Thompson Company is in the process of preparing its budget for the next fiscal year. The company has had problems controlling costs in prior years and has decided to adopt a flexible budgeting system this year. Many of its costs contain both fixed and variable cost components. A method that can be used to separate costs into fixed and variable components is:

a.

Trend analysis.

b.

Monte Carlo simulation.

c.

Regression analysis.

d.

Dynamic programming.

Choice "c" is correct. Regression analysis can be used to separate costs into fixed and variable components by means of least squares. This method mathematically fits a trend line to minimize the distance between the trend line and the actual observations.

Choice "a" is incorrect, because trend analysis is used to project costs (expenses) out into the future.

Choice "b" is incorrect, because Monte Carlo simulation is used to generate individual values for a random variable.

Choice "d" is incorrect, because dynamic programming is used to make a series of interrelated decisions.

There are a variety of ways of classifying costs of an object as either fixed or variable. The most accurate method is considered to be:

a.

The high-low method.

b.

The engineering method.

c.

The account analysis method.

d.

The regression analysis method.

Choice "d" is correct. Regression analysis is a statistical method that fits a line to the data by the method of least squares. It is the most accurate way to classify costs of an object as either fixed or variable.

Choice "b" is incorrect. The engineering method uses such methods as time and motion study to classify costs. It can only be used where there is an observable relationship between the inputs and the outputs.

Choice "c" is incorrect. The account analysis method is merely a review of all the accounts by someone knowledgeable of the activities of the firm. It is only as good as the person making the judgments.

Choice "a" is incorrect. The high-low method is a simplified approach that uses only the points of highest and lowest activity. The regression method considers every point of activity.

In using regression analysis, which measure indicates the extent to which a change in the independent variable explains a change in the dependent variable?

a.

t-statistic.

b.

R-squared.

c.

Standard error.

d.

p-value.

Choice "b" is correct. R-squared is the coefficient of determination and is the proportion of the total variation in a dependent variable (y) explained by the independent variable (x).

Choice "d" is incorrect. The p-value is a statistical measure of the likelihood that tested data could have occurred by chance.

Choice "c" is incorrect. The standard error is a measure of the standard deviation or average variability of a sampling distribution.

Choice "a" is incorrect. The t-statistic is used in hypothesis testing and the computation of confidence levels.

A regression equation:

a.

Ignores the coefficient of determination.

b.

Is based on objective and constraint functions.

c.

Estimates the dependent variables.

d.

Estimates the independent variable.

Choice "c" is correct. A regression equation is a statistical model that estimates the dependent variables based on changes in the independent variable.

Choice "b" is incorrect. Objective and constraint functions are used in linear programming, not in regression analysis.

Choice "d" is incorrect. An independent variable is assumed (not estimated) in regression analysis and is based on activity, rather than costs.

Choice "a" is incorrect. The coefficient of determination is a statistical measure used to evaluate the results of regression analysis.

It is estimated that a particular manufacturing job is subject to an 80 percent learning curve. The first unit required fifty labor hours to complete. What is the cumulative average time per unit after completing four units?

a.

30.0 hours.

b.

40.0 hours.

c.

32.0 hours.

d.

50.0 hours.

Rule: The basic premise of the learning curve is that operating efficiency and/or production increases in repetitive tasks as experience is gained. The rate of improvement, measured by the learning curve, has a regular pattern that can be stated as follows:

As cumulative quantities double, average cost per unit decreases by a specified percent of the previous cost.

Choice "c" is correct. 32.0 hours cumulative average time per unit after completing four units.

~Cumulative # of Units

~Average Time Per Unit

1

50 Hours

2

40 Hours (50 × 0.8)

4

32 Hours (40 × 0.8)

Choices "d", "b", and "a" are incorrect, based on the above calculation.

Given that demand exceeds capacity, that there is no spoilage or waste, and that there is full utilization of a constant number of assembly hours, the number of components needed for an assembly operation with an 80 percent learning curve should

I.

Increase for successive periods.

II.

Decrease per unit of output.

a.

Both I and II.

b.

I only.

c.

Neither I nor II.

d.

II only.

Choice "b" is correct. The learning curve relates to the efficiency with which productive resources, typically labor, are employed, and it suggests that productivity will increase over time. Therefore, the number of components needed for an assembly operation with an 80 percent learning curve will increase for successive periods to accommodate increased production, assuming demand exceeds capacity, there is no spoilage and that there is full utilization of a constant number of assembly hours.

Choice "d" is incorrect. The learning curve relates to the efficiency with which productive resources, typically labor, are employed. Assuming constant hours and no spoilage, the number of components per unit of output will remain unchanged, but productivity will increase. This in turn will cause the number of components needed for assembly to increase for successive periods, to accommodate increased production.

Choice "a" is incorrect. Only the number of units will increase to accommodate increased production. The number of components per unit of output will not decrease since we assume that there is not spoilage or waste. Yield per direct material is unchanged, yield per hour of work and, by extension, demand for components (direct material), will increase.

Choice "c" is incorrect. The number of units will increase to accommodate increased production, but the number of components per unit of output will not decrease since we assume that there is not spoilage or waste. Yield per direct material is unchanged, yield per hour of work and, by extension, demand for components (direct material), will increase.

Multiple regression differs from simple regression in that it:

a.

Provides an estimated constant term.

b.

Allows the computation of the coefficient of determination.

c.

Has more dependent variables.

d.

Has more independent variables.

