Chapter 5: Exercises

Short-Answer Questions, Exercises, and Problems

Short-Answer Questions
➢ Name and describe four cost behavior patterns.
➢ Describe two methods of determining the fixed and variable components of mixed costs.
➢ What is meant by the term break-even point?
➢ What are two ways in which the break-even point can be expressed?
➢ What is the relevant range?
➢ What is the formula for calculating the break-even point in sales revenue?
➢ What formula is used to solve for the break-even point in units?
➢ How can the break-even formula be altered to calculate the number of units that must be sold to achieve a desired level of income?
➢ Why might a business wish to lower its break-even point? How would it go about lowering the break-even point?
➢ What effect would you expect the mechanization and automation of production processes to have on the break-even point?
Real world question Assume your college is considering hiring a lecturer to teach a special class in communication skills. Identify at least two costs that college administrators might consider in deciding whether to hire the lecturer and add the class.
Real world question Two enterprising students are considering renting space and opening a class video recording service. They would hire camera operators to record large introductory classes. The students taking the classes would be charged a fee to rent and view the video on their laptops or smart phones. Identify as many costs of this business as you can and indicate which would be variable and which would be fixed.
Exercises
Exercise A Name and match the types of cost behavior with the appropriate diagram below:Exercise B Research Inc., performs laboratory tests. Use the high-low method to determine the fixed and variable components of a mixed cost, given the following observations:

Volume (number of tests) Total cost
4,800 $6,000
19,200 9,600
Exercise C Compute the break-even point in sales dollars if fixed costs are $200,000 and the total contribution margin is 20% of revenue.

Exercise D Barney Company makes and sells stuffed animals. One product, Michael Bears, sells for $28 per bear. Michael Bears have fixed costs of $100,000 per month and a variable cost of $12 per bear. How many Michael Bears must be produced and sold each month to break even?

Exercise E Peter Garcia Meza is considering buying a company if it will break even or earn net income on revenues of $80,000 per month. The company that Peter is considering sells each unit it produces for $5. Use the following cost data to compute the variable cost per unit and the fixed cost for the period. Calculate the break-even point in sales dollars. Should Peter buy this company?

Volume (units) Cost
8,000 $70,000
68,000 190,000
Exercise F Never Late Delivery currently delivers packages for $9 each. The variable cost is $3 per package, and fixed costs are $60,000 per month. Compute the break-even point in both sales dollars and units under each of the following independent assumptions. Comment on why the break-even points are different.

  1. The costs and selling price are as just given.
  2. Fixed costs are increased to $75,000.
  3. Selling price is increased by 10%. (Fixed costs are $60,000.)
  4. Variable cost is increased to $4.50 per unit. (Fixed costs are $60,000 and selling price is $9.)


Exercise G Best Eastern Motel is a regional motel chain. Its rooms rent for $100 per night, on average. The variable cost is $40 a room per night. Fixed costs are $5,000,000 per year. The company currently rents 200,000 units per year, with each unit defined as one room for one night. Should this company undertake an advertising campaign resulting in a $500,000 increase in fixed costs per year, no change in variable cost per unit, and a 10% increase in revenue (resulting from an increase in the number of rooms rented)? What is the margin of safety before and after the campaign?

Exercise H Fall-For-Fun Company sells three products. Last year's sales were $600,000 for parachutes, $800,000 for hang gliders, and $200,000 for bungee jumping harnesses. Variable costs were: parachutes, $400,000; hang gliders, $700,000; and bungee jumping harnesses, $100,000. Fixed costs were $240,000. Find (a) the break-even point in sales dollars and (b) the margin of safety.

Exercise I Early Horizons Day Care Center has fixed costs of $300,000 per year and variable costs of $10 per child per day. If it charges $25 a child per day, what will be its break-even point expressed in dollars of revenue? How much revenue would be required for Early Horizons Day Care to earn $100,000 net income per year?

Problems

Problem A Assume the local franchise of Togorio Sandwich Company assigns you the task of estimating total maintenance cost on its delivery vehicles. This cost is a mixed cost. You receive the following data from past months:

Month Units Costs
March 8,000 $14,000
April 10,000 14,960
May 9,000 15,200
June 11,000 15,920
July 10,000 15,920
August 13,000 16,880
September 14,000 18,080
October 18,000 19,280
November 20,000 21,200
  1. Using the high-low method, determine the total amount of fixed costs and the amount of variable cost per unit. Draw the cost line.
  2. Prepare a scatter diagram, plot the actual costs, and visually fit a linear cost line to the points. Estimate the amount of total fixed costs and the amount of variable cost per unit.


