CHAPTER 2
COVERAGE OF LEARNING OBJECTIVES
LEARNING OBJECTIVE / FUNDA-MENTAL
ASSIGN-MENT
MATERIAL / CRITICAL THINKING
EXERCISES AND EXERCISES / PROBLEMS / CASES, NIKE 10K, EXCEL,
COLLAB., & INTERNET EXERCISES
LO1: Explain how cost drivers affect cost behavior. / A1,B1 / 24,25, 27 / 41, 43, 45, 48 / 60
LO2: Show how changes in cost-driver levels affect variable and fixed costs. / A1,B1,A2, A3, B2, B3 / 24,25, 28, 29 / 41, 44, 45, 46, 48, 51, 52, 55 / 60, 61, 65
LO3: Calculate break-even sales volume in total dollars and total units. / A2, A3, B2, B3 / 34,35,36 / 42, 44, 46, 47, 49, 51, 53, / 60, 61, 65, 66
LO4: Create a cost-volume-profit graph and understand the assumptions behind it. / 30, 31, 32, 33 / 41
LO5: Calculate sales volume in total dollars and total units to reach a target profit. / A2, A3, B2, B3 / 30, 31, 36, / 42, 44, 46, 47, 49, 51, / 61
LO6: Differentiate between contribution margin and gross margin. / 53
LO7: Explain the effects of sales mix on profits (Appendix 2A). / 37 / 56, 57 / 62
LO8: Compute cost-volume-profit relationships on an after-tax basis (Appendix 2B). / A2, B2 / 38, 39 / 58, 59 / 63
CHAPTER 2
INTRODUCTION TO COST BEHAVIOR AND COST-VOLUME RELATIONSHIPS
2-A1 (20-25 Min.)
1. The cost driver for both resources is square feet cleaned. Labor cost is a fixed-cost resource, and cleaning supplies is a variable cost. Costs for cleaning between 4 and 8 times a month are:
Number of times plant is cleaned / Square Feet Cleaned / Labor Cost / Cleaning Supplies Cost / Total cost / Cost per Square Foot4 / 100,000* / $24,000 / $ 5,000** / $29,000 / $0.290
5 / 125,000 / 24,000 / 6,250*** / 30,250 / 0.242
6 / 150,000 / 24,000 / 7,500 / 31,500 / 0.210
7 / 175,000 / 24,000 / 8,750 / 32,750 / 0.187
8 / 200,000 / 24,000 / 10,000 / 34,000 / 0.170
* 4 x 25,000 square feet
** Cleaning supplies cost per square feet cleaned = $5,000 ÷ 100,000 = $0.05
*** $0.05 per square foot x 125,000
The predicted total cost to clean the plant during the next quarter is the sum of the total costs for monthly cleanings of 5, 6, and 8 times. This is
$30,250 + $31,500 + $34,000 = $95,750
2. If Boeing hires the outside cleaning company, all its cleaning costs will be variable at a rate of $5,900 per cleaning. The cost driver will be “number of times cleaned.” The predicted cost to clean a total of 5 + 6 + 8 = 19 times is 19 x $5,900 = $112,100. Thus, Boeing will not save by hiring the outside cleaning company. The table and chart on the next page show the total costs for the two alternatives. The cost driver for the outsource alternative is different than the cost driver if Boeing cleans the plant with its own employees. If Boeing expects average “times cleaned” to be 6 or more, it would save by cleaning with its own employees.
Boeing Cleans Plant / Outsource Cleaning PlantSquare Feet Cleaned / Boeing / Times Cleaned / Outside
100,000 / $ 29,000 / 4 / $23,600
125,000 / 30,250 / 5 / 29,500
150,000 / 31,500 / 6 / 35,400
175,000 / 32,750 / 7 / 41,300
200,000 / 34,000 / 8 / 47,200
2-A2(20-25 min.)
1.Let N= number of units
Sales= Fixed expenses + Variable expenses + Net income
$1.00 N= $5,000 + $.80 N + 0
$.20 N= $5,000
N= 25,000 units
Let S= sales in dollars
S= $5,000 + .80 S + 0
.20 S= $5,000
S= $25,000
Alternatively, the 25,000 units may be multiplied by the $1.00 to obtain $25,000.
