1. Cost Estimation Chapter 5 McGraw-Hill/Irwin
When managers make decisions they need to compare the costs (and benefits) among alternative actions. In this chapter, we discuss how to estimate the costs required for decision making.
Chapter 5
McGraw-Hill/Irwin

2. Learning Objectives:
1. Understand the reasons for estimating fixed and variable costs.
2. Estimate costs using engineering estimates.
3. Estimate costs using account analysis.
4. Estimate costs using statistical analysis.
5. Interpret the results of regression output.
6. Identify potential problems with regression data.
7. Evaluate the advantages and disadvantages of alternative cost estimates.
After completing Chapter 5 you should: Understand the reasons for estimating fixed and variable costs and be able to estimate costs using engineering estimates, account analysis and statistical analysis. You should be able to interpret the results of regression output and identify potential problems with regression data. You should also be able to evaluate the advantages and disadvantages of alternative cost estimation methods. After completing the Appendix you should be able to use Microsoft Excel to perform analysis.
8. (Appendix A) Use Microsoft Excel to perform a regression analysis.
9. (Appendix B) Understand the mathematical relationship describing the learning phenomenon.

3. Why Estimate Costs?
Managers make decisions and need to compare costs and benefits among alternative actions.
Key Question
What adds value to the firm?
You saw in Chapters 3 and 4 that good decisions require good information about costs. Cost estimates are an important element in helping managers make decisions that add value to the company.
Good decisions

4. Basic Cost Behavior Patterns
LO1 Understand the reasons for estimating fixed and variable costs
Variable costs
Costs behave as either fixed or variable.
COSTS
Variable Costs
Fixed Costs
Fixed costs
Total fixed costs activity changes.
Total variable costs change proportionately as activity changes.
By now you understand the importance of cost behavior. Cost behavior is the key distinction for decision making. Costs behave as either fixed or variable. Fixed costs are fixed in total; variable costs vary in total. On a per-unit basis, fixed costs vary inversely with activity and variable costs stay the same. Are you getting the idea? Cost behavior is critical for decision making.
Per unit fixed costs change inversely as activity changes.
Per unit variable cost remain constant as activity changes.

5. How do we measure activities? By volume
units of output, machine hours, pages typed, miles driven, etc
2. By complexity
the number of different products, the number of components in a product, etc.
By other cost driver
Accounting systems accumulate costs by account, not by cost behavior.
Therefore, only total cost data are available, but not the breakdown of costs into fixed and variable components.

6. Basic Cost Behavior Patterns, Continued. . .
Cost behavior, how costs vary with activity, is the key distinction for decision making. +
variable cost per unit
number of units
Total costs =
fixed costs TC = F V + X
With a change in Activity
In Total
Per Unit
Fixed Cost
Fixed
Vary
Variable
Another way to view cost behavior is in a table format. When the activity level changes fixed costs remain fixed in total and vary per unit while variable costs are just the opposite.

7. Methods to Estimate Cost Behavior
Charlene, owner of Charlene’s Computer Care (3C), wants to estimate the cost of a new computer repair center.
Engineering estimates
Account analysis
Let’s meet Charlene, the owner of Charlene’s Computer Care (3C). In this chapter we are going to help Charlene estimate costs. Three methods used to estimate costs are; engineering estimates, account analysis and statistical methods.
Statistical methods
Which method should we use?
Should we use only one method? If not will results be the same?

8. Engineering Estimates
LO2 Estimate costs using engineering estimates.
Cost estimates are based on measuring and then pricing the work involved in a task.
Identify the activities involved
Labor
Rent
Engineering cost estimates are based on measuring and then pricing the work involved in a task. Managers first identify activities such as labor, rent and insurance and then estimate the time and cost required for each activity.
Insurance
Estimate the time and cost for each activity.

9. Engineering Estimates, Continued. . .
Advantages
Insurance
Details each step required to perform an operation.
Rent
Labor
Permits comparison of other centers with similar operations.
Identifies strengths and weaknesses.
The advantages of engineering estimates are: First, it details each step required to perform an operation. Second, it permits a comparison of other centers with some of our operations. And finally, it identifies strengths and weaknesses. However, engineering estimates can be quite expensive to use and are based on optimal conditions.
Disadvantages
Can be quite expensive to use.

