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Fill in the missing amounts

5-11

Fill in the missing amounts in each of the eight case situations below. Each case is independent of the others. (Hint: One way to find the missing amounts would be to prepare a contribution format income statement for each case, enter the known data, and then compute the missing items.)

  1. Assume that only one product is being sold in each of the four following case situations:

                                                                                                                Contribution                      Net Operating

                                            Units                        Variable         Margin           Fixed            Income

                            Case     Sold         Sales       Expenses        per Unit       Expenses          (Loss)

  • 15,000 $180,000 $120,000         4          $50,000           10,000
  • 4,000 $100,000 60,000             $10      $32,000           $8,000
  • 10,000 200,000           $70,000           $13      118,000           $12,000
  • 6,000 $300,000         210,000           15        $100,000         $(10,000)
  1. Assume that more than one product is being sold in each of the four following case situations:

Average

                                                                                           Contribution                       Net Operating

Variable Margin Fixed Income Case Sales Expenses Ratio Expenses (Loss)

  • $500,000 400,000           20%     93,000              $7,000
  • $400,000 $260,000 35%    $100,000         40,000 
  • 250,000 100,000           60%     $130,000         $20,000
  • $600,000 $420,000 30%    185,000           $(5,000)

5-20

Northwood Company manufactures basketballs. The company has a ball that sells for $25. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $15 per ball, of which 60% is direct labor cost.

Last year, the company sold 30,000 of these balls, with the following results:

                   Sales (30,000 balls)         $750,000

                   Variable expenses             450,000

                    Contribution margin         300,000

                   Fixed expenses                 210,000

Net operating income           $  90,000 Required:

  1. Compute (a) the CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year’s sales level.
  2. Due to an increase in labor rates, the company estimates that variable expenses will increase by $3 per ball next year. If this change takes place and the selling price per ball remains constant at $25, what will be the new CM ratio and breakeven point in balls?
  3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $90,000, as last year?
  4. Refer again to the data in (2) above. The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year, what selling price per ball must it charge next year to cover the increased labor costs?
  5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 40%, but it would cause fixed expenses per year to double. If the new plant is built, what would be the company’s new CM ratio and new break-even point in balls?
  6. Refer to the data in (5) above.
    1. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $90,000, as last year?
    2. Assume the new plant is built and that next year the company manufactures and sells 30,000 balls (the same number as sold last year). Prepare a contribution format income statement and compute the degree of operating leverage.
    3. If you were a member of top management, would you have been in favor of constructing the new plant? Explain
  1. a.

                                    Unit sales to =         Fixed expenses

                                    break even       Unit contribution margin

$210,000

=

$10

                                                     = 21,000 balls                   

  1.      The degree of operating leverage is:

                                           Degree of          = Contribution margin

                                   operating leverage      Net operating income

$300,000

                                                                           =  = 3.33 (rounded)

                                                                    $90,000                             

  1. The new CM ratio will be:

Selling price .............................  $25 100% Variable expenses ....................   18  72%

                                Contribution margin ...............           $ 7        28%

                          Unit sales to =        Fixed expenses

                           break even       Unit contribution margin

$210,000

=  

$7

                                              = 30,000 balls                 

3.

Unit sales to attain = Target profit + Fixed expenses

                                 target profit              Unit contribution margin

$90,000 + $210,000

=  = 42,857 balls

                                                                             $7                                

  1. The contribution margin ratio last year was 40%. If we let P equal the new selling

price, then:

P = $18 + 0.40P

0.60P = $18 P = $18 ÷ 0.60

P = $30

                      To verify:

 Selling price .............................  $30 100%  Variable expenses ...................    18  60%

                                    Contribution margin ...............       $12          40%

      Therefore, to maintain a 40% CM ratio, a $3 increase in variable costs would require a $5 increase in the selling price.

  1. The new CM ratio would be:

Selling price ................................... $25  100% Variable expenses ..........................   9  36%

                                Contribution margin .....................       $16         64%

                      The new break-even point would be:

                          Unit sales to =        Fixed expenses

                           break even      Unit contribution margin

$420,000

                                                       =  = 26,250 balls

                                                        $16                       

      Although this new break-even point is greater than the company’s present breakeven point of 21,000 balls [see Part (1) above], it is less than the break-even point will be if the company does not automate and variable labor costs rise next year [see Part (2) above].

  1. a.

