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Solutions Manual, Chapter 5 195
Chapter 5
Cost Behavior: Analysis and Use
Solutions to Questions
5- a. Variable cost: A variable cost remains con- stant on a per unit basis, but changes into- tal in direct relation to changes in volume. b. Fixed cost: A fixed cost remains constant in total amount. Theaverage fixed cost per unit varies inversely with changes in volume. c. Mixed cost: A mixed cost contains both vari- able and fixed cost elements.
5- a. Unit fixed costs decrease as volume increas- es. b. Unit variable costs remain constant as vol- ume increases. c. Total fixed costs remain constant as volume increases. d. Total variable costs increase as volume in- creases.
5- a. Cost behavior: Cost behavior refers to the way in which costs change in response to changes in a measure of activity such as sales volume, production volume, or orders processed. b. Relevant range: The relevant range is the range of activity within which assumptions about variable and fixed cost behavior are valid.
5-4 An activity base is a measure of what- ever causes the incurrence of a variable cost. Examples of activity bases include units pro- duced, units sold, letters typed, beds in a hospi- tal, meals served in a cafe, service calls made, etc.
5- a. Variable cost: A variable cost remains con- stant on a per unit basis, but increases or
decreasesin total in direct relation to changes in activity. b. Mixed cost: A mixed cost is a cost that con- tains both variable and fixed cost elements. c. Step-variable cost: A step-variable cost is a cost that is incurred in large chunks, and which increases or decreases only in re- sponse to fairly wide changes in activity.
5-6 The linear assumption is reasonably val- id providing that the cost formula is used only within the relevant range. 5-7 A discretionary fixed cost has a fairly short planning horizon—usually a year. Such costs arise from annual decisions by manage- ment to spend on certain fixed cost items, such as advertising, research, and management de- velopment. A committed fixed cost has a long planning horizon—generally many years. Such costs relate to a company’s investment in facili- ties, equipment, and basic organization. Once such costs have been incurred, they are “locked in” for many years.
Cost
Activity
Mixed Cost Variable Cost
Step-Variable Cost
196 Managerial Accounting, 12th Edition
5- a. Committed d. Committed b. Discretionary e. Committed c. Discretionary f. Discretionary
5-9 Yes. As the anticipated level of activity changes, the level of fixed costs needed to sup- port operations may also change. Most fixed costs are adjusted upward and downward in large steps, rather than being absolutely fixed at one level for all ranges of activity.
5-10 The high-low method uses only two points to determine a cost formula. These two points are likely to be less than typical since they represent extremes of activity.
5-11 The formula for a mixed cost is Y = a + bX. In cost analysis, the “a” term represents the fixed cost, and the “b” term represents the vari- able cost per unit of activity.
5-12 The term “least-squares regression” means that the sum of the squares of the devia- tions 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. 5-13 Ordinary single least-squares regression analysis is used when a variable cost is a func- tion of only a single factor. If a cost is a function of more than one factor, multiple regression analysis should be used to analyze the behavior of the cost. 5-14 The contribution approach income statement organizes costs by behavior, first de- ducting variable expenses to obtain contribution margin, and then deducting fixed expenses to obtain net operating income. The traditional ap- proach organizes costs by function, such as pro- duction, selling, and administration. Within a functional area, fixed and variable costs are in- termingled. 5-15 The contribution margin is total sales revenue less total variable expenses.
198 Managerial Accounting, 12th Edition
Exercise 5-2 (30 minutes)
- The completed scattergraph is presented below:
0
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0 2,000 4,000 6,000 8,000 10, Units Processed
Total Cost
Solutions Manual, Chapter 5 199
Exercise 5-2 (continued)
- (Students’ answers will vary considerably due to the inherent impreci- sion and subjectivity of the quick-and-dirty scattergraph method of esti- mating variable and fixed costs.) The approximate monthly fixed cost is $6,000—the point where the straight line intersects the cost axis. The variable cost per unit processed can be estimated as follows using the 8,000-unit level of activity, which falls on the straight line: Total cost at the 8,000-unit level of activity ........... $14, Less fixed costs ................................................... 6, Variable costs at the 8,000-unit level of activity ..... $ 8, $8,000 ÷ 8,000 units = $1 per unit. Observe from the scattergraph that if the company used the high-low method to determine the slope of the line, the line would be too steep. This would result in underestimating the fixed cost and overestimating the variable cost per unit.