10. Account Analysis Identify each cost as either fixed or variable.
LO3 Estimate costs using account analysis.
Identify each cost as either fixed or variable.
Review each account comprising the total cost being analyzed.
Costs ($)
Fixed
Activity level
Estimating costs using account analysis involves a review of each account making up the total costs being analyzed and identifying each cost as either fixed or variable, depending on the relation between the cost and some activity. You know, fixed costs, those costs that are fixed in total regardless of the activity level and variable costs, those costs that vary in total as activity changes.
Variable
Cost ($)
Activity level

11. Example: Account Analysis
3C Cost Estimation Using Account Analysis
Costs for 360 Repair Hours
Account
Total
Variable Cost
Fixed Cost
Office Rent
$3,375
$1,375
$2,000
Utilities
310
100
210
Administration
3,386
186
3,200
Supplies
2,276
2,176
Training
666
316
350
Other
613
257
356
$10,626
$4,410
$6,216
Per Repair Hour
$12.25
An account analysis of 3C shows estimated overhead cost per month for an average location operating at about 360 repair-hours. Each major class of overhead costs is itemized and then divided into estimated variable and fixed components. The rental contract includes a share of the revenue as part of the rent, so a portion of the rent is variable. Other costs are also mixed, having some fixed and some variable elements. Using account analysis, estimated fixed costs are $6,216 and the total variable costs are $4,410 for 360 repair-hours. Because variable costs are directly related to the expected activity level, we can state variable overhead per repair-hour as $12.25 ($4,410 divided by 360 repair-hours).

12. Example: Account Analysis, Continued. . .
3C Cost Estimation Using Account Analysis
variable cost per unit
number of units
Total Cost =
fixed costs +
Costs at 360 Repair-Hours
a unit is a repair- hour
$10,626 =
$6,216 +
$12.25
360
Using account analysis we can now estimate cost for other levels of repair-hours. Estimated costs at 520 repair-hours equals fixed costs of $6,216 plus $12.25 per repair-hour times 520 repair hours (or $6,370 total variable costs). Total estimated costs at 520 repair-hours equals $12,586.
$4,410
Costs at 520 Repair-Hours
Total Cost =
$6,216 +
$12.25
520 = +
$12,586
$6,216
$6,370

13. Account Analysis Advantage
Managers and accountants are familiar with company operations and the way costs react to changes in activity levels.
Disadvantages
Managers and accountants may be biased.
An advantage of using account analysis to estimate costs is that managers and accountants are familiar with company operations and the way costs react to changes in activity levels. However, managers and accountants may be biased. Furthermore, decisions often have major economic consequences for managers and accountants.
Decisions often have major economic consequences for managers and accountants.
Self study 1

14. Statistical Cost Estimation
LO4 Estimate costs using statistical analysis.
Analyze costs within a relevant range.
Relevant range?
The limits within which a cost estimate may be valid.
A statistical cost analysis analyzes costs within the relevant range using statistics. Do you remember how we defined relevant range? A relevant range is the range of activity where a cost estimate is valid. The relevant range for cost estimation is usually between the upper and lower limits of past activity levels for which data is available.
Relevant range for a projection is usually between the upper and lower limits (bounds)of past activity levels for which data is available.

15. Example: Overhead Costs for 3C
The following information is used throughout this chapter:
Month
Overhead Costs
Repair-Hours 1
$9,891
248 2
$9,244 3
$13,200
480 4
$10,555
284 5
$9,054
200 6
$10,662
380 7
$12,883
568 8
$10,345
344 9
$11,217
448 10
$13,269
544 11
$10,830
340 12
$12,607
412 13
$10,871
384 14
$12,816
404 15
$8,464
212
Here we have the overhead costs data for 3C for the last 15 months. Let’s use this data to estimate costs using a statistical analysis.

