A manufacturer may never be able to determine the precise cost of its individual products. The reason is that most of the manufacturing costs (other than materials and some labor) are indirect costs. This means that most of the manufacturing costs are not directly traceable to individual products and will need to be allocated to them. Examples of indirect manufacturing costs include the rent, property taxes, depreciation, heat, lighting, indirect production workers pay and benefits, repairs, maintenance, and others that occur in the factory.
In addition to the manufacturing costs, there are selling, general and administrative (SG&A) expenses and perhaps interest expense. Generally, accountants do not consider these expenses to be product costs. As a result these expenses are reported on the income statement when they occur and without any allocation to the products. However, these expenses are associated with some or all of the products.
The manufacturer can attempt to calculate the costs and expenses of each of its products, but I don't think the result will be the true, precise cost. In addition to the allocations (which are viewed as arbitrary), consider that changes in volume will affect a product's cost. For example, if a company's total fixed costs remain constant but its volume of products decreases by 20%, the cost of each product will increase. If volume increases, the cost of each product will decrease.
Activity-based costing (ABC) is an attempt to improve the allocation of costs by identifying more of the root causes of the costs (rather than merely spreading costs to products based on machine hours). Even with ABC there will be arbitrary allocations which will prevent knowing each product's precise cost.