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## Cost Accounting

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**Cost Accounting**Dr. Baldwin University of Arkansas – Fort Smith Fall 2010**Chapter 10**Determining How Costs Behave**Why understand cost behavior?**• Managers need to understand cost behavior in order to make decisions about strategy and about operations. • For example • Product decisions • Apple iPod, iPhone, iPad • Amazon Kindle • Other decisions • Fort Smith administration enrollment**What do we already know about the nature of costs?**Variable Cost Mixed Cost Cost Fixed Cost Volume of Activity**Assumptions**• Costs are linear • or approximated by linear functions • Each cost has a single cost driver • Are these always true? Not always! • We generally assume they are true within the relevant range. • Exercise 18.**Relevant Range**• The range of the activity in which total cost and the level of activity are related.**How to understand cost behavior?**A cost function is • a mathematical description of how a cost changes with changes in the volume of its cost driver activity. Variable Cost Mixed Cost Cost Fixed Cost Volume of Activity**Linear Cost Functions example**• Let’s assume you are a spin class instructor and you have to provide your own music for class. You spend a lot of time and money downloading songs to use in class. uTunes is providing three different payment options. • Let’s look at the options and identify the cost function for each.**Linear Cost Functions example**• Option A • Pay $5 per song downloaded • Option B • Pay $100 per month for unlimited downloads • Option C • Pay $50 per month plus $0.50 per download • Create a cost function for each option using the generic linear cost function formula.**Create a Linear Cost Function**Formula: Y = a + bX • Where: • Y = total costs • a = fixed costs • b = variable cost per unit of cost driver • X = cost driver • Option A: Y = $0 + $5X • Option B: Y = $100 + $0X • Option C: Y = $50 + $0.50X**How to understand cost behavior?**• Option A: Y = $0 + $5X • Option B: Y = $100 + $0X • Option C: Y = $50 + $0.50X Variable Cost A C Mixed Cost B Cost Fixed Cost Volume of Activity (downloads)**Calculate Total Cost of Each Option**Which option is least expensive? • Assuming 40 downloads a month, what is the total cost per month for each option? • Option A: Y = $0 + $5 * 40 = $200 • Option B: Y = $100 + $0*40 = $100 • Option C: Y = $50 + $0.50*40 = $70 • What happens if you download more or less than 40? 100? 200?**How to understand cost behavior?**• Option A: Y = $0 + $5X • Option B: Y = $100 + $0X • Option C: Y = $50 + $0.50X Variable Cost A C Mixed Cost B Cost 20 Fixed Cost 100 10 Volume of Activity (downloads)**How to understand cost behavior?**Cost Estimation Methods • Many methods to estimate costs • Potential problems in cost estimation • Availability of historical data • Accuracy of data • The estimates are only as good as the data on which they are based.**How to understand cost behavior?**Cost Estimation Methods • Industrial Engineering • Time and motion studies • Conference • Consensus of estimates • Account Analysis • Quantitative Analysis • High-Low Method • Regression **Account Analysis Method**Use knowledge of operations to • Classify cost accounts according to their relationship with the cost driver activity: • variable, fixed, or mixed • Estimate the cost/driver relationship • Example: Lorenzo’s Car Wash (Exercise 20)**Lorenzo’s Car Wash example**• Incoming cars are put on a conveyor belt. • Cars are washed as they are carried by the conveyor belt from start to finish. • The cars are then dried manually. • Workers clean and vacuum car inside. • They are managed by a single supervisor. • Lorenzo serviced 80,000 cars in 2009, for which he reports the following costs:**Lorenzo’s Car Wash example**Use knowledge of operations to • Classify cost accounts according to their relationship with the cost driver activity: • variable, fixed, or mixed • Estimate the costs if 90,000 cars are washed in 2010.**Lorenzo’s Car Wash example**• Classify: variable, fixed, or mixed Variable $412,000 Fixed $110,000**Lorenzo’s Car Wash example**• Variable Costs for 2009 $ 412,000 80,000 cars = $5.15 per car • Fixed Costs $110,000 • Total average cost per car = (412,000 + 110,000) 80,000 cars = $6.53 per car**Lorenzo’s Car Wash example**Estimate Lorenzo’s 2010 costs (90,000 washes) • Variable Costs 90,000 cars * $5.15 per car = $463,500 • Fixed Costs $110,000 • Total costs = $463,500 + $110,000 = $573,500**How to understand cost behavior?