16. Scattergraph Plot of cost and activity levels A visual representation
We will start with a scattergraph. A scattergraph is a plot of cost and activity levels. This gives us a visual representation of costs. Does it look like a relationship exists between repair-hours and overhead cost?
Does it look like a relationship exists between repair-hours and overhead costs?

17. Scattergraph, Continued. . .
Now we “eyeball” the scattergraph to determine the intercept and the slope of a line through the data points. Do you remember graphing our total cost in Chapter 3? Where the total cost line intercepts the horizontal or Y axis represents fixed cost. What we are saying is the intercept equals fixed costs. The slope of the line represents the variable cost per unit. So we use “eyeball judgment” to determine fixed cost and variable cost per unit to arrive at total cost for a given level of activity. As you can imagine, preparing an estimate on the basis of a scattergraph is subject to a high level of error. Consequently, scattergraphs are usually not used as the sole basis for cost estimates but to illustrate the relations between costs and activity and to point out any past data items that might be significantly out of line.
We use “eyeball judgment” to determine the intercept and slope of the line.

18. High-Low Cost Estimation
A method to estimate costs based on two cost observations, usually at the highest and lowest activity level.
The highest and lowest activity.
Choose two data points.
3C Overhead
Repair-Hours
Use the two points to determine the line representing the cost-activity relation.
A simple approach to estimating the relation between cost and activity is to choose two points on the scattergraph. This approach is the high-low method. Using the high-low method, we estimate cost based on costs at the highest activity level and costs at the lowest activity level. Using these two points we can draw the total cost.
Draw a total cost line.

19. Example: High-Low Cost Estimation, Continued. . .
A method to estimate cost based on two cost observations, the highest and lowest activity level.
Month
OH Cost
Repair-
Hours
High
$12,883
568
Low
9,054
200
Change
3,829
368
By definition, the change in cost due to a change in activity is variable cost. So, to calculate unit variable cost:
Δ Total Cost
$3,829
$10.40 = =
Δ Activity
368
VC per unit
To prepare a high-low analysis, select the high and low points and calculate the change in both OH Cost ($3,829) and Repair hours (368). Since the OH Cost change is due to a change in volume (repair hours), it is assumed to be strictly variable cost. To calculate the variable cost per unit all we need to do is divide the change in OH Cost by the change is Repair Hours ($3,829 / 368) which is $10.40 variable cost per unit. Now all we have to do is use either the high or low point and plug in the known values to the total cost equation: Total Cost = variable cost per unit x number of units + fixed cost. We get $9,054 = $10.40(200) + FC. Solve for fixed cost. Fixed cost = $6,974! So, our equation estimating total cost is: Total Cost = ($10.40 x Repair hours) + $6,974.
We could also solve in the format presented on the next two pages.
$9,054 = $2,080 + FC
TC = VC(X) + FC
$9,054 = VC(200) + FC
FC = $6,974
$9,054 = $10.40(200) + FC
TC = $10.40(X) + $6,974

20. Example: High-Low Cost Estimation, Continued. . .
Another approach: Equations
Cost at highest activity
Cost at lowest activity V
Highest activity
Lowest activity F
Highest activity
Total cost at highest activity level V or
The slope of the total cost line estimates the variable cost per unit. Remember from statistics, the slope of the line is the change Y divided by the change in X. So we calculate the slope, or the variable cost per unit as the change in costs divided by the change in activity. The change in cost is cost at the highest activity level minus the cost at the lowest activity level. The change in activity is the highest activity minus the lowest activity. After calculating the variable cost per unit we use the activity level and calculate total variable costs. Total costs minus total variable costs equals fixed cost. We can use the highest activity level or the lowest activity level to calculate fixed costs. Let’s put the numbers in the equations.
Lowest activity
Total cost at lowest activity level V

