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Cost Accounting Chapter 10 Chapter 10 Determining How Costs Behave
• Cost Function – mathematical description of how a cost changes with changes in the level of activity relating to that cost • Estimating cost function two assumptions
– Variations in the level of a single activity explained the variations in the total costs of a costs of a cost object – Cost behavior is approximated by a linear cost function within the relevant range Chapter 10 Chapter 10 Determining How Costs Behave
Linear equation cost: Where: y = estimated total cost a = fixed costs b = variable costs per unit X = level of activity within the relevant range y = a + bX Chapter 10 Chapter 10 Determining How Costs Behave
Atlas Corp. developed the following flexible budget for annual indirect manufacturing labor cost: Total cost = $4,800 + $0.50 (machine hours) The operating budget for the current month is based on 20,000 machine hours. Indirect manufacturing labor cost included in the monthly flexible budget is? Chapter 10 Chapter 10 Determining How Costs Behave
Atlas Corp. developed the following flexible budget for annual indirect manufacturing labor cost: Total cost = $4,800 + $0.50 (machine hours) The operating budget for the current month is based on 20,000 machine hours. Indirect manufacturing labor cost included in the monthly flexible budget is? $4,800 / 12 = $400 per month Total cost = $400 + ($0.50 * 20,000) Total cost = $10,400 Chapter 10 Chapter 10 Determining How Costs Behave
• Cost estimation – analyze past cost • • • • •
behavior as a means for predicting future costs and cost behavior Cause and effect – Industrial engineering method – Conference method – Account analysis method – Quantitative analysis method Chapter 10 Chapter 10 Determining How Costs Behave
• Quantitative analysis method –
– Six steps 1. Choose the dependent variable 2. Identify the independent variable 3. Collect data on the dependent and independent 4. 5. 6. variables Plot the data Estimate the cost function Evaluate the cost driver of the estimated cost function Chapter 10 Chapter 10 Determining How Costs Behave
• The two most common forms of quantitative analysis: – Highlow method (simplest) – Regression analysis (statistical method) measures the average amount of change in the dependent variable associated with a unit of change in one or more independent variables • Simple regression • Multiple regression Chapter 10 Chapter 10 Determining How Costs Behave
Franklin, Inc. is preparing a flexible budget for the coming year and requires the cost of steam used in its plant to be divided into its fixed and variable elements. The following data on the cost of steam used and direct manufacturing labor hours (DMLH) used are available for the last six months: Month Cost of Steam DMLH July $ 15,850 3,000 August 13,400 2,050 September 16,370 2,900 October 19,800 3,650 November 17,600 2,670 December 18,500 2,650 The estimated variable cost of steam per DMLH is: High Low Method Chapter 10 Chapter 10 Determining How Costs Behave
Month July August September October November December Cost of Steam $ 15,850 13,400 16,370 19,800 17,600 18,500 DMLH 3,000 2,050 2,900 3,650 2,670 2,650 The estimated variable cost of steam per DMLH is:
October August 19,800 13,400 6,400 6400 / 1600 = $4.00 3,650 2,050 1,600 Chapter 10 Chapter 10 Determining How Costs Behave
Month July August September October November December Cost of Steam $ 15,850 13,400 16,370 19,800 17,600 18,500 DMLH 3,000 2,050 2,900 3,650 2,670 2,650 The estimated amount of the constant (fixed cost) is: Chapter 10 Chapter 10 Determining How Costs Behave
Month July August September October November December Cost of Steam $ 15,850 13,400 16,370 19,800 17,600 18,500 DMLH 3,000 2,050 2,900 3,650 2,670 2,650 The estimated amount of the constant (fixed cost) is: 6400 / 1600 = $4.00 @ highest level: $19,800 = a + ($4 * 3,650)………..$5,200 @ lowest level: $13,400 = a + ($4 * 2,050)………..$5,200 Chapter 10 Chapter 10 Determining How Costs Behave
• Four criteria used to evaluate and choose cost drivers
– Economic plausibility – Goodness of fit – Significance of independent variable – Specification analysis Chapter 10 Chapter 10 Determining How Costs Behave
Regression Analysis:
Top Flight Airlines provides private jet service to business executives in the Midwest region of the United States. The company’s managers realize that reliable cost forecasts are critical to the company’s future profitability. The company provided the following data about the number of passengers (i.e. seats occupied on a flight) and total costs for the past fiscal year.
