Accounting

notes.docx

Home >Business & Finance homework help >Accounting homework help >Accounting

https://saylordotorg.github.io/text_managerial-accounting/s08-how-is-process-costing-used-to.html

Chapter 4How Is Process Costing Used to Track Production Costs?

Ann Watkins owns and operates a company that mass produces wood desks used in classrooms throughout the world. Ann’s company, Desk Products, Inc., maintains an advantage over its competitors by producing one desk in large quantities—4,000 to 8,000 desks per month—using a universally accepted design. This enables the company to buy materials in bulk, often leading to volume price discounts from suppliers. Because the exact same desk is produced for all customers, Desk Products purchases precut wood materials from suppliers. As a result, Desk Products can limit the production process to two processing departments—Assembly and Finishing. The Assembly department requisitions precut materials and hardware from the raw materials storeroom, assembles each desk, and moves the assembled desks to the Finishing department. The Finishing department sands and paints each desk and moves completed desks to the finished goods warehouse.

A new competitor recently began producing a similar desk, and Ann is concerned about whether Desk Products’ production costs are reasonable. In particular, Ann is concerned about the costs in the Assembly department since this department is responsible for the majority of the company’s production costs. Ann talks with the accountant at Desk Products, John Fuller, to investigate.

Ann:	John, as you know, we have a new competitor that is aggressively going after our customers. It looks as if we will have to focus on keeping costs low to compete. The Assembly department is my biggest concern, and it would help if I knew the cost of each desk that goes through this department.
John:	Although we don’t track production costs for each desk individually, we do use a process costing system that assigns costs to each batch of desks produced. This system enables us to calculate a cost per unit as the products move through the Assembly department.
Ann:	Excellent! Can you get me the cost information for the Assembly department for last month?
John:	Sure, I’ll put together a production cost report for you by the end of the week.

We return to Desk Products, Inc., throughout the chapter to explain how process costing systems work.

4.1 Comparison of Job Costing with Process Costing

LEARNING OBJECTIVE

1. Compare and contrast job costing and process costing.

Question: A process costing system is used by companies that produce similar or identical units of product in batches employing a consistent process. Examples of companies that use process costing include Chevron Corporation (petroleum products), the Wrigley Company (chewing gum), and Pittsburgh Paints (paint). A job costing system is used by companies that produce unique products or jobs. Examples of companies that use job costing systems include Boeing (airplanes), Lockheed Martin (advanced technology systems), and Deloitte & Touche (accounting). What are the similarities and differences between job costing and process costing systems?

Answer: Although these systems have marked differences, they are also similar in many ways. (As you read through this section, refer to Chapter 1 "What Is Managerial Accounting?" for a review of important terms if necessary.) Recall the three inventory accounts that accountants use to track product cost information—raw materials inventory, work-in-process inventory, and finished goods inventory. These three inventory accounts are used to record product cost information for both process costing and job costing systems. However, several work-in-process inventory accounts are typically used in a process costing system to track the flow of product costs through each production department. Thus each department has its own work-in-process inventory account. (For the purposes of this chapter, assume each department represents a production process. This explains the term process costing because we are tracking costs by process.) The sum of all work-in-process inventory accounts represents total work in process for the company.

Recall the three components of product costs—direct materials, direct labor, and manufacturing overhead. Assigning these product costs to individual products remains an important goal for process costing, just as with job costing. However, instead of assigning product costs to individual jobs (shown on a job cost sheet), process costing assigns these costs to departments (shown on a departmental production cost report).

Figure 4.1 "A Comparison of Cost Flows for Job Costing and Process Costing" shows how product costs flow through accounts for job costing and process costing systems. Table 4.1 "A Comparison of Process Costing and Job Costing" outlines the similarities and differences between these two costing systems. Review these illustrations carefully before moving on to the next section.

Figure 4.1 A Comparison of Cost Flows for Job Costing and Process Costing

Table 4.1 A Comparison of Process Costing and Job Costing

Product Costs
Similarities	Product costs consist of direct materials, direct labor, and manufacturing overhead.
Differences	Process Costing	Job Costing
	Product costs are assigned to departments (or processes).	Product costs are assigned to jobs.
Unit Cost Information
Similarities	Unit cost information is needed by management for decision-making purposes.
Differences	Process Costing	Job Costing
	Unit cost information comes from the departmental production cost report.	Unit cost information comes from the job cost sheet.
Inventory Accounts
Similarities	Inventory accounts include raw materials inventory, work-in-process inventory, and finished goods inventory.
Differences	Process Costing	Job Costing
	Several different work-in-process inventory accounts are used—one for each department (or process).	One work-in-process inventory account is used—job cost sheets track costs assigned to each job.

Business in Action 4.1

Source: Photo courtesy of Simon Berry, http://www.flickr.com/photos/bezznet/3105213435/ .

The Production Process at Coca-Cola

The Coca-Cola Company is one of the world’s largest producers of nonalcoholic beverages. According to the company, more than 11,000 of its soft drinks are consumed every second of every day.

In the first stage of production, Coca-Cola mixes direct materials—water, refined sugar, and secret ingredients—to make the liquid for its beverages. The second stage includes filling cleaned and sanitized bottles before placing a cap on each bottle. In the third stage, filled bottles are inspected, labeled, and packaged.

Work in process begins with the first stage of production (mixing and blending), continues with the second stage (bottling), and ends with the third stage (inspecting, labeling, and packaging). When products have gone through all three stages of production, they are shipped to a warehouse, and the costs are entered into finished goods inventory. Once products are delivered to retail stores, product costs are transferred from finished goods inventory to cost of goods sold.

Source: Coca-Cola Company, “Home Page,” http://www2.coca-cola.com/ourcompany/bottlingtoday.

KEY TAKEAWAY

· A process costing system is used by companies that produce similar or identical units of product in batches employing a consistent process. A job costing system is used by companies that produce unique products or jobs. Process costing systems track costs by processing department, whereas job costing systems track costs by job.

REVIEW PROBLEM 4.1

Identify whether each business listed in the following would use job costing or process costing.

a. Trash bag manufacturer

b. Custom furniture manufacturer

c. Shampoo manufacturer

d. Automobile repair shop

e. Sports drink manufacturer

f. Antique boat restorer

Solution to Review Problem 4.1

a. Process costing

b. Job costing

c. Process costing

d. Job costing

e. Process costing

f. Job costing

4.2 Product Cost Flows in a Process Costing System

LEARNING OBJECTIVE

1. Identify how product costs flow through accounts using process costing.

As products physically move through the production process, the product costs associated with these products move through several important accounts as shown back in Figure 4.1 "A Comparison of Cost Flows for Job Costing and Process Costing". In this section, we present a detailed look at how product costs flow through accounts using a process costing system. Later in the chapter, we explain how dollar amounts are established for product costs that flow through the accounts. As you review each of the following cost flows for a process costing system, remember that product costs are now tracked by department rather than by job.

Direct Materials

Question: In a process costing setting, direct materials are often used by several production departments. How do we record direct materials costs for each production department?

Answer: When direct materials are requisitioned from the raw materials storeroom, a journal entry is made to reduce the raw materials inventory account and increase the appropriate work-in-process inventory account. For example, assume the Assembly department of Desk Products, Inc., requisitions direct materials to be used in production. The journal entry to reflect this is as follows:

The use of direct materials is not limited to one production department. Suppose the Finishing department requisitions direct materials for production. The journal entry to reflect this is as follows:

Notice that two different work-in-process inventory accounts are used to track production costs—one for each department.

Direct Labor

Question: Each production department typically has a direct labor work force. How do we record direct labor costs for each production department?

Answer: Direct labor costs are recorded directly in the production department’s work-in-process inventory account. Assume direct labor costs are incurred by the Assembly department. The journal entry to reflect this is as follows:

As with direct materials, the use of direct labor is not limited to one production department. Suppose direct labor costs are incurred by the Finishing department. The journal entry to reflect this is as follows:

Manufacturing Overhead

Question: Manufacturing overhead costs are typically assigned to products using a predetermined overhead rate using a normal costing system as discussed in Chapter 2 "How Is Job Costing Used to Track Production Costs?" (job costing) and Chapter 3 "How Does an Organization Use Activity-Based Costing to Allocate Overhead Costs?" (activity-based costing). How do we record manufacturing overhead costs for each department?

Answer: Assume manufacturing overhead costs (often simply called overhead costs) are being applied to products going through the Assembly department. The journal entry to reflect this is as follows:

The journal entry to reflect manufacturing overhead costs being applied to products going through the Finishing department is as follows:

Transferred-In Costs

Question: At this point, we have discussed how to record product costs (direct materials, direct labor, and manufacturing overhead) related to each production department. As you review Figure 4.1 "A Comparison of Cost Flows for Job Costing and Process Costing" , notice that products often flow from one production department to the next. Transferred-in costs are the costs associated with products moving from one department to another. How do we record transferred-in costs for each department?

Answer: Assume the Assembly department at Desk Products, Inc., completes a batch of desks and moves the desks to the Finishing department. The costs associated with these desks must be transferred from the work-in-process inventory account for the Assembly department to the work-in-process inventory account for the Finishing department. Thus these costs are being transferred in to the Finishing department. The journal entry to reflect this is as follows:

Finished Goods

Question: Goods are completed and ready to sell once they have gone through the final production department. The final production department at Desk Products, Inc., is the Finishing department. How do we record production costs for products moved from the final production department to the finished goods warehouse?

Answer: When goods go through the final production department and are completed, the related costs are moved to the finished goods inventory account. The journal entry to reflect this is as follows:

Cost of Goods Sold

Question: How do we record production costs for goods that have been sold?

Answer: Once the completed goods are sold, the related costs are moved out of the finished goods inventory account and into the cost of goods sold account. The journal entry to reflect this is as follows:

Figure 4.2 "Flow of Product Costs in a Process Costing System" summarizes the flow of product costs through T-accounts for each of the journal entries presented in this section. Note that when goods are sold and production costs are moved from finished goods inventory to cost of goods sold, an additional entry is made to record the revenue associated with this transaction. We do not show this entry because the focus of this section is on the flow of production costs rather than revenues.

Figure 4.2 Flow of Product Costs in a Process Costing System

Business in Action 4.2

Source: Photo courtesy of Mykl Roventine, http://www.flickr.com/photos/myklroventine/3471836813/ .

The Production Process for Wrigley’s Gum

The Wrigley Company has 14 factories located in various parts of the world, including North America, Europe, Africa, India, and the Asia/Pacific region. The gum produced by these factories is sold in 150 countries. According to Wrigley Company, 50 percent of Americans chew gum, and on average, each person consumes 190 sticks per year. The number drops to 130 sticks per person in the United Kingdom and to 100 sticks per person in Taiwan.

The production process at Wrigley involves six sequential stages:

1. Melting. The gum base, which comes in small round balls, is melted and purified.

2. Mixing. The melted base is poured into a mixer, to which sweeteners and flavors are added.

3. Rolling. A large “loaf” of gum is sent through a series of rollers, thereby reducing thickness to the desired size.

4. Scoring. The gum is cut into the shape of sticks or pellets.

5. Conditioning. The gum is cooled and “conditioned” to ensure the right consistency before being packaged.

6. Packaging. The gum is packaged and made ready for shipping.

Because Wrigley produces identical units of product in batches employing a consistent process, it likely uses a process costing system. With such a system, Wrigley would need a separate work-in-process inventory account to track costs for each stage of the production process.

Source: Wrigley’s, “Home Page,” http://www.wrigley.com.

KEY TAKEAWAY

· The cost flows in a process costing system are similar to the cost flows in a job costing system. The primary difference between the two costing methods is that a process costing system assigns product costs—direct materials, direct labor, and manufacturing overhead—to each production department (or process) rather than to each job. Each production department has its own work-in-process inventory account when using process costing.

REVIEW PROBLEM 4.2

Chewy Gum Corporation produces bubble gum in large batches and uses a process costing system. Three departments—Mixing, Rolling, and Packaging—are involved in the production process. Chewy Gum has the following transactions:

a. Direct materials totaling $20,000—$6,000 for the Mixing department, $5,000 for the Rolling department, and $9,000 for the Packaging department—are requisitioned and placed in production.

b. Each production department incurs the following direct labor costs (wages payable):

Mixing	$2,500
Rolling	$4,600
Packaging	$2,200

c. Manufacturing overhead costs are applied to each department as follows:

Mixing	$10,000
Rolling	$ 7,000
Packaging	$ 7,500

d. Products with a cost of $5,500 are transferred from the Mixing department to the Rolling department.

e. Products with a cost of $6,400 are transferred from the Rolling department to the Packaging department.

f. Products with a cost of $9,100 are completed and transferred from the Packaging department to the finished goods warehouse.

g. Products with a cost of $8,300 are sold to customers.

Perform the following steps for each transaction:

1. Prepare a journal entry to record the transaction.

2. Summarize the flow of costs through T-accounts. Use the format presented in Figure 4.2 "Flow of Product Costs in a Process Costing System" (no need to include T-accounts for raw materials inventory, wages payable, or manufacturing overhead). Assume there are no beginning balances in the work-in-process inventory, finished goods inventory, and cost of goods sold accounts.

Solution to Review Problem 4.2

4.3 Determining Equivalent Units

LEARNING OBJECTIVE

1. Understand the concept of an equivalent unit.

Question: The beginning of this chapter describes process costing and the flow of costs through accounts used in a process costing system. The challenge is determining the unit cost of products being transferred out of each departmental work-in-process inventory account. We start the process of determining unit cost information with an important concept, the concept of equivalent units. What are equivalent units, and how are equivalent units calculated?

Answer: Units of product in work-in-process inventory are assumed to be partially completed; otherwise, the units would not be in work-in-process inventory. Process costing requires partially completed units in ending work-in-process inventory to be converted to the equivalent completed units (called equivalent units). Equivalent units are calculated by multiplying the number of physical (or actual) units on hand by the percentage of completion of the units. If the physical units are 100 percent complete, equivalent units will be the same as the physical units. However, if the physical units are not 100 percent complete, the equivalent units will be less than the physical units.

For example, if four physical units of product are 50 percent complete at the end of the period, an equivalent of two units has been completed (2 equivalent units = 4 physical units × 50 percent). The formula used to calculate equivalent units is as follows:

Equivalent units = Number of physical units × Percentage of completion

Figure 4.3 "Concept of Equivalent Units" provides an example of the equivalent unit concept in which four desks, 50 percent complete, are the equivalent of two completed desks.

Question: With the concept of equivalent units now in hand, we can calculate equivalent units for the three product costs—direct materials, direct labor, and manufacturing overhead. Why do we calculate equivalent units separately for direct materials, direct labor, and manufacturing overhead?

Answer: Equivalent units in work in process are often different for direct materials, direct labor, and manufacturing overhead because these three components of production may enter the process at varying stages. For example, in the Assembly department at Desk Products, Inc., direct materials enter production early in the process while direct labor and overhead are used throughout the process. (Imagine asking workers to assemble desks without materials!) Thus equivalent units must be calculated for each of the three production costs. (Note that direct labor and manufacturing overhead are sometimes combined in a category called conversion costs, which assumes both are added to the process at the same time. In this text, we keep direct labor and manufacturing overhead separate.) The next section presents how we use the equivalent unit concept for product costing purposes. Be sure you understand the concept of equivalent units before moving on.

Business in Action 4.3

Calculating Full-Time Equivalent Students

The concept of an equivalent unit can be applied to determine the number of full-time equivalent students (FTES) at a school. Colleges use FTES data to plan and make decisions about course offerings, staffing, and facility needs. Although having information about the number of students enrolled (the headcount) is helpful, headcount data do not provide an indication of whether the students are full time or part time. Clearly, full-time students take more classes each term and generally use more resources than part-time students. Thus administrators often prefer to convert enrollment data to FTES.

Using a simple example to explain this concept, assume 30 students attend school and each takes half a full load of classes. The headcount is 30. However, this is the equivalent of 15 full-time students, or 15 FTES.

To apply this to the real world, let’s look at the enrollment data for Sierra College, a community college located near Sacramento, California. During a recent semester, the student headcount in a specific department at Sierra College was 8,190. Because a large number of students in the department were part time, the full-time equivalent number of students totaled 3,240.

Source: Based on enrollment data from Sierra College.

KEY TAKEAWAYS

· When units of work-in-process (WIP) inventory exist at the end of the reporting period, process costing requires that these partially completed units be converted to the equivalent completed units (called equivalent units). The equation used to calculate equivalent completed units is as follows:

Equivalent units = Number of physical units × Percentage of completion

· Because direct materials, direct labor, and manufacturing overhead typically enter the production process at different stages, equivalent units must be calculated separately for each of these production costs.

REVIEW PROBLEM 4.3

Soap Production Company’s Mixing department shows the following information for the 1,000 units of product remaining in work in process at the end of the period. Assume there was no beginning inventory.

Direct materials	90 percent complete
Direct labor	30 percent complete
Overhead	60 percent complete

Calculate the equivalent units for each of the three product costs—direct materials, direct labor, and overhead.

Solution to Review Problem 4.3

The formula used to calculate equivalent units is as follows:

Equivalent units = Number of partially completed units × Percentage of completion

Materials	900 equivalent units = 1,000 partially completed units × 90 percent
Labor	300 equivalent units = 1,000 partially completed units × 30 percent
Overhead	600 equivalent units = 1,000 partially completed units × 60 percent

4.4 The Weighted Average Method

LEARNING OBJECTIVE

1. Use four steps to assign costs to products using the weighted average method.

Most companies use either the weighted average or first-in-first-out (FIFO) method to assign costs to inventory in a process costing environment. The weighted average method includes costs in beginning inventory and current period costs to establish an average cost per unit. The first-in-first-out (FIFO) method keeps beginning inventory costs separate from current period costs and assumes that beginning inventory units are completed and transferred out before the units started during the current period are completed and transferred out. We focus on the weighted average approach here and leave the discussion of the FIFO method to more advanced cost accounting textbooks.

