Your CEO has asked for your input on making a decision: Machine A costs $500k an

Question

Your CEO has asked for your input on making a decision:

Machine A costs $500k and has an output cost of $.50/unit

Machine B costs $300k and has an output cost of $.70/unit

Machine C costs $200k and has an output cost of $1.00/unit

The sales forecast from the Marketing Department is as follows:

Worst case scenario - 25% probability – 100k units sold

Likely scenario - 50% probability – 200k units sold

Best case scenario - 25% probability – 300k units sold

Assume the machine is amortized over 10 years with no salvage value, and advise your CEO of the best machine to purchase based on the yearly cost.

Explanation / Answer

MACHINE A: SCENARIO Probability [p] Production in units Out put cost per unit (excluding depreciation) Annual Depreciation Total cost [Tc] p*Tc d=TC-E[Tc] d^2 p*d^2 Worst case 0.25 100000 0.5 50000 100000 25000 -50000 2500000000 625000000 Likely 0.50 200000 0.5 50000 150000 75000 0 0 0 Best case 0.25 300000 0.5 50000 200000 50000 50000 2500000000 625000000 150000 1250000000 Expected Total Cost = $150000 Standard deviation = [(p*d^2)]^0.5 = 1250000000^0.5 = $               35,355 Coefficient of variation = SD/E[Tc] = 35355/150000 = 0.2357 MACHINE B: SCENARIO Probability [p] Production in units Out put cost per unit (excluding depreciation) Annual Depreciation Total cost [Tc] p*Tc d=TC-E[Tc] d^2 p*d^2 Worst case 0.25 100000 0.7 30000 100000 25000 -70000 4900000000 1225000000 Likely 0.50 200000 0.7 30000 170000 85000 0 0 0 Best case 0.25 300000 0.7 30000 240000 60000 70000 4900000000 1225000000 170000 2450000000 Expected Total Cost = $170000 Standard deviation = [(p*d^2)]^0.5 = 2450000000^0.5 = $               49,497 Coefficient of variation = SD/E[Tc] = 49497/170000 = 0.2912 MACHINE C: SCENARIO Probability [p] Production in units Out put cost per unit (excluding depreciation) Annual Depreciation Total cost [Tc] p*Tc d=TC-E[Tc] d^2 p*d^2 Worst case 0.25 100000 1 20000 120000 30000 -100000 10000000000 2500000000 Likely 0.50 200000 1 20000 220000 110000 0 0 0 Best case 0.25 300000 1 20000 320000 80000 100000 10000000000 2500000000 220000 5000000000 Expected Total Cost = $220000 Standard deviation = [(p*d^2)]^0.5 =5000000000^0.5 = $               70,711 Coefficient of variation = SD/E[Tc] = 70711/220000 = 0.3214 ADVICE: The best machine is Machine A, as it has the lowest expected tota cost at $150000, with lowest COV of 0.2357.

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