Question & Answer

Cost function judgement and methodology

Suppose you have the responsibility of creating a cost function for the costs of an Internet service provider’s help line.

Required

(a)          What is the cost object? Identify where you might obtain information about past costs for the cost object.

(b)          Identify at least two potential cost drivers. Explain where you might obtain information about past volumes for each cost driver.

(c)           What other information would you like to obtain before estimating the cost function? How might you obtain that information?

(d)          Identify the techniques introduced in this chapter that you would be most likely to use in creating the cost function. Explain why.

          Cost function using account analysis and high-low method

The Elder Clinic, a not-for-profit entity, provides limited medical services to low-income elderly patients. The manager’s summary report for the past four months of operations is reproduced here.

The clinic receives an operating subsidy from the city, but unfortunately, the operating loss that has been incurred through June $(79 392) is larger than anticipated. Part of the problem is the salary increase that went into effect in June, which had been overlooked when the budget was submitted to the city last year. To compound the problem, the cold winter months traditionally bring with them an increase in cold-related health problems. Thus, the clinic is likely to experience an increase in patient visits during July.

The clinic’s managers are considering an increase in patient fees to reduce losses. However, they are reluctant to raise fees because the patients have low incomes. They will raise fees only if it is necessary.

Required

(a)          Use your judgement to classify costs as fixed, variable, or mixed. Explain how you classified each item.

(b)          Create a cost function for the Elder Clinic. Use the high-low method to estimate the function for any mixed costs.

(c)           Use the cost function to estimate July expenses based on a projection of 940 patient visits.

(d)          List reasons why management of the Elder Clinic cannot know with certainty what the expenses will be during July. List as many reasons as you can.

(e)           Describe the pros and cons of using your cost estimate from part (C) to decide whether to raise patient fees.

(f)           The managers need your July cost estimate to decide whether to raise patient fees. Use the information you learned from parts (a) and
(b)  to write a memo to the director of the Elder Clinic presenting your estimate of July costs. Provide the director with appropriate information for understanding your methodology and evaluating the reliability of your cost estimate.

            Scatter plots, cost function using regression, two potential cost drivers

Suppose we need to predict the cost of maintenance for Brush Valley High School for the upcoming school year. From the school district records we gather weekly data about costs and volumes for two potential cost drivers: labour hours used in the maintenance department and number of enrolled students.

Required

(a)          Identify and explain two potential cost drivers for total maintenance cost, in addition to number of students and maintenance hours worked.

(b)          Create a scatter plot, first for maintenance cost against hours worked and then maintenance cost against students.

(c)           Would you eliminate either cost driver based on the plots? Explain.

(d)          Perform regression analysis using each cost driver. Use your judgement to determine the most appropriate cost driver and write out the cost function for maintenance cost.

(e)           Can we know for certain that the cost driver chosen in part (d) is the best cost driver? Why?

          Use of prior year costs; quality of information

Software Solutions is a family-owned business that has been in operation for more than 15 years. The board of directors is comprised of mainly family members, plus a few professionals such as an accountant and lawyer. Regina is a staff accountant who has been working on the budget for the last several weeks. The chief financial officer (CFO) needs to present the budget at the next board meeting and wants a preliminary copy in two days. Regina is certain that she will not be able to finish the budget within two days. Several department heads have not turned in their preliminary figures, and two departments have budgeted large increases in fixed costs for replacing computer equipment. Regina knows she should have alerted the CFO about these budgeted increases, but she has not had time.

One of her co-workers knows that Regina is behind and suggests that she use last year’s budgets for those departments that have not provided information and also for the departments that increased their budgets by large amounts. The co-worker says that the budget can be straightened out later because the board does not pay attention to the details.

Required

(a)          Is this an ethical dilemma for Regina? Why?

(b)          Why might it be important for the board of directors to have as much updated information as possible about the budget?

(c)           What should Regina do, given that not enough time is available to gather high-quality information? Explain your thinking.

Cost function using multiple regression (appendix 2A)

Refer to the data and requirements of Problem 2.23.

Required

(a)          Perform multiple regression using all three cost drivers. Compare the adjusted R-squares and cost functions for the multiple regression with the results of simple regressions for each potential cost driver.

(b)          Which cost drivers do the best job of explaining manufacturing overhead costs? Explain.

(c)           Select only the cost drivers that do the best job of explaining manufacturing overhead costs. Perform multiple regression analysis for those cost drivers and write the cost function.

(d)          Explain why more than one cost driver is plausible for manufacturing overhead costs.

(a)     Multiple regression with all three potential cost drivers:

Comparison of simple and multiple regression results:

(b)     Labour hours does not appear to be a cost driver when using either simple regression or multiple regression; its coefficient is not significantly different from zero in either regression. Also, its coefficient is negative rather than positive in the multiple regression. Thus, labour hours can be eliminated as a potential cost driver.

