Chapter 10: Chapter 10

The controller of the Javier Company is preparing the budget for 2018 and needs to estimate a cost function for delivery costs. Information regarding delivery costs incurred in the prior two months are: $$\begin{array}{lcc}\text { Month } & \text { Miles Driven } & \text { Delivery costs } \\\\\hline \text { August } & 12,000 & \$ 10,000 \\\\\text { September } & 17,000 & \$ 13,000\end{array}$$ 1\. Estimate the cost function for delivery. 2\. Can the constant in the cost function be used as an estimate of fixed delivery cost per month? Explain.

\((\mathrm{CPA}, \text { adapted })\). The vertical axes of the graphs below represent total cost, and the horizontal axes represent units produced during a calendar year. In each case, the zero point of dollars and production is at the intersection of the two axes. Select the graph that matches the numbered manufacturing cost data (requirements 1-9). Indicate by letter which graph best fits the situation or item described. The graphs may be used more than once. 1\. Annual depreciation of equipment, where the amount of depreciation charged is computed by the machine-hours method. 2\. Electricity bill-a flat fixed charge, plus a variable cost after a certain number of kilowatt-hours are used, in which the quantity of kilowatt-hours used varies proportionately with quantity of units produced. 3\. City water bill, which is computed as follows: The gallons of water used vary proportionately with the quantity of production outputt 4\. cost of direct materials, where direct material cost per unit produced decreases with each pound of material used (for example, if 1 pound is used, the costis S10; if 2 pounds are used, the costis \$19.98 3 pounds are used, the cost is \(\$ 29.94\), with a minimum cost per unit of \(\$ 9.20\) 5\. Annual depreciation of equipment, where the amount is computed by the straight-line method. When the depreciation schedule was prepared, it was anticipated that the obsolescence factor would be greater than the wear-and- tear factor. 6\. Rent on a manufacturing plant donated by the city, where the agreement calls for a fixed-fee payment unless 200,000 labor-hours are worked, in which case no rent tis paid. 7\. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours o o less (that is, 0 to 1,000 hours requires one person, 1,001 to 2,000 hours requires two people, and so on 8\. cost of direct materials used (assume no quantity discounts).) 9\. Rent on a manufacturing plant donated by the county, where the agreement calls for rent of \(\$ 100,000\) to be reduced by s1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of \(\$ 20,000\) must be paid.

Stein Corporation wants to find an equation to estimate some of their monthly operating costs for the operating budget for 2018 . The following cost and other data were gathered for 2017 : $$\begin{array}{lcccccc} & \text { Maintenance } & \text { Machine } & \text { Health } & \text { Number of } & \text { Shipping } & \text { Units } \\\\\text { Month } & \text { costs } & \text { Hours } & \text { Insurance } & \text { Employees } & \text { costs } & \text { Shipped } \\ \hline \text { January } & \$ 4,500 & 165 & \$ 8,600 & 68 & \$ 25,776 & 7,160 \\\ \text { February } & \$ 4,452 & 120 & \$ 8,600 & 75 & \$ 29,664 & 8,240 \\ \text { March } & \$ 4,600 & 230 & \$ 8,600 & 92 & \$ 28,674 & 7,965 \\ \text { April } & \$ 4,850 & 318 & \$ 8,600 & 105 & \$ 23,058 & 6,405 \\ \text { May } & \$ 5,166 & 460 & \$ 8,600 & 89 & \$ 21,294 & 5,915 \\ \text { June } & \$ 4,760 & 280 & \$ 8,600 & 87 & \$ 33,282 & 9,245 \\ \text { July } & \$ 4,910 & 340 & \$ 8,600 & 93 & \$ 31,428 & 8,730 \\ \text { August } & \$ 4,960 & 360 & \$ 8,600 & 88 & \$ 30,294 & 8,415 \\ \text { September } & \$ 5,070 & 420 & \$ 8,600 & 95 & \$ 25,110 & 6,975 \\ \text { October } & \$ 5,250 & 495 & \$ 8,600 & 102 & \$ 25,866 & 7,185 \\ \text { November } & \$ 5,271 & 510 & \$ 8,600 & 97 & \$ 20,124 & 5,590 \\ \text { December } & \$ 4,760 & 275 & \$ 8,600 & 94 & \$ 34,596 & 9,610\end{array}$$ 1\. Which of the preceding costs is variable? Fixed? Mixed? Explain. 2\. Using the high-low method, determine the cost function for each cost. 3\. Combine the preceding information to get a monthly operating cost function for the Stein Corporation. 4\. Next month, Stein expects to use 400 machine hours, have 80 employees, and ship 9,000 units. Estimate the total operating cost for the month.

