Question

It costs a company \(\$ 14\) of variable costs and \(\$ 6\) of fixed costs to produce product A that sells for \(\$ 30\). A foreign buyer offers to purchase 3,000 units at \(\$ 18\) each. If the special offer is acceptedand produced with unused capacity, net income will: a. decrease \(\$ 6,000\). c. increase \(\$ 12,000\). b. increase \(\$ 6,000\). d. increase \(\$ 9,000\).

Short answer

Net income will increase by $12,000. (Option c.)

Step-by-step solution

Identify Given Information

We have the following information: 1) Variable cost per unit is $14. 2) Fixed cost per unit is $6. 3) Selling price per unit is $30. The foreign buyer offers to buy 3,000 units at $18 each. These units will be produced with unused capacity, implying no additional fixed costs.

Calculate Relevant Costs and Revenues

Since the fixed costs are incurred already and the production will use unused capacity, only the variable costs and the offered price affect the decision. The relevant cost per unit is $14 (variable cost), and the offered price per unit is $18.

Calculate Contribution Margin per Unit

The contribution margin per unit is the difference between the offered price and the variable cost per unit. It can be calculated as follows: \[ \text{Contribution margin per unit} = 18 - 14 = 4 \]

Calculate Total Contribution Margin for Special Order

Multiply the contribution margin per unit by the number of units in the special offer: \[ \text{Total contribution margin} = 4 \times 3,000 = 12,000 \]

Determine the Effect on Net Income

Since the fixed costs remain unaffected due to unused capacity, the effect on net income is the same as the total contribution margin from the special order, which is $12,000.

Key concepts

Understanding Variable Costs

Variable costs are costs that change with the level of production. In other words, as you produce more units, these costs increase; produce fewer, and they decrease. Typical examples include materials and labor that are directly involved in the production of a product.
In our exercise, the variable cost per unit is given as $14. This means for each unit of the product produced, the cost is $14. The impact is significant when analyzing special sales offers, as only variable costs need to be considered if the production uses unused capacity. This is because, under such conditions, fixed costs are already covered by other production. So, when evaluating a new sales opportunity, understanding how these costs behave is crucial for financial analysis.

The Role of Fixed Costs

Fixed costs, unlike variable costs, do not change with the level of production. Whether you produce zero units or thousands, these costs remain constant. Examples include rent, salaries of permanent staff, and machinery costs.
In this scenario, the fixed cost per unit is $6, but since the new order uses unused capacity, these costs do not increase despite accepting a new order.
This is a critical insight, as accepting the special order means the company does not incur any additional fixed expenses. Understanding fixed costs ensures that businesses make decisions that maximize profit without inadvertently increasing expenses.

Contribution Margin as a Decision Tool

The contribution margin is the amount remaining from sales revenue after variable costs have been deducted, which contributes to covering fixed costs and generating profit. It is calculated by subtracting variable costs from the selling price.
In our case, the foreign buyer offers \(18 per unit; with variable costs at \)14, the contribution margin per unit is calculated as follows:
\[ \text{Contribution margin per unit} = 18 - 14 = 4 \]
Thus, for each unit sold under the special offer, the contribution to fixed costs and profits is $4.
To find the total contribution margin, we multiply by the number of units sold:
\[\text{Total contribution margin} = 4 \times 3,000 = 12,000\]
This metric helps determine the profitability of expanding production or accepting special offers without affecting fixed costs.

Evaluating the Impact on Net Income

Net income is the actual profit after all costs are deducted from total revenue. With the special offer using unused capacity, only the variable costs change, and there's no impact on fixed costs.
Thus, the additional income earned from the special order is entirely due to the contribution margin of \(12,000, as calculated previously.
In this context, since the fixed costs do not increase, the net income impact equals the total contribution margin derived from the special order:
\(\text{Net income impact} = \text{Total contribution margin} = 12,000\)
Therefore, accepting the offer will increase net income by \)12,000, enhancing profitability without any additional fixed cost burden. This makes understanding the relationship between costs and net income essential for sound financial decision-making.