# 2.7: Exercises (Part 1)

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## Questions

- What is a fixed cost? Provide two examples.
- What is the difference between a committed fixed cost and a discretionary fixed cost? Provide examples of each.
- What is a variable cost? Provide two examples.
- What is a mixed cost? Provide two examples.
- Describe the variables in the cost equation \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\).
- How is the cost equation \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) used to estimate future costs?
- Why is it important to identify how costs behave with changes in activity?
- Review Note 5.11 "Business in Action 5.2" Why was the school district’s administration surprised to find out that cost savings from closing a school would be much lower than initially anticipated?
- Explain how account analysis is used to estimate costs.
- Describe the four steps of the high-low method and how these steps are used to estimate costs.
- Why might the high-low method lead to inaccurate results?
- Describe the five steps of the scattergraph method and how these steps are used to estimate costs.
- How can the scattergraph method be used to identify unusual data points?
- Describe how regression analysis is used to estimate costs.
- How does the contribution margin income statement differ from the traditional income statement?
- Review Note 5.27 "Business in Action 5.3" Which costs at Lowe’s are likely to be variable costs?
- Describe the term relevant range. Why is it important to stay within the relevant range when estimating costs?
- Explain how some costs can behave in a nonlinear way.

## Brief Exercises

**Planning at Bikes Unlimited**. Refer to the dialogue at Bikes Unlimited presented at the beginning of the chapter. What is the first step to be taken by Susan and her accounting staff to help in estimating profit for August?**Identifying Cost Behavior**. Vasquez Incorporated is trying to identify the cost behavior of the three costs that follow. Cost information is provided for three months.

Cost A | Cost B | Cost C | |||||
---|---|---|---|---|---|---|---|

Month |
Units Produced |
Total Costs |
Cost per Unit |
Total Costs |
Cost per Unit |
Total Costs |
Cost per Unit |

1 | 1,500 | $1,500 | $4,500 | $3,000 | |||

2 | 3,000 | $1,500 | $5,250 | $6,000 | |||

3 | 750 | $1,500 | $3,750 | $1,500 |

*Required*:

- Calculate the cost per unit, and then identify how the cost behaves for each of the three costs (fixed, variable, or mixed). Explain the reasoning for your answers.
- How does identifying cost behavior patterns help managers?

**Account Analysis**. Cordova Company would like to estimate production costs on an annual basis. Costs incurred for direct materials and direct labor are variable costs. The accounting records indicate that the following production costs were incurred last year for 50,000 units.

Direct materials | $100,000 |

Direct labor | $215,000 |

Manufacturing overhead | $300,000 (20 percent fixed; 80 percent variable) |

*Required*:

Use account analysis to estimate the fixed costs per year, and the variable cost per unit.

**High-Low Method**. The city of Rockville reported the following annual cost data for maintenance work performed on its fleet of trucks.

Reporting Period (Year) | Total Costs | Level of Activity (Miles Driven) |
---|---|---|

Year 1 | $ 750,000 | 225,000 |

Year 2 | $850,000 | 240,000 |

Year 3 | $1,100,000 | 430,000 |

Year 4 | $1,150,000 | 454,000 |

Year 5 | $1,250,000 | 560,000 |

Year 6 | $1,550,000 | 710,000 |

*Required*:

- Use the four steps of the high-low method to estimate total fixed costs per year and the variable cost per mile. State your results in the cost equation form \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\).
- What would the estimated costs be if the trucks drove 500,000 miles in year 7?

**Scattergraph Method**. Refer to the data in Brief Exercise 22 for the city of Rockville.

*Required*:

- Use the five steps of the scattergraph method to estimate total fixed costs per year and the variable cost per mile. State your results in the cost equation form \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- What would the estimated costs be if the trucks drove 500,000 miles in year 7?

**Regression Analysis**. Regression analysis was run using the data in Brief Exercise 22 for the city of Rockville. The output is shown here:

Coefficients | |

y-intercept | 441,013 |

x variable | 1.53 |

*Required*:

- Use the regression output to develop the cost equation \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- What would the city of Rockville’s estimated costs be if its trucks drove 500,000 miles in year 7?

**Contribution Margin Income Statement**. Last year Pod Products, Inc., sold its product for $250 per unit. Production costs totaled $40,000 (25 percent fixed, 75 percent variable). Selling and administrative costs totaled $150,000 (10 percent fixed, 90 percent variable). Pod Products produced and sold 1,000 units last year.

*Required*:

Prepare a contribution margin income statement for Pod Products, Inc.

**Relevant Range**. Jersey Company produces jerseys for athletic teams, and typically produces between 1,000 and 5,000 jerseys annually. The accountant is asked to estimate production costs for this coming year assuming 9,000 jerseys will be produced.

*Required*:

What is meant by the term relevant range, and why is the relevant range important for estimating production costs for this coming year at Jersey Company?

## Exercises: Set A

**Identifying Cost Behavior**. Zhang Corporation is trying to identify the cost behavior of the three costs shown. Cost information is provided for six months.

