 2.5 3.0 Cost 2.5 3.0 Cost 2.5 3.0 3.1 Cost otCost 2.5 3.0 0.4 2.5 3.0 2.5 3.0 2.5 0.6 0.6 a) Which design alternative is most desirable from an expected cost viewpoint? b) Which design alternative is most desirable using the Laplace Criterion?Explanation / Answer
As can be seen from the below tables, in both cases Design 1 is desirable. Reason: Present Value is lower in both the cases.
a
b Laplace: i.e. equal probability of all the 3 scenarios
16.27
Year Design 1 1 2 3 4 5 6 7 8 9 10 11 12 Sum Probability Expected Value F1 0.4 0.6 5 7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 19.40 0.3 Present Value (F1 at 10% interest) 0.4 0.5 3.8 4.8 0.5 0.5 0.4 0.4 0.3 0.3 0.3 0.3 12.31 0.3 3.69 F2 0.6 0.8 1 5 10 1 1 1 1 1 1 1 24.40 0.5 Present Value (F2 at 10% interest) 0.5 0.7 0.8 3.4 6.2 0.6 0.5 0.5 0.4 0.4 0.4 0.3 14.61 0.5 7.30 F3 0.8 0.9 1 7 10 1.2 1.2 1.2 1.2 1.2 1.2 1.2 28.10 0.2 Present Value (F3 at 10% interest) 0.7 0.7 0.8 4.8 6.2 0.7 0.6 0.6 0.5 0.5 0.4 0.4 16.84 0.2 3.37 Total 14.36 Year Design 2 1 2 3 4 5 6 7 8 9 10 11 12 Sum Probability Expected Value F1 0.4 0.4 0.4 1 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 22.70 0.3 Present Value (F1 at 10% interest) 0.4 0.3 0.3 0.7 1.9 1.4 1.3 1.2 1.1 1.0 0.9 0.8 11.10 0.3 3.33 F2 0.6 0.8 3 6 3 3 3 3 3 3 3 3 34.40 0.5 Present Value (F2 at 10% interest) 0.5 0.7 2.3 4.1 1.9 1.7 1.5 1.4 1.3 1.2 1.1 1.0 18.49 0.5 9.25 F3 0.6 0.8 1 5 6 3.1 3.1 3.1 3.1 3.1 3.1 3.1 35.10 0.2 Present Value (F3 at 10% interest) 0.5 0.7 0.8 3.4 3.7 1.7 1.6 1.4 1.3 1.2 1.1 1.0 18.47 0.2 3.69b Laplace: i.e. equal probability of all the 3 scenarios
Year Design 1 1 2 3 4 5 6 7 8 9 10 11 12 Sum Probability Expected Value F1 0.4 0.6 5 7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 19.40 0.333333 Present Value (F1 at 10% interest) 0.4 0.5 3.8 4.8 0.5 0.5 0.4 0.4 0.3 0.3 0.3 0.3 12.31 0.3 4.10 F2 0.6 0.8 1 5 10 1 1 1 1 1 1 1 24.40 0.333333 Present Value (F2 at 10% interest) 0.5 0.7 0.8 3.4 6.2 0.6 0.5 0.5 0.4 0.4 0.4 0.3 14.61 0.3 4.87 F3 0.8 0.9 1 7 10 1.2 1.2 1.2 1.2 1.2 1.2 1.2 28.10 0.333333 Present Value (F3 at 10% interest) 0.7 0.7 0.8 4.8 6.2 0.7 0.6 0.6 0.5 0.5 0.4 0.4 16.84 0.3 5.61 Total 14.59 Year Design 2 1 2 3 4 5 6 7 8 9 10 11 12 Sum Probability Expected Value F1 0.4 0.4 0.4 1 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 22.70 0.333333 Present Value (F1 at 10% interest) 0.4 0.3 0.3 0.7 1.9 1.4 1.3 1.2 1.1 1.0 0.9 0.8 11.10 0.3 3.70 F2 0.6 0.8 3 6 3 3 3 3 3 3 3 3 34.40 0.333333 Present Value (F2 at 10% interest) 0.5 0.7 2.3 4.1 1.9 1.7 1.5 1.4 1.3 1.2 1.1 1.0 18.49 0.3 6.16 F3 0.6 0.8 1 5 6 3.1 3.1 3.1 3.1 3.1 3.1 3.1 35.10 0.333333 Present Value (F3 at 10% interest) 0.5 0.7 0.8 3.4 3.7 1.7 1.6 1.4 1.3 1.2 1.1 1.0 18.47 0.3 6.16 Total 16.02 Total16.27