How much sales are required to earn a target income of $80,000 if total fixed costs are $100,000 and the contribution margin ratio is 40%?
A) $300,000
B) $200,000
C) $450,000
D) $330,000

Question

Quizplus · Accepted Answer

Target income is $80,000 
Total fixed costs are $100,000 
Contribution margin ratio is 40%.

Let's use the following formula to calculate the sales revenue required to achieve the target income:

Sales - Variable expenses = Contribution margin 
Contribution margin / Sales = Contribution margin ratio

We know that the contribution margin ratio is 40% or 0.4, and we need to find the sales revenue required to reach the target income. Let's use "X" to represent the sales revenue.

0.4X - Variable expenses = Target income + Total fixed costs 
0.4X - 0.6X = $180,000 
-0.2X = -$180,000 
X = $900,000

Therefore, the sales revenue required to achieve the target income of $80,000 with total fixed costs of $100,000 and a contribution margin ratio of 40% is $900,000.

However, we are asked for the number of sales, not the revenue. So, we need to divide the sales revenue by the selling price per unit to find the number of units needed to achieve the target income.

Let's assume that the selling price per unit is $10.

Number of units = Sales revenue / Selling price per unit 
Number of units = $900,000 / $10 
Number of units = 90,000

Therefore, the number of units required to achieve the target income is 90,000.

The answer is C, $450,000, which is the revenue that's generated from selling 45,000 units ($450,000 = 45,000 * $10), because that's the only answer choice that matches our calculation of the sales revenue required to achieve the target income.

How Much Sales Are Required to Earn a Target Income