Question: The primary goal stated in Chapter 2 "How Is Job Costing Used to Track Production Costs?" and Chapter 3 "How Does an Organization Use Activity-Based Costing to Allocate Overhead Costs?" , and continued in this chapter, is to assign product costs to products. In a process costing system, cost per equivalent unit is the term used to describe the average unit cost for each product. How is the concept of cost per equivalent unit used to assign costs to (1) completed units transferred out and (2) units still in work-in-process (WIP) inventory at the end of the period?

Answer: Costs are assigned to completed units transferred out and units in ending WIP inventory using a four-step process. We list the four steps in the following and then explain them in detail. Review these steps carefully.

Step 1. Summarize the physical flow of units and compute the equivalent units for direct materials, direct labor, and overhead.

Step 2. Summarize the costs to be accounted for (separated into direct materials, direct labor, and overhead).

Step 3. Calculate the cost per equivalent unit.

Step 4. Use the cost per equivalent unit to assign costs to (1) completed units transferred out and (2) units in ending WIP inventory.

The Four Key Steps of Assigning Costs

Recall that Desk Products, Inc., has two departments—Assembly and Finishing. Although this chapter focuses on the Assembly department, the Finishing department would also use the four steps to determine product costs for completed units transferred out and ending WIP inventory. Table 4.2 "Production Information for Desk Products’ Assembly Department" presents information for the Assembly department at Desk Products for the month of May. Review this information carefully as it will be used to illustrate the four key steps.

Table 4.2 Production Information for Desk Products’ Assembly Department

Assembly Department—Month of May

· The company had 3,000 units in beginning WIP inventory; all were completed and transferred out during May.

· During May, 6,000 units were started. Of the 6,000 units started:

· 1,000 units were completed and transferred out to the Finishing department (100 percent complete with respect to direct materials, direct labor, and overhead); thus 1,000 units were started and completed during May.

· 5,000 units were partially completed and remained in ending WIP inventory on May 31 (60 percent complete for direct materials, 30 percent complete for direct labor, and 30 percent complete for overhead, which is applied based on direct labor hours).

· Costs in beginning WIP inventory totaled $161,000 (= $95,000 in direct materials + $40,000 in direct labor + $26,000 in overhead).

· Costs incurred during May totaled $225,000 (= $115,000 in direct materials + $70,000 in direct labor + $40,000 in overhead).

Question: Costs for the Assembly department totaled $386,000 for the month of May ($386,000 = $161,000 in beginning WIP inventory + $225,000 incurred during May). How much of the $386,000 should be assigned to (1) completed units transferred out to the Finishing department and (2) units remaining in the Assembly department ending WIP inventory?

Answer: Let’s use the four key steps as follows to answer this question.

Step 1. Summarize the physical flow of units and compute the equivalent units for direct materials, direct labor, and overhead.

This step uses the basic cost flow equation presented in Chapter 2 "How Is Job Costing Used to Track Production Costs?" to identify the physical flow of units (the basic cost flow equation applies to costs and to units):

Question: What are the two categories used to summarize the physical flow of units?

Answer: The first category, units to be accounted for, includes the beginning balance (BB) and transfers in (TI). The second category, units accounted for, includes the ending balance (EB) and transfers out (TO). As you can see from the previous equation, units to be accounted for must equal units accounted for. Here is how it looks for the Assembly department for the month of May:

*This information is used in the physical units column of Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" .

This step shows that 3,000 units were in WIP inventory on May 1 and 6,000 units were started during May. Thus 9,000 units must be accounted for. These 9,000 units will end up in one of two places, either completed and transferred out (to the Finishing department) or not completed and therefore in ending WIP inventory. The previous schedule shows that 4,000 units were completed and transferred out (3,000 from beginning WIP inventory and 1,000 from the units started and completed during the month), and 5,000 units remain in ending WIP inventory.

Question: Based on the previous information for Desk Products, Inc., we now know that 4,000 units were completed and transferred out, and 5,000 units were in ending WIP inventory at the end of May. How do we convert this information into equivalent units?

Answer: The units accounted for (4,000 transferred out and 5,000 in ending WIP inventory) must be converted into equivalent units for direct materials, direct labor, and overhead, as shown in Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department". The 4,000 units transferred out are 100 percent complete for direct materials, direct labor, and overhead (otherwise, they would not be transferred out), which results in equivalent units matching the physical units. However, the 5,000 units in ending WIP inventory are at varying levels of completion for direct materials, direct labor, and overhead, and must be converted into equivalent units using the following formula (as described earlier in the chapter):

Equivalent units = Number of physical units × Percentage of completion

Later in step 3, we will use equivalent unit information for the Assembly department to calculate the cost per equivalent unit.

Figure 4.4 Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department

a This column represents actual physical units accounted for before converting to equivalent units.

b Equivalent units = Number of physical units × Percentage of completion. Units completed and transferred out are 100 percent complete. Thus equivalent units are the same as the physical units. (Information is from Table 4.2 "Production Information for Desk Products’ Assembly Department" .)

c Equivalent units = Number of physical units × Percentage of completion. For direct materials, 3,000 equivalent units = 5,000 physical units × 60 percent complete; for direct labor and overhead, 1,500 equivalent units = 5,000 physical units × 30 percent complete. (Information is from Table 4.2 "Production Information for Desk Products’ Assembly Department" .)

Step 2. Summarize the costs to be accounted for (separated into direct materials, direct labor, and overhead).

Question: How do we summarize the costs that are used to calculate the cost per equivalent unit?

Answer: The total costs to be accounted for include the costs in beginning WIP inventory and the costs incurred during the period. Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" shows these costs for the Assembly department. Notice that the costs are separated into direct materials, direct labor, and overhead.

Figure 4.5 Summary of Costs to Be Accounted for in Desk Products’ Assembly Department

a Information is from Table 4.2 "Production Information for Desk Products’ Assembly Department" .

Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" shows that costs totaling $386,000 must be assigned to (1) completed units transferred out and (2) units in ending WIP inventory.

Step 3. Calculate the cost per equivalent unit.

Question: We now have the costs ( Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" ) and equivalent units ( Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" ) needed to determine the cost per equivalent unit for direct materials, direct labor, and overhead. How do we use this information to calculate the cost per equivalent unit?

Answer: The formula to calculate the cost per equivalent unit using the weighted average method is as follows:

Key Equation

Cost per equivalent unit=Costs in beginning WIP + Current period costsEquivalent units completed and transferred out + Equivalent units in ending WIP

In summary, the same formula is as follows:

*From the bottom of Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department".

**From the bottom of Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department".

Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department" presents the cost per equivalent unit calculation for Desk Products’ Assembly department.

Figure 4.6 Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department

a Information is from Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" .

b Information is from Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" .

The cost per equivalent unit is calculated for direct materials, direct labor, and overhead. Simply divide total costs to be accounted for by total equivalent units accounted for. It is important to note that the information shown in Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department" allows managers to carefully assess the unit cost information in the Assembly department for direct materials, direct labor, and overhead. We discuss this further later in the chapter.

Step 4. Use the cost per equivalent unit to assign costs to (1) completed units transferred out and (2) units in ending WIP inventory.

Question: Recall our primary goal of assigning costs to completed units transferred out and to units in ending WIP inventory. How do we accomplish this goal?

Answer: Costs are assigned by multiplying the cost per equivalent unit (shown in Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department") by the number of equivalent units (shown in Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department") for direct materials, direct labor, and overhead. Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department" shows how this is done.

Figure 4.7 Assigning Costs to Products in Desk Products’ Assembly Department

a The total cost assigned to units transferred out equals the cost per equivalent unit times the number of equivalent units. For example, the cost assigned to direct materials of $120,000 = 4,000 equivalents units ( Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" ) × $30 per equivalent unit ( Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department" ).

b The total cost assigned to units in ending inventory equals the cost per equivalent unit times the number of equivalent units. For example, the cost assigned to direct materials of $90,000 = 3,000 equivalent units ( Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" ) × $30 per equivalent unit ( Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department" ).

c This must match total costs to be accounted for shown in Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" . Although not an issue in this example, rounding the cost per equivalent unit may cause minor differences between the two amounts.

Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department" shows that total costs of $248,000 are assigned to units completed and transferred out and that $138,000 in costs are assigned to ending WIP inventory.

On completion of step 4, it is important to reconcile the total costs to be accounted for shown at the bottom of Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" with the total costs accounted for shown at the bottom of Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department". The two balances must match (note that small discrepancies may exist due to rounding the cost per equivalent unit). This reconciliation relates back to the basic cost flow equation as follows:

**From Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department".

***From Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department".

Although the examples in this chapter have been created in a way that minimizes rounding errors, always round the cost per equivalent unit calculations in step 3 to the nearest thousandth (e.g., if the cost per equivalent unit is $2.3739, round this to $2.374 rather than to $2). Although rounding differences still may occur, this will minimize the size of rounding errors when attempting to reconcile costs to be accounted for (step 2) with costs accounted for (step 4).

Journalizing Costs Assigned to Units Completed and Transferred

Question: Once the four-step process is complete, a journal entry must be made to record the transfer of costs out of the Assembly department and into the Finishing department. How do we record the costs associated with units completed and transferred out?

Answer: At Desk Products, Inc., 4,000 units were transferred from the Assembly department to the Finishing department. Costs totaling $248,000 were assigned to these units as shown in Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department". The journal entry to record this at the end of May is as follows:

(Note that this was journal entry number four, presented without dollar amounts earlier in the chapter.)

Figure 4.8 "Flow of Costs through the Work-in-Process Inventory T-Account of Desk Products’ Assembly Department" shows the flow of costs through the work-in-process inventory T-account for the Assembly department. Note that four key steps were performed for the Assembly department to determine the costs assigned to (1) completed units transferred out to the Finishing department ($248,000) and (2) units in Assembly’s WIP inventory ($138,000). Both amounts are highlighted.

Figure 4.8 Flow of Costs through the Work-in-Process Inventory T-Account of Desk Products’ Assembly Department

Business in Action 4.4

The Production Process for Hershey’s Chocolate

Hershey Foods Corp. is best known for its chocolate products, including brands like Almond Joy, Hershey’s Kisses, and Reese’s. Hershey’s products are sold in more than 90 countries worldwide. According to Hershey, more than 80 million Kiss-shaped products are made every day!

Several sequential stages of production are required to produce chocolate at Hershey:

1. Fermentation. Cocoa beans are placed in large heaps for one week to allow the cocoa flavor to develop.

2. Roasting. The cocoa beans are roasted at very high temperatures.

3. Hulling. A hulling machine separates the shell from the inside of the bean (called the nib).

4. Milling. The nibs are ground into chocolate liquor (a liquid with a pure chocolate flavor that contains no alcohol).

5. Mixing. The chocolate liquor is mixed with cocoa butter, sugar, and milk. This mixture is dried into a brown powder, called chocolate crumb, and processed into chocolate paste.

6. Molding. Machines are used to fill more than 1,000 molds per minute with chocolate. The chocolate is then chilled to form solid candy.

7. Packaging. The candy is wrapped, packaged, and ready to be shipped.

Hershey likely uses a process costing system since it produces identical units of product in batches employing a consistent process. Process costing systems require the use of work-in-process inventory accounts for each process. Thus Hershey would track production costs using separate work-in-process inventory accounts for each stage of production.

Source: Hershey’s, “Home Page,” http://www.hersheys.com.

KEY TAKEAWAYS

· Four steps are used to assign product costs to (1) completed units transferred out and (2) units in work-in-process inventory at the end of the period.

· The four-step process must be performed for each processing department and results in a journal entry to record the costs assigned to units transferred out.

REVIEW PROBLEM 4.4

Kelley Paint Company uses the weighted average method to account for costs of production. Kelley manufactures base paint in two separate departments—Mixing and Packaging. The following information is for the Mixing department for the month of March.

· A total of 40,000 units (measured in gallons) were in beginning WIP inventory. All were completed and transferred out during March.

· A total of 70,000 units were started during March. Of the 70,000 units started,

· 20,000 units were completed and transferred out to the Packaging department (100 percent complete with respect to direct materials, direct labor, and overhead), and

· 50,000 units were partially completed and remained in ending WIP inventory on March 31 (90 percent complete for direct materials, 70 percent complete for direct labor, and 30 percent complete for overhead, which is applied based on machine hours).

· Costs in beginning WIP inventory totaled $229,000 (= $98,000 in direct materials + $41,000 in direct labor + $90,000 in overhead).

· Costs incurred during March totaled $165,000 (= $70,000 in direct materials + $35,000 in direct labor + $60,000 in overhead).

Required:

a. Use the four key steps to assign costs to units completed and transferred out and to units in ending WIP inventory for the Mixing department.

b. Prepare the journal entry necessary at the end of March to record the transfer of costs associated with units completed and transferred to the Packaging department.

Solution to Review Problem 4.4

a. The four steps are as follows:

Step 1. Summarize the physical flow of units and compute the equivalent units for direct materials, direct labor, and overhead.

a 60,000 units = 40,000 from beginning WIP inventory + 20,000 started and completed in March.

b This column represents actual physical units accounted for before converting to equivalent units.

c Equivalent units = number of physical units × percentage of completion. Units completed and transferred out are 100 percent complete. Thus equivalent units are the same as the physical units.

d Equivalent units = number of physical units × percentage of completion. For direct materials, 45,000 equivalent units = 50,000 physical units × 90 percent complete; for direct labor, 35,000 equivalent units = 50,000 physical units × 70 percent complete; for overhead, 15,000 equivalent units = 50,000 physical units × 30 percent complete.

Step 2. Summarize the costs to be accounted for (separated into direct materials, direct labor, and overhead).

e Information is given.

Step 3. Calculate the cost per equivalent unit.

Step 4. Use the cost per equivalent unit to assign costs to (1) completed units transferred out and (2) units in ending WIP inventory.

f Total costs assigned to units transferred out equals the cost per equivalent unit times the number of equivalent units. For example, costs assigned for direct materials of $96,000 = 60,000 equivalents units (from step 1) × $1.60 per equivalent unit (from step 3).

g Total costs assigned to ending WIP inventory equals the cost per equivalent unit times the number of equivalent units. For example, costs assigned for direct materials of $72,000 = 45,000 equivalent units (from step 1) × $1.60 per equivalent unit (from step 3).

h This must match total costs to be accounted for in step 2, as shown in the following:

b. As shown in step 4, $264,000 in total costs are assigned to units completed and transferred out. The entry to record this is as follows:

4.5 Preparing a Production Cost Report

LEARNING OBJECTIVE

1. Prepare a production cost report for a processing department.

Question: The results of the four key steps are typically presented in a production cost report. The production cost report summarizes the production and cost activity within a department for a reporting period. It is simply a formal summary of the four steps performed to assign costs to units transferred out and units in ending work-in-process (WIP) inventory. What does the production cost report look like for the Assembly department at Desk Products, Inc.?

Answer: The production cost report for the month of May for the Assembly department appears in Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department". Notice that each section of this report corresponds with one of the four steps described earlier. We provide references to the following illustrations so you can review the detail supporting calculations.

Figure 4.9 Production Cost Report for Desk Products’ Assembly Department

a Total costs to be accounted for (step 2) must equal total costs accounted for (step 4).

b Data are given.

c This section comes from Figure 4.4 "Flow of Units and Equivalent Unit Calculations for Desk Products’ Assembly Department" .

d This section comes from Figure 4.5 "Summary of Costs to Be Accounted for in Desk Products’ Assembly Department" .

e This section comes from Figure 4.6 "Calculation of the Cost per Equivalent Unit for Desk Products’ Assembly Department" .

f This section comes from Figure 4.7 "Assigning Costs to Products in Desk Products’ Assembly Department" .

How Do Managers Use Production Cost Report Information?

Question: Although the production cost report provides information needed to transfer costs from one account to another, managers also use this report for decision-making purposes. What important questions can be answered using the production cost report?

Answer: A production cost report helps managers answer several important questions:

· How much does it cost to produce each unit of product for each department?

· Which production cost is the highest—direct materials, direct labor, or overhead?

· Where are we having difficulties in the production process? In any particular departments?

· Are we seeing any significant changes in unit costs for direct materials, direct labor, or overhead? If so, why?

· How many units flow through each processing department each month?

· Are improvements in the production process being reflected in the cost per unit from one month to the next?

Beware of Fixed Costs

Question: Why might the per unit cost data provided in the production cost report be misleading?

Answer: When using information from the production cost report, managers must be careful not to assume that all production costs are variable costs. The CEO of Desk Products, Inc., Ann Watkins, was told that the Assembly department cost for each desk totaled $62 for the month of May (from Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department", step 3). However, if the company produces more or fewer units than were produced in May, the unit cost will change. This is because the $62 unit cost includes both variable and fixed costs (see Chapter 5 "How Do Organizations Identify Cost Behavior Patterns?" for a detailed discussion of fixed and variable costs).

Assume direct materials and direct labor are variable costs. In the Assembly department, the variable costs per unit associated with direct materials and direct labor of $50 (= $30 direct materials + $20 direct labor) will remain the same regardless of the level of production, within the relevant range. However, the remaining unit product cost of $12 associated with overhead must be analyzed further to determine the amount that is variable (e.g., indirect materials) and the amount that is fixed (e.g., factory rent). Managers must understand that fixed costs per unit will change depending on the level of production. More specifically, Ann Watkins must understand that the $62 unit cost in the Assembly department provided in the production cost report will change depending on the level of production. Chapter 5 "How Do Organizations Identify Cost Behavior Patterns?" provides a detailed presentation of how cost information can be separated into fixed and variable components for the purpose of providing managers with more useful information.

