Given breakeven sales in units of 31,000 and a unit contribution margin of $10, how many units must be sold to reach a target operating income of $15,000?

Question

Quizplus · Accepted Answer

First, we'll calculate the breakeven sales revenue: 
Breakeven sales units x Unit price = Breakeven sales revenue 
31,000 units x $10/unit = $310,000

Next, we'll use the formula for target operating income: 
Target operating income = (Unit contribution margin x Sales volume) - Fixed expenses 
$15,000 = ($10/unit x Sales volume) - Fixed expenses

We need to solve for the sales volume: 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$10/unit

Now we can plug in the numbers: 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$10/unit 
$15,000 + Fixed expenses = $10/unit x Sales volume 
$10/unit = Sales volume - 31,000 units 
$15,000 + Fixed expenses = $10/unit x (Sales volume - 31,000 units) 
$15,000 + Fixed expenses = $10/unit x Sales volume - $310,000 
$10/unit x Sales volume = $15,000 + Fixed expenses + $310,000 
Sales volume = ($15,000 + Fixed expenses + $310,000) / $10/unit

We know that at the breakeven point, the sales revenue is $310,000. So if we subtract that from the sales revenue needed to reach the target operating income, we'll get the additional sales revenue needed: 
Additional sales revenue needed = Target operating income + Breakeven sales revenue 
Additional sales revenue needed = $15,000 + $310,000 
Additional sales revenue needed = $325,000

Now we can solve for the additional units needed to generate that additional sales revenue: 
Additional units needed = Additional sales revenue needed / Unit price 
Additional units needed = $325,000 / $10/unit 
Additional units needed = 32,500 units

Therefore, the answer is C) 32,500 units.

Given Breakeven Sales in Units of 31,000 and a Unit