SOLUTION
(20 min.) Cost-volume-profit and regression analysis.
1a. Average cost of manufacturing =
Total manufacturing costs
Number of drink bottles
=
$808,500
210,000
= $3.85 per bottle
This cost is higher than the $3.75 per bottle that Kraff has quoted.
1b. Rellings cannot take the average manufacturing cost in 2017 of $3.85 per bottle and
multiply it by 225,000 drink bottles to determine the total cost of manufacturing 225,000 drink
bottles. The reason is that some of the $808,500 (or equivalently the $3.85 cost per bottle) are
3. Rellings would need to consider several factors before being confident that the equation
in requirement 2 accurately predicts the cost of manufacturing drink bottles.
a. Is the relationship between total manufacturing costs and quantity of drink bottles
economically plausible? For example, is the quantity of bottles made the only cost
10-1
10-31 Regression analysis, service company. (CMA, adapted) Linda Olson
owns a professional character business in a large metropolitan area. She hires local college
students to play these characters at children’s parties and other events. Linda provides balloons,
cupcakes, and punch. For a standard party the cost on a per-person basis is as follows:
Balloons, cupcakes, and punch $ 7
Labor (0.25 hour $20 per hour) 5
Overhead (0.25 hour $40 per hour 10
Total cost per person $22
Linda is quite certain about the estimates of the materials and labor costs, but is not as
comfortable with the overhead estimate. The overhead estimate was based on the actual data for
the past 9 months, which are presented here. These data indicate that overhead costs vary with
the direct labor-hours used. The $40 estimate was determined by dividing total overhead costs
for the 9 months by total labor-hours.
Month Labor-Hours Overhead
Costs
April 1,400 $ 65,000
May 1,800 71,000
June 2,100 73,000
July 2,200 76,000
August 1,650 67,000
September 1,725 68,000
October 1,500 66,500
10-2
November 1,200 60,000
December 1,900 72,500
Total 15,475 $619,000
Linda has recently become aware of regression analysis. She estimated the following regression
equation with overhead costs as the dependent variable and labor-hours as the independent
variable:
$43,563 $14.66y X= +
Required:
1. Plot the relationship between overhead costs and labor-hours. Draw the regression line and
evaluate it using the criteria of economic plausibility, goodness of fit, and slope of the
regression line.
2. Using data from the regression analysis, what is the variable cost per person for a standard
party?
3. Linda Olson has been asked to prepare a bid for a 20-child birthday party to be given next
month. Determine the minimum bid price that Linda would be willing to submit to recoup
variable costs.
SOLUTION
(25 min.)Regression analysis, service company.
1. Solution Exhibit 10-31 plots the relationship between labor-hours and overhead costs and
shows the regression line.
y = $43,563 + $14.66 X
2. The regression analysis indicates that, within the relevant range of 1,200 to 2,200
labor-hours, the variable cost per person for a birthday party equals:
10-3
3. To earn a positive contribution margin, the minimum bid for a 20-child birthday party
SOLUTION EXHIBIT 10-31
Regression Line of Overhead Costs on Labor-Hours for Linda Olson’s Character Business
1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400
50,000
55,000
60,000
65,000
70,000
75,000
80,000
f(x) = 14.66x + 43563.43
R² = 0.96
Labor-Hours
Overhead Costs
10-32 High-low, regression. 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:
Month Cost of Purchase Quantity Purchased
January $12,675 2,710 parts
February 13,000 2,810
10-4
March 17,653 4,153
April 15,825 3,756
May 13,125 2,912
June 13,814 3,387
July 15,300 3,622
August 10,233 2,298
September 14,950 3,562
Estimated monthly purchases for this part based on expected demand of the two products for the
rest of the year are as follows:
Month Purchase Quantity Expected
October 3,340 parts
November 3,710
December 3,040
Required:
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:
$2,582.6 3.54y 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.
SOLUTION
(25 min.) High-low, regression
1. May will pick the highest point of activity, 4,153 parts (March) at $17,653 of cost, and
the lowest point of activity, 2,298 parts (August) at $10,233.
10-5
Cost driver:
Quantity Purchased Cost
Highest observation of cost driver 4,153 $17,653
Lowest observation of cost driver 2,298 10,233
´
´
´
2. Using the equation above, the expected purchase costs for each month will be:
Month
Purchase
Quantity
Expected Formula
Expected
cost
´
´
´
3. Economic Plausibility: Clearly, the cost of purchasing a part is associated with the
quantity purchased.
SOLUTION EXHIBIT 10-32
10-6
2,000 2,500 3,000 3,500 4,000 4,500
$8,000
$10,000
$12,000
$14,000
$16,000
$18,000
$20,000
f(x) = 3.54x + 2582.57
R² = 0.96
Clayton Manufacturing Purchase Costs for Part #696
Quantity Purchased
Cost of Purchase
4. Using the regression equation, the purchase costs for each month will be:
Month
Purchase
Quantity
Expected Formula Expected cost
October 3,340 parts y = $2,582.60 + ($3.54
´
3,340) $14,406.20
´
Although the two equations are different in both fixed element and variable rate, within the
relevant range they give similar expected costs. This implies that the high and low points of the
data are a reasonable representation of the total set of points within the relevant range.
10-33 Learning curve, cumulative average-time learning model.
Northern Defense manufactures radar systems. It has just completed the manufacture of its first
newly designed system, RS-32. Manufacturing data for the RS-32 follow:
10-7
Required:
Calculate the total variable costs of producing 2, 4, and 8 units.
SOLUTION
(20 min.) Learning curve, cumulative average-time learning model.