Solutions Manual, Chapter 5 201
Exercise 5-4 (20 minutes)
- The Haaki Shop, Inc. Income Statement—Surfboard Department For the Quarter Ended May 31 Sales ................................................................ $800, Variable expenses: Cost of goods sold ($150 per surfboard × 2,000 surfboards*) ....................................... $300, Selling expenses ($50 per surfboard × 2, surfboards) .................................................. 100, Administrative expenses (25% × $160,000) ..... 40,000 440, Contribution margin........................................... 360, Fixed expenses: Selling expenses ............................................. 150, Administrative expenses .................................. 120,000 270, Net operating income ........................................ $ 90, *$800,000 sales ÷ $400 per surfboard = 2,000 surfboards.
- Since 2,000 surfboards were sold and the contribution margin totaled $360,000 for the quarter, the contribution of each surfboard toward fixed expenses and profits was $180 ($360,000 ÷ 2,000 surfboards = $180 per surfboard). Another way to compute the $180 is: Selling price per surfboard .................. $ Less variable expenses: Cost per surfboard .......................... $ Selling expenses.............................. 50 Administrative expenses ($40,000 ÷ 2,000 surfboards) ....... 20 220 Contribution margin per surfboard ...... $
202 Managerial Accounting, 12th Edition
Exercise 5-5 (20 minutes)
The least-squares regression estimates of fixed and variable costs can be computed using any of a variety of statistical and mathematical software packages or even by hand. The solution below uses Microsoft ®^ Excel as il- lustrated in the text.
The intercept provides the estimate of the fixed cost element, $2,296 per month, and the slope provides the estimate of the variable cost element, $3.74 per rental return. Expressed as an equation, the relation between car wash costs and rental returns is Y = $2,296 + $3.74X where X is the number of rental returns. Note that the R 2 is 0.92, which is quite high, and indicates a strong linear relationship between car wash costs and rental returns.
204 Managerial Accounting, 12th Edition
Exercise 5-6 (20 minutes)
- The company’s variable cost per unit would be:
$150, =$2.50 per unit. 60,000 units Taking into account the difference in behavior between variable and fixed costs, the completed schedule would be: Units produced and sold 60,000 80,000 100, Total costs: Variable costs ....................... $150,000 * $200,000 $250, Fixed costs ........................... 360,000 * 360,000 360, Total costs .............................. $510,000 * $560,000 $610, Cost per unit: Variable cost ......................... $2.50 $2.50 $2. Fixed cost ............................. 6.00 4.50 3. Total cost per unit ................... $8.50 $7.00 $6. *Given.
- The company’s income statement in the contribution format would be:
Sales (90,000 units × $7.50 per unit) ............................ $675, Variable expenses (90,000 units × $2.50 per unit) ......... 225, Contribution margin...................................................... 450, Fixed expenses ............................................................ 360, Net operating income ................................................... $ 90,
Solutions Manual, Chapter 5 205
Exercise 5-7 (45 minutes)
- Units Shipped Shipping Expense High activity level ............ 8 $3, Low activity level ............. 2 1, Change .......................... 6 $2, Variable cost element: Change in cost $2, = =$350 per unit Change in activity 6 units Fixed cost element: Shipping expense at the high activity level ................... $3, Less variable cost element ($350 per unit × 8 units)..... 2, Total fixed cost ........................................................... $ 800 The cost formula is $800 per month plus $350 per unit shipped or Y = $800 + $350X, where X is the number of units shipped.
- a. See the scattergraph on the following page.
b. (Note: Students’ answers will vary due to the imprecision and subjec- tive nature of this method of estimating variable and fixed costs.) Total cost at 5 units shipped per month [a point falling on the line in (a)] ...................................... $2, Less fixed cost element (intersection of the Y axis).. 1, Variable cost element............................................. $1, $1,500 ÷ 5 units = $300 per unit. The cost formula is $1,100 per month plus $300 per unit shipped or Y = $1,100 + 300X, where X is the number of units shipped.
Solutions Manual, Chapter 5 207
Exercise 5-8 (30 minutes)
Month
Units Shipped (X)
Shipping Expense (Y) January 4 $2, February 7 $3, March 5 $2, April 2 $1, May 3 $2, June 6 $3, July 8 $3,
A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares re- gression line for the above data. The results are: Intercept (fixed cost) ............... $1, Slope (variable cost per unit) .... $ R 2 ........................................... 0. Therefore, the cost formula is $1,011 per month plus $318 per unit shipped or Y = $1,011 + $318X. Note that the R 2 is 0.96, which means that 96% of the variation in ship- ping costs is explained by the number of units shipped. This is a very high R 2 and indicates a very good fit.
