Introduction to Cost Behavior and Cost-Volume Relationships

CHAPTER 2

COVERAGE OF LEARNING OBJECTIVES

CHAPTER 2

Introduction to Cost Behavior and Cost-Volume Relationships

2-A1 (20-25 Min.)

1. The cost driver for both resources is number of times the plant is 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 plantSquare FeetCleaning SuppliesCost per

is cleanedCleanedLabor CostCost**Total costCleaning

4 200,000* $21,000 $ 8,000*** $29,000 $7,250

5 250,000 21,000 10,000 31,000 $6,200

6 300,000 21,000 12,000 33,000 $5,500

7 350,000 21,000 14,000 35,000 $5,000

8 400,000 21,000 16,000 37,000 $4,625

* 4 × 50,000 square feet

** Cleaning supplies cost per time the plant is cleaned = $8,000 ÷ 4 = $2,000

*** $2,000 per cleaning × number of times plant is cleaned

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

$31,000 + $33,000 + $37,000 = $101,000

2. If Napco hires the outside cleaning company, all its cleaning costs will be variable at a rate of $5,700 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 × $5,700 = $108,300. Thus, Napco will save by not hiring the outside cleaning company.

The table below shows the total costs for the two alternatives. If Napco expects average “times cleaned” to be 6 or more, it would save by cleaning with its own employees. If Napco expects to average 5 or fewer cleanings per month, it would save by outsourcing.

2-A2(20-25 min.)

1.Let N= number of units

Sales= Fixed expenses + Variable expenses + Net income

$1.00 N= $4,000 + $.68 N + 0

$.32 N= $4,000

N= 12,500 units

Let S= sales in dollars

S= $4,000 + .68 S + 0

.32 S= $4,000

S= $12,500

Alternatively, the 12,500 units may be multiplied by the $1.00 to obtain $12,500.

In formula form:

In units

= = 12,500 units

In dollars

= = $12,500

2.The quick way: (45,000 –12,500) × $.32 = $10,400

Compare income statements:

Break-even

Point IncrementTotal

Volume in units 12,500 32,500 45,000

Sales$12,500$32,500$45,000

Deduct expenses:

Variable8,50022,10030,600

Fixed 4,000 --- 4,000

Total expenses 12,500 22,100 34,600

Effect on net income$ 0$ 10,400$ 10,400

3.Total fixed expenses would be $4,000 + $1,600 = $5,600

= 17,500 units; = $17,500 sales

or 17,500 units × $1.00 / unit= $17,500 sales

4.New contribution margin is $1.00 – $.68 – $.07 = $.25 per unit

Breakeven = Fixed cost ÷ contribution margin = $4,000 ÷ $.25 = 16,000 units

16,000 units × $1.00 = $16,000 in sales

5.The quick way: (45,000 –12,500) × $.21 = $6,825. 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 $2.00 - $1.60 = $.40

(1)(2)(3)(4)(5)

(1)×(2)(3)-(4)

RevenueContributionTotal

MilesMargin PerContributionFixedNet

SoldRevenue MileMarginExpensesIncome

1.500,000$.40$200,000$50,000 $ 150,000

2.(a) 500,000 1.00500,00050,000 450,000

(b)650,000 .40260,00050,000 210,000

(c)500,000 (.08)(40,000)50,000 (90,000)

(d)500,000 .40200,00065,000 135,000

(e)575,000 .35201,25050,000 151,250

(f)350,000 .41143,50050,000 93,500

(g)575,000 .40 230,00065,000165,000

2-A4(20-25 min.) Some of these answers are controversial, and reasonable cases can be built for alternative classifications. Class discussion of these answers should lead to worthwhile disagreements about anticipated cost behavior with regard to alternative cost drivers.

1.(b) Fixed cost.

2.(d) Step cost.

3.(a) Variable cost with respect to revenue.

4.(a) Variable cost with respect to miles flown.

5.(c) Mixed cost with respect to miles driven.

6.(b) Fixed cost.

7.(b) Fixed cost.

8.(b) Fixed cost.

9.(a) Variable cost with respect to cases of 7-Up.

10.(b) Fixed cost.

11.(b) Fixed cost.

2-B1 (20-25 Min.)

1. The cost driver for both resources is number of times the restaurant is cleaned. Labor cost is a fixed-cost resource, and cleaning supplies is a variable cost. Costs for cleaning between 35 and 50 times are:

SquareCleaning

TimesFeetLaborSuppliesTotalCost per

CleanedCleanedCostCost**CostCleaning

35 210,000* $21,000 $ 16,800 $37,800 $1,080

40 240,000 21,000 19,200 40,200 $1,005

45 270,000 21,000 21,600 42,600 $ 947

50 300,000 21,000 24,000 45,000 $ 900

* 35 × 6,000

** The cost of cleaning supplies per cleaning = $16,800 ÷ 35 = $480 per cleaning. The cost per square foot is $480 ÷ $6,000 = $.08 or $16,800 ÷ 210,000 = $.08. The total cleaning supplies cost is either $480 × number of cleanings or $.08 × square feet cleaned.

