Managerial Accounting: Ch.5 Cost-Volume-Profit Relationships

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:

Required:

1. Compute (a) last year’s 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 next year’s variable expenses will increase by $3 per ball. If this change takes place and the selling price per ball remains constant at $25, what will be next year’s CM ratio and the break-even 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 (as computed in requirement 1a), 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.

Solution

1. Compute (a) last year’s CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year’s sales level. (Round “Degree of operating leverage” to 2 decimal places.)
   

   CM ratio	40	%
   Unit sales to break even	21,000	balls
   Degree of operating leverage	3.33

   Explanation

   1-a.

   Selling price	25	100 %
   Variable expenses	15	60 %
   Contribution margin	10	40 %

   \(\begin{align*}
   \text{Profit} &= \text{Unit CM} × \text{Q} \ – \ \text{Fixed expenses} \\[6pt] $0 &= $10 × \text{Q} \ − \ $210,000 \\[6pt] $10\text{Q} &= $210,000 \\[6pt] \text{Q} &= $210,000 \ ÷ \ $10 \\[6pt] \text{Q} &= 21{,}000 \ \text{balls}
   \end{align*}\)
   1-b.
   The degree of operating leverage is:
   \(\begin{align*}
   \text{Degree of operating leverage} &= \frac{\text{Contribution margin}}{\text{Net operating income}} \\[6pt] &= \frac{$300{,}000}{$90{,}000} \quad = 3.33 \ \text{(rounded)}
   \end{align*}\)
2. Due to an increase in labor rates, the company estimates that next year’s variable expenses will increase by $3 per ball. If this change takes place and the selling price per ball remains constant at $25, what will be next year’s CM ratio and the break-even point in balls?
   

   CM Ratio	28	%
   Unit sales to break even	30,000	balls

   Explanation

   The new CM ratio will be:
   

   Selling price	25	100 %
   Variable expenses	18	72 %
   Contribution margin	7	28%

   The new break-even point will be:

   \(\begin{align*}
   \text{Profit} &= \text{Unit CM} × \text{Q} \ – \ \text{Fixed expenses} \\[6pt] $0 &= $7 × \text{Q} \ − \ $210{,}000 \\[6pt] $7\text{Q} &= $210{,}000 \\[6pt] \text{Q} &= $210{,}000 ÷ $7 \\[6pt] \text{Q} &= 30{,}000 \ \text{balls}
   \end{align*}\)
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? (Round your answer to the nearest whole unit.)
   

   Number of balls	42,857

   Explanation

   \(\begin{align*}
   \text{Profit} &= \text{Unit CM} × \text{Q} \ – \ \text{Fixed expenses} \\[6pt] $90{,}000 &= $7 × \text{Q} \ − \ $210{,}000 \\[6pt] $7\text{Q} &= $90{,}000 + $210{,}000 \\[6pt] \text{Q} &= $300{,}000 ÷ $7 \\[6pt] \text{Q} &= 42{,}857 \ \text{balls (rounded)}
   \end{align*}\)
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 (as computed in requirement 1a), what selling price per ball must it charge next year to cover the increased labor costs?

   Selling price	30

   Explanation

   The contribution margin ratio last year was 40%. If we let P equal the new selling price, then:

   \(\begin{align*}
   \text{P} &= $18 + 0.40\text{P} \\[6pt] 0.60\text{P} &= $18 \\[6pt] \text{P} &= $18 ÷ 0.60 \\[6pt] \text{P} &= $30
   \end{align*}\)

   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.

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?
   

   CM Ratio	64	%
   Unit sales to break even	26,250	balls

   Explanation

   The new CM ratio would be:

   Selling price	25	100 %
   Variable expenses	9*	36 %
   Contribution margin	16	64 %

   *$15 – ($15 × 40%) = $9

   The new break-even point would be:

   \(\begin{align*}
   \text{Profit} &= \text{Unit CM} × \text{Q} \ – \ \text{Fixed expenses} \\[6pt] $0 &= $16 × \text{Q} \ − \ ($210{,}000 × 2) \\[6pt] $16\text{Q} &= $420{,}000 \\[6pt] \text{Q} &= $420{,}000 ÷ $16 \\[6pt] \text{Q} &= 26{,}250 \ \text{balls}
   \end{align*}\)
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?
      

      Number of balls	31,875

      Solution

      \(\begin{align*}
      \text{Profit} &= \text{Unit CM} × \text{Q} \ – \ \text{Fixed expenses} \\[6pt] $90{,}000 &= $16 × \text{Q} \ − \ $420{,}000 \\[6pt] $16\text{Q} &= $90{,}000 + $420,000 \\[6pt] \text{Q} &= $510{,}000 ÷ $16 \\[6pt] \text{Q} &= 31{,}875 \ \text{balls}
      \end{align*}\)
   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.
      

