Horngren\'s Cost Accounting: A Managerial Emphasis, 16th Global Edition Chapter 10 Questions and solutions PDF

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CHAPTER 10DETERMINING HOW COSTS BEHAVE10-1 What two assumptions are frequently made when estimating a cost function?The two assumptions are Variations in the level of a single activity (the cost driver) explain the variations in the related total costs. Cost behavior is approximated by a linear cost...

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CHAPTER 10 DETERMINING HOW COSTS BEHAVE 10-1

What two assumptions are frequently made when estimating a cost function?

The two assumptions are 1. Variations in the level of a single activity (the cost driver) explain the variations in the related total costs. 2. Cost behavior is approximated by a linear cost function within the relevant range. A linear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity forms a straight line. 10-2

Describe three alternative linear cost functions.

Three alternative linear cost functions are 1. Variable cost function––a cost function in which total costs change in proportion to the changes in the level of activity in the relevant range. 2. Fixed cost function––a cost function in which total costs do not change with changes in the level of activity in the relevant range. 3. Mixed cost function––a cost function that has both variable and fixed elements. Total costs change but not in proportion to the changes in the level of activity in the relevant range. 10-3 What is the difference between a linear and a nonlinear cost function? Give an example of each type of cost function. A linear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity related to that cost is a straight line. An example of a linear cost function is a cost function for use of a videoconferencing line where the terms are a fixed charge of $10,000 per year plus a $2 per minute charge for line use. A nonlinear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity related to that cost is not a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-cost functions, and learning-curve-based costs. 10-4 “High correlation between two variables means that one is the cause and the other is the effect.” Do you agree? Explain. No. High correlation merely indicates that the two variables move together in the data examined. It is essential also to consider economic plausibility before making inferences about cause and effect. Without any economic plausibility for a relationship, it is less likely that a high level of correlation observed in one set of data will be similarly found in other sets of data. 10-5

Name four approaches to estimating a cost function.

Four approaches to estimating a cost function are 10-1

1. 2. 3. 4.

Industrial engineering method. Conference method. Account analysis method. Quantitative analysis of current or past cost relationships.

10-6 Describe the conference method for estimating a cost function. What are two advantages of this method? The conference method estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company (purchasing, process engineering, manufacturing, employee relations, etc.). Advantages of the conference method include 1. The speed with which cost estimates can be developed. 2. The pooling of knowledge from experts across functional areas. 3. The improved credibility of the cost function to all personnel. 10-7

Describe the account analysis method for estimating a cost function.

The account analysis method estimates cost functions by classifying cost accounts in the subsidiary ledger as variable, fixed, or mixed with respect to the identified level of activity. Typically, managers use qualitative, rather than quantitative, analysis when making these costclassification decisions. 10-8 List the six steps in estimating a cost function on the basis of an analysis of a past cost relationship. Which step is typically the most difficult for the cost analyst? The six steps are 1. Choose the dependent variable (the variable to be predicted, which is some type of cost). 2. Identify the independent variable or cost driver. 3. Collect data on the dependent variable and the cost driver. 4. Plot the data. 5. Estimate the cost function. 6. Evaluate the cost driver of the estimated cost function. Step 3 typically is the most difficult for a cost analyst. 10-9 When using the high-low method, should you base the high and low observations on the dependent variable or on the cost driver? Causality in a cost function runs from the cost driver to the dependent variable. Thus, choosing the highest observation and the lowest observation of the cost driver is appropriate in the highlow method. 10-10 Describe three criteria for evaluating cost functions and choosing cost drivers. Three criteria important when choosing among alternative cost functions are 1. Economic plausibility.

10-2

2. 3.

Goodness of fit. Slope of the regression line.

10-11 Define learning curve. Outline two models that can be used when incorporating learning into the estimation of cost functions. A learning curve is a function that measures how labor-hours per unit decline as units of production increase because workers are learning and becoming better at their jobs. Two models used to capture different forms of learning are 1. Cumulative average-time learning model. The cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles. 2. Incremental unit-time learning model. The incremental time needed to produce the last unit declines by a constant percentage each time the cumulative quantity of units produced doubles. 10-12 Discuss four frequently encountered problems when collecting cost data on variables included in a cost function. Frequently encountered problems when collecting cost data on variables included in a cost function are 1. The time period used to measure the dependent variable is not properly matched with the time period used to measure the cost driver(s). 2. Fixed costs are allocated as if they are variable. 3. Data are either not available for all observations or are not uniformly reliable. 4. Extreme values of observations occur. 5. A homogeneous relationship between the individual cost items in the dependent variable cost pool and the cost driver(s) does not exist. 6. The relationship between the cost and the cost driver is not stationary. 7. Inflation has occurred in a dependent variable, a cost driver, or both. 10-13 What are the four key assumptions examined in specification analysis in the case of simple regression? Four key assumptions examined in specification analysis are 1. Linearity of relationship between the dependent variable and the independent variable within the relevant range. 2. Constant variance of residuals for all values of the independent variable. 3. Independence of residuals. 4. Normal distribution of residuals. 10-14 “All the independent variables in a cost function estimated with regression analysis are cost drivers.” Do you agree? Explain. No. A cost driver is any factor whose change causes a change in the total cost of a related cost object. A cause-and-effect relationship underlies selection of a cost driver. Some users of regression analysis include numerous independent variables in a regression model in an attempt 10-3

