A firm has total fixed costs of $60,000 and a profit goal of $40,000. If variable costs per unit are 40 percent of its selling price, the profit goal will be reached if sales are at least $140,000.

Question

Quizplus · Accepted Answer

To determine if the statement is true, we need to calculate the required sales to meet the profit goal. Let's denote the selling price per unit as $P$, the variable cost per unit as $V$, and the number of units sold as $Q$. Given that $V = 0.4P$, the contribution margin per unit is $P - V = P - 0.4P = 0.6P$. The profit ($\Pi$) is given by the equation $\Pi = PQ - VQ - \text{Fixed Costs}$. To achieve a profit goal ($\Pi_{goal}$) of $40,000 with fixed costs of $60,000, we set up the equation: $0.6PQ = \Pi_{goal} + \text{Fixed Costs}$. Without the selling price ($P$) and the number of units ($Q$) specified, we cannot directly calculate the required sales ($PQ$) to be exactly $140,000 to meet the profit goal. The statement simplifies the scenario without providing a direct relationship or enough information to conclusively determine that sales of $140,000 will meet the profit goal, especially since the profit goal also depends on the contribution margin and the volume of sales, not just the total sales value.

A Firm Has Total Fixed Costs of $60,000 and a Profit