**Cost Estimation Methods • Industrial Engineering • Time and motion studies • Conference • Consensus of estimates • Account Analysis • Quantitative Analysis • High-Low Method • Regression **Quantitative Analysis**• Uses formal mathematical methods to fit cost functions to past data observations. • Remember, a cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity. • Total costs = FC + VCUNIT * activity • Lorenzo’s cost function: • $110,000 + $5.15 per car * number of cars**Estimate a Linear Cost Function**• Formula: Y = a + bX • Where: • Y = total costs • a = fixed costs • b = variable cost per unit of cost driver • X = cost driver • Two methods • High-Low Method • Regression Analysis**High-Low Method**• Uses two points (the high and the low) to find the equation of the cost line y = a + bx • slope = b = change in y/change in x • intercept = a = y - bx • Strengths • Simple to compute • Easy to understand • Weaknesses • Only two points used - what if they are not representative of normal relationship? • Exercise 16.**Regression Analysis**• Uses all the observations to find the equation of the cost line y = a + bx • slope = change in y/change in x • intercept = a = y - bx • Regression minimizes the sum of the squared differences between the observed data and the predicted line • Strengths • More accurate than the high-low method**Statistical Output**Larger is better Provides • estimates of the two parameters in the cost function: Y = a + bX • a = intercept = fixed costs • b = slope = variable costs per unit • Measures of goodness of fit • Co-efficient of determination = r2 • Measures the % variation in Y explained by X • T-statistic = b/standard error of estimated co-efficient • t tells us if b is different from zero**Statistical Output**What do we do with it? • Check goodness of fit measures • Want r2 .3 (or perhaps even higher) • Want t 2 • Compare cost drivers to see which is best • Estimate Y (total costs) for future period.**Non-Linear Functions**Costs are not always linear! For example: • Quantity discounts • Costs decrease as volume increases • Step cost functions • Costs increase by discrete amounts over narrow ranges • Step fixed-cost functions • Cost remain the same over wider intervals • Learning curves **Learning Curves**A learning curve is a function that measures how labor-hours per unit decline as unites of production increase because workers are learning and becoming better at their jobs. Two types: • Cumulative average-time learning model • Average time per unit declines at a constant rate • Incremental unit-time learning model • Time to produce last unit decreases at a constant rate Learning curves are given as a percentage**Learning Curves**• Formula: Y = pXq • Where: • Y = cumulative average time or incremental time • p = labor hours on first unit • X = cumulative # of units • q reflects the learning rate (log of learning curve)**Learning Curves**• Learning is faster in which model? • (cumulative model) • Which of these models will predict higher costs? • (incremental model) • Which of these models is better? • It depends! Case by case basis decision.**Learning Curves**• What are implications for product costing? • Charge more initially and decrease price as time to produce declines? • Will the customers put up with that? • Price down the learning curve - set price based on what we expect costs to be in the future • Why might companies do this?**Summary 1**• Managers have to understand cost behavior in order to make decisions about strategy and about operations. • Most of the time we assume costs are linear and each has single cost driver. • A cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity. • Formula: Y = a + bX • Costs are not always linear (e.g. learning curves).**Summary 2**Cost Estimation Methodshelp us understand cost behavior. • Industrial Engineering (Time & motion studies) • Conference (consenses) • Account Analysis • Quantitative Analysis • High-Low Method • Regression**Summary 3**• Many methods to estimate costs • Potential problems in cost estimation • Availability of historical data • Accuracy of data • The estimates are only as good as the data on which they are based. • Don’t forgetto read the appendix which discusses regression.