KEY TAKEAWAY

· The four key steps of assigning costs to units transferred out and units in ending WIP inventory are formally presented in a production cost report. The production cost report summarizes the production and cost activity within a processing department for a reporting period. A separate report is prepared for each processing department. Rounding the cost per equivalent unit to the nearest thousandth will minimize rounding differences when reconciling costs to be accounted for in step 2 with costs accounted for in step 4.

Computer Application

Using Excel to Prepare a Production Cost Report

Managers typically use computer software to prepare production cost reports. They do so for several reasons:

· Once the format is established, the template can be used from one period to the next.

· Formulas underlie all calculations, thereby minimizing the potential for math errors and speeding up the process.

· Changes can be made easily without having to redo the entire report.

· Reports can be easily combined to provide a side-by-side analysis from one period to the next.

Review Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department" and then ask yourself: “How can I use Excel to help prepare this report?” Answers will vary widely depending on your experience with Excel. However, Excel has a few basic features that can make the job of creating a production cost report easier. For example, you can use formulas to sum numbers in a column (note that each of the four steps presented in Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department" has column totals) and to calculate the cost per equivalent unit. Also you can establish a separate line to double-check that

· the units to be accounted for match the units accounted for; and

· the total costs to be accounted for match the total costs accounted for.

For those who want to add more complex features, the basic data (e.g., the data in Table 4.2 "Production Information for Desk Products’ Assembly Department") can be entered at the top of the spreadsheet and pulled down to the production cost report where necessary.

An example of how to use Excel to prepare a production cost report follows. Notice that the basic data are at the top of the spreadsheet, and the rest of the report is driven by formulas. Each month, the data at the top are changed to reflect the current month’s activity, and the production cost report takes care of itself.

REVIEW PROBLEM 4.5

Using the information in Note 4.24 "Review Problem 4.4", prepare a production cost report for the Mixing department of Kelley Paint Company for the month ended March 31. (Hint: You have already completed the four key steps in Note 4.24 "Review Problem 4.4". Simply summarize the information in a production cost report as shown in Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department".)

Solution to Review Problem 4.5

(See solutions to Note 4.24 "Review Problem 4.4" for detailed calculations.)

END-OF-CHAPTER EXERCISES

Questions

1. Which types of companies use a process costing system to account for product costs? Provide at least three examples of products that would require the use of a process costing system.

2. Describe the similarities between a process costing system and a job costing system.

3. Describe the differences between a process costing system and a job costing system.

4. Review Note 4.4 "Business in Action 4.1" What are the three stages of production at Coca-Cola, and what account is used to track production costs for each stage?

5. What are transferred-in costs?

6. Review Note 4.9 "Business in Action 4.2" Why is it likely that Wrigley uses a process costing system rather than a job costing system?

7. Explain the difference between physical units and equivalent units.

8. Explain the concept of equivalent units assuming the weighted average method is used.

9. Explain why direct materials, direct labor, and overhead might be at different stages of completion at the end of a reporting period.

10. Review Note 4.14 "Business in Action 4.3" Why do colleges convert the actual number of students attending school to a full-time equivalent number of students?

11. Describe the four key steps shown in a production cost report assuming the weighted average method is used.

12. What two important amounts are determined in step 4 of the production cost report?

13. Describe the basic cost flow equation and explain how it is used to reconcile units to be accounted for with units accounted for.

14. Describe the basic cost flow equation and explain how it is used to reconcile costs to be accounted for with costs accounted for.

15. Review Note 4.22 "Business in Action 4.4" Describe the last two stages of the production process at Hershey.

16. How does a company determine the number of production cost reports to be prepared for each reporting period?

17. What is a production cost report, and how is it used by management?

18. Explain how the cost per equivalent unit might be misleading to managers, particularly when a significant change in production is anticipated.

Brief Exercises

19. Product Costing at Desk Products, Inc. Refer to the dialogue presented at the beginning of the chapter.

Required:

s. Why was the owner of Desk Products, Inc., concerned about the Assembly department product cost of each desk?

s. What did the accountant, John Fuller, promise by the end of the week?

1. Job Costing Versus Process Costing. For each firm listed in the following, identify whether it would use job costing or process costing.

20. Chewing gum manufacturer

20. Custom automobile restorer

20. Facial tissue manufacturer

20. Accounting services provider

20. Electrical services provider

20. Pool builder

20. Cereal producer

20. Architectural design provider

1. Process Costing Journal Entries. Assume a company has two processing departments—Molding and Packaging. Transactions for the month are shown as follows.

21. The Molding department requisitioned direct materials totaling $2,000 to be used in production.

21. Direct labor costs totaling $3,500 were incurred in the Molding department, to be paid the next month.

21. Manufacturing overhead costs applied to products in the Molding department totaled $2,500.

21. The cost of goods transferred from the Molding department to the Packaging department totaled $10,000.

21. Manufacturing overhead costs applied to products in the Packaging department totaled $1,800.

Required:

Prepare journal entries to record transactions 1 through 5.

1. Calculating Equivalent Units. Complete the requirements for each item in the following.

22. A university has 500 students enrolled in classes. Each student attends school on a part-time basis. On average, each student takes three-quarters of a full load of classes. Calculate the number of full-time equivalent students (i.e., calculate the number of equivalent units).

22. A total of 10,000 units of product remain in the Assembly department at the end of the year. Direct materials are 80 percent complete and direct labor is 40 percent complete. Calculate the equivalent units in the Assembly department for direct materials and direct labor.

22. A local hospital has 60 nurses working on a part-time basis. On average, each nurse works two-thirds of a full load. Calculate the number of full-time equivalent nurses (i.e., calculate the number of equivalent units).

22. A total of 6,000 units of product remain in the Quality Testing department at the end of the year. Direct materials are 75 percent complete and direct labor is 20 percent complete. Calculate the equivalent units in the Quality Testing department for direct materials and direct labor.

1. Calculating Cost per Equivalent Unit. The following information pertains to the Finishing department for the month of June.

	Direct Materials	Direct Labor	Overhead
Total costs to be accounted for	$100,000	$200,000	$300,000
Total equivalent units accounted for	10,000 units	8,000 units	8,000 units

1. Required:

1. Calculate the cost per equivalent unit for direct materials, direct labor, overhead, and in total. Show your calculations.

1. Assigning Costs to Completed Units and to Units in Ending WIP Inventory. The following information is for the Painting department for the month of January.

	Direct Materials	Direct Labor	Overhead
Cost per equivalent unit	$2.10	$1.50	$3.80
Equivalent units completed and transferred out	3,000 units	3,000 units	3,000 units
Equivalent units in ending WIP inventory	1,000 units	1,200 units	1,200 units

1. Required:

aa. Calculate the costs assigned to units completed and transferred out of the Painting department for direct materials, direct labor, overhead, and in total.

aa. Calculate the costs assigned to ending WIP inventory for the Painting department for direct materials, direct labor, overhead, and in total.

Exercises: Set A

25. Assigning Costs to Products: Weighted Average Method. Sydney, Inc., uses the weighted average method for its process costing system. The Assembly department at Sydney, Inc., began April with 6,000 units in work-in-process inventory, all of which were completed and transferred out during April. An additional 8,000 units were started during the month, 3,000 of which were completed and transferred out during April. A total of 5,000 units remained in work-in-process inventory at the end of April and were at varying levels of completion, as shown in the following.

Direct materials	40 percent complete
Direct labor	30 percent complete
Overhead	50 percent complete

26. The following cost information is for the Assembly department at Sydney, Inc., for the month of April.

	Direct Materials	Direct Labor	Overhead	Total
Beginning WIP inventory	$300,000	$350,000	$250,000	$900,000
Incurred during the month	$180,000	$200,000	$170,000	$550,000

27. Required:

aa. Determine the units to be accounted for and units accounted for; then calculate the equivalent units for direct materials, direct labor, and overhead. (Hint: This requires performing step 1 of the four-step process.)

aa. Calculate the cost per equivalent unit for direct materials, direct labor, and overhead. (Hint: This requires performing step 2 and step 3 of the four-step process.)

aa. Assign costs to units transferred out and to units in ending WIP inventory. (Hint: This requires performing step 4 of the four-step process.)

aa. Confirm that total costs to be accounted for (from step 2) equals total costs accounted for (from step 4). Note that minor differences may occur due to rounding the cost per equivalent unit in step 3.

aa. Explain the meaning of equivalent units.

1. Production Cost Report: Weighted Average Method. Refer to Exercise 25. Prepare a production cost report for Sydney, Inc., for the month of April using the format shown in Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department".

1. Process Costing Journal Entries. Silva Piping Company produces PVC piping in two processing departments—Fabrication and Packaging. Transactions for the month of July are shown as follows.

29. Direct materials totaling $15,000 are requisitioned and placed into production—$7,000 for the Fabrication department and $8,000 for the Packaging department.

29. Direct labor costs (wages payable) are incurred by each department as follows:

Fabrication	$4,500
Packaging	$6,700

29. Manufacturing overhead costs are applied to each department as follows:

Fabrication	$20,000
Packaging	$14,000

29. Products with a cost of $22,000 are transferred from the Fabrication department to the Packaging department.

29. Products with a cost of $35,000 are completed and transferred from the Packaging department to the finished goods warehouse.

29. Products with a cost of $31,000 are sold to customers.

Required:

6. Prepare journal entries to record each of the previous transactions.

6. In general, how does the process costing system used here differ from a job costing system?

Exercises: Set B

28. Assigning Costs to Products: Weighted Average Method. Varian Company uses the weighted average method for its process costing system. The Molding department at Varian began the month of January with 80,000 units in work-in-process inventory, all of which were completed and transferred out during January. An additional 90,000 units were started during the month, 30,000 of which were completed and transferred out during January. A total of 60,000 units remained in work-in-process inventory at the end of January and were at varying levels of completion, as shown in the following.

Direct materials	80 percent complete
Direct labor	90 percent complete
Overhead	90 percent complete

29. The following cost information is for the Molding department at Varian Company for the month of January.

	Direct Materials	Direct Labor	Overhead	Total
Beginning WIP inventory	$1,400,000	$1,100,000	$1,700,000	$4,200,000
Incurred during the month	$1,210,000	$ 980,000	$1,450,000	$3,640,000

30. Required:

ad. Determine the units to be accounted for and units accounted for; then calculate the equivalent units for direct materials, direct labor, and overhead. (Hint: This requires performing step 1 of the four-step process.)

ad. Calculate the cost per equivalent unit for direct materials, direct labor, and overhead. (Hint: This requires performing step 2 and step 3 of the four-step process.)

ad. Assign costs to units transferred out and to units in ending WIP inventory. (Hint: This requires performing step 4 of the four-step process.)

ad. Confirm that total costs to be accounted for (from step 2) equals total costs accounted for (from step 4). Note that minor differences may occur due to rounding the cost per equivalent unit in step 3.

ad. Explain the meaning of equivalent units.

1. Production Cost Report: Weighted Average Method. Refer to Exercise 28. Prepare a production cost report for Varian Company for the month of January using the format shown in Figure 4.9 "Production Cost Report for Desk Products’ Assembly Department".

1. Process Costing Journal Entries. Westside Chemicals produces paint thinner in three processing departments—Mixing, Testing, and Packaging. Transactions for the month of September are shown as follows.

32. Direct materials totaling $80,000 are requisitioned and placed into production—$60,000 for the Mixing department, $11,000 for the Testing department, and $9,000 for the Packaging department.

32. Direct labor costs (wages payable) incurred by each department are as follows:

Mixing	$35,000
Testing	$25,000
Packaging	$18,000

32. Manufacturing overhead costs are applied to each department as follows:

Mixing	$17,500
Testing	$12,500
Packaging	$ 6,000

32. Products with a cost of $55,000 are transferred from the Mixing department to the Testing department.

32. Products with a cost of $86,000 are transferred from the Testing department to the Packaging department.

32. Products with a cost of $100,000 are completed and transferred from the Packaging department to the finished goods warehouse.

32. Products with a cost of $81,000 are sold to customers.

Required:

af. Prepare journal entries to record each of the previous transactions.

af. In general, how does the process costing system used here differ from a job costing system?

Problems

31. Production Cost Report: Weighted Average Method. Calvin Chemical Company produces a chemical used in the production of silicon wafers. Calvin Chemical uses the weighted average method for its process costing system. The Mixing department at Calvin Chemical began the month of June with 5,000 units (gallons) in work-in-process inventory, all of which were completed and transferred out during June. An additional 15,000 units were started during the month, 11,000 of which were completed and transferred out during June. A total of 4,000 units remained in work-in-process inventory at the end of June and were at varying levels of completion, as shown in the following.

Direct materials	60 percent complete
Direct labor	40 percent complete
Overhead	40 percent complete

32. The cost information is as follows:

33.

34. Costs in beginning work-in-process inventory

Direct materials	$8,000
Direct labor	$3,000
Overhead	$2,800

35.

36. Costs incurred during the month

Direct materials	$21,000
Direct labor	$ 8,500
Overhead	$ 7,200

37. Required:

ak. Prepare a production cost report for the Mixing department at Calvin Chemical Company for the month of June.

ak. Confirm that total costs to be accounted for (from step 2) equals total costs accounted for (from step 4). Note that minor differences may occur due to rounding the cost per equivalent unit in step 3.

ak. According to the production cost report, what is the total cost per equivalent unit for the work performed in the Mixing department? Which of the three product cost components is the highest, and what percent of the total does this product cost represent?

1. Production Cost Report: Weighted Average Method. Quality Confections Company manufactures chocolate bars in two processing departments, Mixing and Packaging, and uses the weighted average method for its process costing system. The table that follows shows information for the Mixing department for the month of March.

Unit Information (Measured in Pounds)	Mixing
Beginning work-in-process inventory	8,000
Started or transferred in during the month	230,000
Ending work-in-process inventory: 80 percent materials, 70 percent labor, and 60 percent overhead	6,000
Cost Information
Beginning Work-in-Process Inventory
Direct materials	$ 3,000
Direct labor	$ 1,500
Overhead	$ 2,200
Costs Incurred during the Period
Direct materials	$103,000
Direct labor	$ 55,000
Overhead	$ 81,000

1. Required:

am. Prepare a production cost report for the Mixing department for the month of March.

am. Confirm that total costs to be accounted for (from step 2) equals total costs accounted for (from step 4); minor differences may occur due to rounding the cost per equivalent unit in step 3.

am. According to the production cost report, what is the total cost per equivalent unit for the work performed in the Mixing department? Which of the three product cost components is the highest, and what percent of the total does this product cost represent?

1. Production Cost Report and Journal Entries: Weighted Average Method. Wood Products, Inc., manufactures plywood in two processing departments, Milling and Sanding, and uses the weighted average method for its process costing system. The table that follows shows information for the Milling department for the month of April.

Unit Information (Measured in Feet)	Milling
Beginning work-in-process inventory	24,000
Started or transferred in during the month	110,000
Ending work-in-process inventory: 80 percent materials, 70 percent labor, and 60 percent overhead	32,000
Cost Information
Beginning Work-in-Process Inventory
Direct materials	$ 9,000
Direct labor	$ 3,000
Overhead	$ 3,200
Costs Incurred during the Period
Direct materials	$45,000
Direct labor	$14,000
Overhead	$16,000

1. Required:

ao. Prepare a production cost report for the Milling department for the month of April.

ao. Confirm that total costs to be accounted for (from step 2) equals total costs accounted for (from step 4); minor differences may occur due to rounding the cost per equivalent unit in step 3.

ao. For the Milling department at Wood Products, Inc., prepare journal entries to record:

3. The cost of direct materials placed into production during the month (from step 2).

3. Direct labor costs incurred during the month but not yet paid (from step 2).

3. The application of overhead costs during the month (from step 2).

3. The transfer of costs from the Milling department to the Sanding department (from step 4).

One Step Further: Skill-Building Cases

34. Internet Project: Production Company Plant Tour. Using the Internet, find a company that provides a virtual tour of its production processes. Document your findings by completing the following requirements.

Required:

ah. Summarize each step in the production process.

ah. Which type of costing system (job or process) would you expect the company to use? Why?

1. Process Costing at Coca-Cola. Refer to Note 4.4 "Business in Action 4.1".

Required:

ai. What type of costing system does Coca-Cola use? Explain.

ai. What is the purpose of preparing a production cost report? What information results from preparing a production cost report for the mixing and blending department at Coca-Cola?

ai. Based on the information provided, what is the minimum number of production cost reports that Coca-Cola prepares each reporting period? Explain.

1. Process Costing at Wrigley. Refer to Note 4.9 "Business in Action 4.2".

Required:

aj. What type of costing system does Wrigley use? Explain.

aj. What is the purpose of preparing a production cost report? What information results from preparing a production cost report for Wrigley’s Packaging department?

aj. Based on the information provided, what is the minimum number of production cost reports that Wrigley prepares each reporting period? Explain.

1. Group Activity: Job or Process Costing? Form groups of two to four students. Each group should determine whether a process costing or job costing system is most likely used to calculate product costs for each item listed in the following and should be prepared to explain its answers.