January February March April May June July August September October November December Passengers 891.00 1,192.00 1,456.00 1,876.00 1,345.00 1,567.00 1,632.00 1,851.00 1,398.00 1,478.00 1,209.00 1,908.00 17803 Costs 51,346.59 64,651.76 72,367.79 81,761.01 70,981.18 76,652.76 77,895.39 80,098.55 72,557.34 73,447.81 68,992.96 88,993.08 879746.22 Chapter 10 Chapter 10 Determining How Costs Behave
Create a scatterplot: The scatterplot shows a linear relationship between passengers and total costs
Top Flight Airlines
100,000.00 90,000.00 80,000.00 70,000.00 Costs 60,000.00 50,000.00 40,000.00 30,000.00 20,000.00 10,000.00 0 2 4 6 8 10 12 14 Passengers Costs Passengers Summary Output for Regression Analysis
SUMMARY OUTPUT Regression Statistics Multiple R 0.959453854 R Square 0.920551699 Adjusted R Square 0.912606868 Standard Error 2788.267455 Observations 12 ANOVA df Regression Residual Total 1 10 11 SS MS 900808398 9.01E+08 77744354.02 7774435 978552752 Chapter 10 Chapter 10 Determining How Costs Behave F Significance F 115.868 8.0616E07 Intercept Passengers Coefficients Standard Error t Stat Pvalue 29586.17546 4141.146247 7.144441 3.13E05 29.47324128 2.738079892 10.7642 8.06E07 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 20359.12502 38813.2259 20359.12502 38813.2259 23.37241804 35.57406452 23.37241804 35.57406452 Chapter 10 Chapter 10 Determining How Costs Behave
Cost Equation: y = $29,586.17 + $29.47X
To estimate expected costs at 1,400 passengers: y = $29,586.17 + $29.47(1,400) y = $70,844.17 To estimate expected costs at 2,000 passengers: y = $29,586.17 + $29.47(2,000) y = $88,826.17 Chapter 10 Chapter 10 Determining How Costs Behave
Goodness of fit: r2 or the coefficient of determination, the percentage of variation in the dependent variable (the cost) explained by the independent variable (cost driver) (these variables move together) r2 = .920554 Significance of independent variable(s): Is the slope of the regression line, the estimated b statistically significant? The answer depends on the tvalue of the slope coefficient – which is equal to b divided by the standard error of the estimated coefficient $29,586.17 / 2788.267 = 10.610952 Chapter 10 Chapter 10 Determining How Costs Behave
• Nonlinear cost functions:
– Economies or diseconomies of scale can result in variable cost per unit changing as activity levels change (i.e. discounts with material purchases and fixed costs increase as activity level increases such as additional space) – Workers experience a learning curve as they become more efficient • Cumulative average time learning model: based on reduction •
in total or cumulative production time as quantity doubles Incremental unittime learning module: based on a reduction in perunit or incremental production as quantity doubles Chapter 10 Chapter 10 Determining How Costs Behave
GM Manufacturing found that production of a certain product is subject to an 80% learning curve. The product is produced in lots of 100 units and 8 labor hours are required for the first lot. Assuming GM uses the cumulative average time learning model, total time required to produce 400 units is: Chapter 10 Chapter 10 Determining How Costs Behave
GM Manufacturing found that production of a certain product is subject to an 80% learning curve. The product is produced in lots of 100 units and 8 labor hours are required for the first lot. Assuming GM uses the cumulative average time learning model, total time required to produce 400 units is: Cumulative Cumulative Average # units Hours per unit Total Hours 100 8.0 / 100 = 0.0800 200 0.0800 * 80% = 0.0640 400 0.0640 * 80% = 0.0512 Cumulative 8.00 12.80 20.48 Chapter 10 Chapter 10 Determining How Costs Behave
• Problems encountered when estimating costs
– Database relied upon has reliable data points – Data should span as wide a range of activity as possible – Time period represents an accurate frame for measuring cost activity driver Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Five step process to make decisions
1. 2. 3. 4. 5. Obtain historical cost and other information Make predictions about future costs Choose an alternative Implement the decision Evaluate performance Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
• Relevant costs (revenues) – meet two criteria 1) they must be expected future amounts and 2) they must differ between the alternatives being considered • Irrelevant costs (revenues) – those costs and revenues that have already been incurred or realized and/or that don’t differ among alternative courses of action Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
• Quantitative factors – represented in numerical terms (financial) • Qualitative factors – difficult to measure in numerical terms (employee moral, customer goodwill) • Both need to be considered in the decision making process Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Special order: Sandy Company has an annual plant capacity of 2,800,000 units of output. Its regular operations for the year are budgeted as follows: Revenues 2,000,000 units @ $38 $76,000,000 Manufacturing costs: Variable $25 per unit Fixed $18,000,000 Marketing and Admin costs Variable (commission) $6 per unit Fixed $2,000,000 Sandy has been contacted about supplying a one time only special order of 60,000 units at a selling price of $32, subject to half the usual sales commission per unit. Assuming this special order will have no effect on regular sales, should Sandy accept the special order? Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Incremental revenues: 60,000 * $32 Incremental costs (all variable): Manufacturing 60,000 * $25 Sales commission 60,000 * $3 Incremental operating income: $1,920,000 $1,500,000 180,000 $1,680,000 $ 240,000 Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Make or Buy: Captain Company needs 20,000 units of Part K28 to use in its production cycle. The following cost information is provided for part K28: Direct material $ 4 Direct Mfg. Labor 16 Variable OH allocated 8 Fixed OH allocated 10 Total cost $38 Cost to buy the part from Garden Company: $36 If Captain buys the part instead of making it, the released facilities will be idle. Sixty percent of the fixed overhead will continue. Should Captain make or buy the part? Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Relevant items: Make Outside purchase 20,000 * $36 DM, 20,000 * $4 $ 80,000 DML, 20,000 * $16 320,000 Variable OH 20,000 * $8 160,000 Fixed OH 20,000 * $10(1.60) 80,000 Total relevant costs: $640,000 Difference in favor of making $80,000 Buy $720,000 $720,000 Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Discontinue a division: Galaxy Co. plans to discontinue a division with a $48,000 contribution margin, and allocated fixed costs of $96,000, of which $42,000 cannot be eliminated. What is the effect on Galaxy’s operating income of discontinuing this division? Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Discontinue a division: Galaxy Co. plans to discontinue a division with a $48,000 contribution margin, and allocated fixed costs of $96,000, of which $42,000 cannot be eliminated. What is the effect on Galaxy’s operating income of discontinuing this division? Before $48,000 96,000 $(48,000) After $ 42,000 $(42,000) Contribution to fixed costs 0 Deduct allocated fixed costs Operating income of division Difference in favor of discontinuing the division $6,000 Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Merrill Company has an opportunity to acquire a new machine to replace one of its old machines. The new machine costs $90,000 and has an estimated useful life of 5 years, with a zero terminal disposal value. Variable operating costs are $100,000 per year. The old machine has a book value of $50,000 and a remaining useful life of five years. Its disposal value now is $5,000 but would be zero after 5 years. Variable operating costs are $125,000 per year. Considering the five years in total, but ignoring the time value of money and income taxes, what is the difference in operating income by replacing the old machine? Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Relevant items: Variable operating costs Cost of new machine Disposal of old machine Total relevant costs: Keep $625,000 Replace $500,000 90,000 (5,000) $585,000 $625,000 Difference in favor of replacing old machine $40,000 Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Opportunity Cost – The contribution to operating income that is forgone (rejected) by not using a limited resource in its nextbest alternative use. For example, suppose a company uses some of its production capacity to make a product that increases operating income by $20,000 rather than renting out the space for $16,000, the next best alternative. Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Product Mix – Engle Company has 1,440 machinehours of plant capacity available during a particular period for manufacturing two products with the following characteristics: A B Selling Price $42 $75 Variable cost per unit $20 $25 Units mfg per machine hour 8 3 Demand in units 13,500 6,000 Compute the number of available machine hours that should be used to manufacture each product. Chapter 11 Decision Making Chapter 11 Decision Making and Relevant Information
Engle Company has 1,440 machinehours of plant capacity available during a particular period for manufacturing two products with the following characteristics: A B Selling Price $42 $75 Variable cost per unit ($20) ($25) Contribution margin per unit $22 $50 * Units mfg per machine hour 8 3 = Contribution margin per hour of plant capacity $176 $150 All 1,440 machine hours should be used to manufacture product A because A has the higher contribution margin per unit of limited resource (machine hours) and producing 11,520 units of A (1,440 * 8) does not exceed the demand for A of 13,500 units. Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
Capital budgeting – making longrun planning decisions for investments in projects. Six stage process:
1. 2. 3. 4. 5. 6. Identification stage Search stage Information acquisition stage Selection stage Financing stage Implementation and control stage Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
Four methods used in the selection stage: net present value (discounted cash flow method) internal rate of return (discounted cash flow method) payback accrual accounting rate of return Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
The following information is provided on a capital budgeting project: Net initial investment $100,000 Estimated useful life 4 years Est. before tax annual cash flow from operations $ 33,000 Est. terminal disposal value $ 7,000 Required rate of return 12% Income tax rate 30% This firm uses straightline depreciation and ignores the terminal disposal value in computing depreciation for tax purposes. Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
To compute NPV, a key amount needed is annual aftertax cash flow from operations: Annual after tax cash flow (excluding depreciation) $33,000 * (10.30) $23,100 Income tax cash savings from annual depreciation deduction ($100,000 / 4) *.30 7,500 Annual after tax cash flow from operations: $30,600 Net initial investment: Annual after tax cash flow from operations $30,600 * 3.037 (table 4) After tax cash flow from terminal disposal value: $7,000 $0 book value = $7000 $7,000 * (10.30) = $4,900 * 0.636 (table 2) NPV ($100,000) 92,932 3,116 ($3,952) Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
To compute Internal Rate of Return (IRR): Given that NPV (from previous slide) is ($3,952), when the discount rate is 12%, IRR is lower than 12%. Using trial and error: using 10% instead of 12%!! at 10% NPV = $100,000 + (30,600 * 3.170 (table 4)) + ($4,900 * 0.683) = ($100,000) + $97,002 + $3,347 = $349 Slightly above 10% Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
Payback: Initial investment / after tax cash inflows $100,000 / $30,600 = 3.3 years Chapter 21 – Capital Budgeting Chapter 21 – Capital Budgeting and Cost Analysis
Accrual Accounting Rate of Return (AARR): (Est. before tax cash inflow – depreciation)(1 tax rate) initial investment ($33,000 $25,000)(.70) $100,000 $8,000 * .70 $100,000 AARR: 5.6% ...
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 Summer '08
 MONTESARCHIO
 Regression Analysis, Decision Making, Atlas Corp.

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