Choice "d" is correct. Multiple regression analysis is an expansion of simple regression because it allows consideration of more than one independent variable. The other elements are consistent in simple and multiple regression analysis.

Choices "a", "c", and "b" are incorrect based on the above explanation.

Arbor Corporation uses the coefficient of correlation to measure the strength of the cost volume relationships used in planning. When reviewing variable costs and volume, Arbor would be most likely to find a coefficient of correlation equal to:

a.

0.0

b.

-1.0

c.

1.0

d.

-0.5

Choice "c" is correct. Arbor would expect a coefficient of correlation equal to 1.0. The positive measure would reflect the strong direct relationship assumed in CVP analysis, where total variable costs increase proportionally with volume.

Choice "d" is incorrect. A negative coefficient of correlation indicates an inverse relationship. This would illogically presume that variable costs decrease as volume increases. Cost volume relationships are not only positive but are assumed to be proportional.

Choice "b" is incorrect. A coefficient of correlation of -1.0 indicates a perfect inverse relationship. This would imply that costs go down as volume increases. In the relevant range, costs and volume are expected to increase (not decrease) proportionately.

Choice "a" is incorrect. A coefficient of correlation of 0 indicates no relationship between costs and volume. We would expect this relationship for fixed costs, not variable costs.

The regression analysis results for ABC Co. is shown as y = 90x + 45. The standard error (Sb) is 30 and coefficient of determination (r2) is 0.81. The budget calls for production of 100 units. What is ABC's estimate of total costs?

a.

$4,590

b.

$3,090

c.

$9,030

d.

$9,045

Choice "d" is correct. The total cost formula is the formula for a line where total cost, the dependent variable (y), is equal to volume times the independent variable, variable costs (x), plus a constant (fixed costs).

The formula for ABC Company is:

y = 90x + 45

The problem tells us that we plan to produce 100 units so total costs, y, is computed as follows:

y = (90 × 100) + 45

y = 9,045

The coefficient of determination measures the proportion of the total variation in "y" or total cost that is explained by the total variation in the independent variable, x, or variable costs. The coefficient of determination measures the reliability of the formula, but is not used for determining the value of "y".

The standard error (also standard error of the mean) is a measurement used in conjunction with standard deviation computations and is not relevant to this projection.

Choices "b", "a", and "c" are incorrect, based on the above explanation.

Seacraft Inc. received a request for a competitive bid for the sale of one of its unique boating products with a desired modification. Seacraft is now in the process of manufacturing this product but with a slightly different modification for another customer. These unique products are labor intensive and both will have long production runs. Which one of the following methods should Seacraft use to estimate the cost of the new competitive bid?

a.

Learning curve analysis.

b.

Expected value analysis.

c.

Continuous probability simulation.

d.

Regression analysis.

Choice "a" is correct. Learning curve analysis is used to determine increases in efficiency or production as experience is gained. Both products have long production runs, making learning curve analysis the best method for estimating the cost of the competitive bid.

Choice "b" is incorrect. Expected value analysis represents the long-term average of repeated trials and is found by multiplying the probability of each outcome by its payoff and then summing the results.

Choice "d" is incorrect. Regression analysis is a statistical model that can estimate the dependent cost variable based on changes in the independent variable.

Choice "c" is incorrect. Continuous probability simulation is a procedure that studies a problem by creating a model of the process and then, through trial and error solutions, attempts to improve the problem solution.

The coefficient of determination, r squared, in a multiple regression equation is the:

a.

Percentage of variation in the independent variables explained by the variation in the dependent variable.

b.

Coefficient of the independent variable divided by the standard error of regression coefficient.

c.

Measure of the proximity of actual data points to the estimated data points.

d.

Percentage of variation in the dependent variable explained by the variation in the independent variables.

Choice "d" is correct. The coefficient of determination (R2) is the proportion of the total variation in the dependent variable (y) explained by the independent variable (x).

Choice "a" is incorrect. The independent variable is not explained by the dependent variable. Changes in the independent variable drive the variation in the dependent variable. The coefficient of determination (R2) is the proportion of the total variation in the dependent variable (y) explained by the independent variable (x).

Choice "c" is incorrect. The measure of proximity of actual data points to estimated data points is not the coefficient of determination. The coefficient of determination (R2) is the proportion of the total variation in the dependent variable (y) explained by the independent variable (x).

Choice "b" is incorrect. The coefficient of determination (R2) is the proportion of the total variation in the dependent variable (y) explained by the independent variable (x), not the coefficient of the independent variable divided by the standard error of regression coefficient.

Which of the following forecasting methods relies mostly on judgment?

a.

Time-series models.

b.

Econometric models.

c.

Delphi.

d.

Regression.

Choice "c" is correct. The Delphi method of forecasting involves the use of multiple teams in geographically remote locations. Information is shared and gathered in a central point and compiled and then redistributed for comment. The method is highly interpersonal and requires significant judgment.

Choice "a" is incorrect. Although all forecast methods require some judgment regarding both variables used and the evaluation of results, quantitative methods, such as time series models, rely more heavily on mathematical relationships than pure judgment.

Choice "b" is incorrect. Although all forecast methods require some judgment regarding both variables used and the evaluation of results, quantitative methods, such as econometric models, rely more heavily on mathematical relationships than pure judgment.

Choice "d" is incorrect. Although all forecast methods require some judgment regarding both variables used and the evaluation of results, quantitative methods, such as regression analysis, rely more heavily on mathematical relationships than pure judgment.