Unit sales to attain = Target profit + Fixed expenses target profit  Unit contribution margin

= $90,000 + $420,000  

$16

                                                           = 31,875 balls                          

                        Thus, the company will have to sell 1,875 more balls (31,875 – 30,000 = 1,875) than now being sold to earn a profit of $90,000 per year. However, this is still less than the 42,857 balls that would have to be sold to earn a $90,000 profit if the plant is not automated and variable labor costs rise next year [see Part (3) above].

  1. The contribution income statement would be:

Sales (30,000 balls × $25 per ball) .................................... 

$750,000

Variable expenses (30,000 balls × $9 per ball) ................. 

 270,000

Contribution margin ........................................................... 

480,000

Fixed expenses .................................................................... 

 420,000

Net operating income ......................................................... 

$ 60,000

                                    Degree of          = Contribution margin

                           operating leverage        Net operating income

$480,000

                                                                    =  = 8

                                                               $60,000                    

  1. This problem illustrates the difficulty faced by some companies. When variable labor costs increase, it is often difficult to pass these cost increases along to customers in the form of higher prices. Thus, companies are forced to automate resulting in higher operating leverage, often a higher break-even point, and greater risk for the company.

                        There is no clear answer as to whether one should have been in favor of constructing the new plant.

5-22

Due to erratic sales of its sole product—a high-capacity battery for laptop computers—PEM, Inc., has been experiencing financial difficulty for some time. The company’s contribution format income statement for the most recent month is given below:

                    Sales (19,500 units × $30 per unit)            $585,000 

                   Variable expenses                                        409,500 

                    Contribution margin                                    175,500 

                   Fixed expenses                                             180,000 

                   Net operating loss                                     $   (4,500)

Required:

  1. Compute the company’s CM ratio and its break-even point in unit sales and dollar sales.
  2. The president believes that a $16,000 increase in the monthly advertising budget, combined with an intensified effort by the sales staff, will result in an $80,000 increase in monthly sales. If the president is right, what will be the increase (decrease) in the company’s monthly net operating income?
  3. Refer to the original data. The sales manager is convinced that a 10% reduction in the selling price, combined with an increase of $60,000 in the monthly advertising budget, will double unit sales. If the sales manager is right, what will be the revised net operating income (loss)?
  4. Refer to the original data. The Marketing Department thinks that a fancy new package for the laptop computer battery would grow sales. The new package would increase packaging costs by 75 cents per unit. Assuming no other changes, how many units would have to be sold each month to attain a target profit of $9,750?
  5. Refer to the original data. By automating, the company could reduce variable expenses by $3 per unit. However, fixed expenses would increase by $72,000 each month.
    1. Compute the new CM ratio and the new break-even point in unit sales and dollar sales.
    2. Assume that the company expects to sell 26,000 units next month. Prepare two contribution format income statements, one assuming that operations are not automated and one assuming that they are. (Show data on a per unit and percentage basis, as well as in total, for each alternative.)
    3. Would you recommend that the company automate its operations? Explain.
  1. The CM ratio is 30%.

                                                                                                       Total         Per Unit       Percent of Sales

                                Sales (19,500 units) .................    $585,000       $30.00                  100%

                                Variable expenses ....................       409,500          21.00                    70%

                                Contribution margin ...............      $175,500       $ 9.00                    30%

                      The break-even point is:

                              Unit sales to =        Fixed expenses

                                break even      Unit contribution margin

=  = 20,000 units

Dollar sales to = Fixed expenses

                             break even             CM ratio

=  = $600,000 in sales   

  1. Incremental contribution margin:  

                          $80,000 increased sales × 0.30 CM ratio ..........................        $24,000

            Less increased advertising cost ..............................................    16,000              Increase in monthly net operating income ............................   $ 8,000

      Since the company is now showing a loss of $4,500 per month, if the changes are adopted, the loss will turn into a profit of $3,500 each month ($8,000 – $4,500 =

$3,50

3. Sales (39,000 units @ $27.00 per unit) ....................... 

      Variable expenses (39,000 units @ $21.00 per unit) ... 

       Contribution margin ..................................................... 

       Fixed expenses ($180,000 + $60,000) ........................ 

       Net operating loss .......................................................... 

$1,053,000      

    819,000     234,000     

    240,000

$      (6,000)  

4.

