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Chapter 6 Cost Behaviour: Analys Analysis is and Use

Solutions to Questions

6-1 a. Variable cost: A variable cost remains constant on a per unit basis, but changes in total in direct relation to changes in volume. b. Fixed cost: A fixed cost remains constant in total amount, but changes, if expressed on a per unit basis, inversely with changes in volume. c. Mixed cost: A mixed cost contains both variable and fixed cost elements.

of a variable cost. Examples of activity bases include units produced, units sold, letters typed, beds in a hospital, meals served in a cafe, service calls made, etc.

6-2 a. Unit fixed costs will decrease as volume increases. b. Unit variable costs will remain constant as volume increases. c. Total fixed costs will remain constant as volume increases. d. Total variable costs will increase as volume increases. 6-3 a. Cost behaviour: Cost behaviour can be defined as the way in which costs change in response to changes in some underlying activity, such as sales volume, production volume, or orders processed. b. Relevant range: The relevant range can be defined as that range of activity within which assumptions relative to variable and fixed cost behaviour are valid. 6-4 An activity base is a measure of whatever causes the incurrence Copyright © 2017 McGraw-Hill Education. All rights reserved.

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6-8 a. Committed d. Committed b. Discretionary e. Committed c. Discretionary f. Discretionary

6-5 (See the exhibit below.) a. Variable cost: A variable cost remains constant on a per unit basis, but increases or decreases in total in direct relation to changes in activity. b. Mixed cost: A mixed cost is a cost that contains both variable and fixed cost elements. c.

6-9 Yes. As the anticipated level of activity changes, the level of fixed costs needed to support operations will also change. In essence, fixed costs should be viewed as going upward and downward in broad steps, rather than being absolutely fixed at one level for all ranges of activity.

Step-variable cost: A step-variable cost is a cost that is not strictly proportional to a unit change in activity level. Instead it increases or decreases only in response to more than a unitchange in activity level. $5,000

$4,500

6-10 The major disadvantage of the high-low method is that it uses only two points in determining a cost formula and these two points are likely to be less than typical since they represent extremes of activity. If one or both of the points are outliers it can cause a distorted formula.

$4,000

$3,500

Total Cost

$3,000

$2,500

$2,000

$1,500

$1,000

$500

$0 3

4

5

6

7

8

9

10

11

12

13

14

Total Mile age (000)

6-6 The linear assumption is reasonably valid providing the cost formula is used only within the relevant range. 6-7 A discretionary fixed cost is one that has a fairly short planning horizon—usually a year. Such costs arise from annual decisions by management to spend in certain fixed cost areas, such as advertising, research, and management development. A committed fixed cost is one that has a long planning horizon— generally many years. Such costs relate to a company’s investment in facilities, equipment, and basic organization. Once such costs have been incurred, a company becomes “locked in” to the decision for many years.

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6-11 The high-low method, the scattergraph method, and the least-squares regression method are used to analyze mixed costs. The least-squares regression method is generally considered to be most accurate, since it derives the fixed and variable elements of a mixed cost by means of statistical analysis. The scattergraph method derives these elements by visual inspection only, and the high-low method utilizes only two points in doing a cost analysis, making it the least accurate of the three methods. 6-12 The regression line is a line that is fitted to an array of plotted points. A regression line can be expressed in formula form as Y = a + bX. In cost analysis, the “a” term represents the fixed cost element, and the “b” term

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represents the variable cost element per unit of activity. 6-13 The fixed cost element is represented by the point where the regression line intersects the vertical axis on the graph. The variable cost per unit is represented by the slope of the line. 6-14 The term “least-squares regression” means that the sum of the squares of the deviations from the plotted points on a graph to the regression line is smaller than could be obtained from any other line that could be fitted to the data.

6-18 The contribution margin is total sales revenue less total variable expenses. 6-19 The contribution approach to the income statement organizes costs by behaviour, first deducting variable expenses to obtain contribution margin, and then deducting fixed expenses to obtain net income. The traditional approach organizes costs by function, such as production, selling, and administration. Within a functional area, fixed and variable costs are intermingled.

