Two alternative machines are being considered for a cost-reduction project.
• Machine A has a first cost of $60,000 and a salvage value (after tax) of $22,000 at the end of six years of service life. The probabilities of annual after-tax operating costs of this machine are estimated as follows:
Annual O&M Costs Probability
$5,000.............................0.20
8,000..............................0.30
10,000..............................0.30
12,000..............................0.20
Machine B has an initial cost of $35,000, and its estimated salvage value (after tax) at the end of four of service is negligible. The annual after-tax 'rating costs are estimated to be as follows:
Annual O&M Costs Probability
$8,000............................0.10
10.000............................0.30
12.000............................0.40
14.000............................0.20
The MARR on this project is 10%. The required service period of these machines is estimated to be 12 years, and no technological advance in either machine is expected.
(a) Assuming independence, calculate the mean and variance for the equivalent annual cost of operating each machine.
(b) From the results of part (a), calculate the probability that the annual cost of operating machine A will exceed the cost of operating machine B.