Cost A | Cost B | Cost C | |||||
---|---|---|---|---|---|---|---|

Month |
Units Produced |
Total Costs |
Cost per Unit |
Total Costs |
Cost per Unit |
Total Costs |
Cost per Unit |

1 | 18,000 | $36,000 | $19,800 | $5,000 | |||

2 | 16,000 | $32,000 | $19,200 | $5,000 | |||

3 | 14,000 | $28,000 | $18,200 | $5,000 | |||

4 | 12,000 | $24,000 | $16,800 | $5,000 | |||

5 | 10,000 | $20,000 | $14,500 | $5,000 | |||

6 | 8,000 | $16,000 | $12,000 | $5,000 |

*Required*:

- Calculate the cost per unit, and then identify how the cost behaves (fixed, variable, or mixed) for each of the three costs. Explain the reasoning behind your answers.
- Why is it important to identify how costs behave with changes in activity?

**Account Analysis**. Baker Advertising Incorporated would like to estimate costs associated with its clients on an annual basis. Assume costs for supplies and advertising staff are variable costs. The accounting records indicate the following costs were incurred last year for 100 clients:

Supplies | $ 20,000 |

Advertising staff wages (hourly employees) | $170,000 |

Manager salary | $ 90,000 |

Building rent | $ 56,000 |

*Required*:

- Use account analysis to estimate total fixed costs per year, and the variable cost per unit. State your results in the cost equation form \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- Estimate the total costs for this coming year assuming 120 clients will be served.

**High-Low Method**. Castanza Company produces computer printers. Management wants to estimate the cost of production equipment used to produce printers. The company reported the following monthly cost data related to production equipment:

Reporting Period (Month) | Total Costs | Machine Hours |
---|---|---|

January | $ 920,000 | 45,000 |

February | $600,000 | 25,000 |

March | $500,000 | 20,000 |

April | $1,100,000 | 90,000 |

May | $1,140,000 | 95,000 |

June | $620,000 | 30,000 |

July | $880,000 | 38,000 |

August | $910,000 | 48,000 |

September | $1,060,000 | 78,000 |

October | $960,000 | 51,000 |

November | $1,400,000 | 96,000 |

December | $980,000 | 54,000 |

*Required*:

- Use the four steps of the high-low method to estimate total fixed costs per month and the variable cost per machine hour. State your results in the cost equation form \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- What would Castanza Company’s estimated costs be if it used 50,000 machine hours next month?
- What would Castanza Company’s estimated costs be if it used 15,000 machine hours next month? Why should you feel uncomfortable estimating costs for 15,000 machine hours?

**Scattergraph Method**. Castanza Company produces computer printers. Management wants to estimate the cost of production equipment used to produce printers. The company reported the following monthly cost data related to production equipment (this is the same data as the previous exercise):

Reporting Period (Month) | Total Costs | Machine Hours |
---|---|---|

January | $ 920,000 | 45,000 |

February | $600,000 | 25,000 |

March | $500,000 | 20,000 |

April | $1,100,000 | 90,000 |

May | $1,140,000 | 95,000 |

June | $620,000 | 30,000 |

July | $880,000 | 38,000 |

August | $910,000 | 48,000 |

September | $1,060,000 | 78,000 |

October | $960,000 | 51,000 |

November | $1,400,000 | 96,000 |

December | $980,000 | 54,000 |

*Required*:

- Use the five steps of the scattergraph method to estimate total fixed costs per month and the variable cost per machine hour. State your results in the cost equation form \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- What would Castanza Company’s estimated costs be if it used 50,000 machine hours next month?
- What would Castanza Company’s estimated costs be if it used 15,000 machine hours next month?

**Regression Analysis**. Regression analysis was run for Castanza Company resulting in the following output (this is based on the same data as the previous two exercises):

Coefficients | |

y-intercept | 445,639 |

x variable | 8.54 |

*Required*:

**Contribution Margin Income Statement**. Last month Kumar Production Company sold its product for $60 per unit. Fixed production costs were $40,000, and variable production costs amounted to $15 per unit. Fixed selling and administrative costs totaled $26,000, and variable selling and administrative costs amounted to $5 per unit. Kumar Production produced and sold 7,000 units last month.

*Required*:

- Prepare a traditional income statement for Kumar Production Company.
- Prepare a contribution margin income statement for Kumar Production Company.
- Why do companies use the contribution margin income statement format?

**Regression Analysis Using Excel (Appendix)**. Walleye Company produces fishing reels. Management wants to estimate the cost of production equipment used to produce the reels. The company reported the following monthly cost data related to production equipment:

Reporting Period (Month) | Total Costs | Machine Hours |
---|---|---|

January | $1,104,000 | 54,000 |

February | $720,000 | 30,000 |

March | $600,000 | 24,000 |

April | $1,320,000 | 108,000 |

May | $1,368,000 | 114,000 |

June | $744,000 | 36,000 |

July | $1,056,000 | 45,600 |

August | $1,092,000 | 57,600 |

September | $1,272,000 | 93,600 |

October | $1,152,000 | 61,200 |

November | $1,680,000 | 115,200 |

December | $1,176,000 | 64,800 |

*Required*:

- Use Excel to perform regression analysis. Provide a printout of the results.
- Use the regression output to develop the cost equation \(\text{Y} = \mathcal{f} + \mathcal{v} \text{X}\) by filling in the dollar amounts for \(\mathcal{f}\) and \(\mathcal{v}\).
- What would Walleye Company’s estimated costs be if it used 90,000 machine hours this month?