6-15 The least-squares regression method, compared to the high-low method, has two main advantages: (1) it considers all the data points (observations) instead of just the high and the low observations, and (2) it is a statistical technique, and gives an objective measure of the “goodness of fit” of the regression line. 6-16 The main difference between the least-squares regression method and the scattergraph method is that the regression method uses a statistical technique to fit the regression line and compute the coefficients of the constant term and the variable of interest. In contrast, the scattergraph employs a visual fit (approximation) method to draw the regression line which is then used to compute the values of the coefficients. 6-17 True. A higher R2 means that a greater proportion of the variation in the dependent variable (Y) is explained by the variation in the independent variable of interest (X). Copyright © 2017 McGraw-Hill Education. All rights reserved.

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Foundational Fifteen (LO1 – CC1, 3, 6; LO2 – CC7, 9; LO3 – CC12) The following table shows the cost per unit for each of the three months. This table, along with the table in the question, will help in developing the cost equations and computing the required amounts. July Sales in units Sales revenue Direct materials Direct labour Manufacturing overhead Sales commission Other selling expenses Administrative expenses

4,000 $100.00 $ 18.50 $ 22.15 $ 15.87 $ 7.50 $ 10.49 $ 7.89

August

September

4,200

4,800

$100.00

$100.00

$ 18.50

$ 18.50

$ 22.15

$ 22.15

$ 15.51

$ 14.73

$

7.50

$

7.50

$ 10.39

$

9.24

$

$

6.57

7.51

6-1. $100 per unit 6-2. Y = $18.50X (variable cost)1 6-3. Y = $22.15X(variable cost)1 6-4. Y = $27,480 + $9.00X (mixed cost)2 6-5. Y = $7.50X (variable cost)1 6-6. Y = $29,960 + $3.00X (mixed cost)2 6-7. Y = $31,550 (fixed cost)3 6-8. $18.50 + $22.15 + $9.00 = $49.65 6-9. $7.50 + $3.00 = $10.50 6-10. $7.50 x 4,100 = $30,750 6-11. $27,480 + ($9.00 x 4,500) = $67,980 6-12. $88,990 + (60.15 x 4,700) = $371,6954 6-13. $100 - $60.15 = $39.85 6-14. $39.85 x 4,000 = $159,400 6-15. ($39.85 x 4,600) - $88,990 = $94,3205 Notes: 1. As shown in the table above the cost per unit for these three cost items is constant across all months. Therefore, these cost items are classified as variable costs.

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2. The cost per unit for these items is inversely proportional to the sales in units. However, the total cost per month is directly proportional with the sales in units. Therefore, these cost items are classified as mixed costs. The variable portion for each of the two mixed cost items is computed as shown below.

Sales Units High activity – September Low activity July Difference

Observed Costs Manufacturing Other Selling Overhead Expenses

4,800

$70,680

$44,360

4,000

$63,480

$41,960

800

$ 7,200

$2,400

The variable cost portion for Manufacturing Overhead and Other Selling Expenses, respectively, are computed as shown below:

Change in cost $7,200 = =$9 per unit Change in activity 800 units Change in cost $2,400 = =$3 per unit Change in activity 800 units The fixed portion for Manufacturing Overhead and Other Selling Expenses, respectively, are computed as shown below: $70,680 – ($9 ˣ 4,800) $41,960 – ($3 ˣ 4,000)

= $27,480 = $29,960

3. The total cost is constant across all months; therefore this cost item is classified as a fixed cost. 4. The fixed portion of this cost equation is computed as follows: $27,480 + $29,960 + 31,550 The variable portion of this cost equation is computed as follows: $18.50 + $22.15 + $9.00 +7.50 + $3.00

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5. Income is computed as total contribution margin for the 4,600 units sold (@$39.85 per unit as shown in #13 above, multiplied by 4,600) minus the total fixed costs of $88,990 (as shown in #12 above and also Note #4 above).