to maximize goodness of fit, irrespective of the economic plausibility of the independent variables included. Some of the independent variables included may not be cost drivers. 10-15 “Multicollinearity exists when the dependent variable and the independent variable are highly correlated.” Do you agree? Explain. No. Multicollinearity exists when two or more independent variables are highly correlated with each other. 10-16 HL Co. uses the high-low method to derive a total cost formula. Using a range of units produced from 1,500 to 7,500, and a range of total costs from $21,000 to $45,000, producing 2,000 units will cost HL: a. $8,000 c. $23,000

b. $12,000 d. $29,000

SOLUTION Choice "c" is correct. The high-low method is used to estimate both fixed and variable costs, and can then be applied to determine a total cost formula that is used to estimate total costs for any level of production. The difference between the total costs ($45,000 − $21,000) is divided by the difference in units (7,500 – 1,500) to derive a variable cost per unit of $4 ($24,000 / 6,000). Using either end of the range, fixed costs can then be estimated. Using total costs of $45,000 for 7,500 units, with variable costs at $4 per unit, $45,000 − 7,500($4) = $15,000 of fixed costs. The total cost formula for HL will be equal to: $15,000 + [$4.00 × # units]. 2,000 units will produce a total cost of: $15,000 + [$4.00 × 2,000] = $23,000. Choice "a" is incorrect. This calculation fails to account for the fixed costs of $15,000. Choice "b" is incorrect. This calculation incorrectly assumes that because 7,500 units cost $45,000 (or $6 overall per unit), that 2,000 units would cost $12,000 ($6 per unit). Choice "d" is incorrect. This calculation incorrectly applies a variable cost of $7 per unit rather than $4. 10-17 A firm uses simple linear regression to forecast the costs for its main product line. If fixed costs are equal to $235,000 and variable costs are $10 per unit, how many units does it need to sell at $15 per unit to make a $300,000 profit? a. 21,400 c. 60,000

b. 47,000 d. 107,000

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SOLUTION Choice "d" is correct. The regression equation set up will be: y (total costs) = $235,000 + $10x, with x representing volume. In order to make a $300,000 profit, sales ($15x) − costs must equal $300,000. So the full set up will be: $15x − ($235,000 + $10x) = $300,000. Solving for x, $5x = $535,000, or 107,000 units. At 107,000 units, sales will total $1,605,000 and costs will total $1,305,000 for a profit of $300,000. Choice "a" is incorrect. This choice represents a calculation error where the $15 sale price and the $10 variable cost are added together and divided into $535,000. Choice "b" is incorrect. 47,000 is the number of units that is required in order to breakeven. Choice "c" is incorrect. These are the number of units above breakeven that the company must sell in order to make a $300,000 profit. 10-18 In regression analysis, the coefficient of determination: a. Is used to determine the proportion of the total variation in the dependent variable (y) explained by the independent variable (X). b. Ranges between negative one and positive one. c. Is used to determine the expected value of the net income based on the regression line. d. Becomes smaller as the fit of the regression line improves. SOLUTION Choice "a" is correct. This is the definition of the coefficient of determination. It is the square of the coefficient of correlation. The higher the coefficient of determination, the greater the proportion of the total variation in y that is explained by the variation in x. The higher it is, the better is the fit of the regression line. Choice "b" is incorrect. It ranges between 0 and 1. Remember, the coefficient of determination is the square of the coefficient of correlation. Because it is a number squared, it will be positive. Choice "c" is incorrect. This is not a use of the coefficient of determination. Choice "d" is incorrect. It becomes larger as the fit of the regression line improves. 10-19 A regression equation is set up, where the dependent variable is total costs and the independent variable is production. A correlation coefficient of 0.70 implies that: a. b. c. d.

The coefficient of determination is negative. The level of production explains 49% of the variation in total costs There is a slightly inverse relationship between production and total costs. A correlation coefficient of 1.30 would produce a regression line with better fit to the data.

