Question

Bluegill Company sells 7,200 units at $220 per unit. Fixed costs are $79,200, and operating income is $396,000. Determine the following:

a. Variable cost per unit $___
b. Unit contribution margin $___ per unit
c. Contribution margin ratio ___%

Answer 1

The variable cost per unit for Bluegill Company is $176, the unit contribution margin is $44 per unit, and the contribution margin ratio is 20%.

Step-by-step explanation:

Bluegill Company sells 7,200 units at $220 per unit, with fixed costs of $79,200 and operating income of $396,000. To determine the variable cost per unit, unit contribution margin, and contribution margin ratio, let's use the formulas derived from the basic relationships in cost-volume-profit (CVP) analysis.

First, we calculate the total revenue by multiplying the number of units sold by the price per unit:

Total Revenue = 7,200 units * $220/unit = $1,584,000

Next, we can find total variable costs (TVC) by subtracting operating income from total revenue then adding back fixed costs:

Total Variable Costs = Total Revenue - Operating Income + Fixed Costs
= $1,584,000 - $396,000 + $79,200 = $1,267,200

To determine the variable cost per unit, divide total variable costs by the number of units sold:

Variable Cost Per Unit = TVC / Units Sold = $1,267,200 / 7,200 units = $176 per unit

Now we can find the unit contribution margin by subtracting the variable cost per unit from the price per unit:

Unit Contribution Margin = Price Per Unit - Variable Cost Per Unit = $220 - $176 = $44 per unit

Lastly, to determine the contribution margin ratio, divide the contribution margin per unit by the price per unit and multiply by 100 to get a percentage:

Contribution Margin Ratio = (Unit Contribution Margin / Price Per Unit) * 100 = ($44 / $220) * 100 = 20%