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Solutions to Brief Exercise Exercisess Brief Exerci Exercise6-1 se6-1 (15 minutes) (LO1 CC1, 3) 1.

Cups of Coffee Served in a Week 3,000 3,200 3,400 $2,200 $2,200 $2,200 540 576 612 $2,740 $2,776 $2,812 $0.913 $0.868 $0.827

Fixed cost Variable cost Total cost Cost per cup of coffee served * * Total cost ÷ cups of coffee served in a week.

2. The average cost of a cup of coffee declines as the number of cups of coffee served increases because the fixed cost is spread over more cups of coffee.

Brief Exerci Exercise se 6-2 (20 minutes) (LO2 CC9) 1.

Month High activity level (March) Low activity level (October) Change

OccupancyDays 2,536

Electrical Costs $5,383

224 2,312

1,988 $3,395

Variable cost = Change in cost ÷ Change in activity = $3,395 ÷ 2,312 occupancy-days = $1.47 per occupancy-day. Total cost (March).........................................................................$5,383 Variable cost element 3,728 ($1.47 per occupancy-day × 2,536 occupancy-days).................... Fixed cost element........................................................................ $1,655 Cost equation for electrical costs can be stated as follows: Electrical costs (Y) = $1,655 per month + $1.47 per occupancy-day 2. Electrical costs may reflect seasonal factors other than just the variation in occupancy days. For example, common areas such as the reception area must be lighted for longer periods during the winter. This will result in seasonal fluctuations in the fixed electrical costs. Additionally, the fixed costs will be affected by the number of days in a month. In other words, costs like the costs of lighting common Copyright © 2017 McGraw-Hill Education. All rights reserved.

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areas are variable with respect to the number of days in the month, but are fixed with respect to how many rooms are occupied during the month. Other, less systematic, factors may also affect electrical costs such as the frugality of individual guests. Some guests will turn off lights when they leave a room. Others will not.

Brief Exerci Exercise se 6-3 (30 minutes) (LO2 CC10) 1. See the scattergraph on the following page. 2. Students’ answers will vary, depending on their placement of the regression line. The variable cost per unit processed is: Total cost at the 10,000-unit level of activity [approximate amount based on visual inspection]............................................ $48,750 Total cost at the 5,000-unit level of activity [approximate amount based on visual inspection]............................................ $36,250 Change in cost $12,500 Variable cost element per unit produced [$12,500 ÷ 5,000 units produced]...............................................$2.50 Fixed cost element [where the regression line intersects the Y-axis]................................................................................. 25,000 Therefore, the cost formula is $25,000 per month plus $2.50 per unit processed. (Observe from the scattergraph that if the company used the high-low method to determine the slope of the regression line, the line would be too parallel to the line shown in the plot but below it, causing estimated fixed costs to be lower than they should be, and the variable cost per unit to be close to what is computed above.)

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Brief Exerci Exercise se 6-3 (continued)

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Brief Exerci Exercise se 6-4 (20 minutes) (LO2 CC11) The estimates of the fixed and variable costs using least-squares regression is as follows: Fixed cost:

$25,193 per month

Variable cost:$2.42 per unit produced. The R2 is about 92%, which means that the cost manager of Oki Products can be fairly confident that units produced is a reliable basis for estimating processing costs. Students can be asked to compare these estimates with those from the scattergraph method in the previous exercise. The INTERCEPT and SLOPE functions can be used in Excel to calculate the fixed and variable cost numbers, and the RSQ function to calculate R2. Brief Exerci Exercise se 6-5 (10 minutes) minutes)(LO1 CC1, 3; LO3 CC12) Contribution margin income statement. $45,000 27,000 $18,000 12,000 $ 6,000

Sales Less: variable costs1 Contribution margin Less: fixed expenses2 Net income 1

Using sales revenue and average selling price, we can compute the number of units sold as 3,000 ($45,000 ÷ $15). Therefore, total variable costs = 3,000 × $9 = $27,000. 2

Fixed expenses = $39,000 - $27,000 = $12,000

Brief exercise 6-6 (1 (10 0 minutes) (LO1 CC6; LO2 CC7, 8) Cost functions 1, 2, 3, and 4 are linear functions (although 3 is simply a constant function, which means the value of the dependent variable will not vary with any variation in the value of the independent variable). Cost function 5 is a non-linear function.