Gower, Inc., a manufacturer of plastic products, reports the following manufacturing costs and account analysis classification for the year ended December 31,2017. $$\begin{array}{lcr}\text { Account } & \text { Classification } & \text { Amount } \\ \hline \text { Direct materials } & \text { All variable } & \$ 300,000 \\ \text { Direct manufacturing labor } & \text { All variable } & 225,000 \\ \text { Power } & \text { All variable } & 37,500 \\ \text { Supervision labor } & 20 \% \text { variable } & 56,250 \\ \text { Materials-handling labor } & 50 \% \text { variable } & 60,000 \\ \text { Maintenance labor } & 40 \% \text { variable } & 75,000 \\ \text { Depreciation } & 0 \% \text { variable } & 95,000 \\ \text { Rent, property taxes, and administration } & 0 \% \text { variable } & 100,000\end{array}$$ Gower, Inc., produced 75,000 units of product in 2017 . Gower's management is estimating costs for 2018 on the basis of 2017 numbers. The following additional information is available for 2018. a. Direct materials prices in 2018 are expected to increase by \(5 \%\) compared with 2017. b. Under the terms of the labor contract, direct manufacturing labor wage rates are expected to increase by \(10 \%\) in 2018 compared with 2017. c. Power rates and wage rates for supervision, materials handling, and maintenance are not expected to change from 2017 to 2018. d. Depreciation costs are expected to increase by \(5 \%\), and rent, property taxes, and administration costs are expected to increase by \(7 \%\). e. Gower expects to manufacture and sell 80,000 units in 2018 . 1\. Prepare a schedule of variable, fixed, and total manufacturing costs for each account category in 2018 . Estimate total manufacturing costs for 2018. 2\. Calculate Gower's total manufacturing cost per unit in 2017 , and estimate total manufacturing cost per unit in 2018. 3\. How can you obtain better estimates of fixed and variable costs? Why would these better estimates be useful to Gower?

Reisen Travel offers helicopter service from sub-urban towns to John F. Kennedy International Airport in New York City. Each of its 10 helicopters makes between 1,000 and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000 round-trips in the year incurs an average operating cost of \(\$ 350\) per round-trip, and one that has made 2,000 round- trips in the year incurs an average operating cost of \(\$ 300\) per round-trip. 1\. Using the high-low method, estimate the linear relationship \(y=a+b X\), where \(y\) is the total annual operating cost of a helicopter and \(X\) is the number of round-trips it makes to JFK airport during the year. 2\. Give examples of costs that would be included in a and in \(b\). 3\. If Reisen Travel expects each helicopter to make, on average, 1,200 round- trips in the coming year, what should its estimated operating budget for the helicopter fleet be?

Lacy Dallas is examining customer-service costs in the southern region of Camilla Products. Camilla Products has more than 200 separate electrical products that are sold with a 6 -month guarantee of full repair or replacement with a new product. When a product is returned by a customer, a service report is prepared. This service report includes details of the problem and the time and cost of resolving the problem. Weekly data for the most recent 8-week period are as follows: $$\begin{array}{ccc}\text { Week } & \text { Customer-Service Department Costs } & \text { Number of Service Reports } \\\\\hline 1 & \$ 13,300 & 185 \\\2 & 20,500 & 285 \\\3 & 12,000 & 120 \\\4 & 18,500 & 360 \\\5 & 14,900 & 275 \\\6 & 21,600 & 440 \\\7 & 16,500 & 350 \\\8 & 21,300 & 315\end{array}$$ 1\. Plot the relationship between customer-service costs and number of service reports. Is the relationship economically plausible? 2\. Use the high-low method to compute the cost function relating customer- service costs to the number of service reports. 3\. What variables, in addition to number of service reports, might be cost drivers of weekly customer-service costs of Camilla Products?