Problem B

  1. Using the preceding graph, label the relevant range, total costs, fixed costs, break-even point, and profit and loss areas.
  2. At 8,000 units, what are the variable costs, fixed costs, sales, and contribution margin amounts in dollars?
  3. At 8,000 units, is there net income or loss? How much?


Problem C The management of Bootleg Company wants to know the break-even point for its new line hiking boots under each of the following independent assumptions. The selling price is $50 pair of boots unless otherwise stated. (Each pair of boots is one unit.)

  1. Fixed costs are $300,000; variable cost is $30 per unit.
  2. Fixed costs are $300,000; variable cost is $20 per unit.
  3. Fixed costs are $250,000; variable cost is $20 per unit.
  4. Fixed costs are $250,000; selling price is $40; and variable cost is $30 per unit.


Compute the break-even point in units and sales dollars for each of the four independent case.

Problem D Refer to the previous problem. Bootleg Company's sales are $1,100,000. Determine the margin (safety in dollars for cases (a) through (d).

Problem E Using the data in the Bootleg Company problem (a through d), determine the level of sales dollars required achieve a net income of $125,000.

Problem F Bikes Unlimited, Inc., sells three types of bicycles. It has fixed costs of $258,000 per month. The sales and variable costs of these products for April follow:

Bikes
Racing Mountain Touring
Sales $1,00,000 $1,500,000 $2,500,000
Variable costs 700,000 900,000 1,250,000
Compute the break-even point in sales dollars.

Problem G a. Assume that fixed costs of Celtics Company are $180,000 per year, variable cost is $12 per unit, and selling price is $30 per unit. Determine the break-even point in sales dollars.

  1. Hawks Corporation breaks even when its sales amount to $89,600,000. In 2010, its sales were $14,400,000, and its variable costs amounted to $5,760,000. Determine the amount of its fixed costs.
  2. The sales of Niners Corporation last year amounted to $20,000,000, its variable costs were $6,000,000, and its fixed costs were $4,000,000. At what level of sales dollars would the Niners Corporation break even?
  3. What would have been the net income of the Niners Corporation in part (c), if sales volume had been 10% higher but selling prices had remained unchanged?
  4. What would have been the net income of the Niners Corporation in part (c), if variable costs had been 10% lower?
  5. What would have been the net income of the Niners Corporation in part (c), if fixed costs had been 10% lower?
  6. Determine the break-even point in sales dollars for the Niners Corporation on the basis of the data given in (e) and then in (f).


Answer each of the preceding questions.

Problem H After graduating from college, M. J. Orth started a company that produced cookbooks. After three years, Orth decided to analyze how well the company was doing. He discovered the company has fixed costs of $1,200,000 per year, variable cost of $14.40 per cookbook (on average), and a selling price of $26.90 per cookbook (on average).

How many units (that is, cookbooks) must be sold to break even? How many units will the company have to sell to earn $48,000?

Problem I The operating results for two companies follow:

Sierra Olympias
Sales (20,000) units $1,920,000 $1,920,000
Variable costs 480,000 1,056,000
Contribution margin 1,440,000 864,000
Fixed costs 960,000 384,00
Net income 480,000 480,000
  1. Prepare a cost-volume-profit chart for Sierra Company, indicating the break-even point, the contribution margin, and the areas of income and losses.
  2. Compute the break-even point of both companies in sales dollars and units.
  3. Assume that without changes in selling price, the sales of each company decline by 10%. Prepare income statements similar to the preceding statements for both companies.


Problem J Soundoff, Inc., a leading manufacturer of electronic equipment, decided to analyze the profitability of its new portable compact disc (CD) players. On the CD player line, the company incurred $2,520,000 of fixed costs per month while selling 20,000 units at $600 each. Variable cost was $240 per unit.

Recently, a new machine used in the production of CD players has become available; it is more efficient than the machine currently being used. The new machine would reduce the company's variable costs by 20%, and leasing it would increase fixed costs by $96,000 per year.

  1. Compute the break-even point in units assuming use of the old machine.
  2. Compute the break-even point in units assuming use of the new machine.
  3. Assuming that total sales remain at $12,000,000 and that the new machine is leased, compute the expected net income.
  4. Should the new machine be leased? Why?


Problem K Surething CD Company reports sales of $720,000, variable costs of $432,000, and fixed costs of $108,000. If the company spends $72,000 on a sales promotion campaign, it estimates that sales will be increased by $270,000.

Determine whether the sales promotion campaign should be undertaken. Provide calculations.