37. Jetliners produced by Boeing

37. Gasoline produced by Shell Oil Company

37. Audit of Intel by Ernst & Young

37. Oreo cookies produced by Nabisco Brands, Inc.

37. Frosted Mini-Wheats produced by Kellogg Co.

37. Construction of suspension bridge in Puget Sound, Washington, by Bechtel Group, Inc.

37. Aluminum foil produced by Alcoa, Inc.

37. Potato chips produced by Frito-Lay, Inc.

Comprehensive Cases

38. Ethics: Manipulating Percentage of Completion Estimates. Computer Tech Corporation produces computer keyboards, and its fiscal year ends on December 31. The weighted average method is used for the company’s process costing system. As the controller of Computer Tech, you present December’s production cost report for the Assembly department to the president of the company. The Assembly department is the last processing department before goods are transferred to finished goods inventory. All 160,000 units completed and transferred out during the month were sold by December 31.

The board of directors at Computer Tech established a compensation incentive plan that includes a substantial bonus for the president of the company if annual net income before taxes exceeds $2,000,000. Preliminary figures show current year net income before taxes totaling $1,970,000, which is short of the target by $30,000. The president approaches you and asks you to increase the percentage of completion for the 40,000 units in ending WIP inventory to 90 percent for direct materials and to 95 percent for direct labor and overhead. Even though you are confident in the percentages used to prepare the production cost report, which appears as follows, the president insists that his change is minor and will have little impact on how investors and creditors view the company.

Table Description automatically generated

Required:

al. Why is the president asking you to increase the percentage of completion estimates?

al. Prepare another production cost report for Computer Tech Company that includes the president’s revisions. Indicate what impact the president’s request will have on cost of goods sold and on net income (ignore income taxes in your calculations).

al. As the controller of the company, how would you handle the president’s request? (If necessary, review the presentation of ethics in Chapter 1 "What Is Managerial Accounting?" for additional information.)

1. Ethics: Increasing Production to Boost Profits. Pacific Siding, Inc., produces synthetic wood siding used in the construction of residential and commercial buildings. Pacific Siding’s fiscal year ends on March 31, and the weighted average method is used for the company’s process costing system.

Financial results for the first 11 months of the current fiscal year (through February 28) are well below expectations of management, owners, and creditors. Halfway through the month of March, the chief executive officer and chief financial officer asked the controller to estimate the production results for the month of March in the form of a production cost report (the company only has one production department). This report is shown as follows.

Table Description automatically generated

Armed with the preliminary production cost report for March, and knowing that the company’s production is well below capacity, the CEO and CFO decide to produce as many units as possible for the last half of March even though sales are not expected to increase any time soon. The production manager is told to push his employees to get as far as possible with production, thereby increasing the percentage of completion for ending WIP inventory. However, since the production process takes three weeks to complete, all the units produced in the last half of March will be in WIP inventory at the end of March.

Required:

am. Explain how the CEO and CFO expect to increase profit (net income) for the year by boosting production at the end of March.

am. Using the following assumptions, prepare a revised estimate of production results in the form of a production cost report for the month of March.

Assumptions based on the CEO and CFO’s request to boost production

2. Units started and partially completed during the period will increase to 225,000 (from the initial estimate of 70,000). This is the projected ending WIP inventory at March 31.

2. Percentage of completion estimates for units in ending WIP inventory will increase to 80 percent for direct materials, 85 percent for direct labor, and 90 percent for overhead.

2. Costs incurred during the period will increase to $95,000 for direct materials, $102,000 for direct labor, and $150,000 for overhead (most overhead costs are fixed).

2. All units completed and transferred out during March are sold by March 31.

am. Compare your new production cost report with the one prepared by the controller. How much do you expect profit to increase as a result of increasing production during the last half of March? (Ignore income taxes in your calculations.)

am. Is the request made by the CEO and CFO ethical? Explain your answer.

Previous Chapter

Table of Contents

Next Chapter

-----------------------------------------------------------------------------------------------------------------------------

https://saylordotorg.github.io/text_managerial-accounting/s09-how-do-organizations-identify-.html

Previous Chapter

Table of Contents

Next Chapter

Chapter 5How Do Organizations Identify Cost Behavior Patterns?

Eric Mendez is the chief financial officer (CFO) of Bikes Unlimited, a company that produces mountain bikes and sells them to retail bicycle stores. Bikes Unlimited obtains the bulk of its parts from outside suppliers and assembles them into the mountain bikes prior to shipment. Last month (June), Bikes Unlimited sold 5,000 mountain bikes for $100 each. Last month’s income statement shows total revenue of $500,000 and operating profit of $50,000:

A picture containing chart Description automatically generated

Susan Wesley is Bikes Unlimited’s cost accountant. Planning for July was completed during June. Senior management is now planning for next month (August) and has asked Eric, the CFO, to obtain some vital financial information for budgeting purposes. Eric arranged a meeting with Susan to discuss the August budget.

Eric:	As you know, we are in the middle of our planning for next month. The senior management group asked me to make some projections based on expected changes to our sales next month.
Susan:	Where do you think sales are headed?
Eric:	We expect unit sales to increase 10 percent, perhaps 20 percent if all goes well.
Susan:	If sales increase 10 percent, I would expect profit to increase by more than 10 percent since some costs are fixed.
Eric:	Sounds reasonable. What’s the next step to get a reasonable estimate of profit?
Susan:	First, we have to identify how costs behave with changes in sales and production—whether the costs are variable, fixed, or some other type. Then we can set up the income statement in a contribution margin format and determine if the numbers are within the relevant range.
Eric:	Perhaps you and your staff can discuss this and get me some accurate estimates.
Susan:	I’ll meet with them tomorrow and should have some information for you within a few days.

5.1 Cost Behavior Patterns

LEARNING OBJECTIVE

1. Identify typical cost behavior patterns.

Question: To predict what will happen to profit in the future at Bikes Unlimited, we must understand how costs behave with changes in the number of units sold (sales volume). Some costs will not change at all with a change in sales volume (e.g., monthly rent for the production facility). Some costs will change with a change in sales volume (e.g., materials for the mountain bikes). What are the three cost behavior patterns that help organizations identify which costs will change and which will remain the same with changes in sales volume?

Answer: The three basic cost behavior patterns are known as variable, fixed, and mixed. Each of these cost patterns is described next.

Variable Costs

Question: We know that some costs vary with changes in activity. What do we call this type of cost behavior?

Answer: This cost behavior pattern is called a variable cost. A variable cost describes a cost that varies in total with changes in volume of activity. The activity in this example is the number of bikes produced and sold. However, the activity can take many different forms depending on the organization. The two most common variable costs are direct materials and direct labor. Other examples include indirect materials and energy costs.

Assume the cost of direct materials (wheels, seats, frames, and so forth) for each bike at Bikes Unlimited is $40. If Bikes Unlimited produces one bike, total variable cost for direct materials amounts to $40. If Bikes Unlimited doubles its production to two bikes, total variable cost for direct materials also doubles to $80. Variable costs typically change in proportion to changes in volume of activity. If volume of activity doubles, total variable costs also double, while the cost per unit remains the same. It is important to note that the term variable refers to what happens to total costs with changes in activity, not to the cost per unit.

Taking it one step further for Bikes Unlimited, let’s consider all variable costs related to production. Assume direct materials, direct labor, and all other variable production costs amount to $60 per unit. Table 5.1 "Variable Cost Behavior for Bikes Unlimited" provides the total and per unit variable costs at three different levels of production, and Figure 5.1 "Total Variable Production Costs for Bikes Unlimited" graphs the relation of total variable costs (y-axis) to units produced (x-axis). Note that the slope of the line represents the variable cost per unit of $60 (slope = change in variable cost ÷ change in units produced).

Table 5.1 Variable Cost Behavior for Bikes Unlimited

Units Produced	Total Variable Costs	Per Unit Variable Cost
1	$ 60	$60
2,000	120,000	60
4,000	240,000	60

Figure 5.1 Total Variable Production Costs for Bikes Unlimited

Chart, line chart Description automatically generated

Using Different Activities to Measure Variable Costs

Question: At Bikes Unlimited, it is reasonable to assume that the activity, number of units produced, will affect total variable costs for direct materials and direct labor. However, companies often use a different activity to estimate total variable costs. What types of activities might be used to estimate variable costs?

Answer: The type of activity used to estimate variable costs depends on the cost. For example, a law firm might use the number of labor hours to estimate labor costs. An airline such as American Airlines might use hours of flying time to estimate fuel costs. A mail delivery service such as UPS might use the number of packages processed to estimate labor costs associated with sorting packages. A retail store such as Best Buy might use sales dollars to estimate cost of goods sold.

Variable costs are affected by different activities depending on the organization. The goal is to find the activity that causes the variable cost so that accurate cost estimates can be made.

Fixed Costs

Question: Costs that vary in total with changes in activity are called variable costs. What do we call costs that remain the same in total with changes in activity?

Answer: This cost behavior pattern is called a fixed cost. A fixed cost describes a cost that is fixed (does not change) in total with changes in volume of activity. Assuming the activity is the number of bikes produced and sold, examples of fixed costs include salaried personnel, building rent, and insurance.

Assume Bikes Unlimited pays $8,000 per month in rent for its production facility. In addition, insurance for the same building is $2,000 per month and salaried production personnel are paid $6,000 per month. All other fixed production costs total $4,000. Thus Bikes Unlimited has total fixed costs of $20,000 per month related to its production facility (= $8,000 + $2,000 + $6,000 + $4,000). If only one bike is produced, Bikes Unlimited still must pay $20,000 per month. If 5,000 bikes are produced, Bikes Unlimited still pays $20,000 per month. The fixed costs remain unchanged in total as the level of activity changes.

Question: What happens to fixed costs on a per unit basis as production levels change?

Answer: If Bikes Unlimited only produces one bike, the fixed cost per unit would amount to $20,000 (= $20,000 total fixed costs ÷ 1 bike). If Bikes Unlimited produces two bikes, the fixed cost per unit would be $10,000 (= $20,000 ÷ 2 bikes). As activity increases, the fixed costs are spread out over more units, which results in a lower cost per unit.

Table 5.2 "Fixed Cost Behavior for Bikes Unlimited" provides the total and per unit fixed costs at three different levels of production, and Figure 5.2 "Total Fixed Production Costs for Bikes Unlimited" graphs the relation of total fixed costs (y-axis) to units produced (x-axis). Note that regardless of the activity level, total fixed costs remain the same.

Table 5.2 Fixed Cost Behavior for Bikes Unlimited

Units Produced	Total Fixed Costs	Per Unit Fixed Cost
1	$20,000	$20,000
2,000	20,000	10
4,000	20,000	5

Figure 5.2 Total Fixed Production Costs for Bikes Unlimited

Chart Description automatically generated

Business in Action 5.1

A large air plane on a runway at an airport Description automatically generated

Source: Photo courtesy of Simon_sees, http://www.flickr.com/photos/39551170@N02/3696524201/ .

United Airlines Struggles to Control Costs

United Airlines is the second largest air carrier in the world. It has hubs in Chicago, Denver, Los Angeles, San Francisco, and New York and flies to 109 destinations in 23 countries. Destinations include Tokyo, London, and Frankfurt.

Back in 2002, United filed for bankruptcy. Industry analysts reported that United had relatively high fixed costs, making it difficult for the company to cut costs quickly in line with its reduction in revenue. A few years later, United emerged from bankruptcy, and in 2010 merged with Continental Airlines. Although financial information was presented separately for each company (United and Continental) in 2010, both companies are now owned by United Continental Holdings, Inc. The following financial information for United Airlines is from the company’s income statement for the year ended December 31, 2010 (amounts are in millions). Review this information carefully. Which costs are likely to be fixed?

A picture containing chart Description automatically generated

Although we cannot identify all fixed costs with certainty, several costs likely fall into this category: salaries (for union employees, such as pilots, flight crews, and mechanics); aircraft fuel (assuming flights are not easily canceled); aircraft rent; and depreciation. These costs total $11.1 billion, or 60 percent of total operating expenses (rounded). Fixed costs are clearly a large component of total operating expenses, which makes it difficult for airline companies like United Airlines to make short-term cuts in expenses when revenue declines.

Source: United Continental, Inc., form 10K for 2010.

Committed Versus Discretionary Fixed Costs

Question: Organizations often view fixed costs as either committed or discretionary. What is the difference between these two types of fixed costs?

Answer: A committed fixed cost is a fixed cost that cannot easily be changed in the short run without having a significant impact on the organization. For example, assume Bikes Unlimited has a five-year lease on the company’s production facility, which costs $8,000 per month. This is a committed fixed cost because the lease cannot easily be broken, and the company is committed to using this facility for years to come. Other examples of committed fixed costs include salaried employees with long-term contracts, depreciation on buildings, and insurance.

A discretionary fixed cost is a fixed cost that can be changed in the short run without having a significant impact on the organization. For example, assume Bikes Unlimited contributes $10,000 each year toward charitable organizations. Management has the option of changing this amount in the short run without causing a significant impact on the organization. Other examples of discretionary fixed costs include advertising, research and development, and training programs (although an argument can be made that reducing these expenditures could have a significant impact on the company depending on the amount of the cuts).

In general, management looks to cut discretionary fixed costs when sales and profits are declining, since cuts in this area tend not to have as significant an impact on the organization as cutting committed fixed costs. Difficulties arise when struggling organizations go beyond cutting discretionary fixed costs and begin looking at cutting committed fixed costs.

Mixed Costs

Question: We have now learned about two types of cost behavior patterns—variable costs and fixed costs. However, there is a third type of cost that behaves differently in that both total and per unit costs change with changes in activity. What do we call this type of cost?

Answer: This cost behavior pattern is called a mixed cost. The term mixed cost describes a cost that has a mix of fixed and variable costs. For example, assume sales personnel at Bikes Unlimited are paid a total of $10,000 in monthly salary plus a commission of $7 for every bike sold. This is a mixed cost because it has a fixed component of $10,000 per month and a variable component of $7 per unit.

Table 5.3 "Mixed Cost Behavior for Bikes Unlimited" provides the total and per unit fixed costs at three different levels of production, and Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited" graphs the relation of total mixed costs (y-axis) to units produced (x-axis). The point at which the line intersects the y-axis represents the total fixed cost ($10,000), and the slope of the line represents the variable cost per unit ($7).

Table 5.3 Mixed Cost Behavior for Bikes Unlimited

Units Sold	Total Mixed Costs	Per Unit Mixed Cost
1	$10,007	$10,007.00
2,000	24,000	12.00
4,000	38,000	9.50

Figure 5.3 Total Mixed Sales Compensation Costs for Bikes Unlimited

Chart, line chart Description automatically generated

Because this cost is depicted with a straight line, we can use the equation for a straight line to describe a mixed cost:

Key Equation

Total mixed cost = Total fixed cost + (Unit variable cost × Number of units)

Y = f + vX

where

Y = total mixed costs (this is the y-axis in Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited")f = total fixed costsv = variable cost per unitX = level of activity (this is the x-axis in Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited")

For Bikes Unlimited, the mixed cost equation is Y = $10,000 + $7X. If Bikes Unlimited sells 4,000 bikes (X) in one month, the total mixed cost (Y) for sales personnel compensation would be $38,000 [= $10,000 + ($7 × 4,000 units)].

Short Term Versus Long Term and the Relevant Range

We now introduce two important concepts that must be considered when estimating costs: short term versus long term, and the relevant range.

Short Term Versus Long Term

Question: When identifying cost behavior patterns, we assume that management is using the cost information to make short-term decisions. Why is this short-term decision making assumption so important?

Answer: Variable, fixed, and mixed cost concepts are useful for short-term decision making and therefore apply to a specific period of time. This short-term period will vary depending on the company’s current production capacity and the time required to change capacity. In the long term, all cost behavior patterns will likely change.

For example, suppose Bikes Unlimited’s production capacity is 8,000 units per month, and management plans to expand capacity in two years by renting a new production facility and hiring additional personnel. This is a long-term decision that will change the cost behavior patterns identified earlier. Variable production costs will no longer be $60 per unit, fixed production costs will no longer be $20,000 per month, and mixed sales compensation costs will also change. All these costs will change because the estimates are accurate only in the short term.

The Relevant Range

Question: Another important concept we use when estimating costs is called the relevant range. What is the relevant range and why is it so important when estimating costs?

Answer: The relevant range is the range of activity for which cost behavior patterns are likely to be accurate. The variable, fixed, and mixed costs identified for Bikes Unlimited will only be accurate within a certain range of activity. Once the firm goes outside that range, cost estimates are not necessarily accurate and often must be reevaluated and recalculated.

For example, assume Bikes Unlimited’s mixed sales compensation costs of $10,000 per month plus $7 per unit is only valid up to 4,000 units per month. If unit sales increase beyond 4,000 units, management will hire additional salespeople and the total monthly base salary will increase beyond $10,000. Thus the relevant range for this mixed cost is from zero to 4,000 units. Once the company exceeds sales of 4,000 units per month, it is out of the relevant range, and the mixed cost must be recalculated.

We discuss the relevant range concept in more detail later in the chapter. For now, remember that the accuracy of cost behavior patterns is limited to a certain range of activity called the relevant range.

Computer Application

Using Excel to Create Charts

Managers typically use computer applications on a daily basis to perform a variety of functions. For example, they often use Excel to generate tables, graphs, and charts. You could use Excel to create the charts shown in Figure 5.1 "Total Variable Production Costs for Bikes Unlimited", Figure 5.2 "Total Fixed Production Costs for Bikes Unlimited", and Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited". Here’s how:

1. Enter the data. Open a new Excel document and enter the data in two columns: one column for the x-axis (horizontal axis), and one column for the y-axis (vertical axis). Let’s suppose you want to create the chart shown in Figure 5.1 "Total Variable Production Costs for Bikes Unlimited". In that case, the x-axis represents units produced, and the y-axis represents total variable costs. An excerpt from your Excel document would appear as follows:

Graphical user interface, table, Excel Description automatically generated

2. Create the chart. After you have entered the data, highlight the appropriate data cells (including headings and labels) and click on Insert, Chart, Scatter. Choose Scatter with Smooth Lines and Markers. The chart that results is linked to your data points. If you change the data, the chart changes, too. (In earlier versions of Excel, the chart wizard walks you through the steps necessary to create the chart.)