Dr. Young, of Young and Associates, LLP, is examining how overhead costs behave as a function of monthly physician contact hours billed to patients. The historical data are as follows: $$\begin{array}{cc}\text { Total 0verhead costs } & \text { Physician Contact Hours Billed to Patients } \\ \hline \$ 90,000 & 150 \\\105,000 & 200 \\\111,000 & 250 \\\125,000 & 300 \\\137,000 & 350 \\\150,000 & 400\end{array}$$ 1\. Compute the linear cost function, relating total overhead costs to physician contact hours, using the representative observations of 200 and 300 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of Young and Associates? Why? 2\. What would be the predicted total overhead costs for (a) 150 hours and (b) 400 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 150 and 400 hours. 3\. Dr. Young had a chance to do some school physicals that would have boosted physician contact hours billed to patients from 200 to 250 hours. Suppose Dr. Young, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of \(\$ 9,000\), before deducting the predicted increase in total overhead cost, \(\$ 10,000\). What is the total contribution margin actually forgone?

What is the difference between a linear and a nonlinear cost function? Give an example of each type of cost function.

Relling Corporation manufactures a drink bottle, model CL24. During 2017 , Relling produced 210,000 bottles at a total cost of \(\$ 808,500\). Kraff Corporation has offered to supply as many bottles as Relling wants at a cost of \(\$ 3.75\) per bottle. Relling anticipates needing 225,000 bottles each year for the next few years. 1\. a. What is the average cost of manufacturing a drink bottle in \(2017 ?\) How does it compare to Kraff's offer? b. Can Relling use the answer in requirement 1a to determine the cost of manufacturing 225,000 drink bottles? Explain. 2\. Relling's cost analyst uses annual data from past years to estimate the following regression equation with total manufacturing costs of the drink bottle as the dependent variable and drink bottles produced as the independent variable: $$y=\$ 445,000+\$ 1.75 x$$ During the years used to estimate the regression equation, the production of bottles varied from 200,000 to \(235,000 .\) Using this equation, estimate how much it would cost Relling to manufacture 225,000 drink bottles. How much more or less costly is it to manufacture the bottles than to acquire them from Kraff? 3\. What other information would you need to be confident that the equation in requirement 2 accurately predicts the cost of manufacturing drink bottles?

696, used i… # May Blackwell is the new manager of the materials storeroom for Clayton Manufacturing. May has been asked to estimate future monthly purchase costs for part #696, used in two of Clayton's products. May has purchase cost and quantity data for the past 9 months as follows: $$\begin{array}{lcc} \text { Month } & \text { cost of Purchase } & \text { Quantity Purchased } \\\ \hline \text { January } & \$ 12,675 & 2,710 \text { parts } \\ \text { February } & 13,000 & 2,810 \\ \text { March } & 17,653 & 4,153 \\ \text { April } & 15,825 & 3,756 \\ \text { May } & 13,125 & 2,912 \\ \text { June } & 13,814 & 3,387 \\ \text { July } & 15,300 & 3,622 \\ \text { August } & 10,233 & 2,298 \\ \text { September } & 14,950 & 3,562 \end{array}$$ Estimated monthly purchases for this part based on expected demand of the two products for the rest of the year are as follows: $$\begin{array}{lc} \text { Month } & \text { Purchase Quantity Expected } \\ \hline \text { October } & 3,340 \text { parts } \\ \text { November } & 3,710 \\ \text { December } & 3,040 \end{array}$$ 1\. The computer in May's office is down, and May has been asked to immediately provide an equation to estimate the future purchase cost for part #696. May grabs a calculator and uses the high-low method to estimate a cost equation. What equation does she get? 2\. Using the equation from requirement 1 , calculate the future expected purchase costs for each of the last 3 months of the year. 3\. After a few hours May's computer is fixed. May uses the first 9 months of data and regression analysis to estimate the relationship between the quantity purchased and purchase costs of part #696. The regression line May obtains is as follows: $$y=\$ 2,582.6+3.54 x$$ Evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Compare the regression equation to the equation based on the high-low method. Which is a better fit? Why? 4\. Use the regression results to calculate the expected purchase costs for October, November, and December. Compare the expected purchase costs to the expected purchase costs calculated using the high-low method in requirement 2. Comment on your results.