Both machine hours and raw materials are positive and significantly different from zero when using simple regression and also when using multiple regression. The adjusted R-Square is far higher in the multiple regression (0.806) than in either of the simple regressions (0.352 and 0.226) for these two cost drivers. A combination of cost drivers does a much better job of explaining the variation in manufacturing overhead costs than either cost driver alone.

(c)     Multiple regression using machine hours and raw materials as cost drivers:

The cost function is: TC = $60 678 + $48.74×Machine hours + $82.93×Raw materials

(d)    Manufacturing can be a complex activity requiring a number of different tasks. Each task includes different activities. Costs for these activities are likely related to specific cost drivers. In this example, machine hours and raw materials explain different activity costs, such as machining work on units, and materials handling for the units. A better understanding of the manufacturing process improves the ability to determine the types and number of cost drivers that can be used in a more complete cost function.

Cost function using regression; scatter plots; three potential cost drivers

Laura Mills is the controller of Peer Jets International, a manufacturer of small corporate jets. She has undertaken a project to study the behaviour of overhead cost. She has assembled factory overhead data for the last 30 months from the company’s manufacturing facility. Laura has asked you to develop a model to predict the level of manufacturing overhead.

Required

(a)          Create a scatter plot of manufacturing overhead for each of the potential cost drivers.

(b)          Would you eliminate any of the potential cost drivers based on the scatter plots? Why?

(c)           Explain why you create a scatter plot of the data before you perform regression analysis.

(d)          To practice your regression analysis skills, perform a simple regression analysis of manufacturing overhead for each of the three potential cost drivers. Write the cost function from each regression.

(e)           Based on the simple regression results, which cost driver does the best job of explaining manufacturing overhead costs? Explain.

(f)           Do your regression results support your answer to part (b)? Explain.

Cost behaviour; scatter plot

Polar Bear Ski Wear is a shop that sells skiwear at a ski resort. Its cost accountant developed the following scatter plot for the cost of electricity for lights, heating, and cooling against retail sales revenue.

Required

(a)          In a business such as retail sales, what usually causes the cost of electricity to vary?

(b)          In what time of year would most skiwear be sold at a ski resort?

(c)           In the scatter plot, the cost of electricity appears to be related to volume of retail sales. If this shop specialised in selling swimwear, would the scatter plot look different? Explain what would change.

(d)          Identify and explain another cost that is similar in nature to the cost of electricity. When you plot the cost against a cost driver, a relationship becomes apparent. However, the cost varies with something other than the cost driver. (Think of other situations where this type of relationship might occur.)

          Cost categories; cost function

The Leyland Hospital Cafe has been reporting losses in past months. In July, for example, the loss was $5000.

The Cafe purchases prepared food directly from Hospital Food Services. This charge varies proportionately with the number and kind of meals served. Personnel who are paid by the Cafe serve the food, tend the cash register, waiting and clean tables, and wash dishes. The staffing levels in the cafe rarely change; the existing staff can usually handle daily fluctuations in volume. Administrative costs are primarily the salaries of the Cafe manager and her office staff. The hospital charges the Cafe a surcharge of 10 per cent of its revenue. Utility costs are the costs of cooling, heating, and lighting the Cafe during its normal operating hours.

The hospital’s management is considering shutting the Cafe down because it has been operating at a loss.

Required

(a)          List the fixed expenses of the Cafe.

(b)          List the variable expenses of the Cafe and the most likely cost driver for each expense.

(c)           Write out the cost function for running the Cafe.

(d)          Estimate the profit or loss for August if the revenues of the Cafe increase to $80 000.

(e)           Explain why the original data show a loss but part (d) shows a profit. Be specific.

          Cost driver; cost categories; appropriateness of regression; relevant information

Susan looked at her long-distance telephone bill with dismay. After leaving her job last year to become a self-employed consultant, her long-distance charges had grown considerably. She had not changed long-distance plans for years, partly because she hated taking the time to review the range of service providers and plans. However, the size of her long-distance bill made it clear that it was time to make a change. She had recently seen numerous advertisements by telephone companies offering much lower rates than she was currently paying, but she was sure that at least some of those plans offered low rates only for night and weekend calls.

Susan called her current long-distance service provider and asked how she could obtain a lower rate. She mentioned hearing that a competitor was currently offering long distance at 5c per minute. In responding to the service representative’s questions, Susan verified that most of her long-distance calls are weekday and out of state. She also agreed that her activity over the past two months—approximately 500 minutes of long distance per month—was her best estimate for future calling activity. Given this information, the service representative suggested that Susan buy the following long-distance service plan:

                               (i)                             Up to 500 minutes of long distance for a flat fee of $20 per month.

                             (ii)                             No refunds would be provided for usage less than 500 minutes per month.