21. Example: High-Low Cost Estimation, Continued. . .
$12,883
$9,054 V
$10.40/RH
568
200
$12,883
$10.40
568
$6,976 F or
Using the high-low cost estimation, calculate variable cost per unit. The highest activity level for 3C over the last 15 months was 560 repair-hours and the lowest activity level was 200 repair-hours. Costs of $12,883 at 568 repair-hours minus cost of $9,054 at 200 repair-hours divided by repair-hours gives us a variable cost per repair-hour of $ Knowing $10.40 per repair-hour is the variable cost per unit we can calculate the total fixed cost for 3C. Fixed costs equals total cost minus total variable costs. At the highest activity level total variable costs are $5,907 ($10.40 times 568 repair-hours). Total costs of $12,883 - $5,907 equals fixed cost of $6,976. Or at the lowest activity level, total costs of $9,054 minus variable cost per unit of $10.40 times 200 units equals fixed costs of $6,974. The difference between $6,976 and $6,974 is simply a rounding difference.
200
$9,054
$10.40
$6,974
Rounding Difference

22. Example: High-Low
Estimated manufacturing overhead with 520 repair-hours. TC = F + V X TC =
$6,976 +
$10.40
520
$12,384
Estimated overhead with 720 repair-hours?
Now that we know the estimated fixed costs are $6,976 and the estimated variable cost per unit is $10.40 we can estimate manufacturing overhead for a level of 520 repair-hours. Total manufacturing overhead at 520 repair-hours equals $6,976 plus $10.40 per unit times 520 units or $12,384. Can we estimate overhead at 720 repair-hours? Remember our data for the last 15 months included repair hours between the activity levels of 200 and 568 repair-hours. So 720 repair-hours is out of the relevant range for a projection. The cost sructure may change once the activity goes beyond 568 repair-hours.
Relevant range for a projection is usually between the upper and lower limits of past activity levels for which data is available.
Not sure.

23. Statistical Cost Estimation Using Regression Analysis
Statistical procedure to determine the relationship between variables.
High-Low Method
Uses two data points.
Regression
Uses all the data points.
3C Overhead
Although the high-low method allows a computation of estimates of the fixed and variable costs, it ignores most of the information available to the analyst. The high-low method uses two data points to estimate costs, regression is a statistical procedure that uses all the data points to estimate costs.

24. Regression Analysis The relationship between activities and costs
Independent variable
The X term, or predictor. The activity that predicts (causes) the change in costs.
Activities
Repair-hours
Regression statistically measures the relationship between two variables, activities and costs. Regression techniques are designed to generate a line that best fits a set of data points. In addition, regression techniques generate information that helps a manager determine how well the estimated regression equation describes the relations between costs and activities. For 3C, repair-hours are the activities, the independent variable or predictor variable. In regression, the independent variable or predictor variable is identified as the X term. Overhead costs is the dependent variable or Y term. What we are saying is; overhead costs are dependent on repair-hours, or predicted by repair-hours.
Dependent variable
The Y term. The dependent variable. The cost to be estimated.
Costs
Overhead costs

25. Regression, Continued. . . The Regression Equation Y = a + b X + Y
Intercept
Slope X =
You already know that an estimate for the costs at any given activity level can be computed using the equation TC = F + VX. The regression equation, Y= a bX represents the cost equation. Y equals the intercept plus the slope times the number of units. When estimating overhead costs for 3C, total overhead costs equals fixed costs plus the variable cost per unit of repair-hours times the number of repair-hours. OH =
Fixed costs + V
Repair-hours

26. Interpreting Regression
LO5 Interpret the results of regression output.
Interpreting regression output allows us to estimate total overhead costs. The intercept of 6,472 is total fixed costs and the coefficient, 12.52, is the variable cost per repair-hours. F V Y =
Intercept
Slope X = + Y F V X

27. Interpreting Regression, Continued. . .
Correlation coefficient
“R” measures the linear relationship between variables. The closer R is to 1.0 the closer the points are to the regression line. The closer R is to zero, the poorer the regression line.
“R2” The square of the correlation coefficient. The proportion of the variation in the dependent variable (Y) explained by the independent variable(s)(X).
Coefficient of determination
T-Statistic
The t-statistic is the value of the estimated coefficient, b, divided by its standard error. Generally, if it is over 2, then it is considered significant. If significant, the cost is NOT totally fixed.
Continuing to interpret the regression output, the Multiple R is called the correlation coefficient and measures the linear relationship between the independent and dependent variables. R Square, the square of the correlation cost efficient, determines and identifies the proportion of the variation in the dependent variable, in this case, overhead costs, that is explained by the independent variable, in this case, repair-hours.

