Question

Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 500,000 units at a price of 94 per unit during the current year. Its Income statement is as follows: Sales Cost of goods sold Gross profit Expenses: $47,000,000 25,000,000 $22,000,000 Selling expenses Administrative expenses 3,000,000 $4,000,000 Total expenses 7,000,000 Income from operations $15,000,000 The division of costs between variable and fixed is as follows: Variable 70% 75% 5096 Fixed 30% 25% 5096 Cost of goods sold Selling expenses Administrative expenses Management is considering a plant expansion program for the following year that wll permit an increase of $3,760,000 in yearly sales. The expansion will Increase fixed costs by $1,800,000 but will not affect the relationship between sales and variable costs. Required: 1. Detemine the total variable costs and the total fixed costs for the current year Total variable costs

Answer 1

Concepts and reason

Accounting: Accounting is a process of recording transactions, classifying them in a specific manner, and then it is the process of summarizing and analyzing to interpret the results. It is a process of preserving the accounts.

Marginal Cost: Marginal cost is the change in the cost of production as output is changed. It is the cost altered by adding a single unit of goods or involving change in the service provided. Thus, the total cost of production is changed.

Cost: Cost is any value spent to produce a product or to render any service. The types of costs are fixed cost and variable cost.

Income: Income refers to any revenue earned or accrued through the related sources for the services rendered or any sales done. It is derived after covering the expenses of the period.

Fundamentals

Cost of goods sold: The costs that are incurred by a business to sell products in a particular period are called as cost of goods sold. It is also known as cost of sales. It is considered as the expense of the current period.

Selling price: Selling price is the price at which products are sold in the market. It includes the total cost incurred on the product and profit.

Sales: Sales is an activity of selling the goods in amarket, which is sold by a seller and purchased by a buyer. It is the main source of revenue for a company. It is necessary to have consideration for sales.

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 a company that does not depend on the activities concerned with that 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 a company that depends on the activities concerned with the business.

Contribution margin: The balance when the sales are deducted by the variable costs is known as contribution margin. The management uses the contribution margin to develop the weight of sales mix for multiple products. The contribution margin signifies the profit earned before deducting the fixed costs.

Break-even point: Break-even point is the stage where the income earned and expense incurred is equal. Thus, the net income at break-even point remains zero.

Gross profit: Gross profit is the excess amount of sales price over estimated costs. It is the profit after deducting the manufacturing costs of product. Thus, it is the net of sales and cost of goods sold.

1)

Calculate the total variable costs and fixed costs:

$\begin{array}{c}\\{\rm{Total Variable Costs = }}\left( \begin{array}{l}\\{\rm{(Cost of Goods Sold \times 70\% ) }}\\\\{\rm{ + (Selling expenses }} \times {\rm{75\% ) }}\\\\{\rm{ + (Administration Expenses }} \times {\rm{50\% }})\\\end{array} \right){\rm{ }}\\\\{\rm{ = }}\left( \begin{array}{l}\\\left( {{\rm{\$ 25,000,000 x 70\% }}} \right){\rm{ + }}\left( {{\rm{\$ 4,000,000 x 75\% }}} \right){\rm{ }}\\\\{\rm{ + }}\left( {{\rm{\$ 3,000,000 x 50\% }}} \right)\\\end{array} \right)\\\\{\rm{ = \$ 17,500,000 + \$ 3,000,000 + \$ 1,500,000}}\\\\{\rm{ = \$ 22,000,000}}\\\end{array}$

Therefore, the total variable cost is $22,000,000.

Calculate the total fixed cost:

$\begin{array}{c}\\{\rm{Total Fixed Costs = }}\left( \begin{array}{l}\\{\rm{(Cost of Goods Sold \times 30\% ) + (Selling expenses }} \times {\rm{75\% ) }}\\\\{\rm{ + (Administration Expenses }} \times {\rm{50\% }})\\\end{array} \right)\\\\ = \left[ \begin{array}{l}\\\left( {{\rm{\$ 25,000,000 x 30\% }}} \right){\rm{ + }}\left( {{\rm{\$ 4,000,000 x 25\% }}} \right){\rm{ }}\\\\{\rm{ + }}\left( {{\rm{\$ 3,000,000 x 50\% }}} \right)\\\end{array} \right]\\\\ = {\rm{\$ 7,500,000 + \$ 1,000,000 + \$ 1,500,000}}\\\\ = {\rm{\$ 10,000,000}}\\\end{array}$

Therefore, the total variable cost is $10,000,000.