Unit sales to attain = Target profit + Fixed expenses

                                          target profit                      CM per unit

$9,750 + $180,000

=  

$8.25**

                                                                 = 23,000 units                         

  1. a. The new CM ratio would be:

                                                                                                  Per Unit          Percent of Sales

Sales .....................................  $30.00 100% Variable expenses ................   18.00  60%

                                 Contribution margin ............        $12.00                        40%

                            The new break-even point would be:

                              Unit sales to =        Fixed expenses

                               break even      Unit contribution margin

$180,000 + $72,000

=  

$12.00

= 21,000 units

Dollar sales to = Fixed expenses

                             break even            CM ratio

$180,000 + $72,000

=  

0.40

                                                  = $630,000                    

  1.     Comparative income statements follow:

                                                                                         Not Automated                              Automated

Sales (26,000

Per

     Total          Unit

%         

Total

Per Unit

%

units) ................... 

$780,000 $30.00

100      

$780,000

$30.00

100

Variable expenses .. 

Contribution

 546,000       21.00

 70       

 468,000

 18.00

 60

margin ................. 

234,000 $ 9.00

 30       

312,000

$12.00

 40

Fixed expenses ....... 

Net operating

 180,000                   

 252,000

income ................ 

$ 54,000                   

$ 60,000

5-28

Carbex, Inc., produces cutlery sets out of high-quality wood and steel. The company makes a Standard set and a Deluxe set and sells them to retail department stores throughout the country. The Standard set sells for $60, and the Deluxe set sells for $75. The variable expenses associated with each set are given below.

                                                                    Standard

Deluxe

                   Variable production costs                            $15.00      $30.00

Sales commissions (15% of sales price) $9.00 $   11.25   The company’s fixed expenses each month are:

                    Advertising         $105,000

                   Depreciation        $ 21,700

                   Administrative      $63,000

Mary Parsons, the financial vice president, watches sales commissions carefully and has noted that they have risen steadily over the last year. For this reason, she was shocked to find that even though sales have increased, profits for the current month—May—are down substantially from April. Sales, in sets, for the last two months are given below:

                Standard

Deluxe

Total

                    April      4,000       2,000     6,000

                    May         1,000      5,000     6,000

Required:

  1. Prepare contribution format income statements for April and May. Use the following headings:

                  Standard                    Deluxe                         Total

                       Amount Percent   Amount Percent   Amount Percent

Sales                                                                                             Etc.                                                                                                     

Place the fixed expenses only in the Total column. Do not show percentages for the fixed expenses.

  1. Explain the difference in net operating incomes between the two months, even though the same total number of sets was sold in each month.
  2. What can be done to the sales commissions to improve the sales mix?
    1. Using April’s sales mix, what is the break-even point in dollar sales?
    2. Without doing any calculations, explain whether the break-even point in May would be higher or lower than the break-even point in April. Why?

1.

Carbex, Inc.

Income Statement For April

                                                                                      Standard                   Deluxe                         Total

                                                                         Amount        %        Amount       %        Amount          %

                Sales ......................................     $240,000    100        $150,000 100  $390,000        100.0

                Variable expenses:                                                                                                                            

                     Production ........................          60,000       25         60,000      40        120,000       30.8

                     Sales commission ..............          36,000       15          22,500       15          58,500        15.0

                Total variable expenses ........          96,000      40          82,500      55         178,500       45.8

                 Contribution margin ............      $144,000        60  $  67,500        45       $211,500       54.2

                Fixed expenses:                                                                                                                                 

                     Advertising ........................                                                                           105,000                

                      Depreciation .....................                                                                              21,700                

                     Administrative ..................                                                                             63,000                

                Total fixed expenses .............                                                                            189,700                

                Net operating income ...........                                                                         $ 21,800                 

Carbex, Inc.

Income Statement For May

                                                                                           Standard                    Deluxe                            Total

                                                                      Amount       %         Amount         %           Amount           %

                  Sales ......................................  $60,000     100       $375,000      100        $435,000     100.0

                Variable expenses:                                                                                                                              

                     Production ........................        15,000      25         150,000       40           165,000       37.9

Sales commission ..............    9,000  15     56,250  15     65,250  15.0 Total variable expenses ........   24,000  40   206,250  55   230,250  52.9

                  Contribution margin ............  $36,000       60        $168,750        45           204,750        47.1

                Fixed expenses:                                                                                                                                   

Advertising ........................        105,000  Depreciation .....................        21,700 

Administrative ..................                                                             63,000         Total fixed expenses .............                                                      189,700          

                Net operating income ...........                                                                            $ 15,050                 

