Question

In the month of March, Style Salon services 550 clients at an average price of $180. During the month, fixed costs were $25,866 and variable costs were 70% of sales.

(a) Determine the contribution margin in dollars, per unit, and as a ratio.

Contribution margin		$
Contribution margin per unit		$
Contribution margin ratio			%

(b) Using the contribution margin technique, compute the break-even point in dollars and in units.

Break-even sales		$
Break-even sales			units

Answer 1

Concepts and reason

CVP analysis: CVP is one of the techniques of decision accounting to achieve the targeted profits by changing different variables. The relationship between cost, profit, and sales volume provides the basis for the managers to take effective steps about the future profits.

Fixed cost: Fixed cost is a cost that remains the same irrespective of the increase or decrease in the value of goods or any services rendered. It is the cost paid by the company that does not depend on the activities concerned with the business.

Variable cost: Variable cost is a cost that varies according to the output produced or any service rendered. It is the cost paid by the company that depends on the activities concerned with the business.

Sales revenue: The amount received by sale of goods or rendering services is known as sales revenue. This is the most earned revenue of a company. This is also called as the sales revenue on gross. When gross sales revenue is deducted by any return, allowance, and discount, it is termed to be as net sales.

Fundamentals

Contribution margin: The difference of value between the sales and the variable costs is known as contribution margin. The management uses contribution margin to develop the weight of sales mix for multiple products. The contribution margin signifies the profit earned before deducting the fixed costs.

Contribution margin per unit: The contribution margin per unit is calculated by dividing the contribution margin by the number of units.

Contribution margin ratio: The percentage of sales remaining after the variable expenses are paid off is called as contribution margin ratio. The following is the formula to calculate the contribution margin ratio:

${\rm{Contribution margin ratio = }}\left( {\frac{{{\rm{Selling price -- Variable expenses}}}}{{{\rm{Selling price}}}}} \right){\rm{ }} \times {\rm{ 100}}$

Break-even point: Break-even point is the stage where the income earned and expenses incurred are equal. Thus, the net income at break-even point remains as Zero.

Break-even point in dollars: The point that represents sales dollars where total revenue equals total costs is referred to as break-even point in dollars.

${\rm{Break - even point in dollars = }}\frac{{{\rm{Fixed cost}}}}{{{\rm{Contribution margin ratio}}}}$

1)

Calculate the contribution margin in dollars:

Therefore, the contribution margin in dollars is $29,700.

Calculate the contribution margin per unit:

$\begin{array}{c}\\{\rm{Contribution margin per unit = }}\frac{{{\rm{Contribution margin}}}}{{{\rm{Number of clients}}}}\\\\{\rm{ = }}\frac{{{\rm{\$ 29,700}}}}{{{\rm{550}}}}\\\\{\rm{ = \$ 54}}\\\end{array}$

Therefore, the contribution margin per unit is $54.

Calculate the contribution margin ratio:

$\begin{array}{c}\\{\rm{Contribution margin ratio = }}\frac{{{\rm{Contribution margin}}}}{{{\rm{Sales}}}}{\rm{ \times 100}}\\\\{\rm{ = }}\frac{{{\rm{\$ 29,700}}}}{{{\rm{\$ 99,000}}}}{\rm{ \times 100}}\\\\{\rm{ = 30\% }}\\\end{array}$

Therefore, the contribution margin ratio is 30%.

2)

Calculate the break-even sales in dollars:

$\begin{array}{c}\\{\rm{Break - even sales in dollars = }}\frac{{{\rm{Fixed costs}}}}{{{\rm{Contribution margin ratio}}}}\\\\{\rm{ = }}\frac{{{\rm{\$ 25,866}}}}{{{\rm{30\% }}}}\\\\{\rm{ = \$ 86,220}}\\\end{array}$

Therefore, the break-even sales in dollars are $86,220.

Calculate the break-even sales in units:

$\begin{array}{c}\\{\rm{Break - even sales in units = }}\frac{{{\rm{Break - even sales in dollars}}}}{{{\rm{Average price}}}}\\\\{\rm{ = }}\frac{{{\rm{\$ 86,220}}}}{{{\rm{\$ 180}}}}\\\\{\rm{ = 479 units}}\\\end{array}$

Therefore, the break-even sales in units are 479 units.

Ans: Part 1

Part 2