Variable Cost per Unit
Fixed Cost per Month Quick-and-dirty scattergraph method ... $300 $1, High-low method................................ $350 $ Least-squares regression method ........ $318 $1, Note that the high-low method gives estimates that are quite different from the estimates provided by least-squares regression.
208 Managerial Accounting, 12th Edition
Exercise 5-9 (20 minutes)
Miles Driven
Total An- nual Cost* High level of activity ............ 120,000 $13, Low level of activity ............. 80,000 10, Change ............................... 40,000 $ 3,
- 120,000 miles × $0.116 per mile = $13, 80,000 miles × $0.136 per mile = $10, Variable cost per mile: Change in cost $3, = =$0.076 per mile Change in activity 40,000 miles Fixed cost per year: Total cost at 120,000 miles .................................. $13, Less variable cost element: 120,000 miles × $0.076 per mile ....................... 9, Fixed cost per year .............................................. $ 4,
2. Y = $4,800 + $0.076X
- Fixed cost ............................................................... $ 4, Variable cost: 100,000 miles × $0.076 per mile ......... 7, Total annual cost ..................................................... $12,
210 Managerial Accounting, 12th Edition
Exercise 5-11 (30 minutes)
- The scattergraph appears below.
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0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8, Number of X-Rays Taken
Cost of X-Rays
Solutions Manual, Chapter 5 211
Exercise 5-11 (continued)
- (Note: Students’ answers will vary considerably due to the inherent lack of precision and subjectivity of the quick-and-dirty method.) Total costs at 5,000 X-rays per month [a point falling on the line in (1)] .................................................. $23, Less fixed cost element (intersection of the Y axis)..... 6, Variable cost element................................................ $16, $16,500 ÷ 5,000 X-rays = $3.30 per X-ray. The cost formula is therefore $6,500 per month plus $3.30 per X-ray taken. Written in equation form, the cost formula is: Y = $6,500 + $3.30X, where X is the number of X-rays taken.
- The high-low method would not provide an accurate cost formula in this situation, since a line drawn through the high and low points would have a slope that is too flat. Consequently, the high-low method would over- estimate the fixed cost and underestimate the variable cost per unit.
Solutions Manual, Chapter 5 213
Exercise 5-13 (30 minutes)
- Units
(X)
Total Glazing Cost (Y) 8 $ 5 $ 10 $ 4 $ 6 $ 9 $
A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares re- gression line for the above data. The results are: Intercept (fixed cost) ............... $107. Slope (variable cost per unit) .... $20. R 2 ........................................... 0. 98 Therefore, the cost formula is $107.50 per week plus $20.36 per unit. Note that the R 2 is 0.98, which means that 98% of the variation in glaz- ing costs is explained by the number of units glazed. This is a very high R 2 and indicates a very good fit.
- Y = $107.50 + $20.36X, where X is the number of units glazed.
- Total expected glazing cost if 7 units are processed:
Variable cost: 7 units × $20.36 per unit ................ $142. Fixed cost ........................................................... 107. Total expected cost .............................................. $250.
214 Managerial Accounting, 12th Edition
Problem 5-14 (45 minutes)
- Number of Leagues
(X)
Total Cost (Y) 5 $13, 2 $7, 4 $10, 6 $14, 3 $10, A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares re- gression line for the above data. The results are: Intercept (fixed cost) .................. $4, Slope (variable cost per unit) ....... $1, R 2 .............................................. 0. Therefore, the variable cost per league is $1,700 and the fixed cost is $4,100 per year. Note that the R 2 is 0.96, which means that 96% of the variation in cost is explained by the number of leagues. This is a very high R 2 and indi- cates a very good fit.
- Y = $4,100 + $1,700X
- The expected total cost for 7 leagues would be:
Fixed cost ......................................................... $ 4, Variable cost (7 leagues × $1,700 per league)..... 11, Total cost .......................................................... $16, The problem with using the cost formula from (2) to estimate total cost in this particular case is that an activity level of 7 leagues may be out- side the relevant range—the range of activity within which the fixed cost is approximately $4,100 per year and the variable cost is approximately $1,700 per league. These approximations appear to be reasonably accu- rate within the range of 2 to 6 leagues, but they may be invalid outside this range.
