Question

The Fashion Shoe Company operates a chain of women’s shoe shops that carry many styles of shoes that are all sold at the same price. Sales personnel in the shops are paid a substantial commission on each pair of shoes sold (in addition to a small base salary) in order to encourage them to be aggressive in their sales efforts.

The following worksheet contains cost and revenue data for Shop 48 and is typical of the company’s many outlets:

	Per Pair of Shoes
Selling price	$	20.00
Variable expenses:
Invoice cost	$	7.00
Sales commission		3.00
Total variable expenses	$	10.00
		Annual
Fixed expenses:
Advertising	$	32,000
Rent		21,000
Salaries		105,000
Total fixed expenses	$	158,000

Required:
1.	Calculate the annual break-even point in unit sales and in dollar sales for Shop 48.

     

3.	If 15,200 pairs of shoes are sold in a year, what would be Shop 48’s net operating income or loss?

       

4.	The company is considering paying the store manager of Shop 48 an incentive commission of 70 cents per pair of shoes (in addition to the salesperson’s commission). If this change is made, what will be the new break-even point in unit sales and in dollar sales? (Do not round intermediate calculations. Round your final answers to the nearest whole number.)

        

5.	Refer to the original data. As an alternative to (4) above, the company is considering paying the store manager 45 cents commission on each pair of shoes sold in excess of the break-even point. If this change is made, what will be the shop’s net operating income or loss if 18,400 pairs of shoes are sold? (Do not round intermediate calculations.)

        

6.	Refer to the original data. The company is considering eliminating sales commissions entirely in its shops and increasing fixed salaries by $30,500 annually.

     

a.	If this change is made, what will be the new break-even point in unit sales and in dollar sales for Shop 48? (Do not round intermediate calculations.)

            

Answer 1

Concepts and reason

CVP analysis: It is used to identify how much changes in volume and costs affect the operating income of the company and net income. It plays a very significant role in decision making in management and is a significant way of determining and describing the selling price and breakeven point. It consists managerial approaches of determining sales revenue, net profit and capacity of production.

Fundamentals

Contribution margin ratio (CM Ratio): It is the relationship between contribution and sales. It is computed as the difference between selling price and variable costs and expressed as a percentage of sales.

Breakeven point: It is the point of sales where no profit or loss is incurred. It also states that cost is equal to the income of the company. It is the point in sales dollars that can be computed by dividing fixed expenses of the company by the contribution margin ratio of the company.

Variable cost: The cost and expenses which change with the level of activity are the variable expenses. These expenses change with every extra unit produced. More the production more will be the variable cost.

‎Fixed cost: The cost and expenses which doesn’t change with the change in the level of activity are fixed costs. The expenses whose amount and nature of the occurrence, both are fixed. If the company does not produce any output, still the fixed expenses need to be paid.

Net Operating Income: The resultant amount after reducing all expenses regarding the company’s operations whether direct or indirect for the period from the revenues earned is termed as net operating income. Net income can be computed by deducting all the operating expenses involved in doing business from total revenues.

(1)

(1)

The computation of the break-even point (in units) is given below:

$\begin{array}{c}\\{\rm{Break - even point}} = \frac{{{\rm{Fixed Costs}}}}{{{\rm{Contribution Margin}}}}\\\\ = \frac{{{\rm{Fixed Costs}}}}{{\left( {{\rm{Selling Price}} - {\rm{Variable Cost}}} \right)}}\\\\ = \frac{{\$ 158,000}}{{\left( {\$ 20 - \$ 10} \right)}}\\\end{array}$

$\begin{array}{c}\\ = \frac{{\$ 158,000}}{{\$ 10}}\\\\ = \$ 15,800{\rm{ units}}\\\end{array}$

The computation of the break-even point (in dollar) is given below:

$\begin{array}{c}\\{\rm{Break - eve}}{{\rm{n}}_{\left( {{\rm{Dollars}}} \right)}} = {\rm{Break - eve}}{{\rm{n}}_{\left( {{\rm{Units}}} \right)}} \times {\rm{Selling Price}}\\\\ = 15,800{\rm{ units}} \times \$ 20\\\\ = \$ 316,000\\\end{array}$

(3)

The computation of the net operating loss for Shop 48 is given below:

Compute the amount of sales:

$\begin{array}{c}\\{\rm{Sales}} = {\rm{Sales per unit}} \times {\rm{Sold Units}}\\\\ = \$ 20 \times 15,200{\rm{ units}}\\\\ = \$ 304,000\\\end{array}$

Compute the amount of variable cost:

$\begin{array}{c}\\{\rm{Variable cost}} = {\rm{Variable cost per unit}} \times {\rm{Sold Units}}\\\\ = \$ 10 \times 15,200{\rm{ units}}\\\\ = \$ 152,000\\\end{array}$