                           (iii)                             Any minutes over 500 per month would be billed at 10c per minute.

                           (iv)                             No service change fee or cancellation fee would apply.

Required

(a)          What is the cost driver for Susan’s long-distance telephone costs, assuming that the cost object is her consulting business?

(b)          In the proposed service plan, which of the costs are fixed and which are variable? Explain.

(c)           Would regression analysis be an appropriate tool for Susan to use in deciding whether to buy the new service plan? Why?

(d)          Is the cost of Susan’s current long-distance service plan relevant to this decision? Why?

(e)           Explain why Susan cannot be certain whether the new service plan will reduce her long-distance costs.

(f)           List additional information that might be relevant to Susan in deciding whether to buy the new service plan.

(g)          Are Susan’s long-distance services most likely a discretionary cost? Explain.

(h)          Are Susan’s long-distance services most likely a direct or indirect cost, assuming that the cost object is an individual consulting job? Explain.

(i)            Describe the pros and cons of the new service plan.

Scatter plot; cost function using regression

The following scatter plot and simple regression results used revenue as a potential cost driver for research and development costs.

Required

(a)          Discuss whether the scatter plot suggests that revenue is a cost driver for research and development costs.

(b)          Using the regression results, write the cost function for research and development costs.

(c)           Based on the regression results, discuss whether it would be appropriate to use total revenue as a cost driver for research and development costs.

(d)          If you use the cost function from part (b) to estimate next month’s research and development costs, what assumptions are you making? Identify at least three assumptions and discuss their reasonableness.

Cost function using high-low and regression; quality of cost estimates

Following are sales and administrative cost data for Big Jack Burgers for four months:

 Administrative cost is a mixed cost, and sales is a potential cost driver.

Required

(a)          Using the high-low method, create a cost function for administrative costs.

(b)          In your own words, explain why the high-low method might not be a good method for estimating the cost function.

(c)           Create a scatter plot and add a trend line. After examining the plot, use your judgement to determine whether the cost is fixed, variable, or mixed.

(d)          Perform regression analysis to create a cost function for administrative costs.

(e)           Can we know for certain that the cost function from part (d) provides a good estimate for next month’s administrative costs? Why or why not?

(f)           Discuss whether sales are an economically plausible driver for administration costs for Big Jack Burgers.(a)     Total revenue (TR) instead of quantity (Q) in the cost function because sales is a potential cost driver. Under the high-low method, the cost function is calculated using the highest and lowest values of the cost driver. First, the variable cost is calculated:

($68 333 – $43 333)/($1 132 100 – $632 100)

= $25 000/$500 000

= 0.05  or 5% of sales

The fixed cost is determined by substituting the variable cost into one of the high-low data points:

$68 333 = F + 5%×$1 132 100

F = $68 333 – $56 605 = $11 728

Thus, the total cost function is:

TC = $11 728 + 5%×Sales

(b)        The high-low method uses the most extreme cost driver values, which could

be outliers, that is, not represent the cost most of the time. That means that the cost function might not represent the actual cost, on average. Therefore, this cost function might provide poor estimates of future costs.

(c)     Chart of data with trend line added by Excel; trend line extended to Y-axis (dashed line) using Word:

It appears that the cost is most likely mixed. There is a general downward slope     (variable cost) that appears to meet the intercept enough above zero to suggest a    fixed cost. The upward slope of the line indicates that there are variable costs.

(d)     Following is the regression output. A t-statistic greater than 2 is often interpreted as meaning that the coefficient is significantly different from zero. Notice that the t-statistic for the intercept coefficient is 2.172, but the p-value is greater than 10% at 0.162. Based on the p-value, there is a 16% probability that the intercept (fixed cost) is not different from zero. Because this regression has few observations, the p-value result for the t-statistic is atypical. Additional judgement is required to decide whether it is appropriate to include a fixed cost in the cost function.

          Analysis at the account level can be used to increase the understanding of this cost. If this cost pool includes items such as salaries and other fixed costs (insurance, etc.), the regression intercept can be used as an estimate of the fixed costs. Then, the cost function would be TC = $16 800 + 4.5% × sales. Alternatively, analysis at the account level might indicate that there are few fixed costs. In that case, fixed costs are likely to be zero and would be excluded from the cost function. Then, the cost function would be: TC = 4.5% × sales

(e)     Because of unforeseen changes in cost behaviour, a cost function may not provide a good estimate for the next month’s costs. The past costs used for estimation might not be representative, especially because so few observations were used in the estimation. Sales might not be the activity that drives administrative costs. There might be a change in business operations or in the economy that would cause future costs to be different than in the past. There might be a large discretionary component in administrative costs, causing fluctuations in cost that are unrelated to any cost driver.