28. Interpreting Regression, Continued. . .
Correlation Coefficient
Coefficient of Determination
T-Statistic
The Multiple R, the correlation coefficient, of .91 tells us that a linear relationship does exist between repair-hours and overhead costs. The R Square, or coefficient of determination, tells us that 82.8% of the changes in overhead costs can be explained by changes in repair-hours. Can you use this regression output to estimate overhead costs for 3C at 520 repair-hours?
.91
A linear relationship does exists between repair hours and overhead costs.
.828
82.8% of the changes in overhead costs can be explained by changes in repair-hours.
10.7 & 7.9
Both have t-statistics that are greater than 2, so the cost is not totally fixed.

29. Example: Regression Estimate 3C’s overhead with 520 repair hours. TC =
Total overhead costs would equal fixed costs of $6,472 plus $12.52 variable cost per repair-hours times 520 repair-hours. Estimated overhead costs for 3C at 520 repair-hours is $12,982. TC = F + V X TC =
$6,472 + $
520 TC
$12,982 =

30. Is repair-hours the only activity that drives overhead costs at 3C?
Multiple Regression
Multiple Regression:
When more than one predictor (x) is in the model.
Is repair-hours the only activity that drives overhead costs at 3C?
Predictors:
X1: Repair-hours
X2: Parts Cost
Multiple regression is used when more than one predictor is needed to adequately predict the value. For example, it might lead to more precise results if 3C uses both repair hours and the cost of parts in order to predict the total cost. Let’s look at this example.
Equation:
TC = VC(X1) + VC(X2) + FC

31. Multiple Regression, Continued. . .
3C Cost Information
Month
OH Costs
Repair-Hours (X1)
Parts (X2) 1
$9,891
248
$1,065 2
$9,244
$1,452 3
$13,200
480
$3,500 4
$10,555
284
$1,568 5
$9,054
200
$1,544 6
$10,662
380
$1,222 7
$12,883
568
$2,986 8
$10,345
344
$1,841 9
$11,217
448
$1,654 10
$13,269
544
$2,100 11
$10,830
340
$1,245 12
$12,607
412
$2,700 13
$10,871
384
$2,200 14
$12,816
404
$3,110 15
$8,464
212
$ 752
Charlene, the owner of 3C, raises a good question. Is repair-hours the only activity that drives the overhead costs of repairing computers? What about the cost of parts? Multiple regression is used to analyze the relationship between more than one independent or predictor variable and a dependent variable.

32. Multiple Regression Output
Adjusted Correlation Coefficient
Adjusted R Square
In multiple regression, the Adjusted R Square is the correlation coefficient squared and adjusted for the number of independent variables used to make the estimate. Reading this output tells us that 89% of the changes in overhead costs can be explained by changes in repair-hours and the cost of parts. Remember 82.8% of the changes in overhead costs were explained when one independent variable, repair-hours, was used to estimate the costs. Can you use this regression output to estimate overhead costs for 520 repair-hours and $3,500 cost of parts?
Correlation coefficient squared and adjusted for the number of independent variables used to make the estimate.
.89
89% of the changes in overhead costs can be explained by changes in repair-hours and parts costs.

