Step 1: Identify the Total Cost Formula
The formula to calculate the total annual cost for each location is:
Total Cost (TC) = Annual Fixed Costs (FC) + (Total Variable Cost per unit (VC) × Quantity (Q))
Step 2: Calculate Total Variable Cost (VC) per unit for each site.
- Site A VC: $50 (Labour) + $80 (Material) + $10 (Transport) = $140 per unit
- Site B VC: $45 (Labour) + $80 (Material) + $25 (Transport) = $150 per unit
Step 3: Calculate Total Annual Cost (TC) for Site A.
- FC = $120,000
- VC = $140
- Q = 6,000 units
- TC (Site A) = $120,000 + ($140 × 6,000) = $120,000 + $840,000 = $960,000
Step 4: Calculate Total Annual Cost (TC) for Site B.
- FC = $70,000
- VC = $150
- Q = 6,000 units
- TC (Site B) = $70,000 + ($150 × 6,000) = $70,000 + $900,000 = $970,000
Step 5: Recommendation
Based on the quantitative analysis, Site A has a lower total annual cost ($960,000) compared to Site B ($970,000) at the forecast production level of 6,000 units. Therefore, Site A is the more cost-effective option.
Further Analysis (Evaluation):
It's also useful to find the break-even output level between the two sites:
$120,000 + 140Q = $70,000 + 150Q
50,000=10Q
Q = 5,000 units.
This means if output is expected to be above 5,000 units, Site A is cheaper. If it falls below 5,000, Site B becomes the cheaper option due to its lower fixed costs. The decision depends on the confidence in the sales forecast.