chapter 5

Units to Be Sold to Earn the Target Profit Formula

= (Target Profit + FE Unit) / CM

Degree of OL Formula

= CM / NOI

Expected % Increase in NOI Formula

= Expected % Increase in Sales × Degree of OL

Percentage Increase in NOI Formula

= Increase in NOI / Old NOI

Profit Formula

= Unit CM × Q − FE

Voltar Company manufactures and sells a specialized cordless telephone for high electromagnetic radiation environments. The company's contribution format income statement for the most recent year is given below: Total Per Unit Percent of Sales Sales (20,000 units) . . . . . . . . . . . $1,200,000 $60 100% Variable expenses. . . . . . . . . . . . . 900,000 45 ? % Contribution margin . . . . . . . . . . . 300,000 $15 ? % Fixed expenses . . . . . . . . . . . . . . . 240,000 Net operating income. . . . . . . . . . $ 60,000 Management is anxious to increase the company's profit and has asked for an analysis of a number of items. 6. a. Compute the company's degree of operating leverage at the present level of sales. b. Assume that through a more intense effort by the sales staff, the company's unit sales increase by 8% next year. By what percentage would you expect net operating income to increase? Use the degree of operating leverage to obtain your answer. c. Verify your answer to (b) by preparing a new contribution format income statement showing an 8% increase in unit sales.

6a.) Step 1 of 2 Degree of operating leverage (OL) determines how the net operating income (NOI) responds to a change in the sales. To calculate the degree of OL, the NOI for a given level of sales and contribution margin (CM) needs to be identified. Fixed expenses will not be considered to have an effect on NOI because they do not change with a change in sales. NOI = $60,000 CM=$300,000NOICM​=$60,000=$300,000​ Step 2 of 2 The degree of OL is calculated by dividing the CM of $300,000 by the NOI of $60,000. Degree of OL = CM / NOI =$300,000 / $60,000 = 5 ----------------- 6b.) Step 1 of 2 Identify the expected percentage increase in sales and the degree of operating leverage (DL) that are required to calculate the expected percentage increase in net operating income (NOI). Expected % Increase in Sales = 8% Degree of OL = 5 Step 2 of 2 The expected percentage increase in NOI is calculated by multiplying the 8% expected increase in sales by the degree of OL. Expected % Increase in NOI = Expected % Increase in Sales × Degree of OL =8% × 5 = 40% ------------------- 6c). Step 1 of 4 Global Explanation: The new contribution format income statement is calculated by increasing the units sold by 8%. When the sales increase by 8%, the variable expenses will also increase by 8%. The fixed expenses of $240,000 will remain the same because the fixed costs do not change when the level of production or sales change. The percentage increase in net operating income (NOI) is calculated by dividing the increase in the NOI by the old NOI. Percentage Increase in NOI = Increase in NOI / Old NOI = ($84,000−$60,000) / $60,000 = 40% Step 1: An increase in the number of units sold is calculated by multiplying the number of units sold of 20,000 units by the 8% increase in sales. Increase in the Number of Units Sold = Number of Units Sold × Percentage Increase in Sales = 20,000 Units × 8%=1,600 Step 2 of 4 The increased number of units sold is calculated by adding the old unit sales of 20,000 units and 1,600 units increase in the number of units sold. Increased Number of Unit Sales=Old Unit Sales+Increase in Unit Sales=20,000 Units+1,600 Units=21,600 UnitsIncreased Number of Unit Sales​=Old Unit Sales+Increase in Unit Sales=20,000 Units+1,600 Units=21,600 Units​ Step 3 of 4 The amount of increased sales is calculated by multiplying the increased number of unit sales by the selling price per unit. Increased Sales=Increased Number of Units Sold×Selling Price per Unit=21,600 Units×$60=$1,296,000Increased Sales​=Increased Number of Units Sold×Selling Price per Unit=21,600 Units×$60=$1,296,000​ Step 4 of 4 The amount of increased variable expenses is calculated by multiplying the increased number of unit sales by the variable cost per unit. Increased Variable Expenses=Increased Number of Units Sold×Variable Cost Price per Unit=21,600 Units×$45=$972,000Increased Variable Expenses​=Increased Number of Units Sold×Variable Cost Price per Unit=21,600 Units×$45=$972,000​

Contribution Margin Formula

Contribution Margin Ratio ​= Unit Selling Price / Unit Contribution Margin

Variable Expense Ratio Formula

Variable Expense Ratio = VE per Unit / Selling Price per Unit

Voltar Company manufactures and sells a specialized cordless telephone for high electromagnetic radiation environments. The company's contribution format income statement for the most recent year is given below: Total Per Unit Percent of Sales Sales (20,000 units) . . . . . . . . . . . $1,200,000 $60 100% Variable expenses. . . . . . . . . . . . . 900,000 45 ? % Contribution margin . . . . . . . . . . . 300,000 $15 ? % Fixed expenses . . . . . . . . . . . . . . . 240,000 Net operating income. . . . . . . . . . $ 60,000 Management is anxious to increase the company's profit and has asked for an analysis of a number of items. 1). Compute the company's CM ratio and variable expense ratio. 2). Compute the company's break-even point in both unit sales and dollar sales. Use the equation method

