Two alternative machines are being considered for a cost reduction project. Mach
ID: 2662860 • Letter: T
Question
Two alternative machines are being considered for a cost reduction project.Machine A has a first cost of $60,000 and a salvage value of $22,000 at the end of it 6 year service life. Annual operating costs of this machine and the associated probabilities 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 a first cost of $35,000 and its salvage value at the end of it 4-year service life is negligible. Annual operating costs of this machine and the associated probabilities are estimated 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 is estimated to be 12 years. Assuming independence, calculate the mean and variance for the equivalent annual cost of operating each machine.
Explanation / Answer
Solution:
(a)
• Machine A:
CR(10%) of A = ($60,000 - $22,000) (A/P, 10%,6)
+ (0.10) ($22,000)
= $10,924
E[NAW(10%)] of A = ($5,000) (0.20) + ($8,000) (0.30)
+ ($10, 000) (0.30) + ($12,000) (0.20)
+ $10,924
= $19,725
Var[NAW(10%)] of A = (15,924 - 19,725)2 (0.20)
+ (18,924 - 19, 725)2 (0.30)
+ (20,924 - 19, 725)2 (0.30)
+ (22,924 - 19, 725)2 (0.20)
= 5,560,000
• Machine B:
CR(10%) of B = $35,000 (A/P, 10%, 4)
= $11,042
E[NAW(10%)] of B= ($8,000) (0.10) + ($10,000) (0.30)
+ ($12,000) (0.40) + ($14,000) (0.20)
+ $11,042
= $22,442
Var[NAW(10%)] of B = (19,042 - 22,442)2 (0.10)
+ (21,042 - 22,442)2 (0.30)
+ (23,042 - 22,442)2 (0.40)
+ (25,042 - 22,442)2 (0.20)
= 3,240,000
(b) Prob[NAW(10%) of A> NAW(10%) of B]:
Joint event Joint probability