In formula form:
In units
= = 25,000 units
In dollars
= = $25,000
2.The quick way: (36,000 - 25,000) x $.20 = $2,200
Compare income statements:
Break-even
Point IncrementTotal
Volume in units 25,000 11,000 36,000
Sales$25,000$11,000$36,000
Deduct expenses:
Variable20,0008,80028,800
Fixed 5,000 --- 5,000
Total expenses$25,000$8,800$33,800
Effect on net income$ 0$ 2,200$ 2,200
3.Total fixed expenses would be $5,000 + $1,152 = $6,152
= 30,760units; = $30,760 sales
or 30,760 x $1.00= $30,760 sales
4.New contribution margin is $.18 per unit;
$5,000 ÷ $.18 = 27,778 units
27,778 units x $1.00 = $27,778 in sales
5.The quick way: (36,000 - 25,000) x $.16 = $1,760. On a graph, the slope of the total cost line would have a kink upward, beginning at the break-even point.
2-A3(20-30 min.)
The following format is only one of many ways to present a solution. This situation is really a demonstration of "sensitivity analysis," whereby a basic solution is tested to see how much it is affected by changes in critical factors. Much discussion can ensue, particularly about the final three changes.
The basic contribution margin per revenue mile is $1.50 - $1.30 = $.20
(1)(2)(3)(4)(5)
(1)x(2)(3)-(4)
RevenueContributionTotal
MilesMargin PerContributionFixedNet
SoldRevenue MileMarginExpensesIncome
1.800,000$.20$160,000$110,000 $ 50,000
2.(a) 800,000.35280,000110,000 170,000
(b)880,000.20176,000110,000 66,000
(c)800,000.0756,000110,000 (54,000)
(d)800,000.20160,000121,000 39,000
(e)840,000.17142,800110,000 32,800
(f)720,000.25180,000110,000 70,000
(g)840,000.20168,000121,000 47,000
2-B1 (20-25 Min.)
1. The cost driver for both resources is square feet cleaned. Labor cost is a fixed-cost resource, and cleaning supplies is a variable cost. Costs for cleaning between 35 and 50 times are:
Times Cleaned / Square Feet Cleaned / Labor Cost / Cleaning Supplies Cost / Total cost / Cost per Square Foot35 / 140,000* / $18,000 / $ 8,400** / $26,400 / $0.189
40 / 160,000 / 18,000 / 9,600 / 27,600 / 0.173
45 / 180,000 / 18,000 / 10,800 / 28,800 / 0.160
50 / 200,000 / 18,000 / 12,000 / 30,000 / 0.150
* 35 x 4,000
** The cost of cleaning supplies per square feet cleaned = $8,400 ÷ 140,000 = $0.06 per square foot. Cleaning supplies cost = $0.06 x 140,000 = $8,400.
The predicted total cost to clean during the November and December is the sum of the total costs for monthly cleanings of 45 and 50 times. This is
$28,800 + $30,000 = $58,800
2. If Outback hires the outside cleaning company, all its cleaning costs will be variable at a rate of $0.17 per square foot cleaned. The predicted cost to clean a total of 45 + 50 = 95 times is 95 x 4,000 x $0.17 = $64,600. Thus Outback will not save by hiring the outside cleaning company.
To determine whether outsourcing is a good decision on a permanent basis Outback needs to know the expected demand for the cost driver over an extended time frame. As the following table and graph show, outsourcing becomes less attractive when cost driver levels are high. If average demand for cleaning is expected to be more than about 164,000 ÷ 4,000 = 41 times a month, Outback should continue to do its own cleaning. Outback should also consider such factors as quality and cost control when an outside cleaning company is used.
(1) Times Cleaned / (2) Square Feet Cleaned / (3) Outback Total Cleaning Cost* / Outside Cleaning Cost$.17 x (2)
35 / 140,000 / $26,400 / $23,800
40 / 160,000 / 27,600 / 27,200
45 / 180,000 / 28,800 / 30,600
50 / 200,000 / 30,000 / 34,000
* From requirement 1., total cost is the fixed cost of $18,000 +
variable costs of $.06 x square feet cleaned
2-B2(15-20 min.)