10-5

SOLUTION Choice "b" is correct. A correlation coefficient (used to measure the strength in the linear relationship between independent and dependent variables) of 0.70 implies that the coefficient of determination is 0.49. A coefficient of determination of 0.49 equates to the independent variable (level of production) explaining 49 percent of the variation in the dependent variable (total costs). Choice "a" is incorrect. The coefficient of determination will always be a number between 0 and 1. Choice "c" is incorrect. A positive correlation coefficient implies a direct relationship between the two variables. Choice "d" is incorrect. The correlation coefficient can only be between -1 and 1. 10-20 What would be the approximate value of the coefficient of correlation between advertising and sales where a company advertises aggressively as an alternative to temporary worker layoffs and cuts off advertising when incoming jobs are on backorder? a. 1.0 c. –1.0

b. 0 d. –100

SOLUTION Choice "c" is correct. The coefficient of correlation measures the strength and direction of the relationship between two variables. Since the company increases advertising when sales are low and decreases advertising when sales are high, the movement is in directly opposite directions and the coefficient would be close to - 1.0. Choice "a" is incorrect. A coefficient of correlation of 1.0 would imply that both variables move in the same direction at approximately the same rate. An increase in advertising when sales are increasing would be characteristic of a correlation of coefficient of 1.0. Choice "b" is incorrect. A coefficient of correlation of 0 would imply that there is no relationship between advertising and sales. There is an inverse relationship between advertising and sales. Choice "d" is incorrect. A relationship exists between advertising and sales. According to the facts of the question, the relationship is an inverse relationship. The coefficient of correlation is expressed as a range between 1.0 and +1.0. 10-21 Estimating a cost function. The controller of the Ijiri Company wants you to estimate a cost function from the following two observations in a general ledger account called Maintenance:

10-6

Month

Miles Driven

Delivery Costs

January

6,000

$4,000

February

10,000

5,400

Required: 1. Estimate the cost function for maintenance. 2. Can the constant in the cost function be used as an estimate of fixed maintenance cost per month? Explain. SOLUTION (10 min.) 1.

Estimating a cost function.

Slope coefficient = $ 5,400−$ 4,000 10,000 −6,000 $ 1,400 = $0.35 per machine-hour = 4,000 Constant = Total cost – (Slope coefficient  Quantity of cost driver) = $5,400 – ($0.3510,000) = $1,900 = $4,000 – ($0.356,000) = $1,900 =

The cost function based on the two observations is Maintenance costs = $1,900 + $0.35 Machine-hours 2. The cost function in requirement 1 is an estimate of how costs behave within the relevant range, not at cost levels outside the relevant range. If there are no months with zero machinehours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machine-hours level. Rather, the constant component of the cost function provides the best available starting point for a straight line that approximates how a cost behaves within the relevant range. 10-22 Identifying variable-, fixed-, and mixed-cost functions. The Bengal Corporation operates car rental agencies at more than 20 airports across India. Customers can choose from one of three contracts for car rentals of one day or less:  Contract 1: $50 for the day  Contract 2: $30 for the day plus $0.20 per mile traveled  Contract 3: $1 per mile traveled Required: 1. Plot separate graphs for each of the three contracts, with costs on the vertical axis and miles traveled on the horizontal axis.

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2. Express each contract as a linear cost function of the form y = a + bX. 3. Identify each contract as a variable-, fixed-, or mixed-cost function. SOLUTION (15 min.)

Identifying variable-, fixed-, and mixed-cost functions.

1.

See Solution Exhibit 10-22.

2.

Contract 1: y = $50 Contract 2: y = $30 + $0.20X Contract 3: y = $1X where X is the number of miles traveled in the day.

3.

Contract 1 2 3

Cost Function Fixed Mixed Variable

SOLUTION EXHIBIT 10-22 Plots of Car Rental Contracts Offered by The Bengal Corp.

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10-23 Various cost-behavior patterns. (CPA, 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.

Required:

10-9

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 kilowatthours 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: First 1,000,000 gallons or less

$1,000 flat fee

Next 10,000 gallons

$0.003 per gallon used

Next 10,000 gallons

$0.006 per gallon used

Next 10,000 gallons

$0.009 per gallon used

and so on

and so on

The gallons of water used vary proportionately with the quantity of production output. 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 cost is $10; if 2 pounds are used, the cost is $19.98; if 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 is paid. 7. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours or 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 $1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of $20,000 must be paid. SOLUTION (20 min.) Various cost-behavior patterns. 1. K 2. B 3. G 4. J Note that A is incorrect because, although the cost per pound eventually equals a constant at $9.20, the total dollars of cost increases linearly from that point onward.

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5. 6. 7. 8. 9.

I L F K C

The total costs will be the same regardless of the volume level. This is a classic step-cost function.

10-24 Matching graphs with descriptions of cost and revenue behavior. (D. Green, adapted) Given here are a number of graphs.

Required: The horizontal axis of each graph represents the units produced over the year, and the vertical axis represents total cost or revenues. Indicate by number which graph best fits the situation or item described (a–h). Some graphs may be used more than once; some may not apply to any of the situations. Direct material costs Supervisors’ salaries for one shift and two shifts A cost–volume–profit graph Mixed costs—for example, car rental fixed charge plus a rate per mile driven Depreciation of plant, ...