# 2.3: Cost Estimation Methods

Skills to Develop

• 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?

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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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 analysis7 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?

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:

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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. Thus the mixed cost equation used to estimate future production costs is $$\text{Y} = \ 30,000 + \ 52 \text{X}$$ 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?

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:

1. Describe the production costs in the equation form $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$.
2. Assume Alta intends to produce 400 units next month. Calculate total production costs for the month.
1. Because $$\mathcal{f}$$ represents total fixed costs, and $$\mathcal{v}$$ 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: $$\begin{split} \text{Y} &= \ 7,000 + (\ 1,428.57 \times 400\; \text{units}) \\ &= \ 7,000 + \ 571,428 \\ &= \ 578,428 \end{split}$$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 method8. 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. 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

Using the low activity level of 2,900 units and $200,000, $$\begin{split} \text{Y} &= \mathcal{f} + \mathcal{v} \text{X} \\ \ 200,000 &= \mathcal{f} + (\ 60 \times 2,900\; \text{units}) \\ \mathcal{f} &= \ 200,000 - (\ 60 \times 2,900\; \text{units}) \\ &= \ 200,000 - \ 174,000 \\ &= \ 26,000 \end{split}$$ 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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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 $$\text{Y} = \ 26,000 + \ 60 \text{X}$$ 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:

$$\begin{split} \text{Y} &= \ 26,000 + (\ 60 \times 6,000\; \text{units}) \\ &= \ 26,000 + \ 360,000 \\ &= \ 386,000 \end{split}$$

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?

In reviewing Figure 5.4, 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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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? Answer: 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 ($$\mathcal{v}$$). $$\begin{split} \text{Unit variable cost} &= \text{Change in cost} \div \text{Change in activity} \\ &= (\ 700,000 - \ 250,000) \div (450\; \text{units} - 150\; \text{units}) \\ &= \ 1,500 \end{split}$$ #### Step 3. Calculate the total fixed cost ($$\mathcal{f}$$). After completing step 2, the equation to describe the line is partially complete and stated as Y = $$\mathcal{f}$$ +$1,500X. The goal of step 3 is to calculate a value for total fixed cost ($$\mathcal{f}$$). Simply select either the high or low activity level, and fill in the data to solve for $$\mathcal{f}$$ (total fixed costs), as shown.

Using the high activity level,

$$\begin{split} \text{Y} &= \mathcal{f} + \mathcal{v} \text{X} \\ \ 700,000 &= \mathcal{f} + (\ 1,500 \times 450\; \text{units}) \\ \mathcal{f} &= \ 700,000 - (\ 1,500 \times 450\; \text{units}) \\ &= \ 700,000 - \ 675,000 \\ &= \ 25,000 \end{split}$$

Thus total fixed cost is $25,000. #### Step 4. State the results in equation form $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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 $$\text{Y} = \ 25,000 + \ 1,500 \text{X}$$ 1. Using the equation from part 1, simply substitute 400 units for X, as follows: $$\begin{split} \text{Y} &= \ 25,000 + (\ 1,500 \times 400\; \text{units}) \\ &= \ 25,000 + \ 600,000 \\ &= \ 625,000 \end{split}$$Thus total production costs are expected to be$625,000 for next month.
2. 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 method9 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?

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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. Using the same data for Bikes Unlimited shown in Table 5.4, we will follow the five steps associated with the scattergraph method:

#### Step 5. State the results in equation form $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$.

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

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 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

#### Step 4. Calculate the variable cost per unit ($$\mathcal{v}$$).

After completing step 3, the equation to describe the line is partially complete and stated as Y = $45,000 + $$\mathcal{v}$$X. The goal of step 4 is to calculate a value for variable cost per unit ($$\mathcal{v}$$). 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 $$\mathcal{v}$$ (variable cost per unit) as follows:

$$\begin{split} \text{Y} &= \mathcal{f} + \mathcal{v} \text{X} \\ \230,000 &= \ 45,000 + (\mathcal{v} \times 3,500) \\ \ 230,000 - \ 45,000 &= \mathcal{v} \times 3,500 \\ \ 185,000 &= \mathcal{v} \times 3,500 \\ \mathcal{v} &= \ 185,000 \div 3,500 \\ &= \ 52.86\; \text{(rounded)} \end{split}$$

Thus variable cost per unit is $52.86. #### Step 5. State the results in equation form $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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: $$\text{Y} = \ 45,000 + \ 52.86 \text{X}$$ 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$362,160:

$$\begin{split} \text{Y} &= \ 45,000 + (\ 52.86 \times 6,000\; \text{units}) \\ &= \ 45,000 + \ 317,160 \\ &= \ 362,160 \end{split}$$

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?

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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$. 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 yintercept (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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$.
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?
1. The five steps are as follows:

#### Step 3. Estimate the total fixed costs ($$\mathcal{f}$$).

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 ($$\mathcal{v}$$).

After completing step 3, the equation to describe the line is partially complete and stated as Y = $5,000 + $$\mathcal{v}$$X. The goal of this step is to calculate a value for variable cost per unit ($$\mathcal{v}$$). 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 $$\mathcal{v}$$ (variable cost per unit):

$$\begin{split} \text{Y} &= \mathcal{f} + \mathcal{v} \text{X} \\ \ 480,000 &= \ 5,000 + (\mathcal{v} \times 330) \\ \ 480,000 - \ 5,000 &= \mathcal{v} \times 330 \\ \ 475,000 &= \mathcal{v} \times 330 \\ \mathcal{v} &= \ 475,000 \div 330 \\ &= \ 1,439.39\; \text{(rounded)} \end{split}$$

#### Step 5. State the results in equation form $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$.

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:

$$\text{Y} = \ 5,000 + \ 1,439.39 \text{X}$$

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).

1. Using the equation, simply substitute 400 units for X, as follows: $$\begin{split} \text{Y} &= \ 5,000 + (\ 1,439.39 \times 400\; \text{units}) \\ &= \ 5,000 + \ 575,756 \\ &= \ 580,756 \end{split}$$Thus total production costs are expected to be $580,756 for next month. 2. 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 analysis10 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, 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: $$\text{Y} = \ 43,276 + \ 53.42 \text{X}$$ 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$363,796:

$$\begin{split} \text{Y} &= \ 43,276 + (\ 53.42 \times 6,000\; \text{units}) \\ &= \ 43,276 + \ 320,520 \\ &= \ 363,796 \end{split}$$

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 $$\text{Y} = \mathcal{f} + \mathcal{v} \text{X}$$.
2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.
1. The cost equation using the data from regression analysis is: $$\text{Y} = \ 703 + \ 1,442.97 \text{X}$$