  1. The sales mix has shifted over the last year from Standard sets to Deluxe sets. This shift has caused a decrease in the company’s overall CM ratio from 54.2% in April to 47.1% in May. For this reason, even though total sales (in dollars) are greater, net operating income is lower.
  1. Sales commissions could be based on contribution margin rather than on sales price. A flat rate on total contribution margin, as the text suggests, might encourage the salespersons to emphasize the product with the greatest contribution to the profits.
  1. The break-even in dollar sales can be computed as follows:

Dollar sales to = Fixed expenses = $189,700 = $350,000

                            break even               CM ratio              0.542                      

  1. The break-even point in May would be higher than the break-even point in April. This occurs because the sales mix has shifted from the more profitable to the less profitable units, which in turn decreases the company’s overall CM ratio.

5-30

Angie Silva has recently opened The Sandal Shop in Brisbane, Australia, a store that specializes in fashionable sandals. In time, she hopes to open a chain of sandal shops. As a first step, she has gathered the following data for her new store:

                    Sales price per pair of sandals                            $40

                   Variable expenses per pair of sandals                  16

Contribution margin per pair of sandals       $24 Fixed expenses per year:

                       Building rental                                         $ 15,000

                       Equipment depreciation                               7,000

                       Selling                                                        20,000

                       Administrative                                           18,000

Total fixed expenses            $60,000 Required:

  1. What is the break-even point in unit sales and dollar sales?
  2. Prepare a CVP graph or a profit graph for the store from zero pairs up to 4,000 pairs of sandals sold each year. Indicate the break-even point on your graph.
  3. Angie has decided that she must earn a profit of $18,000 the first year to justify her time and effort. How many pairs of sandals must be sold to attain this target profit?
  4. Angie now has two salespersons working in the store—one full time and one part time. It will cost her an additional $8,000 per year to convert the part-time position to a full-time position. Angie believes that the change would increase annual sales by $25,000. Should she convert the position? Use the incremental approach. (Do not prepare an income statement.)
  5. Refer to the original data. During the first year, the store sold only 3,000 pairs of sandals and reported the following operating results:

                            Sales (3,000 pairs)          $120,000

                           Variable expenses              48,000

                            Contribution margin           72,000

                           Fixed expenses                   60,000

                           Net operating income      $ 12,000

  1. What is the store’s degree of operating leverage?
  2. Angie is confident that with a more intense sales effort and with a more creative advertising program she can increase sales by 50% next year. Using the degree of operating leverage, what would be the expected percentage increase in net operating income if Angie is able to increase sales by 50%?

  1.

Unit sales to = Fixed expenses = $60,000 = 2,500 pairs

                          break even         CM per unit         $24.00                    

Dollar sales to = Fixed expenses = $60,000 = $100,000  break even     CM ratio     0.60 

  1. See the graphs at the end of this solution.

3.

Unit sales to attain = Target profit + Fixed expenses

                                 target profit               Unit contribution margin

$18,000 + $60,000

=  = 3,250 pairs

                                                                           $24.00                            

4. Incremental contribution margin:

$25,000 increased sales × 60% CM ratio ................. 

$15,000

       Incremental fixed salary cost ........................................ 

   8,000

       Increased net income .................................................... 

$ 7,000

                      Yes, the position should be converted to a full-time basis.

  1. a. Degree of           = Contribution margin = $72,000 = 6

                                        operating leverage      Net operating income       $12,000       

  1. 6 × 50% sales increase = 300% increase in net operating income. Thus, net operating income next year would be: $12,000 + ($12,000 × 300%) =

$48,000.

5-33

Pittman Company is a small but growing manufacturer of telecommunications equipment. The company has no sales force of its own; rather, it relies completely on independent sales agents to market its products. These agents are paid a sales commission of 15% for all items sold.

Barbara Cheney, Pittman’s controller, has just prepared the company’s budgeted income statement for next year as follows:

Pittman Company

Budgeted Income Statement

For the Year Ended December 31

                    Sales                                                                                $   16,000,000

                    Manufacturing expenses:                                                             

                    Variable                                                  $7,200,000                               

Fixed overhead          2,340,000                   9,540,000 Gross margin                                 6,460,000

                   Selling and administrative expenses:                                                      

                   Commissions to agents                             2,400,000                               

                    Fixed marketing expenses                          120,000*                              

                    Fixed administrative expenses                 1,800,000              4,320,000

                   Net operating income                                                             2,140,000

                    Fixed interest expenses                                                             540,000

                   Income before income taxes                                                   1,600,000

                   Income taxes (30%)                                                                   480,000

                   Net income                                                                    $    1,120,000

 

*Primarily depreciation on storage facilities.