1. = = 1,000 units
2.Contribution margin: = 25%
$7,500 ÷ 25% = $30,000
3. = = 2,500 units
4. ($50,000 - $20,000)(110%)= $33,000 contribution margin;
$33,000 - $20,000= $13,000
or
(10% x $50,000) x .6 = $3,000 more net income. The current $10,000 net income plus the $3,000 additional net income equal $13,000 total net income.
5.New contribution margin:$40 - ($30 - 20% of $30)
=$40 - ($30 - $6) = $16;
New fixed expenses: $80,000 x 110% = $88,000;
= = 6,750 units
2-B3(15-25 min.)
1.176 x ($30 - $10) - $2,300 = $3,520 - $2,300 = $1,220
2.a.198 x ($30 - $10) - $2,300 = $3,960 - $2,300 = $1,660
or (22 x $20) + $1,220 = $440 + $1,220 = $1,660
b.176 x ($30 - $11) - $2,300 = $3,344 - $2,300 = $1,044
or $1,220 - ($1 x 176) = $1,044
c.$1,220 - $200 = $1,020
d.[(9.5 x 22) x ($30 - $10)] - ($2,300 + $300) = $4,180 - $2,600 = $1,580
e.[(7 x 22) x ($33 - $10)] - $2,300 = $3,542 - $2,300 = $1,242
2-1This is a good characterization of cost behavior. Identifying cost drivers will identify activities that affect costs, and the relationship between a cost driver and costs specifies how the cost driver influences costs.
2-2Two rules of thumb to use are:
a. Total fixed costs remain unchanged regardless of changes in cost-driver activity level.
b. The per-unit variable cost remains unchanged regardless of changes in cost-driver activity level.
2-3Examples of variable costs are the costs of merchandise, materials, parts, supplies, sales commissions, and many types of labor. Examples of fixed costs are real estate taxes, real estate insurance, many executive salaries, and space rentals.
2-4Fixed costs, by definition, do not vary in total as volume changeswithin the relevant range and during the time period specified (a month, year, etc.). However, when the cost-driver level is outside the relevant range (either less than or greater than the limits) management must decide whether to decrease or increase the capacity of the resource, expressed in cost-driver units. In the long run, all costs are subject to change. For example, the costs of occupancy such as a long-term non-cancellable lease cannot be changed for the term of the lease, but at the end of the lease management can change this cost. In a few cases, fixed costs may be changed by entities outside the company rather than by internal management – an example is the fixed, base charge for some utilities that is set by utility commissions.
2-5Yes. Fixed costs per unit change as the volume of activity changes. Therefore, for fixed cost per unit to be meaningful, you must identify an appropriate volume level. In contrast, total fixed costs are independent of volume level.
2-6No. Cost behavior is much more complex than a simple dichotomy into fixed or variable. For example, some costs are not linear, and some have more than one cost driver. Division of costs into fixed and variable categories is a useful simplification, but it is not a complete description of cost behavior in most situations.
2-7No. The relevant range pertains to both variable and fixed costs. Outside a relevant range, some variable costs, such as fuel consumed, may behave differently per unit of activity volume.
2-8The major simplifying assumption is that we can classify costs as either variable or fixed with respect to a single measure of the volume of output activity.
2-9The same cost may be regarded as variable in one decision situation and fixed in a second decision situation. For example, fuel costs are fixed with respect to the addition of one more passenger on a bus because the added passenger has almost no effect on total fuel costs. In contrast, total fuel costs are variable in relation to the decision of whether to add one more mile to a city bus route.
2-10No. Contribution margin is the excess of sales over all variable costs, not fixed costs. It may be expressed as a total, as a ratio, as a percentage, or per unit.
2-11A "break-even analysis" does not describe the real value of a CVP analysis, which shows profit at any volume of activity within the relevant range. The break-even point is often only incidental in studies of cost-volume relationships. It predicts how managers’ decisions will affect sales, costs, and net income. It is an important part of a company’s planning process.
2-12No. break-even points can vary greatly within an industry. For example, Rolls Royce has a much lower break-even volume than does Honda (or Ford, Toyota, and other high-volume auto producers).
