Answer :
1. Equipment cost rate for the machine is $40.94 per hour.
2. (a) Cycle time is 4,563 seconds.
(b) Average production rate without setup time is 6.35 stampings/sec.
Average production rate with setup time is 0.88 stampings/sec.
(c) Cost per stamping produced is approximately $580.18.
3. (a) Production rate is approximately 0.78 parts/sec.
(b) Finished part cost is approximately $5.91 per part.
4. The production rate and part cost remain the same at 0.78 parts/sec and $5.91 per part.
1. Equipment cost rate for the machine:
To calculate the equipment cost rate, we need to consider the initial purchase cost, repairs, and the remaining years of useful life. The formula to calculate the equipment cost rate is:
Equipment Cost Rate = (Initial Cost + Repairs) / (Remaining Years * Annual Usage)
Initial Cost = $530,000
Repairs = $125,000
Remaining Years = 4
Annual Usage = 4,000 hours
Substituting the values into the formula:
Equipment Cost Rate = ($530,000 + $125,000) / (4 * 4,000) = $655,000 / 16,000 = $40.94/hour
Therefore, the equipment cost rate for the machine is $40.94 per hour.
2. (a) Cycle time:
The cycle time is the total time required to complete one batch of stampings, including setup time and operation time.
Cycle time = Setup time + Operation time + Unloading time
Setup time = 75 min = 75 * 60 sec = 4,500 sec
Operation time = Press stroke time + Loading time
Press stroke time = 8 sec
Loading time = 42 sec
Unloading time = 13 sec
Cycle time = 4,500 sec + (8 sec + 42 sec + 13 sec) = 4,500 sec + 63 sec = 4,563 sec
(b) Average production rate with and without setup time included:
Average production rate is the number of stampings produced per unit of time.
Without setup time:
Average production rate = Batch size / (Cycle time - Setup time)
Batch size = 400 stampings
Average production rate = 400 / (4,563 sec - 4,500 sec) = 400 / 63 sec ≈ 6.35 stampings/sec
With setup time:
Average production rate = Batch size / Cycle time
Average production rate = 400 / 4,563 sec ≈ 0.88 stampings/sec
(c) Cost per stamping produced:
Cost per stamping produced includes the labor cost, equipment cost, material cost, and overhead costs.
Cost per stamping produced = (Labor cost + Equipment cost + Material cost) / Batch size
Labor cost = Labor rate * Cycle time * (1 + Labor overhead rate)
Equipment cost = Equipment cost rate * Cycle time * (1 + Equipment overhead rate)
Material cost = Starting blanks cost
Labor rate = $15.00/hr
Labor overhead rate = 42%
Equipment cost rate = $22.50/hr
Equipment overhead rate = 20%
Starting blanks cost = $0.23/pc
Batch size = 400 stampings
Substituting the values into the formula:
Labor cost = $15.00/hr * 4,563 sec * (1 + 42%) = $15.00/hr * 4,563 sec * 1.42 = $97,446.30
Equipment cost = $22.50/hr * 4,563 sec * (1 + 20%) = $22.50/hr * 4,563 sec * 1.20 = $123,177.00
Material cost = $0.23/pc * 400 = $92.00
Cost per stamping produced = ($97,446.30 + $123,177.00 + $92.00) / 400 ≈ $580.18/stamping
3. (a) Production rate:
Production rate is the number of finished parts produced per unit of time.
Production rate = 60 / Cycle time
Cycle time = 1.28 min = 1.28 * 60 sec =76.8 sec
Production rate = 60 / 76.8 sec ≈ 0.78 parts/sec
(b) Finished part cost:
Finished part cost includes the labor cost, equipment cost, tooling cost, material cost, and overhead costs.
Finished part cost = (Labor cost + Equipment cost + Tooling cost + Material cost) / Production rate
Labor cost = Labor cost rate * Cycle time
Equipment cost = Equipment cost rate * Cycle time
Tooling cost = $0.05/pc
Labor cost rate = $28.00/hr
Equipment cost rate = $44.00/hr
Tooling cost = $0.05/pc
Material cost = $0.65/pc
Substituting the values into the formula:
Labor cost = $28.00/hr * 1.28 min = $28.00/hr * 1.28 * 60 sec = $2,073.60
Equipment cost = $44.00/hr * 1.28 min = $44.00/hr * 1.28 * 60 sec = $3,302.40
Tooling cost = $0.05/pc
Material cost = $0.65/pc
Finished part cost = ($2,073.60 + $3,302.40 + $0.05/pc + $0.65/pc) / 0.78 ≈ $5.91/part
4. If machine availability = 100% and scrap rate = 0%:
The production rate and finished part cost will remain the same as calculated in part 3 since machine availability and scrap rate do not affect these parameters. Therefore, the production rate will still be approximately 0.78 parts/sec, and the finished part cost will still be approximately $5.91/part.
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