Alternate problems

Alternate problem A Hear Right Company has identified certain variable and fixed costs in its production of hearing aids. Management wants you to divide one of its mixed costs into its fixed and variable portions. Here are the data for this cost:

Month Units Costs
January 20,800 $57,600
February 20,000 54,000
March 22,000 58,500
April 25,600 57,600
May 28,400 58,500
June 30,000 62,100
July 32,800 63,900
August 35,600 68,400
September 37,600 72,000
October 40,000 77,400
  1. Using the high-low method, determine the total amount of fixed costs and the amount of variable cost per unit. Draw the cost line.
  2. Prepare a scatter diagram, plot the actual costs, and visually fit a linear cost line to the points. Estimate the amount of total fixed costs and the variable cost per unit.


Alternate problem B

  1. Using the preceding graph, label the relevant range, total costs, fixed costs, break-even point, and profit and loss areas.
  2. At 18,000 units, what would sales revenue, total costs, fixed and variable costs be?
  3. At 18,000 units, would there be a profit or loss? How much?


Alternate problem C Jefferson Company has a plant capacity of 100,000 units, at which level variable costs are $720,000. Fixed costs are expected to be $432,000. Each unit of product sells for $12.

  1. Determine the company's break-even point in sales dollars and units.
  2. At what level of sales dollars would the company earn net income of $144,000?
  3. If the selling price were raised to $14.40 per unit, at what level of sales dollars would the company earn $144,000?


Alternate problem D a. Determine the break-even point in sales dollars and units for Cowboys Company that has fixed costs of $63,000, variable cost of $24.50 per unit, and a selling price of $35.00 per unit.

  1. Wildcats Company breaks even when sales are $280,000. In March, sales were $670,000, and variable costs were $536,000. Compute the amount of fixed costs.
  2. Hoosiers Company had sales in June of $84,000; variable costs of $46,200; and fixed costs of $50,400. At what level of sales, in dollars, would the company break even?
  3. What would the break-even point in sales dollars have been in (c) if variable costs had been 10% higher?
  4. What would the break-even point in sales dollars have been in (c) if fixed costs had been 10% higher?
  5. Compute the break-even point in sales dollars for Hoosiers Company in (c) under the assumptions of (d) and (e) together.


Answer each of the preceding questions.

Alternate problem E See Right Company makes contact lenses. The company has a plant capacity of 200,000 units. Variable costs are $4,000,000 at 100% capacity. Fixed costs are $2,000,000 per year, but this is true only between 50,000 and 200,000 units.

  1. Prepare a cost-volume-profit chart for See Right Company assuming it sells its product for $40 each. Indicate on the chart the relevant range, break-even point, and the areas of net income and losses.
  2. Compute the break-even point in units.
  3. How many units would have to be sold to earn $200,000 per year?


Alternate problem F Mr Feelds Cookies has fixed costs of $360,000 per year. It sells three types of cookies. The cost and revenue data for these products follow:

Cookies
Cream cake Goo fill Sweet tooth
Sales $64,000 $95,0000 $131,000
Variable costs 38,400 55,100 66,000
Compute the break-even point in sales dollars.

Beyond the numbers—Critical thinking

Business decision case A Quality Furniture Company is operating at almost 100% of capacity. The company expects sales to increase by 25% in 2011. To satisfy the demand for its product, the company is considering two alternatives: The first alternative would increase fixed costs by 15% but not affect variable costs. The second alternative would not affect fixed costs but increase variable costs to 60% of the selling price of the company's product.

This is Quality Furniture Company's condensed income statement for 2010:

Sales $3,600,000
Costs:
Variable $1,620,000
Fixed 330,000 1,950,000
Income before taxes $1,650,000
  1. Determine the break-even point in sales dollars for 2011 under each of the alternatives.
  2. Determine projected income for 2011 under each of the alternatives.
  3. Which alternative would you recommend? Why?


Business decision case B When the Weidkamp Company's plant is completely idle, fixed costs amount to $720,000. When the plant operates at levels of 50% of capacity or less, its fixed costs are $840,000; at levels more than 50% of capacity, its fixed costs are $1,200,000. The company's variable costs at full capacity (100,000 units) amount to $1,800,000.

  1. Assuming that the company's product sells for $60 per unit, what is the company's break-even point in sales dollars?
  2. Using only the data given, at what level of sales would it be more economical to close the factory than to operate it? In other words, at what level would operating losses approximate the losses incurred if the factory closed down completely?
  3. Assume that Weidkamp Company is operating at 50% of its capacity and decides to reduce the selling price from $60 per unit to $36 per unit to increase sales. At what percentage of capacity must the company operate to break even at the reduced sales price?