2-13No. The CVP technique you choose is a matter of personal preference or convenience. The equation technique is the most general, but it may not be the easiest to apply. All three techniques yield the same results.
2-14Three ways of lowering a break-even point, holding other factors constant, are: decrease total fixed costs, increase selling prices, and decrease unit variable costs.
2-15No. In addition to being quicker, incremental analysis is simpler. This is important because it keeps the analysis from being cluttered by irrelevant and potentially confusing data.
2-16An increase in demand for a company’s products will drive almost all other cost-driver levels higher. This will cause cost drivers to exceed capacity or the upper end of the relevant range for its fixed-cost resources. Since fixed-cost resources must be purchased in “chunks” of capacity, the proportional increase in cost may exceed the proportional increase in the use of the related cost-driver. Thus cost per cost-driver unit may increase.
2-17Operating leverage is a firm's ratio of fixed to variable costs. A highly leveraged company has relatively high fixed costs and low variable costs. Such a firm is risky because small changes in volume lead to large changes in net income.
2-18No. In retailing, the contribution margin is likely to be smaller than the gross margin. For instance, sales commissions are deducted in computing the contribution margin but not the gross margin. In manufacturing companies the opposite is likely to be true because there are many fixed manufacturing costs deducted in computing gross margin.
2-19No. CVP relationships pertain to both profit-seeking and nonprofit organizations. In particular, managers of nonprofit organizations must deal with tradeoffs between variable and fixed costs. To many government department managers, lump-sum budget appropriations are regarded as the available revenues.
2-20Contribution margin could be lower because the proportion of sales of the product bearing the higher unit contribution margin declines.
2-21
=
2-22
= x x (1 - tax rate)
2-23No. The individual is confused. Definitions of variable and fixed cost behavior are based on total cost behavior, not unit cost behavior.
2-24The key to determining cost behavior is to ask, “If there is a change in the level of the cost driver, will the total cost of the resource change immediately?” If the answer is yes, the resource cost is variable. If the answer is no, the resource cost is fixed. Using this question as a guide, the cost of advertisements is normally variable as a function of the number of advertisements. Note that because the number of advertisements may not vary with the level of sales, advertising cost may be fixed with respect to the cost driver “level of sales.” Salaries of marketing personnel are a fixed cost. Travel costs and entertainment costs can be either variable or fixed depending on the policy of management. The key question is whether it is necessary to incur additional travel and entertainment costs to generate added sales.
2-25The key to determining cost behavior is to ask, “If there is a change in the level of the cost driver, will the total cost of the resource change immediately?” If the answer is yes, the resource cost is variable. If the answer is no, the resource cost is fixed. Using this question as a guide, the cost of labor can be fixed or variable as a function of the number of hours worked. Regular wages may be fixed if there is a commitment to the laborers that they will be paid for normal hours regardless of the workload. However, overtime and temporary labor wages are variable. The depreciation on plant and machinery is not a function of the number of machine hours used and so this cost is fixed.
2-26Suggested value chain functions are listed below.
New Products / New Technology / New Positioning Strategies / New PricingMarketing
R & D
Design / R & D
Design / Marketing
Support functions / Marketing
2-27(5 –10 min.)
Situation / Best Cost Driver / Justification1. / Number of Setups / Because each setup takes the same amount of time, the best cost driver is number of setups. Data is both plausible, reliable, and easy to maintain.
2. / Setup Time / Longer setup times result in more consumption of mechanics’ time. Simply using number of setups as in situation 1 will not capture the diversity associated with this activity.
3. / Cubic Feet / Assuming that all products are stored in the warehouse for about the same time (that is inventory turnover is about the same for all products), and that products are stacked, the volume occupied by products is the best cost driver.
4. / Cubic Feet Weeks / If some types of product are stored for more time than others, the volume occupied must be multiplied by a time dimension. For example, if product A occupies 100 cubic feet for an average of 2 weeks and product B occupies only 40 cubic feet but for an average of 10 weeks, product B should receive twice as much allocation of warehouse occupancy costs.
2-28(5-10 min.)
1.Contribution margin = $900,000 - $500,000= $400,000
Net income = $400,000 - $350,000= $ 50,000
2.Variable expenses = $800,000 - $350,000= $450,000
Fixed expenses = $350,000 - $ 80,000= $270,000
3.Sales = $600,000 + $340,000= $940,000
Net income = $340,000 - $250,000= $ 90,000
2-29(10-20 min.)
