To determine if the investment is viable, we must compare the total annual costs of both production methods at the expected output level of 2,000 units.
Step 1: Calculate Total Annual Cost for the Labour-Intensive Method
This method has lower fixed costs but higher variable costs per unit.
- Formula: Total Cost = (Variable Cost per Unit × Quantity) + Fixed Costs
- Calculation: Total Cost = ($200 × 2,000) + $20,000
- Total Cost = $400,000 + $20,000 = $420,000
Step 2: Calculate Total Annual Cost for the Capital-Intensive Method
This method involves a high initial investment, leading to higher fixed costs, but reduces the variable cost per unit.
- Annual Fixed Costs:
- Depreciation: $150,000 / 5 years = $30,000
- Maintenance: $10,000
- Existing Rent: $20,000
- Total Fixed Costs: $30,000 + $10,000 + $20,000 = $60,000
- Variable Cost per Unit: $100
- Formula: Total Cost = (Variable Cost per Unit × Quantity) + Fixed Costs
- Calculation: Total Cost = ($100 × 2,000) + $60,000
- Total Cost = $200,000 + $60,000 = $260,000
Step 3: Compare and Conclude
- Labour-Intensive Total Annual Cost: $420,000
- Capital-Intensive Total Annual Cost: $260,000
Conclusion: By investing in the automated machine, FineWoods could reduce its total annual production costs by $160,000 ($420,000 - $260,000) at an output of 2,000 units. From a purely cost-based perspective, the investment is highly recommended.
Further Analysis (Break-Even Point):
We can find the output level where both methods cost the same:
($200 × Q) + $20,000 = ($100 × Q) + $60,000
100Q=40,000
Q = 400 units.
This means the investment is more cost-effective for any output level above 400 units per year.