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Cost functions 1, 2, and 5 are mixed cost functions in that they include a constant term and a variable term. The remaining two cost functions are not mixed (#3 has only a fixed cost element and #4 has only a variable cost element). Brief Exerci Exercise se 6-7 (15 minutes) (LO2 CC9) Pizzas Cost High activity level Low activity level Change Variable portion

32,000 24,000 12,520 8,000 3,520

16,040

= Change in cost÷change in activity = $3,520 ÷ 8,000 = $0.44 per pizza.

Fixed portion: High Total cost $16,040 Less variable portion @$0.44 per pizza 14,080 Fixed cost element $ 1,960

Low $12,520 10,560 $ 1,960

Cost equation can be stated as follows: Utilitycosts (Y) = $1,960 per month + $0.44 per pizza

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Brief Exerci Exercise se 6-8 (20 minutes) (LO3 CC12) 1. THE ALPINE HOUSE, INC. Income Statement—Ski Department For the Quarter Ended March 31 Sales............................................................................................ Less variable expenses: Cost of goods sold ($450 per pair × 800 pairs*).......................... $360,000 Selling expenses ($50 per pair × 800 pairs)................................. 40,000 Administrative expenses (20% × $20,000)..................................4,000 Contribution margin...................................................................... Less fixed expenses: Cost of goods sold [$390,000 – ($450 per pair × 800 pairs] 30,000 Selling expenses [$60,000 – ($50 per pair × 800 pairs)]..................................... 20,000 Administrative expenses (80% × $20,000).................................. 16,000 Net income...................................................................................

$560,000

404,000 156,000

66,000 $ 90,000

*$560,000 ÷ $700 per pair = 800 pairs. 2. Since 800 pairs of skis were sold and the contribution margin totalled $156,000 for the quarter, the contribution of each pair of skis toward covering fixed costs and toward profits was $195 ($156,000 ÷ 800 pairs).

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Solutions to Exe Exercises rcises Exercise 6-1 (30 minutes) (LO2 CC9) 1.

GuestDays 28,500 12,500 16,000

High activity level (June) Low activity level (April) Change

Custodial Supplies Expense $28,850 19,250 $ 9,600

Variable cost portion: Change in expense ÷Change in activity = $9,600÷16,000 = $0.60 per guest day

Fixed cost portion: Custodial supplies expense at high activity level.............................. $28,850 Less variable cost element 28,500 guest-days × $0.60 per guest-day................................... 17,100 Total fixed cost............................................................................. $11,750 The cost formula is $11,750 per month plus $0.60 per guest-day or Y = $11,750 + $0.60x. 2. Custodial supplies expense for 13,000 guest-days: Variable cost 13,000 guest-days × $0.60 per guest-day................................... $ 7,800 Fixed cost..................................................................................... 11,750 Total cost..................................................................................... $19,550

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Exercise 6-2 ((30 30 minutes) (LO2 CC11) The use of a spreadsheet to conduct the least-squares regression analysis returns the following results: Fixed cost:

$11,591

Variable cost:$0.62 per guest-day occupied. Cost formula:Y = $11,591 + $0.62 x. Custodial supplies expense for 13,000 guest-days: Variable cost 13,000 guest-days × $0.62 per guest-day................................... $ 8,060 Fixed cost..................................................................................... 11,591 Total cost..................................................................................... $19,651

The estimated cost for 13,000 guest-days using least-squares regression is slightly higherthan the estimate using high-low method. Least-squares regression is a superior method be...