33. Multiple Regression Output, Continued. . .= F + V1 X1 + V2 X2
Estimated overhead costs for 520 repair-hours and $3,500 parts cost equals fixed costs of $6,416 plus $8.61 per repair-hours times 520 repair-hours plus $0.77 per parts dollar times 3,500 parts dollars. TC =
$6,416 +
$ 8.61
520 +
$ 0.77
3,500 TC =
$13,588

34. Implementation Problems
LO6 Identify potential problems with regression data.
1. Curvilinear costs
2. Outliers
Curvilinear costs
3. Spurious relations
4. Assumptions
It’s easy to be over confident when interpreting regression output. It all looks so official. But beware of some potential problems with regression data. We already discussed in earlier chapters that costs are curvilinear and cost estimations are only valid within the relevant range. Data may also include outliers and the relationships may be spurious. Let’s talk a bit about each.
Identify relevant range
Relevant Range
Analyze relevant range

35. Implementation Problems, Continued. . .
1. Curvilinear costs
Problem:
Attempting to fit a linear model to nonlinear data. Likely to occur near full-capacity.
Curvilinear costs
Solution:
Define a more limited relevant range (example: from 25 – 75% capacity) or design a nonlinear model.
If the cost function is curvilinear, then a linear model contains weaknesses. This generally occurs when the firm is at or near capacity.
Relevant Range

36. Implementation Problems, Continued. . .
2. Outliers
Solution:
Prepare a scatter-graph, analyze the graph and eliminate highly unusual observations before running the regression.
Problem:
Outlier moves the regression line.
outlier
Regression line with outlier
Because regression calculates the line that best fits the data points, observations that lie a significant distance away from the line could have an overwhelming effect on the regression estimate. Here we see the effect of one significant outlier. The computed regression line is a substantial distance from most of the points. The outlier moves the regression line.
True regression line

37. Implementation Problems, Continued. . .
3. Spurious relations
Problem:
Using too many variables in the regression. For example, using direct labor to explain materials costs. Although the association is very high, actually both are driven by output.
Solution:
Carefully analyze each variable and determine the relationship among all elements before using in the regression.
4. Assumptions
Problem:
Although there may be solutions for spurious relations, it appears that there are no clear cut solutions to the problem of assumptions. If you increase your data size then accuracy increases, but the time covered also increases which could cause a curvilinear problem. If you decrease your sample, then you may get rid of the curvilinear problem, but you weaken the output due to less observations.
If the assumptions in the regression are not satisfied then the regression is not reliable.
Solution:
No clear solution. Limit time to help assure costs behavior remains constant, yet this causes the model to be weaker due to less data.

38. Statistical Cost Estimation
LO7 Evaluate the advantages and disadvantages of alternative cost estimation methods.
Advantages
Reliance on historical data is relatively inexpensive.
Computational tools allow for more data to be used than for non-statistical methods.
Disadvantages
Using regression to estimate costs relies on past data that is relatively inexpensive. Computational tools allow for more data to be used than for nonstatistical methods. However, analysts must be alert to cost-activity changes.
Reliance on historical data may be the only readily available, cost-effective basis for estimating costs.
Analysts must be alert to cost-activity changes.

39. Choosing an Estimation Method*
Estimated manufacturing overhead with 520 repair-hours.
Account Analysis
$12,586
High-Low
$12,384
Regression
$12,982
Multiple Regression
$13,588*
Each cost estimation method can yield a different estimate of the costs that are likely to result from a particular management decision. This underscores the advantage of using more than one method to arrive at a final estimate. Which method is the best? Management must weigh the cost-benefit related to each method.
The more sophisticated methods yield more accurate cost estimates than the simple methods. *
520 repair-hours and $3,500 parts costs

40. Allocated and discretionary costs
Data Problems
Missing data
Outliers
Allocated and discretionary costs
Inflation
Mismatched time periods
No matter what method is used to estimate costs, the results are only as good as the data used. Collecting appropriate data is complicated by missing data, outliers, allocated and discretionary costs, inflation and mismatched time periods.

41. Appendix A: Microsoft as a Tool
LO8 (Appendix A) Use Microsoft Excel to perform a regression analysis.
Many software programs exist to aid in performing regression analysis. In order to use Microsoft Excel, the Analysis Tool Pak must be installed.
Data is entered and the user then selects the data and type of regression analysis to be generated.
The analyst must be well schooled in regression in order to determine the meaning of the output!
As we saw in Chapter 3 (CVP), there are software packages that allow users to easily generate a regression analysis. If, however, the user has little or no knowledge regarding regression, the output will be of little use.