Compute the amount of contribution margin:

$\begin{array}{c}\\{\rm{Contribution Margin}} = {\rm{Sales}} - {\rm{Variable Cost}}\\\\ = \$ 304,000 - \$ 152,000\\\\ = \$ 152,000\\\end{array}$

Compute the amount of net operating income:

$\begin{array}{c}\\{\rm{Net operating income}} = {\rm{Contribution margin}} - {\rm{Fixed cost}}\\\\ = \$ 152,000 - \$ 158,000\\\\ = \left( {\$ 6,000} \right)\\\end{array}$

(4)

(1)

The computation of the revised break-even point (in units) is given below:

$\begin{array}{c}\\{\rm{Break - even point}} = \frac{{{\rm{Fixed Costs}}}}{{{\rm{Contribution Margin}}}}\\\\ = \frac{{{\rm{Fixed Costs}}}}{{\left( {{\rm{Selling Price}} - {\rm{Revised Variable Cost}}} \right)}}\\\\ = \frac{{\$ 158,000}}{{\left( {\$ 20 - \$ 10.70} \right)}}\\\end{array}$

$\begin{array}{c}\\ = \frac{{\$ 158,000}}{{\$ 9.3}}\\\\ = \$ 16,989{\rm{ units}}\\\end{array}$

Working Notes:

Compute the amount revised variable cost per unit:

$\begin{array}{c}\\{\rm{Revised Variable Cost}} = {\rm{Vairable Cost}} + {\rm{Incentive Commission}}\\\\ = \$ 10 + \$ 0.70\\\\ = \$ 10.70\\\end{array}$

The computation of the revised break-even point (in dollars) is given below:

$\begin{array}{c}\\{\rm{Revised Break - eve}}{{\rm{n}}_{\left( {{\rm{Dollars}}} \right)}} = {\rm{Break - eve}}{{\rm{n}}_{\left( {{\rm{Units}}} \right)}} \times {\rm{Selling Price}}\\\\ = 16,989{\rm{ units}} \times \$ 20\\\\ = \$ 339,780\\\end{array}$

(5)

The computation of the net operating loss/income is given below:

$\begin{array}{c}\\{\rm{Net Operating Loss/Income}} = \left( {{\rm{Units sold}} - {\rm{Break - even point}}} \right) \times \\\\\left( {{\rm{Sales per unit}} - {\rm{Revised Variable Cost per unit}}} \right)\\\\ = \left( {18,400 - 15,800} \right) \times \left( {\$ 20 - \left( {\$ 10 + \$ 0.45} \right)} \right)\\\\ = 2,600 \times \left( {\$ 20 - \$ 10.45} \right)\\\end{array}$

$\begin{array}{c}\\ = 2,600 \times \$ 9.55\\\\ = \$ 24,830\\\end{array}$

(6)

(a)

The computation of the break-even point (in units) is given below:

$\begin{array}{c}\\{\rm{Break - even point}} = \frac{{{\rm{Revised Fixed Costs}}}}{{{\rm{Contribution Margin}}}}\\\\ = \frac{{{\rm{Fixed Costs}} + {\rm{Increase amount}}}}{{\left( {{\rm{Selling Price}} - {\rm{Invoice Cost}}} \right)}}\\\\ = \frac{{\$ 158,000 + \$ 30,500}}{{\left( {\$ 20 - \$ 7} \right)}}\\\end{array}$

$\begin{array}{c}\\ = \frac{{\$ 188,500}}{{\$ 13}}\\\\ = \$ 14,500{\rm{ units}}\\\end{array}$

The computation of the revised break-even point (in dollars) is given below:

$\begin{array}{c}\\{\rm{Revised Break - eve}}{{\rm{n}}_{\left( {{\rm{Dollars}}} \right)}} = {\rm{Break - eve}}{{\rm{n}}_{\left( {{\rm{Units}}} \right)}} \times {\rm{Selling Price}}\\\\ = 14,500{\rm{ units}} \times \$ 20\\\\ = \$ 290,000\\\end{array}$

Ans: Part 1.1

The break-even point (in units) for Shop 48 is 15,800 units.

Part 1.2

The break-even point (in dollars) is $316,000.

Part 3

The amount of net operating loss is $6,000.

Part 4.1

The break-even point (in units) for Shop 48 is 16,989 units.

Part 4.2

The break-even point (in dollars) for Shop 48 is $339,780.

Part 5

The amount of net operating income after the payment of commission is $24,830.

Part 5.a.1

The break-even point (in units) for Shop 48 is 14,500 units.

Part 5.a.2

The break-even point (in dollars) for Shop 48 is $290,000.