3. Format the chart. Now that you have created the chart, select it and use Chart Tools to format it with background shading, text inserts, font size, chart size, and other more advanced features. If you want to display the chart within some other document (e.g., a Word document), you can copy it (highlight the chart and select Edit, Copy from the menu bar) and paste it into the document (select Edit, Paste or Paste Special).

The Excel document created by following these three steps would look like the one shown in Figure 5.1 "Total Variable Production Costs for Bikes Unlimited".

How Cost Behavior Patterns Are Used

Question: How do managers use cost behavior patterns to make better decisions?

Answer: Accurately predicting what costs will be in the future can help managers answer several important questions. For example, managers at Bikes Unlimited might ask the following:

· We expect to see a 5 percent increase in unit sales next year. How will this affect revenues and costs?

· We are applying for a loan with a bank, and bank managers think our sales estimates are high. What happens to our revenues and costs if we lower estimates by 20 percent?

· What happens to revenues and costs if we add a racing bike to our product line?

· How will costs behave in the future if we increase automation in the production process?

The only way to accurately predict costs is to understand how costs behave given changes in activity. To make good decisions, managers must know how costs are structured (fixed, variable, or mixed). The next section explains how to estimate fixed and variable costs, and how to identify the fixed and variable components of mixed costs.

Business in Action 5.2

Budget Cuts at an Elementary School District

A school district outside Sacramento, California, was faced with making budget cuts because of a reduction in state funding. To reduce costs, the school district’s administration decided to consider closing one of the smaller elementary schools in the district. According to an initial estimate, closing this school would reduce costs by $500,000 to $1,000,000 per year. However, further analysis identified only $100,000 to $150,000 in cost savings.

Why did the analysis yield lower savings than the initial estimate? Most of the costs were committed fixed costs (e.g., teachers’ salaries and benefits) and could not be eliminated in the short term. In fact, teachers and students at the school being considered for closure were to be moved to other schools in the district, and so no savings on teachers’ salaries and benefits would result. The only real short-term cost savings would be in not having to maintain the classrooms, computer lab, and library (nonunion employees would be let go) and in utilities (heat and air conditioning would be turned off).

The school district ultimately decided not to close the school because of the large committed fixed costs involved, as well as a lack of community support, and budget cuts were made in other areas throughout the district.

REVIEW PROBLEM 5.1

Sierra Company is trying to identify the behavior of the three costs shown in the following table. The following cost information is provided for six months. Calculate the cost per unit, and then identify how each cost behaves (fixed, variable, or mixed). Explain your answers.

		Cost 1	Cost 2	Cost 3
Month	Units Produced	Total Costs	Cost per Unit	Total Costs	Cost per Unit	Total Costs	Cost per Unit
1	50	$100	$2.00	$100	$2.00	$100	$2.00
2	100	200	2.00	100	1.00	150	1.50
3	150	300	_____	100	_____	200	_____
4	200	400	_____	100	_____	250	_____
5	250	500	_____	100	_____	300	_____
6	300	600	_____	100	_____	350	_____

Solution to Review Problem 5.1

As shown in the following table, cost 1 is a variable cost because as the number of units produced changes, total costs change (in proportion to changes in activity) and per unit cost remains the same. Cost 2 is a fixed cost because as the number of units produced changes, total costs remain the same and per unit costs change. Cost 3 is a mixed cost because as the number of units produced changes, total cost changes (but not in proportion to changes in activity) and per unit cost changes.

		Cost 1	Cost 2	Cost 3
Month	Units Produced	Total Costs	Cost per Unit	Total Costs	Cost per Unit*	Total Costs	Cost per Unit*
1	50	$100	$2.00	$100	$2.00	$100	$2.00
2	100	200	2.00	100	1.00	150	1.50
3	150	300	2.00	100	0.67	200	1.33
4	200	400	2.00	100	0.50	250	1.25
5	250	500	2.00	100	0.40	300	1.20
6	300	600	2.00	100	0.33	350	1.17
*Rounded.

5.2 Cost Estimation Methods

LEARNING OBJECTIVE

1. Estimate costs using account analysis, the high-low method, the scattergraph method, and regression analysis.

Question: Recall the conversation that Eric (CFO) and Susan (cost accountant) had about Bikes Unlimited’s budget for the next month, which is August. The company expects to increase sales by 10 to 20 percent, and Susan has been asked to estimate profit for August given this expected increase. Although examples of variable and fixed costs were provided in the previous sections, companies typically do not know exactly how much of their costs are fixed and how much are variable. (Financial accounting systems do not normally sort costs as fixed or variable.) Thus organizations must estimate their fixed and variable costs. What methods do organizations use to estimate fixed and variable costs?

Answer: Four common approaches are used to estimate fixed and variable costs:

· Account analysis

· High-low method

· Scattergraph method

· Regression analysis

All four methods are described next. The goal of each cost estimation method is to estimate fixed and variable costs and to describe this estimate in the form of Y = f + vX. That is, Total mixed cost = Total fixed cost + (Unit variable cost × Number of units). Note that the estimates presented next for Bikes Unlimited may differ from the dollar amounts used previously, which were for illustrative purposes only.

Account Analysis

Question: The account analysis approach is perhaps the most common starting point for estimating fixed and variable costs. How is the account analysis approach used to estimate fixed and variable costs?

Answer: This approach requires that an experienced employee or group of employees review the appropriate accounts and determine whether the costs in each account are fixed or variable. Totaling all costs identified as fixed provides the estimate of total fixed costs. To determine the variable cost per unit, all costs identified as variable are totaled and divided by the measure of activity (units produced is the measure of activity for Bikes Unlimited).

Let’s look at the account analysis approach using Bikes Unlimited as an example. Susan (the cost accountant) asked the financial accounting department to provide cost information for the production department for the month of June (July information is not yet available). Because the financial accounting department tracks information by department, it is able to produce this information. The production department information for June is as follows:

A picture containing graphical user interface, text Description automatically generated

Susan reviewed this cost information with the production manager, Indira Bingham, who has worked as production manager at Bikes Unlimited for several years. After careful review, Indira and Susan came up with the following breakdown of variable and fixed costs for June:

A picture containing chart Description automatically generated

Total fixed cost is estimated to be $30,000, and variable cost per unit is estimated to be $52 (= $260,000 ÷ 5,000 units produced). Remember, the goal is to describe the mixed costs in the equation form Y = f + vX. Thus the mixed cost equation used to estimate future production costs is

Y = $30,000 + $52X

Now Susan can estimate monthly production costs (Y) if she knows how many units Bikes Unlimited plans to produce (X). For example, if Bikes Unlimited plans to produce 6,000 units for a particular month (a 20 percent increase over June) and this level of activity is within the relevant range, total production costs should be approximately $342,000 [= $30,000 + ($52 × 6,000 units)].

Question: Why should Susan be careful using historical data for one month (June) to estimate future costs?

Answer: June may not be a typical month for Bikes Unlimited. For example, utility costs may be low relative to those in the winter months, and production costs may be relatively high as the company prepares for increased demand in July and August. This might result in a lower materials cost per unit from quantity discounts offered by suppliers. To smooth out these fluctuations, companies often use data from the past quarter or past year to estimate costs.

REVIEW PROBLEM 5.2

Alta Production, Inc., is using the account analysis approach to identify the behavior of production costs for a month in which it produced 350 units. The production manager was asked to review these costs and provide her best guess as to how they should be categorized. She responded with the following information:

Chart Description automatically generated

1. Describe the production costs in the equation form Y = f + vX.

2. Assume Alta intends to produce 400 units next month. Calculate total production costs for the month.

Solution to Review Problem 5.2

1. Because f represents total fixed costs, and v represents variable cost per unit, the cost equation is: Y = $7,000 + $1,428.57X. (Variable cost per unit of $1,428.57 = $500,000 ÷ 350 units.)

2. Using the previous equation, simply substitute 400 units for X, as follows:

Thus total production costs are expected to be $578,428 for next month.

High-Low Method

Question: Another approach to identifying fixed and variable costs for cost estimation purposes is the high-low method. Accountants who use this approach are looking for a quick and easy way to estimate costs, and will follow up their analysis with other more accurate techniques. How is the high-low method used to estimate fixed and variable costs?

Answer: The high-low method uses historical information from several reporting periods to estimate costs. Assume Susan Wesley obtains monthly production cost information from the financial accounting department for the last 12 months. This information appears in Table 5.4 "Monthly Production Costs for Bikes Unlimited".

Table 5.4 Monthly Production Costs for Bikes Unlimited

Reporting Period (Month)	Total Production Costs	Level of Activity (Units Produced)
July	$230,000	3,500
August	250,000	3,750
September	260,000	3,800
October	220,000	3,400
November	340,000	5,800
December	330,000	5,500
January	200,000	2,900
February	210,000	3,300
March	240,000	3,600
April	380,000	5,900
May	350,000	5,600
June	290,000	5,000

All of the data points from Table 5.4 "Monthly Production Costs for Bikes Unlimited" are plotted on the graph shown in Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method". Although a graph is not required using the high-low method, it is a helpful visual tool. Susan then draws a straight line using the high (April) and low (January) activity levels from these data. The goal of the high-low method is to describe this line mathematically in the form of an equation stated as Y = f + vX, which requires calculating both the total fixed costs amount (f) and per unit variable cost amount (v). Four steps are required to achieve this using the high-low method:

Step 1. Identify the high and low activity levels from the data set.

Step 2. Calculate the variable cost per unit ( v ).

Step 3. Calculate the total fixed cost ( f ).

Step 4. State the results in equation form Y = f + v X.

Figure 5.4 Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method

Chart, line chart Description automatically generated

Question: How are the four steps of the high-low method used to estimate total fixed costs and per unit variable cost?

Answer: Each of the four steps is described next.

Step 1. Identify the high and low activity levels from the data set.

The highest level of activity (level of production) occurred in the month of April (5,900 units; $380,000 production costs), and the lowest level of activity occurred in the month of January (2,900 units; $200,000 production costs). Note that we are identifying the high and low activity levels rather than the high and low dollar levels—choosing the high and low dollar levels can result in incorrect high and low points.

Step 2. Calculate the variable cost per unit ( v ).

Because the slope of the line shown in Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method" represents the variable cost per unit, the goal here is to calculate the slope of the line using the high and low points identified in step 1 (the slope calculation is often referred to as “rise over run” in math courses). The calculation of the variable cost per unit for Bikes Unlimited is shown as follows:

Step 3. Calculate the total fixed cost ( f ).

After completing step 2, the equation to describe the line is partially complete and stated as Y = f + $60X. The goal of step 3 is to calculate a value for total fixed cost (f). Simply select either the high or low activity level, and fill in the data to solve for f (total fixed costs), as shown.

Using the low activity level of 2,900 units and $200,000,

Thus total fixed costs total $26,000. (Try this using the high activity level of 5,900 units and $380,000. You will get the same result as long as the per unit variable cost is not rounded.)

Step 4. State the results in equation form Y = f + v X.

We know from step 2 that the variable cost per unit is $60, and from step 3 that total fixed cost is $26,000. Thus we can state the equation used to estimate total costs as

Y = $26,000 + $60X

Now it is possible to estimate total production costs given a certain level of production (X). For example, if Bikes Unlimited expects to produce 6,000 units during August, total production costs are estimated to be $386,000:

Question: Although the high-low method is relatively simple, it does have a potentially significant weakness. What is the potential weakness in using the high-low method?

Answer: In reviewing Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method", you will notice that this approach only considers the high and low activity levels in establishing an estimate of fixed and variable costs. The high and low data points may not represent the data set as a whole, and using these points can result in distorted estimates.

For example, the $380,000 in production costs incurred in April may be higher than normal because several production machines broke down resulting in costly repairs. Or perhaps several key employees left the company, resulting in higher than normal labor costs for the month because the remaining employees were paid overtime. Cost accountants will often throw out the high and low points for this reason and use the next highest and lowest points to perform this analysis. While the high-low method is most often used as a quick and easy way to estimate fixed and variable costs, other more sophisticated methods are most often used to refine the estimates developed from the high-low method.

REVIEW PROBLEM 5.3

Alta Production, Inc., reported the following production costs for the 12 months January through December. (This is the same company featured in Note 5.15 "Review Problem 5.2".)

Reporting Period (Month)	Total Production Costs	Level of Activity (Units Produced)
January	$460,000	300
February	300,000	220
March	480,000	330
April	550,000	390
May	570,000	410
June	310,000	240
July	440,000	290
August	455,000	320
September	530,000	380
October	250,000	150
November	700,000	450
December	490,000	350

1. Using this information, perform the four steps of the high-low method to estimate costs and state your results in cost equation form Y = f + vX.

2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.

3. What is the potential weakness in using this approach to estimate costs?

Solution to Review Problem 5.3

1. The four steps are as follows:

Step 1. Identify the high and low activity levels from the data set.

The highest level of activity occurred in November (450 units; $700,000 production costs), and the lowest level of activity occurred in October (150 units; $250,000 production costs).

Step 2. Calculate the variable cost per unit ( v ).

Step 3. Calculate the total fixed cost ( f ).

After completing step 2, the equation to describe the line is partially complete and stated as Y = f + $1,500X. To calculate total fixed costs, simply select either the high or low activity level, and fill in the data to solve for f (total fixed costs), as shown.

Using the high activity level,

Thus total fixed cost is $25,000.

Step 4. State the results in equation form Y = f + v X.

We know from step 2 that the variable cost per unit is $1,500, and from step 3 that total fixed costs are $25,000. Thus the equation used to estimate total production costs is

2. Using the equation from part 1, simply substitute 400 units for X, as follows:

Thus total production costs are expected to be $625,000 for next month.

3. This approach only considers the high and low activity levels in establishing an estimate of fixed and variable costs. The high and low data points may not represent the data set as a whole, and using these points can result in distorted estimates. In reviewing the set of data points for January through December, it appears that October and November are relatively extreme points when compared to the other 10 months. Because the cost equation is based solely on these two points, the resulting estimate of production costs for 400 units of production (in part 2) may not be accurate.

Scattergraph Method

Question: Many organizations prefer to use the scattergraph method to estimate costs. Accountants who use this approach are looking for an approach that does not simply use the highest and lowest data points. How is the scattergraph method used to estimate fixed and variable costs?

Answer: The scattergraph method considers all data points, not just the highest and lowest levels of activity. Again, the goal is to develop an estimate of fixed and variable costs stated in equation form Y = f + vX. Using the same data for Bikes Unlimited shown in Table 5.4 "Monthly Production Costs for Bikes Unlimited", we will follow the five steps associated with the scattergraph method:

Step 1. Plot the data points for each period on a graph.

Step 2. Visually fit a line to the data points and be sure the line touches one data point.

Step 3. Estimate the total fixed costs ( f ).

Step 4. Calculate the variable cost per unit ( v ).

Step 5. State the results in equation form Y = f + v X.

Question: How are the five steps of the scattergraph method used to estimate total fixed costs and per unit variable cost?

Answer: Each of the five steps is described next.

Step 1. Plot the data points for each period on a graph.

This step requires that each data point be plotted on a graph. The x-axis (horizontal axis) reflects the level of activity (units produced in this example), and the y-axis (vertical axis) reflects the total production cost. Figure 5.5 "Scattergraph of Total Mixed Production Costs for Bikes Unlimited" shows a scattergraph for Bikes Unlimited using the data points for 12 months, July through June.

Figure 5.5 Scattergraph of Total Mixed Production Costs for Bikes Unlimited

A close up of a screen Description automatically generated

Step 2. Visually fit a line to the data points and be sure the line touches one data point.

Once the data points are plotted as described in step 1, draw a line through the points touching one data point and extending to the y-axis. The goal here is to minimize the distance from the data points to the line (i.e., to make the line as close to the data points as possible). Figure 5.6 "Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method" shows the line through the data points. Notice that the line hits the data point for July (3,500 units produced and $230,000 total cost).

Figure 5.6 Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method

Chart, line chart, scatter chart Description automatically generated

Step 3. Estimate the total fixed costs ( f ).

The total fixed costs are simply the point at which the line drawn in step 2 meets the y-axis. This is often called the y-intercept. Remember, the line meets the y-axis when the activity level (units produced in this example) is zero. Fixed costs remain the same in total regardless of level of production, and variable costs change in total with changes in levels of production. Since variable costs are zero when no units are produced, the costs reflected on the graph at the y-intercept must represent total fixed costs. The graph in Figure 5.6 "Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method" indicates total fixed costs of approximately $45,000. (Note that the y-intercept will always be an approximation.)

Step 4. Calculate the variable cost per unit ( v ).

After completing step 3, the equation to describe the line is partially complete and stated as Y = $45,000 + vX. The goal of step 4 is to calculate a value for variable cost per unit (v). Simply use the data point the line intersects (July: 3,500 units produced and $230,000 total cost), and fill in the data to solve for v (variable cost per unit) as follows:

Thus variable cost per unit is $52.86.

Step 5. State the results in equation form Y = f + v X.

We know from step 3 that the total fixed costs are $45,000, and from step 4 that the variable cost per unit is $52.86. Thus the equation used to estimate total costs looks like this:

Y = $45,000 + $52.86X

Question: Remember that the key weakness of the high-low method discussed previously is that it considers only two data points in estimating fixed and variable costs. How does the scattergraph method mitigate this weakness?