42. Learning Phenomenon Example:
L09 (Appendix B) Understand the mathematical relationship describing the learning phenomenon.
Learning Phenomenon:
The systematic relationship between the amount of experience in performing a task and the time required to perform it.
Example:
Unit
Time to Produce
Calculation of Time
First Unit
100 hours
(assumed)
Second Unit
80 hours
(80 percent x 100 hours
Fourth Unit
64 hours
(80 percent x 80 hours)
Eighth Unit
51.2 hours
(80 percent x 64 hours)
Another element that can change the shape of the total cost curve is the notion of a learning phenomenon. As workers become more skilled they are able to produce more output per hour. This will impact the total cost curve since it leads to a lower per unit cost, the higher the output.
Impact:
Causes the unit price to decrease as production increases. This implies a nonlinear model.

44. Self study question 1
Use account analysis method to prepare three analysis of overhead costs,
Calculate the monthly average fixed costs and the variable rate per1) direct labor hour 2) machine hour, 3) unit of output
The data are based on two years of operation
Indirect materials
27200
Indirect labor
44300
Lease
56000
Utilities
19200
Power to run machines
18500
Insurance
16400
Maintenance
14500
Depreciation
9000
Total over head
205100
All costs are fixed except indirect material, indirect labor and power to run machines
Direct labor hours
12000
Direct labor costs
180000
Machine hours
14400
Units produced
20000

45. Exercise 5-23 Costs for the past year -Production was 210,000 units
Direct materials
210,000
Direct labor
175,000
Variable overhead
154,000
-Production was 210,000 units
-Fixed manufacturing overhead was 240,000
For the coming year costs are expected to increase as follow
-direct material costs by 20%
-direct labor by 4%
-fixed manufacturing overhead by 10%

46. Cost/unit last year=…………. Cost/unit this year=…………
Cost Item
Last Year’s Cost (1)
Cost Change (1 + Cost Increase) (2)
This Year’s Cost (at last year’s volume) (1) x (2) = (3)
Growth in Volume (4)
This Year’s Cost (3) x (4) = (5)
Direct materials 
210,000 
120% =
252,000
220,000
= $264,000
Direct labor
175,000
104%
182,000
= 190,666
Variable overhead
154,000
100%
154,000 
= ,333
Fixed Overhead
240,000
110%
264,000
(fixed)
= 264,000
Total costs
$779,000
$879,999
Cost/unit last year=………….
Cost/unit this year=…………

47. Exercise 5-23 b) Maintenance costs= 167.50 + 1.5*2600
Number of visitors per year
Maintenance costs (000)
1825
2,925
2007
3,225
2375
3,750
a) Variable cost = (Cost at highest activity – cost at lowest activity)/
(Highest activity – lowest activity)
=(3750–2925)/( )=1.5
Fixed costs=3750-(1.5*2375)=167.5
b) Maintenance costs= *2600
Is this estimate reliable? c)

48. Example
John, a cost analyst for a manufacturing firm, was asked to estimate the overhead costs at one of the factories. He interviewed the supervisor and several workers there to get a feel of how overhead costs changed. His experience with the cost accounting system pointed to the use of machine hours as the cost driver. Over the last 12 months, the total overhead costs were $103,918, out of which John determined $4,620 to be fixed cost per month and the rest variable cost. For the same period of time, 4,519 machine hours were incurred in that factory.
Required:
Please help John determine the general cost equation that describes the relation between overhead costs and machine hours in that factory.
If the factory expects to spend 400 machine hours next month, how much will the overhead be?

49. Solution:
The variable cost component for the last 12 months had a total of $48,478 = $103,918 - $4,620 × 12, which can be divided by the machine hours involved to get the variable overhead per unit of machine hour. That is, V = $48,478 ÷ 4,519 machine hours = $10.73 per machine hour. The cost equation can be stated as
Overhead costs = $4,620 per month + $10.73 × Number of machine hours spent.
For 400 machine hours to be spent next month, the overhead costs are expected to be
$4,620 per month + $10.73 × 400 machine hours = $8,912.