1). Step 1 of 2 The contribution margin (ratio for a company that produces and sells only one product is calculated by dividing the contribution margin per unit by the selling price per unit. The contribution margin ratio of Company V that deals with a specialized cordless telephone, i.e., only one product, is calculated as follows: Contribution Margin Ratio = Unit Contribution Margin / Unit Selling Price =$15 / $60 = 25% -------------------- Step 2 of 2 The variable expense ratio is calculated by dividing the variable expense per unit by the selling price per unit. Per unit cost is used because Company V produces and sells only one product. Variable Expense Ratio = VE per Unit / Selling Price per Unit =$45/ $60 = 75% ------------------- 2). Step 1 of 2 The equation method of determining the break-even point (BEP) is used when only one product is produced and sold. The BEP is the point where the profit is zero. Under this method, contribution margin (CM) per unit of $15 and total fixed expenses (FE) of $240,000 are required to calculate BEP units. In the equation, BEP units is represented as Q. Profit = Unit CM × Q − FE $0 = $15 × Q - $240,000 $15Q = $240,000Q = $240,000 / $15Q = 16,000 units ------------------- Step 2 of 2 The BEP in dollars is the break-even sales that is calculated by multiplying the BEP units, i.e., Q, by the selling price per unit of $60. BEP in Dollars = Q × Unit Selling Price =16,000 units × $60 = $960,000.

Voltar Company manufactures and sells a specialized cordless telephone for high electromagnetic radiation environments. The company's contribution format income statement for the most recent year is given below: Total Per Unit Percent of Sales Sales (20,000 units) . . . . . . . . . . . $1,200,000 $60 100% Variable expenses. . . . . . . . . . . . . 900,000 45 ? % Contribution margin . . . . . . . . . . . 300,000 $15 ? % Fixed expenses . . . . . . . . . . . . . . . 240,000 Net operating income. . . . . . . . . . $ 60,000 Management is anxious to increase the company's profit and has asked for an analysis of a number of items. 3). Assume that an increase in unit sales causes total sales to increase by $400,000 next year. If cost behavior patterns remain unchanged, by how much will the company's net operating income increase? Use the CM ratio to compute your answer. 4). Refer to the original data. Assume that next year management wants the company to earn a profit of at least $90,000. How many units will have to be sold to earn this target profit? 5). Refer to the original data. Compute the company's margin of safety in both dollar and percentage form.

3). Step 1 of 2 To calculate the increase in net operating income (NOI) when there is an increase in sales, the increase in sales and the contribution margin (CM) ratio needs to be identified. Increase in Sales= $400,000 CM Ratio = 25% --------------- Step 2 of 2 The increase in NOI can be calculated by multiplying the $400,000 increase in sales by the CM ratio of 25%. It is given that the cost behavior remains the same when the sales increases. Therefore, fixed expenses will not vary and will not affect the increase in NOI. Increase in NOI = $400,000 × 25% = $100,000 -------------------- 4). Step 1 of 2 Under the equation method, Q is the number of units sold to earn profit. Therefore, to find the number of units to be sold to achieve the target profit, $90,000 is used as the profit. Unit contribution margin (CM) of $15 and total fixed expenses (FE) of $240,000 will be used to calculate Q. Profit = Unit CM × Q −FE $90,000= $15 × Q - $240,000 $15Q = $90,000 + $240,000Q =$330,000 / $15Q = 22,000 Units Step 2 of 2 The formula method can also be used to determine the number of units to be sold to earn a target profit of $90,000. Units to Be Sold to Earn the Target Profit = (Target Profit + FE Unit) / CM Units to Be Sold to Earn $90,000 = ($90,000 + $240,000) / $15 = $330,000 / $15 = 22,000 Units ------------------------------ 5). Step 1 of 2 Margin of safety (MoS) is the amount of total sales made during the period after the break-even point (BEP) is achieved. Therefore, MoS in dollars is calculated by subtracting the BEP in dollars of $960,000 from the total sales of $1,200,000 made during the period. MoS in Dollars = Total Sales - Break-even Sales =$1,200,000 − $960,000 = $240,000 ​ Step 2 of 2 MoS as percentage is calculated by dividing the MoS in dollars $240,000 by the total sales $1,200,000 made during the year. MoS as Percentage = MoS in Dollars / Total Sales = $240,000 / $1,200,000 = 20%

MoS as Percentage Formula

= MoS in Dollars / Total Sales

BEP (Breakeven Point) in Dollars Formula​

= Q × Unit Selling Price

MoS (Margin of Safety) in Dollars Formula

= Total Sales - Break-even Sales