1.d= c(a - b)
$720,000= 120,000($25 - b)
b= $19
f= d - e
= $720,000 - $640,000 = $80,000
2.d= c(a - b)
= 100,000($10 - $6) = $400,000
f= d - e
= $400,000 - $320,000 = $80,000
3.c= d ÷ (a - b)
= $100,000 ÷ $5 = 20,000 units
e= d - f
= $100,000 - $15,000 = $85,000
4.d= c(a - b)
= 70,000($30 - $20)
= $700,000
e= d - f
= $700,000 - $12,000 = $688,000
5.d= c(a - b)
$160,000= 80,000(a - $9)
a= $11
f= d - e
= $160,000 - $110,000 = $50,000
2-30 (10 min.)
Using the graph above, the estimated breakeven point in total units sold is about 80,000. The estimated net income for 100,000 units sold is $80,000 ($1,000,000 - $920,000).
2-31 (10 min.)
Using the graph above, the estimated breakeven point in total units sold is about 65,000 (actual breakeven volume is 68,800). The estimated net loss for 50,000 units sold is about $200,000 ($1,500,000 - $1,700,000). Actual net loss is $500,000 - $688,000 = $188,000.
2-32 (20–25 min.)
Square Feet / Labor Cost / Labor Cost per Square Foot / Supplies Cost / Supplies Cost per Square Foot100,000 / $24,000 / $ 0.240 / $ 5,000 / $0.050*
125,000 / 24,000 / $ 0.192 / 6,250 / 0.050
150,000 / 24,000 / $ 0.160 / 7,500 / 0.050
175,000 / 24,000 / $ 0.137 / 8,750 / 0.050
200,000 / 24,000 / $ 0.120 / 10,000 / 0.050
* At 100,000 square feet on the second graph, the total supplies cost is $5,000 so the slope of the line is $0.05.
2-33 (20-25 min.)
140,000 / $0.13 / $18,200 / $0.06 / $ 8,400
160,000 / 0.11 / 17,600 / 0.06 / 9,600
180,000 / 0.10 / 18,000 / 0.06 / 10,800
200,000 / 0.09 / 18,000 / 0.06 / 12,000
* The estimates for labor cost per square foot yield slightly different total labor cost estimates. In the graph below, $18,000 is used.
2-34(10 min.)
1.Let TR= total revenue
TR - .30(TR) -$42,000,000= 0
.70(TR)= $42,000,000
TR= $60,000,000
2.Daily revenue per patient = $60,000,000 ÷ 50,000 = $1,200. This may appear high, but it includes the room charge plus additional charges for drugs, x-rays, and so forth.
2-35(15 min.)
1.100% Full50% Full
Room revenue @ $50 $7,300,000 a $3,650,000 b
Variable costs @ $10 1,460,000 730,000
Contribution margin 5,840,000 2,920,000
Fixed costs 3,200,000 3,200,000
Net income (loss) $2,640,000 $ (280,000)
a400 x 365 = 146,000 rooms per year
146,000 x $50 = $7,300,000
b50% of $7,300,000 = $3,650,000
2.Let N= number of rooms
$50N -$10N - $3,200,000 = 0
N= $3,200,000 ÷ $40 = 80,000 rooms
Percentage occupancy= 80,000 ÷ 146,000 = 54.8%
2-36(15 min.)
1.$28. To compute this, let X be the variable cost that generates $1 million in profits:
($48 - X ) x 800,000 - $15,000,000 = $1,000,000
($48 - X) = ($1,000,000 + $15,000,000) ÷ 800,000
$48 – X= $160 ÷ 8 = $20
X= $48 - $20 = $28
2.Loss of $600,000:
($48 - $30) x 800,000 - $15,000,000
= ($18 x 800,000) - $15,000,000
= $14,400,000 - $15,000,000
= ($600,000)
2-37 (15-20 min.)