Business decision case C Monroe Company has recently been awarded a contract to sell 25,000 units of its product to the federal government. Monroe manufactures the components of the product rather than purchasing them. When the news of the contract was released to the public, President Mary Monroe, received a call from the president of the McLean Corporation, Carl Cahn. Cahn offered to sell Monroe 25,000 units of a needed component, Part J, for $15.00 each. After receiving the offer, Monroe calls you into her office and asks you to recommend whether to accept or reject Cahn's offer.

You go to the company's records and obtain the following information concerning the production of Part J.

Costs at current production

level (200,000 units)
Direct labor $1,248,000
Direct materials 576,000
Manufacturing overhead 600,000
Total cost $2,424,000
You calculate the unit cost of Part J to be $12.12 or ($2,424,000/200,000). But you suspect that this unit cost may not hold true at all production levels. To find out, you consult the production manager. She tells you that to meet the increased production needs, equipment would have to be rented and the production workers would work some overtime. She estimates the machine rental to be $60,000 and the total overtime premiums to be $108,000. She provides you with the following information:

Costs at current production

level (225,000 units)
Direct labor $1,404,000
Direct materials 648,000
Manufacturing overhead

(including equipmental rental and overtime premiums)
828,000
Total cost $2,880,000
The production manager advises you to reject Cahn's offer, since the unit cost of Part J would be only $12.80 or ($2,880,000/225,000 units) with the additional costs of equipment rental and overtime premiums. This amount still is less than the $15.00 that Cahn would charge. Undecided, you return to your office to consider the matter further.

  1. Using the high-low method, compute the variable cost portion of manufacturing overhead. (Remember that the costs of equipment rental and overtime premiums are included in manufacturing overhead. Subtract these amounts before performing the calculation).
  2. Compute the total costs to manufacture the additional units of Part J. (Note: include overtime premiums as a part of direct labor.)
  3. Compute the unit cost to manufacture the additional units of Part J.
  4. Write a report recommending that Monroe accept or reject Cahn's offer.


Business decision case D Refer to the "A broader perspective: Major television networks are finding it harder to break even" discussion of cost-volume-profit analysis for television networks. Write a memo to your instructor describing how the networks can reduce their break-even points.

Group project E In teams of two or three students, develop a cost-volume-profit equation for a new business that you might start. Examples of such businesses are a portable espresso bar, a pizza stand, a campus movie theater, a package delivery service, a campus-to-airport limousine service, and a T-shirt printing business.

Your equation should be in the form: Profits = (Price per unit X Volume) – (Variable cost per unit X Volume) - Fixed costs per period. Pick a period of time, say one month, and project the unit price, volume, unit variable cost, and fixed costs for the period. From this information, you will be able to estimate the profits—or losses—for the period. Select one spokesperson for your team to tell the class about your proposed business and its profits or losses. Good luck, and have fun.

Group project F Refer to "A broader perspective: Even colleges use CVP" discussion of how cost-volume-profit analysis is used by colleges. In teams of two or three students, write a memo to your instructor defining step costs and explain why the step costs identified in the case are classified as such. Also include in your memo how the school might lower its break-even point.

Group project G In teams of two or three students, address the following questions:

  • Why would a company consider increasing automation and decreasing the use of labor if the result would be an increase in the break-even point?
  • Would an increase in automation increase fixed costs over the short-run, long-run, or both?


Write a memo to your instructor that addresses both questions. Be sure to explain your answers.

Using the Internet—A view of the real world

Visit the website for Intel Corporation, a high technology manufacturing company.

http://www.intel.com

Go to the company's most recent financial statements and review the consolidated statement of income. What additional information, if any, would you need to perform cost-volume-profit analysis? Why is this information excluded from Intel's income statement?

Visit the website for Wal-Mart Corporation, a retail company.

http://www.walmart.com

Go to the company's most recent financial statements and review the statement of income. What additional information, if any, would you need to perform cost-volume-profit analysis? Why is this information excluded from Wal-Mart Corporation's income statement?

level (225,000 units)Direct labor$1,404,000Direct materials648,000

Manufacturing overhead

(including equipmental rental and overtime premiums)

828,000Total cost$2,880,000

The production manager advises you to reject Cahn's offer, since the unit cost of Part J would be only $12.80 or ($2,880,000/225,000 units) with the additional costs of equipment rental and overtime premiums. This amount still is less than the $15.00 that Cahn would charge. Undecided, you return to your office to consider the matter further.

  1. Using the high-low method, compute the variable cost portion of manufacturing overhead. (Remember that the costs of equipment rental and overtime premiums are included in manufacturing overhead. Subtract these amounts before performing the calculation).
  2. Compute the total costs to manufacture the additional units of Part J. (Note: include overtime premiums as a part of direct labor.)
  3. Compute the unit cost to manufacture the additional units of Part J.
  4. Write a report recommending that Monroe accept or reject Cahn's offer.


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