As Barbara handed the statement to Karl Vecci, Pittman’s president, she commented, “I went ahead and used the agents’ 15% commission rate in completing these statements, but we’ve just learned that they refuse to handle our products next year unless we increase the commission rate to 20%.”

“That’s the last straw,” Karl replied angrily. “Those agents have been demanding more and more, and this time they’ve gone too far. How can they possibly defend a 20% commission rate?”

“They claim that after paying for advertising, travel, and the other costs of promotion, there’s nothing left over for profit,” replied Barbara.

“I say it’s just plain robbery,” retorted Karl. “And I also say it’s time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at?”

“We’ve already worked them up,” said Barbara. “Several companies we know about pay a 7.5% commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $2,400,000 per year, but that would be more than offset by the $3,200,000 (20% × $16,000,000) that we would avoid on agents’ commissions.”

The breakdown of the $2,400,000 cost follows:

Salaries:

                       Sales manager                  $    100,000

                       Salespersons                           600,000

                   Travel and entertainment            400,000

                    Advertising                             1,300,000

                    Total                                      $2,400,000

“Super,” replied Karl. “And I noticed that the $2,400,000 equals what we’re paying the agents under the old 15% commission rate.”

“It’s even better than that,” explained Barbara. “We can actually save $75,000 a year because that’s what we’re paying our auditors to check out the agents’ reports. So our overall administrative expenses would be less.”

“Pull all of these numbers together and we’ll show them to the executive committee tomorrow,” said Karl. “With the approval of the committee, we can move on the matter immediately.”

Required:

  1. Compute Pittman Company’s break-even point in dollar sales for next year assuming:
    1. The agents’ commission rate remains unchanged at 15%.
    2. The agents’ commission rate is increased to 20%.
    3. The company employs its own sales force.
  2. Assume that Pittman Company decides to continue selling through agents and pays the 20% commission rate. Determine the dollar sales that would be required to generate the same net income as contained in the budgeted income statement for next year.
  3. Determine the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents (at a 20% commission rate) or employs its own sales force.
  4. Compute the degree of operating leverage that the company would expect to have at the end of next year assuming:
    1. The agents’ commission rate remains unchanged at 15%.
    2. The agents’ commission rate is increased to 20%.
    3. The company employs its own sales force.

Use income before income taxes in your operating leverage computation.

  1. Based on the data in (1) through (4) above, make a recommendation as to whether the company should continue to use sales agents (at a 20% commission rate) or employ its own sales force. Give reasons for your answer.

  

Before proceeding with the solution, it is helpful first to restructure the data into contribution format for each of the three alternatives. (The data in the statements below are in thousands.)

                                                                              15% Commission     20% Commission        Own Sales Force

Sales ............................................... 

$16,000

100%

$16,000

100%

$16,000.00 100.0%

Variable expenses:

             

Manufacturing ........................... 

7,200

7,200

      7,200.00               

Commissions (15%, 20% 7.5%) . 

   2,400

   3,200

    1,200.00                

Total variable expenses ................. 

   9,600

 60%

 10,400

 65%

    8,400.00  52.5%

Contribution margin ..................... 

   6,400

 40%

   5,600

 35%

    7,600.00  47.5%

Fixed expenses:

             

Manufacturing overhead ........... 

2,340

2,340

      2,340.00               

Marketing .................................. 

120

120

      2,520.00               

Administrative ........................... 

1,800

1,800

       1,725.00               

Interest ....................................... 

      540

     540

       540.00                 

Total fixed expenses ...................... 

   4,800

   4,800

    7,125.00                 

Income before income taxes ......... 

1,600

800

          475.00               

Income taxes (30%) ...................... 

      480

     240

      142.50                  

Net income .................................... 