(f)      The cons of the high-low method as an estimation technique were discussed in Part B above. If there are only two or three data points, however, the high-low method may be the best option available. This method can be used in cases where there is not enough data to perform regression, and it can be further improved by adopting more representative data points than the highest and lowest values of the cost driver. If there are more data points, regression analysis incorporates all of the observations into the analysis. Therefore, the results rely on more complete information and provide a better estimate, on average. Both methods assume that the cost function is linear and that all data points come from a single relevant range. If these assumptions do not hold, then both methods may be unsuitable for estimating future costs. In addition, both of these methods assume that the data points are representative of future costs. Unusual cost items are assumed to continue in the future, and possible changes in costs such as those described in Part E are ignored.

Cost function using regression; other potential cost drivers

The new cost analyst in your accounting department just received a computer-generated report that contains the results of a simple regression analysis. The analyst was estimating the costs of the marketing department using units sold as the cost driver. Summary results of the report are shown below.

Required

(a)          Write an equation for the cost function based on the regression analysis.

(b)          What does the adjusted R-square tell you?

(c)           What other cost drivers could potentially explain marketing costs? Explain.

          Fixed, variable, and mixed costs

Spencer and Church is a CPA entity engaged in local practice. Some selected items from its chart of accounts are listed here.

Required

For each account, indicate whether the account represents a fixed, variable, or mixed cost for the operations of the local practice office. If mixed, indicate whether it is predominantly fixed or variable. Explain your answers.

  (LO2)

[Note about problem complexity: These are difficult questions because students will need to first visualise the costs (with very little information) and then apply chapter concepts. The Step 2 questions (A, B, and F) are the ones requiring significant assumptions to generate an answer.]

          Cost function; opportunity cost; relevant costs

Yummy Yoghurt sells yogurt cones in a variety of natural flavours. Data for a recent month follow:

Required

(a)          Categorise each cost as fixed or variable.

(b)          Create a cost function.

Piecewise linear cost function; regression measurement error

The following is the description of a cost: Total fixed costs are $50 000 per month and the variable cost per unit is $10.00 when production is under 1000 units. The variable cost drops to $9.00 per unit after the first 1000 units are produced.

Required

(a)          Write the algebraic expression of the cost function and graph it.

(b)          Assume that the cost function just described is a reasonable representation of total costs. If the accountant performed regression analysis on weekly observations of this cost and did not realise that there were two relevant ranges, what problems would arise in the cost function that was produced? In other words, how would the cost function be mismeasured?

          Cost function and assumptions

Express Lunch is a small food van that sells a variety of sandwiches and beverages. Total fixed costs are $20 000 per month. Last month total variable costs were $8000 when total sales were $32 000.

Required

(a)          Write out the algebraic expression for the cost function.

(b)          What assumptions do we make when we develop this cost function?

          Linear, stepwise linear, and piecewise linear cost functions

(a)          Total fixed costs are $10 000 per week and the variable cost per unit is $8. Write the algebraic expression for the cost function and graph it. What are the assumptions of the cost function?

(b)          Total fixed costs are $25 000 per week up to 2000 units a week and then jump up to $35 000 per week. The variable cost per unit is $8. Write the algebraic expression for the cost function and graph it.

(c)           The average cost to produce 10,000 units is $45 and the average cost to produce 12 000 units is $44. Estimate the average cost to produce 15 000 units.

(d)          The total cost function for Hot Dog Days, a hot dog cart business in Centennial Park, is TC = $5000 + 45% ´ total revenues. Estimate the total cost for a month when total revenues are $10 000.

          Fixed, variable, and mixed costs

Bridges and Roads is an entity engaged in road construction. Some selected items from its chart of accounts are listed below.

Required

For each account, indicate whether the account represents a fixed, variable, or mixed cost for the operation of road construction activity. If mixed, indicate whether it is predominantly fixed or variable. Explain your answers.

  (LO2)

[Note about problem complexity: These are difficult questions because students will need to first visualise the costs (with very little information) and then apply chapter concepts. The Step 2 questions (A, B, and F) are the ones requiring significant assumptions to generate an answer.]

The trend line developed using regression analysis provides a more accurate representation of a mixed cost function than the two-point or high-low methods. Explain why.

Why might some have trouble classifying costs as fixed or variable?

List two examples of non-linear cost functions and describe a method of developing a cost function for each one.

          Explain the analysis at the account level approach to developing a cost function.

Explain how information from a scatter plot helps in categorising a cost as fixed, variable, or mixed.

You are about to start a coffee shop business. What do you understand by ‘cost behaviour’? Explain how your accountants could help you in building an understanding of cost behaviour. Identify the likely key costs and classify each as fixed or variable.         

          At two levels of activity within the relevant range, average costs are $192 and $188, respectively. Assuming the cost function is linear, what can be said about the existence of fixed and variable costs?