Answer :
Final answer:
Vault-Tec's break-even level of sales is calculated by adding the annual fixed costs and depreciation to find total fixed costs, then setting up an equation where total sales cover these costs along with variable costs that are 75% of sales. Solving this equation yields a break-even level of sales of $5,000,000.
Explanation:
To calculate the break-even level of sales for Vault-Tec, we need to determine the total sales required to cover all costs, including both fixed and variable costs. The total fixed costs are given as $1,000,000, and we also have depreciation, which is another fixed cost, of $250,000. These two amounts combined give us total fixed costs of $1,250,000. The variable costs are equal to 75% of sales, which means for every dollar of sales, $0.75 goes toward variable costs. At the break-even point, total revenues (sales) are equal to total costs (fixed costs plus variable costs).
Let's denote the break-even level of sales as 'S'. The total costs at this level will be the sum of fixed costs and variable costs, which can be expressed as $1,250,000 + 0.75S. Because we are looking for the break-even point, total costs will equal total sales (S), giving us the equation 1,250,000 + 0.75S = S.
To solve for S, we rearrange the equation: S - 0.75S = 1,250,000, which simplifies to 0.25S = 1,250,000. Dividing both sides by 0.25, we find that S = 5,000,000. Therefore, Vault-Tec's break-even level of sales is $5,000,000, which corresponds to option D.
