Question

Piedmont Company segments its business into two regions—North and South. The company prepared the contribution format segmented income statement shown below:

		Total Company		North		South
Sales	$	600,000	$	400,000	$	200,000
Variable expenses		360,000		280,000		80,000
Contribution margin		240,000		120,000		120,000
Traceable fixed expenses		132,000		66,000		66,000
Segment margin		108,000	$	54,000	$	54,000
Common fixed expenses		56,000
Net operating income	$	52,000

Required:

1.	Compute the companywide break-even point in dollar sales .

      

       

2.	Compute the break-even point in dollar sales for the North region.

    

       

3.	Compute the break-even point in dollar sales for the South region. (Round your break-even dollar sales to the nearest whole number.)

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 manager 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 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 ratio: The percentage of sales that remain 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 in dollars: The point, which 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 companywide break-even point in dollar sales:

$\begin{array}{c}\\{\rm{Break - even point in dollars = }}\frac{{{\rm{Fixed cost}}}}{{{\rm{Contribution margin ratio}}}}\\\\{\rm{ = }}\left( {\frac{{\left( {{\rm{\$ 132,000 + \$ 56,000}}} \right)}}{{{\rm{40\% }}}}} \right)\\\\{\rm{ = \$ 470,000}}\\\end{array}$

Working note:

Calculate the contribution margin ratio:

$\begin{array}{c}\\{\rm{Contribution margin ratio = }}\left( {\frac{{{\rm{Contribution margin}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{{\rm{Sales - Variable costs}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 600,000{\rm{ }} - {\rm{ }}\$ 360,000}}{{\$ 600,000}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 240,000}}{{{\rm{\$ 600,000}}}}} \right) \times 100\\\\{\rm{ = 40\% }}\\\end{array}$

2)

Calculate the break-even point in dollar sales for the North region:

$\begin{array}{c}\\{\rm{Break - even point in dollars = }}\frac{{{\rm{Fixed cost}}}}{{{\rm{Contribution margin ratio}}}}\\\\{\rm{ = }}\left( {\frac{{\$ 66,000}}{{{\rm{30\% }}}}} \right)\\\\{\rm{ = \$ 220,000}}\\\end{array}$

Hence, the break-even point in dollars for the North region is $220,000.

Working note:

Calculate the contribution margin ratio for the North region:

$\begin{array}{c}\\{\rm{Contribution margin ratio = }}\left( {\frac{{{\rm{Contribution margin}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{{\rm{Sales - Variable costs}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 400,000 - \$ 280,000}}{{\$ 400,000}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 120,000}}{{{\rm{\$ 400,000}}}}} \right) \times 100\\\\{\rm{ = 30\% }}\\\end{array}$

3)

Calculate the break-even point in dollar sales for the South region:

$\begin{array}{c}\\{\rm{Break - even point in dollars = }}\frac{{{\rm{Fixed cost}}}}{{{\rm{Contribution margin ratio}}}}\\\\{\rm{ = }}\left( {\frac{{\$ 66,000}}{{{\rm{60\% }}}}} \right)\\\\{\rm{ = \$ 110,000}}\\\end{array}$

Hence, the break-even point in dollars for the South region is $110,000.

Working note:

Calculate the contribution margin ratio for the South region:

$\begin{array}{c}\\{\rm{Contribution margin ratio = }}\left( {\frac{{{\rm{Contribution margin}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{{\rm{Sales - Variable costs}}}}{{{\rm{Sales}}}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 200,000 - \$ 80,000}}{{\$ 200,000}}} \right) \times 100\\\\{\rm{ = }}\left( {\frac{{\$ 120,000}}{{{\rm{\$ 200,000}}}}} \right) \times 100\\\\{\rm{ = 60\% }}\\\end{array}$

Ans: Part 1

The break-even point in dollars is $470,000.

Part 2

The break-even point in dollars for the North region is $220,000.

Part 3

The break-even point in dollars for the South region is $110,000.