The direct manufacturing labor-hours (DMLH) required to produce the first 2, 4, and 8 units
given the assumption of a cumulative average-time learning curve of 85%, is as follows:
85% Learning Curve
Cumulative Cumulative Cumulative
Number Average Time Total Time:
of Units (X) per Unit (y): Labor Hours Labor-Hours
(1) (2)
(3) = (1)
´
(2)
1 4,400 4,400
´
Alternatively, to compute the values in column (2) we could use the formula
where a = 4,400, X = 2, 4, or 8, and b = – 0.234465, which gives
10-8
´
Variable Costs of Producing
2 Units 4 Units 8 Units
10-34 Learning curve, incremental unit-time learning model. Assume
the same information for Northern Defense as in Exercise 10-33, except that Northern Defense
uses an 85% incremental unit-time learning model as a basis for predicting direct manufacturing
labor-hours. (An 85% learning curve means b = –0.234465.)
Required:
1. Calculate the total variable costs of producing 2, 3, and 4 units.
2. If you solved Exercise 10-33, compare your cost predictions in the two exercises for 2 and 4
units. Why are the predictions different? How should Northern Defense decide which model
it should use?
SOLUTION
(20 min.) Learning curve, incremental unit-time learning model.
1. The direct manufacturing labor-hours (DMLH) required to produce the first 2, 3, and 4
units, given the assumption of an incremental unit-time learning curve of 85%, is as follows:
85% Learning Curve
Cumulative
Number of Units (X)
Individual Unit Time for Xth
Unit (y): Labor Hours
Cumulative Total Time:
Labor-Hours
(1) (2) (3)
1 4,400 4,400
Variable Costs of Producing
2 Units 3 Units 4 Units
10-9
2. Variable Costs of
Producing
2 Units 4 Units
Total variable costs for manufacturing 2 and 4 units are lower under the cumulative
average-time learning curve relative to the incremental unit-time learning curve. Direct
10-35 High-low method. Wayne Mueller, financial analyst at CELL Corporation, is
examining the behavior of quarterly utility costs for budgeting purposes. Mueller collects the
following data on machine-hours worked and utility costs for the past 8 quarters:
Quarter Machine-Hours Utility Costs
1 120,000 $215,000
2 75,000 150,000
3 110,000 200,000
4 150,000 270,000
5 90,000 170,000
6 140,000 250,000
7 130,000 225,000
8 100,000 195,000
Required:
1. Estimate the cost function for the quarterly data using the high-low method.
2. Plot and comment on the estimated cost function.
3. Mueller anticipates that CELL will operate machines for 125,000 hours in quarter 9.
Calculate the predicted utility costs in quarter 9 using the cost function estimated in
10-10
requirement 1.
SOLUTION
(25 min.) High-low method.
1. Machine-Hours Utility Costs
Utility costs = a + b
´
Machine-hours
Slope coefficient (b) =
$120,000
75,000
= $1.60 per machine-hour
Constant (a) = $270,000 – ($1.60 × 150,000)
or Constant (a) = $150,000 – ($1.60 × 75,000)
2.
SOLUTION EXHIBIT 10-35
Plot and High-Low Line of Utility Costs as a Function of Machine-Hours
10-11
60,000 80,000 100,000 120,000 140,000 160,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
$220,000
$240,000
$260,000
$280,000
Machine-Hours
utility Costs
Solution Exhibit 10-35 presents the high-low line.
Economic plausibility. The cost function shows a positive economically plausible relationship
Goodness of fit. The high-low line appears to “fit” the data well. The vertical differences between
Slope of high-low line. The slope of the line appears to be reasonably steep indicating that, on
3. Using the cost function estimated in 1, predicted utility costs would be:
Mueller should budget $230,000 in quarter 9 because the relationship between
10-36 High-low method and regression analysis. Market Thyme, a cooperative
of organic family-owned farms, has recently started a fresh produce club to provide support to
the group’s member farms and to promote the benefits of eating organic, locally produced food.
Families pay a seasonal membership fee of $100 and place their orders a week in advance for a
price of $40 per order. In turn, Market Thyme delivers fresh-picked seasonal local produce to
several neighborhood distribution points. Five hundred families joined the club for the first
season, but the number of orders varied from week to week.
Tom Diehl has run the produce club for the first season. Tom is now a farmer but remembers
a few things about cost analysis from college. In planning for next year, he wants to know how
many orders will be needed each week for the club to break even, but first he must estimate the
club’s fixed and variable costs. He has collected the following data over the club’s first season of
10-12
operation:
Week Number of Orders per Week Weekly Total Costs
1 415 $26,900
2 435 27,200
3 285 24,700
4 325 25,200
5 450 27,995
6 360 25,900
7 420 27,000
8 460 28,315
9 380 26,425
10 350 25,750
Required:
1. Plot the relationship between number of orders per week and weekly total costs.
2. Estimate the cost equation using the high-low method, and draw this line on your graph.
3. Tom uses his computer to calculate the following regression formula:
Weekly total costs = $18,791 + ($19.97 Number of orders per week)
Draw the regression line on your graph. Use your graph to evaluate the regression line using
the criteria of economic plausibility, goodness of fit, and significance of the independent
variable. Is the cost function estimated using the high-low method a close approximation of
the cost function estimated using the regression method? Explain briefly.
4. Did Market Thyme break even this season? Remember that each of the families paid a
seasonal membership fee of $100.
5. Assume that 500 families join the club next year and that prices and costs do not change.
How many orders, on average, must Market Thyme receive each of 10 weeks next season to
break even?
10-13