The design of a system is to be pursued from one of the available alternatives.
ID: 438636 • Letter: T
Question
The design of a system is to be pursued from one of the available alternatives. Each alternative has a life cycle cost associated with an expected future. The costs for the corresponding futures are given in the following table (in millions of dollars). If the probabilities of occurrence of the futures are 30%, 50% and 20% respectively which alternative is most desirable from an expected cost viewpoint? Assume interest 10%.
Design 1 Years
Future 1 2 3 4 5 6 7 8 9 10 11 12
Optimistic 0.4 0.6 5.0 7.0 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
Expected 0.6 0.8 1.0 5.0 10.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
Pessimistic 0.8 0.9 1.0 7.0 10.0 1.2 1.2 1.2 1.2 1.2 1.2 1.2
Design 2 Years
Future 1 2 3 4 5 6 7 8 9 10 11 12
Optimistic 0.4 0.4 0.4 1.0 3.0 2.5 2.5 2.5 2.5 2.5 2.5 2.5
Expected 0.6 0.8 1.0 3.0 6.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
Pessimistic 0.6 0.8 1.0 5.0 6.0 3.1 3.1 3.1 3.1 3.1 3.1 3.1
Explanation / Answer
design 1
Optimistic NPV (millions)= 0.4/1.1 + 0.6/1.12 + ...........+0.8/1.111 + 0.8/1.112
similarily calculate NPV for Expected and pessimistic
now design 1 expected cost= 0.3*(NPV-optimistic) + 0.5*(NPV-Expected)+ 0.2*(NPV-pessimistic)
repeat the same procedure for design 2 and calculate expected cost
which ever is less of the two costs is the choosen alternative
since i dunnot have calculator right now i am only mentioning the procedure. this one is correct procedure