Questions: Current operating income for Bay Area Cycles Company is 52,000. Selling price per unit is 100, the contribution margin ratio is 20%, and fixed expense is 208,000. Required: 1. Calculate Bay Area Cycle's per unit variable expense and contribution margin. How many units are currently being sold? 2. How many additional unit sales would be necessary to achieve operating income of 130,000?

Solution Steps

• The selling price per unit is $\$100$.
• The contribution margin ratio is $20\%$, so the contribution margin per unit is: $$\text{Contribution margin per unit} = \text{Selling price per unit} \times \text{Contribution margin ratio} = 100 \times 0.20 = \$20$$
• The variable expense per unit is: $$\text{Variable expense per unit} = \text{Selling price per unit} - \text{Contribution margin per unit} = 100 - 20 = \$80$$

• The total contribution margin is: $$\text{Total contribution margin} = \text{Operating income} + \text{Fixed expense} = 52,000 + 208,000 = \$260,000$$
• The number of units sold is: $$\text{Number of units sold} = \frac{\text{Total contribution margin}}{\text{Contribution margin per unit}} = \frac{260,000}{20} = 13,000 \text{ units}$$

• The required total contribution margin for the new operating income is: $$\text{Required total contribution margin} = \text{Desired operating income} + \text{Fixed expense} = 130,000 + 208,000 = \$338,000$$
• The additional contribution margin needed is: $$\text{Additional contribution margin needed} = 338,000 - 260,000 = \$78,000$$
• The additional units needed to achieve this are: $$\text{Additional units needed} = \frac{\text{Additional contribution margin needed}}{\text{Contribution margin per unit}} = \frac{78,000}{20} = 3,900 \text{ units}$$

Final Answer