Chapter 6 – Cost Behavior6.1Cost Behavior— How costs change as volume changesThere are three common cost behaviors: 1. Variable costs2. Fixed Costs3. Mixed costsVariable Costs:• Total variable costs change in direct proportion to changes in volume• Variable cost per unit remains constant • Total variable cost (y) = xor or y = vxAssume you have a cellphone plan that charges you 5 cents for every text you make. We can graph therelationship between the number of texts in a month and the total monthly cost:- The total variable cost line begins at the Origin - zero volume and zero cost- The slope of the total variable cost line is the variable cost per unit.However, if we graphed the cost per unit at varying levels of volume, the graph would be as follows:Volume of activity (x)Variable cost perunit of activity (v) 0 100 200 300 400 $0 $20 $40 Number of textsTotal cost 0 100 200 300 400 $0.00 $0.05 $0.10 $0.15 $0.20 Number of textsCost per textFixed Costs: • Total fixed costs remain constant with changes in volume• Fixed costs per unit of activity varies inversely with changes in volumeY = f where f = total fixed costsAssume your cellphone plan includes unlimited minutes of talk time. The TOTAL COST for voice servicewould be graphed as follows:However, the COST PERMINUTE talked would decrease as the number of minutes talked increases as follows:Mixed Costs• Total mixed costs increase as volume increases (but not proportionately)• Total mixed costs can be expressed as a combination of the variable and fixed cost equations: Total mixed cost = + Or Y = vx + f Total VariableCostTotal FixedCost0 100 200 300 400 $0 $10 $20 $30 $40 Minutes talkedTotal cost50 100 200 300 400 $0.000$0.100$0.200$0.300$0.400$0.500$0.600Minutes talkedCost per minuteThe fixed cost component of $30 for unlimited minutes of talk is represented by the horizontal line. Thevariable costs component varies in direct proportion to the volume of texts.- Total mixed costs increase as volume increases because of the variable cost component.- Total mixed cost graphs slope upwards, and they intersect at the y-axis at the level of the fixed costs. Identify each cost as variable, fixed, or mixedStep Costs- Step costs are fixed fora SMALL range ofvolume and then jumpto a new fixed level with moderate changes in volume.- An example is the caregiver-to-child ratio in a day care center. States usually require a limit ofstudents per care giver. Curvilinear CostsActivity level Cost Behavior5,000 Units 6,000 units 7,000 units F, V, M1 Total Cost A $15,000 $16,000 $17,0002 Total Cost B $5,000 $6,000 $7,0003 Total Cost C $15,000 $15,000 $15,0004 Per Unit Cost D $2.00 $2.00 $2.005 Per Unit Cost E $3.00 $2.50 $2.140 100 200 300 400 $0 $20 $40 $60 Total textsTotal cellphone bill $0 $15,000 $30,000 $45,000 $60,000 Number of UnitsTotal Costs $0 $15,000 $30,000 $45,000 $60,000 Number of UnitsTotal Costs- Curvilinear costs are not linear, and therefore, do not fit into any neat pattern. - When a cost behaves this way, it is necessary to approximate this type of cost as a mixed cost. Identify the graph that most closely represents the cost behavior pattern described below: 1 2 3 4 5 6 7 8 9 10 11 12a. Straight line depreciation of equipmentb. Monthly electric bill which consists of a flat monthly service charge plus $.002 per kilowatt hour usedc. Factory rent of $3000 per month, which will be forgiven by the City if the company employs 12 disadvantage youth. The x-axis is the number of disadvantaged youth employed by the company.d. Office rent of $1500 (x-axis is units sold)e. Tuition is $385 per semester credit hour up to 10 credit hours; tuition for 11 credit hours or more is $4,215 per semester.f. Salaries of delivery workers, where delivery person is needed for every 200 deliveriesscheduled in a given month.g. Cost of direct materials for picnic tables when the wood costs $45 for each tableh. Cost of water used in plant with that has a flat fee of $10 per month plus the following price schedule per gallon of water:Up to 10,000- gallons $.005 per gallon10,001 – 20,000 gallons $.006 per gallonMore than 20,000 gallons $.008 per galloni. Cell phone bill of $29.99 per month for 450 minutes plus $.25 per minute above 450j. Assembly line workers are paid $15 per hour6.2Cost EquationMathematical equation for a straight line to predict total costTotal cost = total variable cost + total fixed cost.Or Y + vx + f WhereY = total mixed costv = variable cost per unit of activityx = volume of activityf = total fixed cost over a given period of timeUsing Cost Behavior for Decision-MakingRelevant Range- The normal range of operating activity.- Band of volume where o Total fixed costs remain constanto Variable costs per unit remain constanto The cost equation remains valid- Managers must be sure that planned activity is within the relative rangeCommitted Fixed Costs- Fixed costs that cannot be changed in the short-term .- Examples: depreciation, signed leaseDiscretionary Fixed Costs- Fixed costs that can be changed in the short-term.- Examples: Advertising, training-Complete the following schedule related to a dry cleaning business for the three volumes shown:2,000 3,500 5,000garments garments garmentsTotal variable costs$2,625Total fixed costsTotal operating costsVariable cost per garmentFixed cost per garment2.00Average cost per garment 2. Why does the average cost per garment change? Suppose the owner erroneously uses the average cost per unit at FULL CAPACITY to predict total costsat a volume of 2,000 garments. Would he overestimate or underestimate total costs? By how much?Mailbox Magic produces decorative mailboxes. The company’s average cost per unit is$26.43 when it produces 1,000 mailboxes.1. What is the total cost of producing 1,000 mailboxes? 2. If $18,000 of the total cost is fixed, what is the variable cost of producing each mailbox?3. Write Mailbox Magic’s cost equation.4. If the plant manager uses average cost to predict total costs, determine is forecast for 1,200