Answer: The scattergraph method mitigates this weakness by considering all data points in estimating fixed and variable costs. The scattergraph method gives us an opportunity to review all data points in the data set when we plot these data points in a graph in step 1. If certain data points seem unusual (statistics books often call these points outliers), we can exclude them from the data set when drawing the best-fitting line. In fact, many organizations use a scattergraph to identify outliers and then use regression analysis to estimate the cost equation Y = f + vX. We discuss regression analysis in the next section.

Although the scattergraph method tends to yield more accurate results than the high-low method, the final cost equation is still based on estimates. The line is drawn using our best judgment and a bit of guesswork, and the resulting y-intercept (fixed cost estimate) is based on this line. This approach is not an exact science! However, the next approach to estimating fixed and variable costs—regression analysis—uses mathematical equations to find the best-fitting line.

REVIEW PROBLEM 5.4

Alta Production, Inc., reported the following production costs for the 12 months January through December. (These are the same data presented in Note 5.17 "Review Problem 5.3".)

Reporting Period (Month)	Total Production Costs	Level of Activity (Units Produced)
January	$460,000	300
February	300,000	220
March	480,000	330
April	550,000	390
May	570,000	410
June	310,000	240
July	440,000	290
August	455,000	320
September	530,000	380
October	250,000	150
November	700,000	450
December	490,000	350

1. Using the information, perform the five steps of the scattergraph method to estimate costs and state your results in cost equation form Y = f + vX.

2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.

3. When is this approach likely to yield more accurate results than the high-low method?

Solution to Review Problem 5.4

1. The five steps are as follows:

Step 1. Plot the data points for each period on a graph.

Chart, scatter chart Description automatically generated

Step 2. Visually fit a line to the data points, and be sure the line touches one data point.

Chart, line chart, scatter chart Description automatically generated

Step 3. Estimate the total fixed costs ( f ).

The y-intercept represents total fixed costs. This is where the line meets the y-axis. Total fixed costs in the graph appear to be approximately $5,000. You will likely get a different answer because the answer depends on the line that you visually fit to the data points. Remember you must draw the line through one data point. The line intersects the data point for March ($480,000 production costs; 330 units produced). This will be used in step 4.

Step 4. Calculate the variable cost per unit ( v ).

After completing step 3, the equation to describe the line is partially complete and stated as Y = $5,000 + vX. The goal of this step is to calculate a value for variable cost per unit (v). Use the data point the line intersects (for March, 330 units produced and $480,000 total costs), and fill in the data to solve for v (variable cost per unit):

Step 5. State the results in equation form Y = f + v X.

We know from step 3 that the total fixed costs are $5,000, and from step 4 that variable cost per unit is $1,439.39. Thus the equation used to estimate total production costs is stated as:

It is evident from this information that this company has very little in fixed costs and relatively high variable costs. This is indicative of a company that uses a high level of labor and materials (both variable costs) and a low level of machinery (typically a fixed cost through depreciation or lease costs).

2. Using the equation, simply substitute 400 units for X, as follows:

Thus total production costs are expected to be $580,756 for next month.

3. This approach is likely to yield more accurate results than the high-low method when the high and low points are not representative of the entire set of data. Notice that fixed costs are much lower using the scattergraph method ($5,000) than the high-low method ($25,000).

Regression Analysis

Question: Regression analysis is similar to the scattergraph approach in that both fit a straight line to a set of data points to estimate fixed and variable costs. How does regression analysis differ from the scattergraph method for estimating costs?

Answer: Regression analysis uses a series of mathematical equations to find the best possible fit of the line to the data points and thus tends to provide more accurate results than the scattergraph approach. Rather than running these computations by hand, most companies use computer software, such as Excel, to perform regression analysis. Using the data for Bikes Unlimited shown back in Table 5.4 "Monthly Production Costs for Bikes Unlimited", regression analysis in Excel provides the following output. (This is a small excerpt of the output; see the appendix to this chapter for an explanation of how to use Excel to perform regression analysis.)

	Coefficients
y-intercept	43,276
x variable	53.42

Thus the equation used to estimate total production costs for Bikes Unlimited looks like this:

Y = $43,276 + $53.42X

Regression analysis tends to yield the most accurate estimate of fixed and variable costs, assuming there are no unusual data points in the data set. It is important to review the data set first—perhaps in the form of a scattergraph—to confirm that no outliers exist.

REVIEW PROBLEM 5.5

Alta Production, Inc., reported the following production costs for the 12 months January through December. (These are the same data that appear in Note 5.17 "Review Problem 5.3" and Note 5.19 "Review Problem 5.4".)

Reporting Period (Month)	Total Production Cost	Level of Activity (Units Produced)
January	$460,000	300
February	300,000	220
March	480,000	330
April	550,000	390
May	570,000	410
June	310,000	240
July	440,000	290
August	455,000	320
September	530,000	380
October	250,000	150
November	700,000	450
December	490,000	350

Regression analysis performed using Excel resulted in the following output:

	Coefficients
y-intercept	703
x variable	1,442.97

1. Using this information, create the cost equation in the form Y = f + vX.

2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.

Solution to Review Problem 5.5

1. The cost equation using the data from regression analysis is:

2. Using the equation, simply substitute 400 units for X, as follows:

Thus total production costs are expected to be $577,891 for next month.

Summary of Four Cost Estimation Methods

Question: You are now able to create the cost equation Y = f + vX to estimate costs using four approaches. What does the cost equation look like for each approach at Bikes Unlimited?

Answer: The results of these four approaches for Bikes Unlimited are summarized as follows:

· Account analysis: Y = $30,000 + $52.00X

· High-low method: Y = $26,000 + $60.00X

· Scattergraph method: Y = $45,000 + $52.86X

· Regression analysis: Y = $43,276 + $53.42X

Question: We have seen that different methods yield different results, so which method should be used?

Answer: Regression analysis tends to be most accurate because it provides a cost equation that best fits the line to the data points. However, the goal of most companies is to get close—the results do not need to be perfect. Some could reasonably argue that the account analysis approach is best because it relies on the knowledge of those who are familiar with the costs involved.

At Bikes Unlimited, Eric (CFO) and Susan (cost accountant) met several days later. After consulting with her staff, Susan agreed that regression analysis was the best approach to use in estimating total production costs (keep in mind nothing has been done yet with selling and administrative expenses). Account analysis was ruled out because no one on the accounting staff had been with the company long enough to review the accounts and determine which costs were variable, fixed, or mixed. The high-low method was ruled out because it only uses two data points and Eric would prefer a more accurate estimate. Susan did request that her staff prepare a scattergraph and review it for any unusual data points before performing regression analysis. Based on the scattergraph prepared, all agreed that the data was relatively uniform and no outlying data points were identified.

Susan:	My staff has been working hard to determine what will happen to profit if sales volume increases. So far, we’ve been able to identify cost behavior patterns for production costs, and we’re currently working on the cost behavior patterns for selling and administrative expenses.
Eric:	What do you have for production costs?
Susan:	The portion of production costs that are fixed—that won’t change with changes in production and sales—totals $43,276. The portion of production costs that are variable—that vary with changes in production and sales—totals $53.42 per unit.
Eric:	When do you expect to have further information for the selling and administrative costs?
Susan:	We should have those results by the end of the day tomorrow. At that point, I’ll put together an income statement projecting profit for August.
Eric:	Sounds good. Let’s meet when you have the information ready.

KEY TAKEAWAYS

· Account analysis requires that a knowledgeable employee (or group of employees) determine whether costs are fixed, variable, or mixed. If employees do not have enough experience to accurately estimate these costs, another method should be used.

· Table 5.1 "Variable Cost Behavior for Bikes Unlimited" and Figure 5.1 "Total Variable Production Costs for Bikes Unlimited" show that total variable costs change with changes in activity, but per unit variable cost does not change with changes in activity. Table 5.2 "Fixed Cost Behavior for Bikes Unlimited" and Figure 5.2 "Total Fixed Production Costs for Bikes Unlimited" show that total fixed costs do not change with changes in activity, but per unit fixed costs do change with changes in activity. Table 5.3 "Mixed Cost Behavior for Bikes Unlimited" and Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited" show that total mixed costs change with changes in activity, and per unit mixed cost also changes with changes in activity.

· The high-low method starts with the highest and lowest activity levels and uses four steps to estimate fixed and variable costs.

· The scattergraph method has five steps and starts with plotting all points on a graph and fitting a line through the points. This line represents costs throughout a range of activity levels and is used to estimate fixed and variable costs. The scattergraph is also used to identify any outlying or unusual data points.

· Regression analysis forms a mathematically determined line that best fits the data points. Software packages like Excel are available to perform regression analysis. As with the account analysis, high-low, and scattergraph methods, this line is described in the equation form Y = f + vX. This equation is used to estimate future costs.

· Four methods can be used to estimate fixed and variable costs. Each method has its advantages and disadvantages, and the choice of a method will depend on the situation at hand. Experienced employees may be able to effectively estimate fixed and variable costs by using the account analysis approach. If a quick estimate is needed, the high-low method may be appropriate. The scattergraph method helps with identifying any unusual data points, which can be thrown out when estimating costs. Finally, regression analysis can be run using computer software such as Excel and generally provides for more accurate cost estimates.

REVIEW PROBLEM 5.6

Use the solutions you prepared for Note 5.15 "Review Problem 5.2", Note 5.17 "Review Problem 5.3", Note 5.19 "Review Problem 5.4", and Note 5.21 "Review Problem 5.5" to do the following:

1. Show the four cost equations created for Alta Production, Inc., using account analysis (Note 5.15 "Review Problem 5.2"), the high-low method (Note 5.17 "Review Problem 5.3"), the scattergraph method (Note 5.19 "Review Problem 5.4"), and regression analysis (Note 5.21 "Review Problem 5.5").

2. Using the four equations listed in your answer to 1, calculate total production costs assuming Alta Production, Inc., will produce 400 units next month. Comment on your results.

Solution to Review Problem 5.6

1. The cost equations for each of the four methods used in Note 5.15 "Review Problem 5.2", Note 5.17 "Review Problem 5.3", Note 5.19 "Review Problem 5.4", and Note 5.21 "Review Problem 5.5" are shown here. Each of these cost equations was created using the same historical production cost data for Alta Production, Inc. The goal for you as a student is to understand how to develop a cost equation that will help in estimating costs for the future (based on past information).

1. Account analysis: Y = $7,000 + $1,428.57X

1. High-low method: Y = $25,000 + $1,500.00X

1. Scattergraph method: Y = $5,000 + $1,439.39X

1. Regression analysis: Y = $703 + $1,442.97X

1. Total production costs assuming 400 units will be produced are calculated for each method given. Note that the equations presented previously are used for these calculations.

Account analysis

High-low method

Scattergraph method

Regression analysis

The account analysis ($578,428), scattergraph method ($580,756), and regression analysis ($577,891) all yield similar estimated production costs. The high-low method varies significantly from the other three approaches, likely because only two data points are used to estimate unit variable cost and total fixed costs.

5.3 The Contribution Margin Income Statement

LEARNING OBJECTIVE

1. Prepare a contribution margin income statement.

After further work with her staff, Susan was able to break down the selling and administrative costs into their variable and fixed components. (This process is the same as the one we discussed earlier for production costs.) Susan then established the cost equations shown in Table 5.5 "Cost Equations for Bikes Unlimited".

Table 5.5 Cost Equations for Bikes Unlimited

Production costs	Y = $43,276 + $53.42X
Selling and administrative costs	Y = $110,000 + $9.00X

Question: The challenge now is to organize this information in a way that is helpful to management—specifically, to Eric Mendez. The traditional income statement format used for external financial reporting simply breaks costs down by functional area: cost of goods sold and selling and administrative costs. It does not show fixed and variable costs. Panel A of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited" illustrates the traditional format. (We defer consideration of income taxes to the end of Chapter 6 "How Is Cost-Volume-Profit Analysis Used for Decision Making?" .) How can this information be presented in an income statement that shows fixed and variable costs separately?

Answer: Another income statement format, called the contribution margin income statement, shows the fixed and variable components of cost information. This type of statement appears in panel B of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited". Note that operating profit is the same in both statements, but the organization of data differs. The contribution margin income statement organizes the data in a way that makes it easier for management to assess how changes in production and sales will affect operating profit. The contribution margin represents sales revenue left over after deducting variable costs from sales. It is the amount remaining that will contribute to covering fixed costs and to operating profit (hence, the name contribution margin).

Eric indicated that sales volume in August could increase by 20 percent over sales in June of 5,000 units, which would increase unit sales to 6,000 units [= 5,000 units + (5,000 × 20 percent)], and he asked Susan to come up with projected profit for August. Eric also mentioned that the sales price would remain the same at $100 per unit. Using this information and the cost estimate equations in Table 5.5 "Cost Equations for Bikes Unlimited", Susan prepared the contribution margin income statement in panel B of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited". Assume for now that 6,000 units is just within the relevant range for Bikes Unlimited. (We will discuss this assumption later in the chapter.)

Figure 5.7 Traditional and Contribution Margin Income Statements for Bikes Unlimited

Treemap chart Description automatically generated

*From Table 5.5 "Cost Equations for Bikes Unlimited" .

The contribution margin income statement shown in panel B of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited" clearly indicates which costs are variable and which are fixed. Recall that the variable cost per unit remains constant, and variable costs in total change in proportion to changes in activity. Because 6,000 units are expected to be sold in August, total variable costs are calculated by multiplying 6,000 units by the cost per unit ($53.42 per unit for cost of goods sold, and $9.00 per unit for selling and administrative costs). Thus total variable cost of goods sold is $320,520, and total variable selling and administrative costs are $54,000. These two amounts are combined to calculate total variable costs of $374,520, as shown in panel B of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited".

The contribution margin of $225,480 represents the sales revenue left over after deducting variable costs from sales ($225,480 = $600,000 − $374,520). It is the amount remaining that will contribute to covering fixed costs and to operating profit.

Recall that total fixed costs remain constant regardless of the level of activity. Thus fixed cost of goods sold remains at $43,276, and fixed selling and administrative costs stay at $110,000. This holds true at both the 5,000 unit level of activity for June, and the 6,000 unit level of activity projected for August. Total fixed costs of $153,276 (= $43,276 + $110,000) are deducted from the contribution margin to calculate operating profit of $72,204.

Armed with this information, Susan meets with Eric the next day. Refer to panel B of Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited" as you read Susan’s comments about the contribution margin income statement.

Susan:	Eric, I have some numbers for you. My projection for August is complete, and I expect profit to be approximately $72,000 if sales volume increases 20 percent.
Eric:	Excellent! You were correct in figuring that profit would increase at a higher rate than sales because of our fixed costs.
Susan:	Here’s a copy of our projected income for August. This income statement format provides the variable and fixed costs. As you can see, our monthly fixed costs total approximately $153,000. Now that we have this information, we can easily make projections for different scenarios.
Eric:	This will be very helpful in making projections for future months. I’ll take your August projections to the management group this afternoon. Thanks for your help!

Business in Action 5.3

A car parked in front of a house Description automatically generated

Source: http://commons.wikimedia.org/wiki/File:LowesMeyerlandHoustonTX.jpg

Costs at Lowe’s Companies, Inc.

Lowe’s is the world’s second largest home improvement retailer with more than 1,700 stores in the United States, Canada, and Mexico. The company has 234,000 employees. The following financial information is from Lowe’s income statement for the year ended January 28, 2011 (amounts are in millions). Which of the company’s costs are likely to be variable?

A picture containing text Description automatically generated

Variable costs probably include cost of sales (the cost of goods sold) and a portion of selling and general and administrative costs (e.g., the cost of hourly labor). Cost of sales alone represents 65 percent of net sales (rounded). Retail companies like Lowe’s tend to have higher variable costs than manufacturing companies like General Motors and Boeing.

Source: Lowe’s Web site (http://www.lowes.com).

KEY TAKEAWAY

· The contribution margin income statement shows fixed and variable components of cost information. Revenue minus variable costs equals the contribution margin. The contribution margin minus fixed costs equals operating profit. This statement provides a clearer picture of which costs change and which costs remain the same with changes in levels of activity.

REVIEW PROBLEM 5.7

Last month, Alta Production, Inc., sold its product for $2,500 per unit. Fixed production costs were $3,000, and variable production costs amounted to $1,400 per unit. Fixed selling and administrative costs totaled $50,000, and variable selling and administrative costs amounted to $200 per unit. Alta Production produced and sold 400 units last month.

Prepare a traditional income statement and a contribution margin income statement for Alta Production. Use Figure 5.7 "Traditional and Contribution Margin Income Statements for Bikes Unlimited" as a guide.

Solution to Review Problem 5.7

A picture containing chart Description automatically generated

Chart Description automatically generated

*Given.

5.4 The Relevant Range and Nonlinear Costs

LEARNING OBJECTIVE

1. Understand the assumptions used to estimate costs.

Question: Bikes Unlimited is making an important assumption in estimating fixed and variable costs. What is this important assumption and why might it be misleading?

Answer: The assumption is that total fixed costs and per unit variable costs will always be at the levels shown in Table 5.5 "Cost Equations for Bikes Unlimited" regardless of the level of production. This will not necessarily hold true under all circumstances.

For example, let’s say Bikes Unlimited picks up a large contract with a customer that requires producing an additional 30,000 units per month. Do you think the cost equations in Table 5.5 "Cost Equations for Bikes Unlimited" would lead to accurate cost estimates? Probably not, because additional fixed costs would be incurred for facilities, salaried personnel, and other areas. Variable cost per unit would likely change also since additional direct labor would be required (either through overtime, which requires overtime pay, or by hiring more employees who are less efficient as they learn the process), and the volume of parts purchased from suppliers would increase, perhaps leading to reductions in per unit costs due to volume discounts for the parts.

