Final answer:
The total annual cost for the epoxy and associated expenses such as freight and carrying costs for manufacturing 156 kayaks is $71,040. This includes $52,960 for the epoxy itself, $7,488 for the freight, and $10,592 for the carrying cost.
Step-by-step explanation:
The small boatyard built 156 epoxy kayaks last year. Each kayak requires 12 kg of epoxy, which is purchased in six-kg barrels at $170 each, with freight costs of $18 per shipment plus $1/kg. The annual carrying cost is estimated to be 20% of the inventory value. To calculate the total cost, we must include the cost of the epoxy, the freight cost, and the carrying cost.
First, we calculate the total amount of epoxy needed for all kayaks and then determine the cost:
- Amount of epoxy required for 156 kayaks: 156 kayaks × 12 kg/kayak = 1872 kg.
- Number of barrels required: 1872 kg ÷ 6 kg/barrel = 312 barrels.
- Cost of epoxy: 312 barrels × $170/barrel = $52,960.
- Freight costs for the barrels: $18/shipment × 312 shipments = $5,616.
- Additional freight cost per kg: 1872 kg × $1/kg = $1,872.
- Total freight cost: $5,616 + $1,872 = $7,488.
- Total cost of epoxy and freight: $52,960 + $7,488 = $60,448.
Next, we calculate the annual carrying cost:
- Annual carrying cost: 20% of $52,960 (value of the epoxy) = $10,592.
Therefore, the total annual cost for the epoxy and its associated costs is $60,448 (epoxy and freight) + $10,592 (carrying cost) = $71,040.