Question

Astro company sold 28,500 units of its only product and reported income of $57,900 for the current year. During a planning session for next year's activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by $142,000. Total units sold and the selling price per unit will not change. What will be the effect on the company's income for the next year if it installs the machine?

1) The company's income will increase by $28,950
2) The company's income will decrease by $28,950
3) The company's income will increase by $57,900
4) The company's income will decrease by $57,900

Answer 1

The company's income will decrease because the additional fixed costs from installing the machine are not fully offset by the savings in variable costs.

Step-by-step explanation:

To determine the effect on the company's income for the next year if it installs the machine, we need to first calculate the current variable costs. Since the installation of the machine would reduce variable costs by 50% but increase annual fixed costs by $142,000, we can calculate the new income as follows:

Let's denote the current total variable costs as 'VC'. The income can be represented as:

Income = (Selling Price per Unit * Units Sold) - (VC + Fixed Costs)

We are given that the income currently is $57,900. Therefore:

$57,900 = (Selling Price per Unit * 28,500) - (VC + Current Fixed Costs)

With the machine installed:

New Income = (Selling Price per Unit * 28,500) - (0.5 * VC + Current Fixed Costs + $142,000)

We can rearrange to find the 'New Income':

New Income = Income + (0.5 * VC) - $142,000

Substituting the current income, we get:

New Income = $57,900 + (0.5 * VC) - $142,000

Since the only unknown in the equation is VC, we can conclude that the new income will be less than the current income by the amount of $142,000, assuming VC > 0.

Therefore, the company's income will decrease for the next year by the amount of fixed costs added minus the savings from variable costs.