$ 1,120

$   560

$    332.50                 

  1. When the income before taxes is zero, income taxes will also be zero and net income will be zero. Therefore, the break-even calculations can be based on the income before taxes.
  1. Break-even point in dollar sales if the commission remains 15%:

Dollar sales to = Fixed expenses = $4,800,000 = $12,000,000 break even CM ratio       0.40  

  1. Break-even point in dollar sales if the commission increases to 20%:

Dollar sales to = Fixed expenses = $4,800,000 = $13,714,286 break even CM ratio       0.35  

  1. Break-even point in dollar sales if the company employs its own sales force:

Dollar sales to = Fixed expenses = $7,125,000 = $15,000,000 break even CM ratio       0.475

  1. In order to generate a $1,120,000 net income, the company must generate

$1,600,000 in income before taxes. Therefore,

Dollar sales to = Target income before taxes + Fixed expenses

                           attain target                                      CM ratio

$1,600,000 + $4,800,000

                                                         =  

0.35

$6,400,000

=  = $18,285,714

                                                                      0.35                                                             

  1. To determine the volume of sales at which net income would be equal under either the 20% commission plan or the company sales force plan, we find the volume of sales where costs before income taxes under the two plans are equal. See the next page for the solution.

                                                                 X = Total sales revenue

                               0.65X + $4,800,000 = 0.525X + $7,125,000

                                                        0.125X = $2,325,000

                                                                 X = $2,325,000 ÷ 0.125

                                                                 X = $18,600,000

      Thus, at a sales level of $18,600,000 either plan would yield the same income before taxes and net income. Below this sales level, the commission plan would yield the largest net income; above this sales level, the sales force plan would yield the largest net income.

  1. , b., and c.

15% 

Commission

20% 

Commission

Own 

Sales Force

Contribution margin (Part 1) (a) .............. 

$6,400,000

$5,600,000

$7,600,000

Income before taxes (Part 1) (b) ................

$1,600,000

$800,000

$475,000

Degree of operating leverage: (a) ÷ (b) .... 

4

7

16

  1. We would continue to use the sales agents for at least one more year, and possibly for two more years. The reasons are as follows:

                           First, use of the sales agents would have a less dramatic effect on net income.

                        Second, use of the sales agents for at least one more year would give the company more time to hire competent people and get the sales group organized.

                        Third, the sales force plan doesn’t become more desirable than the use of sales agents until the company reaches sales of $18,600,000 a year. This level probably won’t be reached for at least one more year, and possibly two years.

                        Fourth, the sales force plan will be highly leveraged since it will increase fixed costs (and decrease variable costs). One or two years from now, when sales have reached the $18,600,000 level, the company can benefit greatly from this leverage. For the moment, profits will be greater and risks will be less by staying with the agents, even at the higher 20% commission rate.

5A-4

To prepare a scattergraph plot in Excel, begin by highlighting the data in cells B4 through C10 (as shown in Exhibit 5A4). From the Charts group within the Insert tab, select the “Scatter” subgroup and then click on the choice that has no lines connecting the data points. This should produce a scattergraph plot similar to the one shown in Exhibit 5A5. Notice that the number of patient-days is plotted on the X-axis and the maintenance cost is plotted on the Y-axis.7 As we saw verified earlier in Exhibit 5A1, the data is approximately linear, so it makes sense to proceed with estimating a regression equation that minimizes the sum of the squared errors.

  1. The scattergraph appears below:

Yes, there is an approximately linear relationship between the number of units shipped and the total shipping expense.

  1. The high-low estimates and cost formula are computed as follows:

                                                                         Units Shipped       Shipping Expense

                                     

       High activity level (June) .............                 8                             $2,700

            Low activity level (July) ...............             2           1,200             Change ..........................................  6          $1,500

      Variable cost element:

                                                          Change in expense    $1,500

                                                                                                                =           =$250 per unit.

                                                            Change in activity    6 units                       

  Fixed cost element:

Shipping expense at high activity level ........................................         $2,700 Less variable cost element ($250 per unit × 8 units) ..................      2,000

                Total fixed cost .............................................................................            $ 700

                                                                         The cost formula is $700 per month plus $250 per unit shipped or Y = $700 + $250X,

      where X is the number of units shipped.

      The scattergraph on the following page shows the straight line drawn through the high and low data points.

Units Shipped

  1. The high-low estimate of fixed costs is $210.71 (= $910.71 – $700.00) lower than the estimate provided by least-squares regression. The high-low estimate of the variable cost per unit is $32.14 (= $250.00 – $217.86) higher than the estimate provided by least-squares regression. A straight line that minimized the sum of the squared errors would intersect the Y-axis at $910.71 instead of $700. It would also have a flatter slope because the estimated variable cost per unit is lower than the high-low method.
  1. The cost of shipping units is likely to depend on the weight and volume of the units shipped and the distance traveled as well as on the number of units shipped. In addition, higher cost shipping might be necessary to meet a deadline.

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