Step 1: Calculate Total Cost for Batch Production
- Number of batches:
100,000 packs / 1,000 packs per batch = 100 batches
- Total setup costs:
100 batches * $200/batch = $20,000
- Total variable costs:
100,000 packs * $0.80/pack = $80,000
- Total Annual Cost (Batch):
Fixed Costs + Total Setup Costs + Total Variable Costs
$50,000 + $20,000 + $80,000 = $150,000
Step 2: Calculate Cost per Unit for Batch Production
- Unit Cost (Batch):
Total Annual Cost / Total Packs
$150,000 / 100,000 packs = $1.50 per pack
Step 3: Calculate Total Cost for Flow Production
- Annual machinery cost (depreciation):
$250,000 / 5 years = $50,000 per year
- Total fixed costs:
Annual Fixed Costs + Annual Machinery Cost
$80,000 + $50,000 = $130,000
- Total variable costs:
100,000 packs * $0.30/pack = $30,000
- Total Annual Cost (Flow):
Total Fixed Costs + Total Variable Costs
$130,000 + $30,000 = $160,000
Step 4: Calculate Cost per Unit for Flow Production
- Unit Cost (Flow):
Total Annual Cost / Total Packs
$160,000 / 100,000 packs = $1.60 per pack
Step 5: Recommendation
Based on these calculations, Batch Production is the more cost-effective method at an annual output of 100,000 units. It has a lower total annual cost ($150,000 vs $160,000) and a lower cost per unit ($1.50 vs $1.60). The high initial investment and fixed costs of flow production are not justified at this production volume.