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

$42,600 + $45,000 = $87,600

2. If Applejack hires the outside cleaning company, all its cleaning costs will be variable at a rate of $0.25 per square foot cleaned. The predicted cost to clean a total of 45 + 50 = 95 times is 95 × 6,000 × $0.25 = $142,500. Thus,Applejack will not save by hiring the outside cleaning company.

To determine whether outsourcing is a good decision on a permanent basis, Applejack needs to know the expected demand for the cost driver over an extended time frame. As the following table shows, outsourcing becomes less attractive when cost driver levels are high. If average demand for cleaning is expected to be more than the number of cleanings at which the cost of outsourcing equals the internal cost, Applejack should continue to do its own cleaning. This point is C cleanings, where:

$.25 × C × 6,000 = $21,000 + ( $.08 × C × 6,000)

C = $21,000 ÷ ($.17× 6,000) = 20.588 cleanings

Applejack should also consider such factors as quality and cost control when an outside cleaning company is used.

* From requirement 1, total cost is $21,000 + $.08 x square feet cleaned

2-B2(15-25 min.)

1. $2,340 ÷ ($30 - $12) = 130 child-days

or 130 × $30 = $3,900 revenue.

2.176 × ($30 - $12) - $2,340 = $3,168 - $2,340 = $828

3.a.198 × ($30 - $12) - $2,340 = $3,564 - $2,340 = $1,224

or (22 × $18) + $828 = $396 + $828 = $1,224

b.176 × ($30 - $14) - $2,340 = $2,816 - $2,340 = $476

or $828 - ($2 × 176) = $476

c.$828 - $220 = $608

d.[(9.5 × 22) × ($30 - $12)] - ($2,340 + $300) = $3,762 - $2,640 = $1,122

e.[(7 × 22) × ($33 - $12)] - $2,340 = $3,234 - $2,340 = $894

2-B3(15-20 min.)

1. = = 1,300 units

2.Contribution margin ratio: = 30%

$8,400 ÷ 30% = $28,000

3. = = 2,400 units

4.($51,000 - $18,000) × (120%)= $39,600 contribution margin;

$39,600 - $18,000= $21,600

5.New contribution margin:$48 - ($36 - 25% of $36)

=$48 - ($36 - $9) = $21;

New fixed expenses: $106,000 × 115% = $121,900;

= = 6,900 units

2-B4(20-25 min.)

The following classifications are open to debate. With appropriate assumptions, other answers could be equally supportable. For example, in #2, the health insurance would be a fixed cost if the number of employees will not change. This problem provides an opportunity to discuss various aspects of cost behavior. Students should make an assumption regarding the time period involved. For example, if the time period is short, say one month, more costs tend to be fixed. Over longer periods, more costs are variable. They also must assume something about the nature of the cost. For example, consider #4. Repairs and maintenance are often thought of as a single cost. However, repairs are more likely to vary with the amount of usage, making them variable, while maintenance is often on a fixed schedule regardless of activity, making them fixed.

Another important point to make is the cost/benefit criterion applied to determining “true” cost behavior. A manager may accept a cost driver that is plausible but may have less reliability than an alternative due to the cost associated with maintaining data for the more reliable cost driver.

Cost Cost Behavior Likely Cost Driver(s)

1. X-ray operating costMixedNumber of x-rays

2. InsuranceStep (or variable)Number of employees

3. Cancer researchFixed

4. RepairsVariableNumber of patients

5. Training costFixed

6. DepreciationFixed

7. ConsultingFixed

8. Nursing supervisorsStepNumber of nurses, patient-days

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 and supervisor salaries, and space rentals.

2-4Fixed costs, by definition, do not vary in total as volume changes within 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. CVP analysis predicts how managers’ decisions will affect sales, costs, and net income. It can be 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.

2-16Operating 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. This is good when volume increases but can be disastrous when volumes fall.

2-17An 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.

2-18 The margin of safety shows how far sales can fall before losses occur – that is before the company reaches the break-even sales level.

2-19No. 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.

2-20No. 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.

2-21Contribution margin could be lower because the proportion of sales of the product bearing the higher unit contribution margin is lower than the proportion budgeted.

2-22

=

2-23

= × × (1 - tax rate)

2-24The fixed salary portion of the compensation is a fixed cost. It is independent of how much is sold. In contrast, the 5% commission is a variable cost. It varies directly with the amount of sales. Because the compensation is part fixed cost and part variable cost, it is considered a mixed cost.

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 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.

2-26The 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.

2-27Suggested value chain functions are listed below.

2-28(10-15 min.)

2-29(5-10 min.)

1.Contribution margin = $960,000 - $533,000= $427,000

Net income= $427,000 - $310,000= $117,000

2.Variable expenses = $550,000 - $300,000= $250,000

Fixed expenses = $300,000 - $ 46,000= $254,000

3.Sales = $500,000 + $520,000= $1,020,000

Net income = $520,000 - $200,000= $320,000

2-30(5-10 min.)

The $278,000 annual advertising fee is a fixed cost. The $6,100 cost for each advertisement is a variable cost.

If the total number of ads is 46 the total cost of advertising is

$278,000 + 46 × $6,100 = $558,600

If the total number of ads is 92 the total cost of advertising is

$278,000 + 92 × $6,100 = $839,200.

The total cost of advertising does not double in response to a doubling of the number of ads because the fixed costs do not change.