2)

Calculate the variable cost unit:

$\begin{array}{c}\\{\rm{Unit Variable Cost = }}\frac{{{\rm{Total Variable Costs}}}}{{{\rm{Total units sold}}}}{\rm{ }}\\\\{\rm{ = }}\frac{{{\rm{\$ 22,000,000}}}}{{{\rm{500,000 units}}}}{\rm{ }}\\\\{\rm{ = \$ 44}}\\\end{array}$

Therefore, the unit variable cost is $44.

Calculate the unit contribution margin.

$\begin{array}{c}\\{\rm{Unit Contribution margin = Sale Price per unit }} - {\rm{Unit Variable cost}}\\\\{\rm{ = \$ 94}} - {\rm{\$ 44}}\\\\{\rm{ = \$ 50}}\\\end{array}$

Therefore, the contribution margin unit is $50.

3)

Calculate the break-even sales unit for the current year:

$\begin{array}{c}\\{\rm{Break - even Sales Units = }}\frac{{{\rm{Total Fixed Costs }}}}{{{\rm{Unit Contribution margin}}}}\\\\{\rm{ = }}\frac{{{\rm{\$ 10,000,000 }}}}{{{\rm{\$ 50 }}}}\\\\{\rm{ = 200,000 units }}\\\end{array}$

Therefore, the break-even sales unit for the current year is 200,000.

4)

Calculate the break-even sales unit for the following year:

$\begin{array}{c}\\{\rm{Break - even sales = }}\frac{{{\rm{(Total Fixed Cost + Increased Fixed Cost)}}}}{{{\rm{Unit Contribution margin}}}}{\rm{ }}\\\\{\rm{ = }}\frac{{\left( {{\rm{\$ 10,000,000 + \$ 1,800,000}}} \right)}}{{{\rm{\$ 50 }}}}{\rm{ }}\\\\{\rm{ = }}\frac{{{\rm{\$ 11,800,000}}}}{{{\rm{\$ 50}}}}\\\\{\rm{ = 236,000units}}\\\end{array}$

Therefore, the break-even sales unit for the following year is 236,000.

5)

Calculate the amount of sales units:

$\begin{array}{c}\\{\rm{Amount of sales }}\left( {{\rm{units}}} \right){\rm{ = }}\frac{{\left( \begin{array}{l}\\{\rm{Desired Income + Total Fixed Cost + }}\\\\{\rm{Increased Fixed Cost}}\\\end{array} \right)}}{{{\rm{Unit Contribution margin}}}}{\rm{ }}\\\\{\rm{ = }}\frac{{\left( {{\rm{\$ 15,000,000 + \$ 10,000,000 + \$ 1,800,000}}} \right)}}{{{\rm{\$ 50 }}}}\\\\{\rm{ = }}\frac{{{\rm{\;\$ 26,800,000 }}}}{{{\rm{\$ 50}}}}\\\\{\rm{ = 536,000 units }}\\\end{array}$

Therefore, the amount of sales units is 536,000.

6)

Determine the maximum net income for the expanded unit:

Therefore, the net income is $15,200,000.

Working notes:

Calculation is given below:

Calculate the increase in sales units:

$\begin{array}{c}\\{\rm{Increase in Sales units = }}\left( {\frac{{{\rm{Increase in sales }}}}{{{\rm{Selling Price per unit}}}}} \right){\rm{ + Current Year Sales Unit}}\\\\{\rm{ = }}\left( {\frac{{{\rm{\$ 3,760,000}}}}{{{\rm{\$ 94}}}}} \right){\rm{ + 500,000}}\\\\{\rm{ = 40,000 + 500,000}}\\\\{\rm{ = 540,000}}\\\end{array}$

Therefore, the increase in sales unit is 540,000.

7)

Determine the profit or loss for the following year accepting the proposals:

$\begin{array}{c}\\{\rm{Income in the following year = \$ 15,000,000}} - {\rm{\$ 1,800,000}}\\\\{\rm{ = \$ 13,200,000}}\\\end{array}$

Therefore, the profit for the following year is $13,200,000.

Ans: Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7