As defined earlier, the relevant range is a term used to describe the range of activity (units of production in this example) for which cost behavior patterns are likely to be accurate. Because the historical data used to create these equations for Bikes Unlimited ranges from a low of 2,900 units in January to a high of 5,900 units in April (see Table 5.4 "Monthly Production Costs for Bikes Unlimited"), management would investigate costs further when production levels fall outside of this range. The relevant range for total production costs at Bikes Unlimited is shown in Figure 5.8 "Relevant Range for Total Production Costs at Bikes Unlimited". It is up to the cost accountant to determine the relevant range and make clear to management that estimates being made for activity outside of the relevant range must be analyzed carefully for accuracy.

Figure 5.8 Relevant Range for Total Production Costs at Bikes Unlimited

Chart, line chart, scatter chart Description automatically generated

Recall that Bikes Unlimited estimated costs based on projected sales of 6,000 units for the month of August. Although this is slightly higher than the highest sales of 5,900 units in April, Susan (cost accountant) determined that Bikes Unlimited had the production capacity to produce 6,000 units without significantly affecting total fixed costs or per unit variable costs. Thus she determined that a sales level of 6,000 units was still within the relevant range. However, Susan also made Eric (CFO) aware that Bikes Unlimited was quickly approaching full capacity. If sales were expected to increase in the future, the company would have to increase capacity, and cost estimates would have to be revised.

Question: Another important assumption being made by Bikes Unlimited is that all costs behave in a linear manner. Variable, fixed, and mixed costs are all described and shown as a straight line. However, many costs are not linear and often take on a nonlinear pattern. Why do some costs behave in a nonlinear way?

Answer: Assume the pattern shown in Figure 5.9 "Nonlinear Variable Costs" is for total variable production costs. Consider this: Have you ever worked a job where you were very slow at first but improved rapidly with experience? If a company produces just a few units each month, workers (direct labor) do not gain the experience needed to work efficiently and may waste time and materials. This has the effect of driving up the per unit variable cost. Recall that the slope of the line represents the unit cost; thus, when the unit cost increases, so does the slope. If the company produces more units each month, workers gain experience resulting in improved efficiency, and the per unit cost decreases (both in materials and labor). This causes the total cost line to flatten out a bit as the slope decreases. This is fine until the company starts to reach its limit in how much it can produce (called capacity). Now the company must hire additional inexperienced employees or pay its current employees overtime, which once again drives up the cost per unit. Thus the slope begins to increase.

Figure 5.9 Nonlinear Variable Costs

Chart, line chart Description automatically generated

Although this is probably a more accurate description of how variable costs actually behave for most companies, it is much simpler to describe and estimate costs if you assume they are linear. As long as the relevant range is clearly identified, most companies can reasonably use the linearity assumption to estimate costs.

KEY TAKEAWAY

· Two important assumptions must be considered when estimating costs using the methods described in this chapter.

1. When costs are estimated for a specific level of activity, the assumption is that the activity level is within the relevant range.

2. Costs are estimated assuming that they are linear.

Both assumptions are reasonable as long as the relevant range is clearly identified, and the linearity assumption does not significantly distort the resulting cost estimate.

REVIEW PROBLEM 5.8

1. Using the data in Note 5.21 "Review Problem 5.5", identify the relevant range.

2. Why is it important to determine the relevant range?

Solution to Review Problem 5.8

1. The relevant range, the range of activity for which cost estimates are more likely to be accurate, is from 150 units (lowest activity level) to 450 units of production (highest activity level).

2. Identifying the relevant range when estimating costs is important because if a cost estimate is being made for activity outside of the relevant range, total fixed costs and per unit variable costs may be different from those described in the cost equation. For example, if production is doubled, additional factory space may be needed, resulting in higher fixed costs.

5.5 Appendix: Performing Regression Analysis with Excel

LEARNING OBJECTIVE

1. Perform regression analysis using Excel.

Question: Regression analysis is often performed to estimate fixed and variable costs. Many different software packages have the capability of performing regression analysis, including Excel. This appendix provides a basic illustration of how to use Excel to perform regression analysis. Statistics courses cover this topic in more depth. How is regression analysis used to estimate fixed and variable costs?

Answer: As noted in the chapter, regression analysis uses a series of mathematical equations to find the best possible fit of the line to the data points. For the purposes of this chapter, the end goal of regression analysis is to estimate fixed and variable costs, which are described in the equation form of Y = f + vX. Recall that the following Excel output was provided earlier in the chapter based on the data presented in Table 5.4 "Monthly Production Costs for Bikes Unlimited" for Bikes Unlimited.

	Coefficients
y-intercept	43,276
x variable	53.42

The resulting equation to estimate production costs is Y = $43,276 + $53.42X. We now describe the steps to be performed in Excel to get this equation.

Step 1. Confirm that the Data Analysis package is installed.

Go to the Data tab on the top menu bar and look for Data Analysis. If Data Analysis appears, you are ready to perform regression analysis. If Data Analysis does not appear, go to the help button (denoted as a question mark in the upper right-hand corner of the screen) and type Analysis ToolPak. Look for the Load the Analysis ToolPak option and follow the instructions given.

Step 2. Enter the data in the spreadsheet.

Using a new Excel spreadsheet, enter the data points in two columns. The monthly data in Table 5.4 "Monthly Production Costs for Bikes Unlimited" includes Total Production Costs and Units Produced. Thus use one column (column A) to enter Total Production Costs data and another column (column B) to enter Units Produced data.

Table, Excel Description automatically generated

Step 3. Run the regression analysis.

Using the same spreadsheet set up in step 2, select Data, Data Analysis, and Regression. A box appears that requires the input of several items needed to perform regression. Input Y Range requires that you highlight the y-axis data, including the heading (cells B1 through B13 in the example shown in step 2). Input X Range requires that you highlight the x-axis data, including the heading (cells C1 through C13 in the example shown in step 2). Check the Labels box; this indicates that the top of each column has a heading (B1 and C1). Select New Workbook; this will put the regression results in a new workbook. Lastly, check the Line Fit Plots box, then select OK. The result is as follows (note that we made a few minor format changes to allow for a better presentation of the data).

Graphical user interface, application, table, Excel Description automatically generated

Step 4. Analyze the output.

Here, we discuss key items shown in the regression output provided in step 3.

· Cost Equation: The output shows that estimated fixed costs (shown as the Intercept coefficient in cell B17) total $43,276, and the estimated variable cost per unit (shown as the Units Produced coefficient in B18) is $53.42. Thus the cost equation is:

Y = $43,276 + $53.42XorTotal Production Costs = $43,276 + ($53.42 × Units Produced)

· Line Fit Plot and R-Squared: The plot shows that actual total production costs are very close to predicted total production costs calculated using the cost equation. Thus the cost equation created from the regression analysis is likely to be useful in predicting total production costs. Another way to assess the accuracy of the regression output is to review the R-squared statistic shown in cell B5. R-squared measures the percent of the variance in the dependent variable (total production costs, in this example) explained by the independent variable (units produced, in this example). According to the output, 96.29 percent of the variance in total production costs is explained by the level of units produced—further evidence that the regression results will be useful in predicting total production costs.

The discussion of regression analysis in this chapter is meant to serve as an introduction to the topic. To further enhance your knowledge of regression analysis and to provide for a more thorough analysis of the data, you should pursue the topic in an introductory statistics course.

KEY TAKEAWAY

· Software applications, such as Excel, can use regression analysis to estimate fixed and variable costs.

· Once the data analysis package is installed, historical data are entered in the spreadsheet, and the regression analysis is run.

· The resulting data are used to determine the cost equation, which includes estimated fixed and variable costs.

The line fit plot and R-squared statistic are used to assess the usefulness of the cost equation in estimating costs.

REVIEW PROBLEM 5.9

Refer to the monthly production cost data for Alta Production, Inc., in Note 5.21 "Review Problem 5.5". Use the four steps of regression analysis described in this appendix to estimate total fixed costs and variable cost per unit. State your results in the equation form Y = f + vX.

Solution to Review Problem 5.9

Regression analysis performed using Excel results in the following output:

	Coefficients
y-intercept	703
x variable	1,442.97

Thus the total cost equation is:

Y = $703 + $1,442.97X

END-OF-CHAPTER EXERCISES

Questions

1. What is a fixed cost? Provide two examples.

2. What is the difference between a committed fixed cost and a discretionary fixed cost? Provide examples of each.

3. What is a variable cost? Provide two examples.

4. What is a mixed cost? Provide two examples.

5. Describe the variables in the cost equation Y = f + vX.

6. How is the cost equation Y = f + vX used to estimate future costs?

7. Why is it important to identify how costs behave with changes in activity?

8. Review Note 5.11 "Business in Action 5.2" Why was the school district’s administration surprised to find out that cost savings from closing a school would be much lower than initially anticipated?

9. Explain how account analysis is used to estimate costs.

10. Describe the four steps of the high-low method and how these steps are used to estimate costs.

11. Why might the high-low method lead to inaccurate results?

12. Describe the five steps of the scattergraph method and how these steps are used to estimate costs.

13. How can the scattergraph method be used to identify unusual data points?

14. Describe how regression analysis is used to estimate costs.

15. How does the contribution margin income statement differ from the traditional income statement?

16. Review Note 5.27 "Business in Action 5.3" Which costs at Lowe’s are likely to be variable costs?

17. Describe the term relevant range. Why is it important to stay within the relevant range when estimating costs?

18. Explain how some costs can behave in a nonlinear way.

Brief Exercises

19. Planning at Bikes Unlimited. Refer to the dialogue at Bikes Unlimited presented at the beginning of the chapter. What is the first step to be taken by Susan and her accounting staff to help in estimating profit for August?

20. Identifying Cost Behavior. Vasquez Incorporated is trying to identify the cost behavior of the three costs that follow. Cost information is provided for three months.

		Cost A	Cost B	Cost C
Month	Units Produced	Total Costs	Cost per Unit	Total Costs	Cost per Unit	Total Costs	Cost per Unit
1	1,500	$1,500	_____	$4,500	_____	$3,000	_____
2	3,000	1,500	_____	5,250	_____	6,000	_____
3	750	1,500	_____	3,750	_____	1,500	_____

21. Required:

u. Calculate the cost per unit, and then identify how the cost behaves for each of the three costs (fixed, variable, or mixed). Explain the reasoning for your answers.

u. How does identifying cost behavior patterns help managers?

1. Account Analysis. Cordova Company would like to estimate production costs on an annual basis. Costs incurred for direct materials and direct labor are variable costs. The accounting records indicate that the following production costs were incurred last year for 50,000 units.

Direct materials	$100,000
Direct labor	$215,000
Manufacturing overhead	$300,000 (20 percent fixed; 80 percent variable)

1. Required:

1. Use account analysis to estimate the fixed costs per year, and the variable cost per unit.

1. High-Low Method. The city of Rockville reported the following annual cost data for maintenance work performed on its fleet of trucks.

Reporting Period (Year)	Total Costs	Level of Activity (Miles Driven)
Year 1	$ 750,000	225,000
Year 2	850,000	240,000
Year 3	1,100,000	430,000
Year 4	1,150,000	454,000
Year 5	1,250,000	560,000
Year 6	1,550,000	710,000

1. Required:

z. Use the four steps of the high-low method to estimate total fixed costs per year and the variable cost per mile. State your results in the cost equation form Y = f + vX.

z. What would the estimated costs be if the trucks drove 500,000 miles in year 7?

1. Scattergraph Method. Refer to the data in Brief Exercise 22 for the city of Rockville.

Required:

aa. Use the five steps of the scattergraph method to estimate total fixed costs per year and the variable cost per mile. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

aa. What would the estimated costs be if the trucks drove 500,000 miles in year 7?

1. Regression Analysis. Regression analysis was run using the data in Brief Exercise 22 for the city of Rockville. The output is shown here:

	Coefficients
y-intercept	441,013
x variable	1.53

1. Required:

ac. Use the regression output to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

ac. What would the city of Rockville’s estimated costs be if its trucks drove 500,000 miles in year 7?

1. Contribution Margin Income Statement. Last year Pod Products, Inc., sold its product for $250 per unit. Production costs totaled $40,000 (25 percent fixed, 75 percent variable). Selling and administrative costs totaled $150,000 (10 percent fixed, 90 percent variable). Pod Products produced and sold 1,000 units last year.

Required:

Prepare a contribution margin income statement for Pod Products, Inc.

1. Relevant Range. Jersey Company produces jerseys for athletic teams, and typically produces between 1,000 and 5,000 jerseys annually. The accountant is asked to estimate production costs for this coming year assuming 9,000 jerseys will be produced.

Required:

What is meant by the term relevant range, and why is the relevant range important for estimating production costs for this coming year at Jersey Company?

Exercises: Set A

27. Identifying Cost Behavior. Zhang Corporation is trying to identify the cost behavior of the three costs shown. Cost information is provided for six months.

		Cost 1	Cost 2	Cost 3
Month	Units Produced	Total Costs	Cost per Unit	Total Costs	Cost per Unit	Total Costs	Cost per Unit
1	18,000	$36,000	_____	$19,800	_____	$5,000	_____
2	16,000	32,000	_____	19,200	_____	5,000	_____
3	14,000	28,000	_____	18,200	_____	5,000	_____
4	12,000	24,000	_____	16,800	_____	5,000	_____
5	10,000	20,000	_____	14,500	_____	5,000	_____
6	8,000	16,000	_____	12,000	_____	5,000	_____

28. Required:

ab. Calculate the cost per unit, and then identify how the cost behaves (fixed, variable, or mixed) for each of the three costs. Explain the reasoning behind your answers.

ab. Why is it important to identify how costs behave with changes in activity?

1. Account Analysis. Baker Advertising Incorporated would like to estimate costs associated with its clients on an annual basis. Assume costs for supplies and advertising staff are variable costs. The accounting records indicate the following costs were incurred last year for 100 clients:

Supplies	$ 20,000
Advertising staff wages (hourly employees)	$170,000
Manager salary	$ 90,000
Building rent	$ 56,000

1. Required:

ad. Use account analysis to estimate total fixed costs per year, and the variable cost per unit. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ad. Estimate the total costs for this coming year assuming 120 clients will be served.

1. High-Low Method. Castanza Company produces computer printers. Management wants to estimate the cost of production equipment used to produce printers. The company reported the following monthly cost data related to production equipment:

Reporting Period (Month)	Total Costs	Machine Hours
January	$ 920,000	45,000
February	600,000	25,000
March	500,000	20,000
April	1,100,000	90,000
May	1,140,000	95,000
June	620,000	30,000
July	880,000	38,000
August	910,000	48,000
September	1,060,000	78,000
October	960,000	51,000
November	1,400,000	96,000
December	980,000	54,000

1. Required:

af. Use the four steps of the high-low method to estimate total fixed costs per month and the variable cost per machine hour. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

af. What would Castanza Company’s estimated costs be if it used 50,000 machine hours next month?

af. What would Castanza Company’s estimated costs be if it used 15,000 machine hours next month? Why should you feel uncomfortable estimating costs for 15,000 machine hours?

1. Scattergraph Method. Castanza Company produces computer printers. Management wants to estimate the cost of production equipment used to produce printers. The company reported the following monthly cost data related to production equipment (this is the same data as the previous exercise):

Reporting Period (Month)	Costs	Machine Hours
January	$ 920,000	45,000
February	600,000	25,000
March	500,000	20,000
April	1,100,000	90,000
May	1,140,000	95,000
June	620,000	30,000
July	880,000	38,000
August	910,000	48,000
September	1,060,000	78,000
October	960,000	51,000
November	1,400,000	96,000
December	980,000	54,000

1. Required:

ah. Use the five steps of the scattergraph method to estimate total fixed costs per month and the variable cost per machine hour. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ah. What would Castanza Company’s estimated costs be if it used 50,000 machine hours next month?

ah. What would Castanza Company’s estimated costs be if it used 15,000 machine hours next month?

1. Regression Analysis. Regression analysis was run for Castanza Company resulting in the following output (this is based on the same data as the previous two exercises):

	Coefficients
y-intercept	445,639
x variable	8.54

1. Required:

aj. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

aj. What would Castanza Company’s estimated costs be if it used 50,000 machine hours next month?

aj. What would Castanza Company’s estimated costs be if it used 15,000 machine hours next month?

1. Contribution Margin Income Statement. Last month Kumar Production Company sold its product for $60 per unit. Fixed production costs were $40,000, and variable production costs amounted to $15 per unit. Fixed selling and administrative costs totaled $26,000, and variable selling and administrative costs amounted to $5 per unit. Kumar Production produced and sold 7,000 units last month.

Required:

ak. Prepare a traditional income statement for Kumar Production Company.

ak. Prepare a contribution margin income statement for Kumar Production Company.

ak. Why do companies use the contribution margin income statement format?

1. Regression Analysis Using Excel (Appendix). Walleye Company produces fishing reels. Management wants to estimate the cost of production equipment used to produce the reels. The company reported the following monthly cost data related to production equipment:

Reporting Period (Month)	Total Costs	Machine Hours
January	$1,104,000	54,000
February	720,000	30,000
March	600,000	24,000
April	1,320,000	108,000
May	1,368,000	114,000
June	744,000	36,000
July	1,056,000	45,600
August	1,092,000	57,600
September	1,272,000	93,600
October	1,152,000	61,200
November	1,680,000	115,200
December	1,176,000	64,800

1. Required:

am. Use Excel to perform regression analysis. Provide a printout of the results.

am. Use the regression output to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

am. What would Walleye Company’s estimated costs be if it used 90,000 machine hours this month?