1.Let R = pints of raspberries and 2R = pints of strawberries
sales - variable expenses - fixed expenses = zero net income
$1.00(2R) + $1.35(R) - $.65(2R) - $.85(R) - $14,400 = 0
$2.00R + $1.35R - $1.30R - $.85R -$14,400 = 0
$1.2R - $14,400= 0
R= 12,000 pints of raspberries
2R = 24,000 pints of strawberries
2.Let S = pints of strawberries
($1.00 - $.65) x S - $14,400 = 0
.35S - $14,400 = 0
S = 41,143 pints of strawberries
3.Let R = pints of raspberries
($1.35 - $.85) x R - $14,400 = 0
$.50R - $14,400 = 0
R = 28,800 pints of raspberries
2-38(10 min.)
1.$1.50N - $1.20N - $18,000 =
$.30N = $18,000 +
$.30N = $18,000 + $1,080
N = $19,080 ÷ $.30 = 63,600 units
2.$1.50N - $1.20N - $18,000 =
$.30N = $18,000 +
$.30N = $18,000 + $1,800
N = $19,800 ÷ $.30 = 66,000 units
2-39(15 min.)
Several variations of the following general approach are possible:
Sales - Variable expenses - Fixed expenses =
S - .7S - $440,000 =
.3S = $440,000 + $70,000
S = $510,000 ÷ .3 = $1,700,000
Check:Sales$1,700,000
Variable expenses (70%) 1,190,000
Contribution margin510,000
Fixed expenses 440,000
Income before taxes$ 70,000
Income taxes @ 40% 28,000
Net income$ 42,000
2-40 (30-40 min.)
1. The cost of labor and depreciation is fixed at $18,000 per month. Cleaning supplies cost varies in proportion to the number of times the store is cleaned. The cost per cleaning is $10,200 ÷ 60 = $170.
Number of times store is cleaned / Labor & Depreciation Cost / Cleaning Supplies Cost $170 per Cleaning / Total cost / Cost per Cleaning35 / $18,000 / $ 5,950 / $23,950 / $684.29
40 / 18,000 / 6,800 / 24,800 / 620.00
45 / 18,000 / 7,650 / 25,650 / 570.00
50 / 18,000 / 8,500 / 26,500 / 530.00
55 / 18,000 / 9,350 / 27,350 / 497.27
60 / 18,000 / 10,200 / 28,200 / 470.00
The total cost of cleaning for the next quarter is:
Total cost =Total Fixed Cost + Total Variable Cost
=3 x $18,000 + (50 + 46 + 35) x $170 per Cleaning
=$54,000 + $22,270
=$76,270
2.
3.
Number of times store is cleaned / Labor & Depreciation Cost / Cleaning Supplies Cost / Total cost
35 / $18,000 / $ 5,950 / $23,950 / $18,900
46 / 18,000 / 7,820 / 25,820 / 24,840
50 / 18,000 / 8,500 / 26,500 / 27,000
$76,270 / $70,740
Kroger will save $76,270 - $70,740 = $5,530 by using the outside cleaning company as shown in the above schedule.
2-41(10-15 min.)
The answer is $1,100,000.
Refined analysis:
$1,200,000
1,100,000
1,000,000
$2,000,000$2,400,000billings
Practical analysis:
$1,200,000
1,100,000
1,000,000
$2,000,000$2,400,000billings
Relevant Range
2-42(15-20 min.)
1. Microsoft: ($39,788 - $6,200) ÷ $39,788 = .84 or 84%
Procter & Gamble: ($68,222 - $33,125) ÷ $68,222) = .51 or 51%
There is very little variable cost for each unit of software sold by Microsoft, while the variable cost of the soap, cosmetics, foods, and other products of Procter & Gamble is substantial.
2. Microsoft: $10,000,000 x .84 = $8,400,000
Procter & Gamble: $10,000,000 x .51 = $5,100,000
3. By assuming that changes in sales volume do not move the volume outside the relevant range, we know that the total contribution margin generated by any added sales will be added to the operating income. Thus, we can simply multiply the contribution margin percentage by the changes in sales to get the change in operating income.
The main assumptions we make when we assume that the sales volume remains in the relevant range are that total fixed costs do not change and unit variable cost remain unchanged. This generally means that such predictions will apply only to small changes in volume – changes that do not cause either the addition or reduction of capacity.