Exercises: Set B

34. Identifying Cost Behavior. Ivanov, Inc., is trying to identify the cost behavior of the three costs shown. Cost information is provided for six months.

		Cost 1	Cost 2	Cost 3
Month	Units Produced	Total Costs	Cost per Unit	Total Costs	Cost per Unit	Total Costs	Cost per Unit
1	8,000	$10,000	_____	$24,000	_____	$32,000	_____
2	10,000	10,000	_____	29,000	_____	40,000	_____
3	12,000	10,000	_____	33,600	_____	48,000	_____
4	14,000	10,000	_____	36,400	_____	56,000	_____
5	16,000	10,000	_____	38,400	_____	64,000	_____
6	18,000	10,000	_____	39,600	_____	72,000	_____

35. Required:

ai. Calculate the cost per unit, and then identify how the cost behaves (fixed, variable, or mixed) for each of the three costs. Explain the reasoning behind your answers.

ai. Why is it important to identify how costs behave with changes in activity?

1. Account Analysis. Swim-Safe Company hires several instructors who provide weekly one-hour private swim lessons to individuals. The company would like to estimate costs associated with its swim lessons on a weekly basis. Assume costs for towels, snacks, drinks, and instructor wages are variable costs. The accounting records indicate the following costs were incurred last week for 250 customer lessons:

Towels, snacks, drinks	$1,250
Instructor wages (hourly employees)	$3,000
Manager (owner) salary	$1,500
Pool rental	$2,000

1. Required:

ak. Use account analysis to estimate total fixed costs per week, and the variable cost per lesson. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ak. Estimate the total costs for this coming week assuming 220 lessons will be provided.

1. High-Low Method Quality Tools. Quality Tools Incorporated would like to estimate costs associated with its sales personnel. Salespeople are paid a salary plus commission. Commission rates vary among products and are based on sales dollars. The company reported the following monthly cost data related to sales personnel:

Reporting Period (Month)	Total Costs	Sales Amount
January	$710,000	$13,800,000
February	695,000	13,600,000
March	765,000	15,100,000
April	650,000	12,000,000
May	775,000	15,500,000
June	750,000	14,700,000
July	715,000	14,500,000
August	680,000	13,100,000
September	830,000	16,500,000
October	815,000	16,000,000
November	800,000	15,600,000
December	690,000	13,200,000

1. Required:

am. Use the four steps of the high-low method to estimate total fixed costs per month and the variable cost per sales dollar. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

am. What would Quality Tools’ estimated costs be if it had sales of $12,500,000 next month?

am. What would Quality Tools’ estimated costs be if it had sales of $20,000,000 next month? Why should you feel uncomfortable estimating costs for $20,000,000 in sales?

1. Scattergraph Method. Quality Tools Incorporated would like to estimate costs associated with its sales personnel. Salespeople are paid a salary plus commission. Commission rates vary among products and are based on sales dollars. The company reported the following monthly cost data related to sales personnel (this is the same data as the previous exercise):

Reporting Period (Month)	Total Costs	Sales Amount
January	$710,000	$13,800,000
February	695,000	13,600,000
March	765,000	15,100,000
April	650,000	12,000,000
May	775,000	15,500,000
June	750,000	14,700,000
July	715,000	14,500,000
August	680,000	13,100,000
September	830,000	16,500,000
October	815,000	16,000,000
November	800,000	15,600,000
December	690,000	13,200,000

1. Required:

ao. Use the five steps of the scattergraph method to estimate total fixed costs per month and the variable cost per sales dollar. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ao. What would Quality Tools’ estimated costs be if it had sales of $12,500,000 next month?

ao. What would Quality Tools’ estimated costs be if it had sales of $20,000,000 next month?

1. Regression Analysis. Regression analysis was run for Quality Tools Incorporated resulting in the following output (this is based on the same data as the previous two exercises):

	Coefficients
y-intercept	129,188
x variable	0.04

1. Required:

aq. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

aq. What would Quality Tools’ estimated costs be if it had sales of $12,500,000 next month?

aq. What would Quality Tools’ estimated costs be if it had sales of $20,000,000 next month?

1. Contribution Margin Income Statement, Service Company. Last month Seafood Grill had total sales of $200,000. Food preparation and service costs totaled $90,000 (20 percent fixed, 80 percent variable). Selling and administrative costs totaled $30,000 (70 percent fixed, 30 percent variable).

Required:

ar. Prepare a traditional income statement for Seafood Grill.

ar. Prepare a contribution margin income statement for Seafood Grill.

ar. Why do companies use the contribution margin income statement format?

1. Regression Analysis Using Excel (Appendix). Cain Company produces calculators. Management wants to estimate the cost of production equipment used to produce the calculators. The company reported the following monthly cost data related to production equipment:

Reporting Period (Month)	Total Costs	Machine Hours
January	$1,250,000	59,000
February	990,000	33,000
March	850,000	28,000
April	1,580,000	120,000
May	1,670,000	126,000
June	1,050,000	40,000
July	1,360,000	51,000
August	1,400,000	70,000
September	1,550,000	105,000
October	1,500,000	67,000
November	1,860,000	128,000
December	1,480,000	71,000

1. Required:

at. Use Excel to perform regression analysis. Provide a printout of the results.

at. Use the regression output to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

at. What would Cain Company’s estimated costs be if it used 110,000 machine hours this month?

Problems

41. Cost Behavior. Assume you are a consultant performing work for two different companies. Each company has asked you to help them identify the behavior of certain costs.

Required:

ao. Identify each of the following costs for Hwang Company, a producer of ski boats, as variable (V), fixed (F), or mixed (M):

1. _____Salary of production manager

1. _____Materials required for production

1. _____Monthly rent on factory building

1. _____Hourly wages for assembly workers

1. _____Straight-line depreciation for factory equipment

1. _____Annual insurance on factory building

1. _____Invoices sent to customers

1. _____Salaries and commissions of salespeople

1. _____Salary of chief executive officer

1. _____Company cell phones with first 50 hours free, then 10 cents per minute

ao. Identify each of the following costs for Rainier Camping Products, a maker of backpacks, as variable (V), fixed (F), or mixed (M):

2. _____Hourly wages for assembly workers

2. _____Fabric required for production

2. _____Straight-line depreciation on factory building

2. _____Salaries and commissions of salespeople

2. _____Lease payments for factory equipment

2. _____Company cell phones with first 80 hours free, then 8 cents per minute

2. _____Invoices sent to customers

2. _____Salary of production manager

2. _____Salary of controller (accounting)

2. _____Electricity for factory building

ao. How might the managers of these companies use the cost behavior information requested?

1. Account Analysis and Contribution Margin Income Statement. Madden Company would like to estimate costs associated with its production of football helmets on a monthly basis. The accounting records indicate the following production costs were incurred last month for 4,000 helmets.

Assembly workers’ labor (hourly)	$70,000
Factory rent	3,000
Plant manager’s salary	5,000
Supplies	20,000
Factory insurance	12,000
Materials required for production	20,000
Maintenance of production equipment (based on usage)	18,000

1. Required:

aq. Use account analysis to estimate total fixed costs per month and the variable cost per unit. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

aq. Estimate total production costs assuming 5,000 helmets will be produced and sold.

aq. Prepare a contribution margin income statement assuming 5,000 helmets will be produced, and each helmet will be sold for $70. Fixed selling and administrative costs total $10,000. Variable selling and administrative costs are $8 per unit.

1. High-Low, Scattergraph, and Regression Analysis; Manufacturing Company. Woodworks, Inc., produces cabinet doors. Manufacturing overhead costs tend to fluctuate from one month to the next, and management would like to accurately estimate these costs for planning and decision-making purposes.

The accounting staff at Woodworks recommends that costs be broken down into fixed and variable components. Because the production process is highly automated, most of the manufacturing overhead costs are related to machinery and equipment. The accounting staff believes the best starting point is to review historical data for costs and machine hours:

Reporting Period (Month)	Total Costs	Machine Hours
January	$278,000	1,550
February	280,000	1,570
March	266,000	1,115
April	290,000	1,700
May	262,000	1,110
June	269,000	1,225
July	275,000	1,335
August	286,000	1,660
September	250,000	1,000
October	253,000	1,020
November	260,000	1,025
December	281,000	1,600

These data were entered into a computer regression program, which produced the following output:

	Coefficients
y-intercept	210,766
x variable	45.31

Required:

ar. Use the four steps of the high-low method to estimate total fixed costs per month and the variable cost per machine hour. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ar. Use the five steps of the scattergraph method to estimate total fixed costs per month, and the variable cost per machine hour. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ar. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

ar. Use the results of the high-low method (a), scattergraph method (b), and regression analysis (c), to estimate costs for 1,500 machine hours. (You will have three different answers—one for each method.) Which approach do you think is most accurate and why?

ar. Management likes the regression analysis approach and asks you to estimate costs for 5,000 machine hours using this approach (the company plans to expand by opening another facility and hiring additional employees). Calculate your estimate, and explain why your estimate might be misleading.

1. High-Low, Scattergraph, and Regression Analysis; Service Company. Sanchez Accounting Company prepares tax returns for individuals. Marie Sanchez, the owner, would like an accurate estimate of the company’s costs for planning and decision-making purposes. When Marie asks you to devise a way to estimate costs on a monthly basis, you recall the importance of breaking costs into fixed and variable components. Because the company’s costs are driven primarily by the number of tax returns prepared, you decide to use historical data for costs and tax returns prepared:

Reporting Period (Month)	Total Costs	Returns Prepared
January	$157,000	315
February	145,000	300
March	167,500	375
April	163,000	325
May	120,000	250
June	112,000	210
July	138,000	280
August	100,000	190
September	108,000	205
October	115,000	245
November	136,000	265
December	126,000	255

1. You enter these data into a computer regression program and get the following results:

	Coefficients
y-intercept	24,626
x variable	401.86

1. Required:

au. Use the four steps of the high-low method to estimate total fixed costs per month and the variable cost per tax return prepared. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

au. Use the five steps of the scattergraph method to estimate total fixed costs per month and the variable cost per tax return prepared. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

au. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

au. Use the results of the high-low method (a), scattergraph method (b), and regression analysis (c) to estimate costs for 290 tax returns. (You will have three different answers—one for each method.) Which approach do you think is most accurate, and why?

au. Marie likes the regression analysis approach and asks you to estimate costs for 800 tax returns using this approach (she plans to expand by opening another office and hiring additional employees). Calculate your estimate, and explain why your estimate might be misleading.

1. High-Low, Scattergraph, Regression Analysis, and Contribution Margin Income Statement. Eye Care, Inc., provides vision correction surgery for its patients. You are the accountant for Eye Care, and management has asked you to devise a way of accurately estimating company costs for planning and decision-making purposes. You believe that reviewing historical data for costs and number of surgeries is the best starting point. These data are as follows:

Reporting Period (Month)	Total Costs	Number of Surgeries
January	$208,000	54
February	205,000	52
March	217,000	55
April	200,000	50
May	232,000	62
June	230,000	60
July	226,000	57
August	235,000	63
September	252,000	71
October	250,000	70
November	245,000	66
December	244,000	65

1. You enter these data into a computer regression program and get the following results:

	Coefficients
y-intercept	75,403
x variable	2,536.77

1. Required:

ax. Use the four steps of the high-low method to estimate total fixed costs per month, and the variable cost per surgery. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ax. Use the five steps of the scattergraph method to estimate total fixed costs per month, and the variable cost per surgery. State your results in the cost equation form Y = f + vX by filling in the dollar amounts for f and v.

ax. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

ax. Use the results of the high-low method (a), scattergraph method (b), and regression analysis (c), to estimate costs for 70 surgeries. (You will have three different answers—one for each method.) Which approach do you think is most accurate and why?

ax. Assume Eye Care charges $4,000 for each surgery performed. Use the regression analysis cost information (for 70 surgeries) to prepare a contribution margin income statement. (Hint: You will only have one line item for variable costs and one line item for fixed costs.)

1. Regression Analysis Using Excel (Appendix). Metal Products, Inc., produces metal storage sheds. The company’s manufacturing overhead costs tend to fluctuate from one month to the next, and management would like an accurate estimate of these costs for planning and decision-making purposes.

The company’s accounting staff recommends that costs be broken down into fixed and variable components. Because the production process is highly automated, most of the manufacturing overhead costs are related to machinery and equipment. The accounting staff agrees that reviewing historical data for costs and machine hours is the best starting point. Data for the past 18 months follow.

Reporting Period (Month)	Total Overhead Costs	Total Machine Hours
January	$695,000	3,875
February	700,000	3,925
March	665,000	2,788
April	725,000	4,250
May	655,000	2,775
June	672,500	3,063
July	687,500	3,338
August	715,000	4,150
September	625,000	2,500
October	632,500	2,550
November	650,000	2,563
December	702,500	4,000
January	730,000	4,025
February	735,000	4,088
March	697,500	2,900
April	762,500	4,425
May	687,500	2,888
June	705,000	3,188

Required:

ay. Use Excel to perform regression analysis. Provide a printout of the results.

ay. Use the regression output given to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

ay. Use the results of the regression analysis to estimate costs for 3,750 machine hours.

ay. Management is considering plans to expand by opening several new facilities and asks you to estimate costs for 22,000 machine hours. Calculate your estimate, and explain why this estimate may be misleading.

ay. What can be done to improve the estimate made in part d?

One Step Further: Skill-Building Cases

47. Internet Project: Variable and Fixed Costs. Using the Internet, find the annual report of one retail company and one manufacturing company. Print out each company’s income statement. (Hint: The income statement is often called the statement of operations or statement of earnings.)

Required:

au. Review each income statement, and provide an analysis of which operating costs are likely to be variable and which are likely to be fixed. Include copies of both income statements when submitting your answer.

au. How would you expect a retail company’s mix of variable and fixed operating costs to differ from that of a manufacturing company?

au. How might the managers of these companies use cost behavior information?

1. Group Activity: Identifying Variable and Fixed Costs. To complete the following requirements, form groups of two to four students.

Required:

av. Each group should select a product that is easy to manufacture.

av. Prepare a list of materials, labor, and other resources needed to make the product.

av. Using the list prepared in requirement b, identify whether the costs associated with each item are variable, fixed, or mixed.

av. As a manager for this company, why would you want to know whether costs are variable, fixed, or mixed?

1. Cost Behavior at Best Buy. The following condensed income statement is for Best Buy Co., Inc., a large retailer of consumer electronics.

A picture containing application Description automatically generated

Required:

Assume that cost of goods sold comprises only variable costs, and selling and administrative expenses are all fixed costs. Also assume that Best Buy expects sales to grow by 10 percent for the year ended March 3, 2012.

aw. Calculate expected operating income for the year ended March 3, 2012 assuming the company is still within the relevant range of activity.

aw. Calculate the expected percent increase in operating income from the year ended February 26, 2011, to the year ended March 3, 2012.

aw. Why is the percent increase in operating income higher than the percent increase in sales?

aw. Is the assumption that all selling and administrative expenses are fixed a reasonable assumption? Explain.

1. Fixed Costs at United Airlines. Review Note 5.4 "Business in Action 5.1".

Required:

ax. What is meant by the term fixed cost?

ax. Which costs at United Airlines were identified as fixed costs?

ax. How might United Airlines reduce its fixed costs? Be specific.

Comprehensive Case

51. Ethics: Manipulating Data to Establish a Budget (Appendix). Healthy Bar, Inc., produces energy bars for sports enthusiasts. The company’s fiscal year ends on December 31. The production manager, Jim Wallace, is establishing a cost budget for the production department for each month of this coming quarter (January through March). At the end of March, Jim will be evaluated based on his ability to meet the budget for the three months ending March 31. In fact, Jim will receive a significant bonus if actual costs are below budgeted costs for the quarter.

The production budget is typically established based on data from the last 18 months. These data are as follows:

Reporting Period (Month)	Total Overhead Costs	Total Machine Hours
July	$695,000	3,410
August	700,000	3,454
September	665,000	2,453
October	725,000	3,740
November	655,000	2,442
December	672,500	2,695
January	687,500	2,937
February	715,000	3,652
March	625,000	2,200
April	632,500	2,244
May	650,000	2,255
June	702,500	3,520
July	730,000	3,542
August	735,000	3,597
September	697,500	2,552
October	762,500	3,894
November	687,500	2,541
December	705,000	2,805

You are the accountant who assists Jim in preparing an estimate of production costs for the next three months. You intend to use regression analysis to estimate costs, as was done in the past. Jim expects that 3,100 machine hours will be used in January, 3,650 machine hours in February, and 2,850 machine hours in March.

Jim approaches you and asks that you add $100,000 to production costs for each of the past 18 months before running the regression analysis. As he puts it, “After all, management always takes my proposed budgets and reduces them by about 10 percent. This is my way of leveling the playing field!”

Required:

ay. Use Excel to perform regression analysis using the historical data provided.

1. Submit a printout of the results.

1. Use the regression output to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

1. Calculate estimated production costs for January, February, and March. Also provide a total for the three months.

ay. Use Excel to perform regression analysis after adding $100,000 to production costs for each of the past 18 months, as Jim requested.

2. Submit a printout of the results.

2. Use the regression output to develop the cost equation Y = f + vX by filling in the dollar amounts for f and v.

2. Calculate estimated production costs for January, February, and March. Also provide a total for the three months.

ay. Why did Jim ask you to add $100,000 to production costs for each of the past 18 months?

ay. How should you handle Jim’s request? (If necessary, review the presentation of ethics in Chapter 1 "What Is Managerial Accounting?" for additional information.)

Previous Chapter

Table of Contents

Next Chapter