      Northwood Company
      Contribution Income Statement
      Sales	750,000
      Variable expenses	270,000
      Contribution margin	480,000
      Fixed expenses	420,000
      Net operating income	60,000
      Degree of operating leverage	8

      Solution

      \( \text{Sales:} \ (30{,}000 \ \text{balls} × $25 \ \text{per ball}) = $750{,}000 \\[6pt] \text{Variable expenses:} \ (30{,}000 \ \text{balls} × $9 \ \text{per ball}) = $270{,}000 \\[6pt] \)
      \(\begin{align*}
      \text{Degree of operating leverage} &= \frac{\text{Contribution margin}}{\text{Net operating income}} \\[6pt] &= \frac{$480{,}000}{$60{,}000} = 8
      \end{align*}\)

Gold Star Rice, Ltd., of Thailand exports Thai rice throughout Asia. The company grows three varieties of rice—White, Fragrant, and Loonzain. Budgeted sales by product and in total for the coming month are shown below:

\( \text{Dollar sales to break-even} = \frac{\text{Fixed expenses}}{\text{CM ratio}} = \frac{$449{,}280}{0.64} = $702{,}000
\) As shown by these data, net operating income is budgeted at $30,720 for the month and the estimated break-even sales is $702,000.

Assume that actual sales for the month total $750,000 as planned; however, actual sales by product are: White, $300,000; Fragrant, $180,000; and Loonzain, $270,000.

Required:

1. Prepare a contribution format income statement for the month based on the actual sales data.
2. Compute the break-even point in dollar sales for the month based on your actual data.

Solution

1. Prepare a contribution format income statement for the month based on the actual sales data.
   

   Gold Star Rice, Ltd.
   Contribution Income Statement
   	Product
   	White		Fragrant		Loonzain		Total
   Percentage of total sales	40 %		24 %		36 %		100 %
   Sales	300,000	100 %	180,000	100 %	270,000	100 %	750,000	100 %
   Variable expenses	216,000	72 %	36,000	20 %	108,000	40 %	360,000	48 %
   Contribution margin	84,000	28 %	144,000	80 %	162,000	60 %	390,000	52 %
   Fixed expenses							449,280
   Net operating loss							(59,280)

   Total contribution margin: $390,000 ÷ $750,000 = 52%
   
2. Compute the break-even point in dollar sales for the month based on your actual data. (Do not round intermediate calculations.)

   Break-even point in dollar sales	864,000

   Explanation

   Break-even sales would be:

   \(\begin{align*}
   \text{Dollar sales to break even} &= \frac{\text{Fixed expenses}}{\text{CM ratio}} \\[6pt] &= \frac{$449{,}280}{0.52} = $864{,}000
   \end{align*}\)

Feather Friends, Inc., distributes a high-quality wooden birdhouse that sells for $20 per unit. Variable expenses are $8 per unit, and fixed expenses total $180,000 per year. Its operating results for last year were as follows:

Required:
Answer each question independently based on the original data:

1. What is the product’s CM ratio?
2. Use the CM ratio to determine the break-even point in dollar sales.
3. Assume this year’s unit sales and total sales increase by 3,750 units and $75,000, respectively. If the fixed expenses do not change, how much will net operating income increase?
4. 1. What is the degree of operating leverage based on last year’s sales?
   2. Assume the president expects this year’s unit sales to increase by 20%. Using the degree of operating leverage from last year, what percentage increase in net operating income will the company realize this year?
5. The sales manager is convinced that a 10% reduction in the selling price, combined with a $30,000 increase in advertising, would increase this year’s unit sales by 25%.
   1. If the sales manager is right, what would be this year’s net operating income if his ideas are implemented?
   2. If the sales manager’s ideas are implemented, how much will net operating income increase or decrease over last year?
6. The president does not want to change the selling price. Instead, he wants to increase the sales commission by $1 per unit. He thinks that this move, combined with some increase in advertising, would increase this year’s unit sales by 25%. How much could the president increase this year’s advertising expense and still earn the same $60,000 net operating income as last year?

Solution

1. What is the product’s CM ratio?
   

   CM ratio	60	%

   Explanation

   The CM ratio is 60%:
   

   Sales price	20.00	100 %
   Variable expenses	8.00	40 %
   Contribution margin	12.00	60 %

2. Use the CM ratio to determine the break-even point in dollar sales. (Do not round intermediate calculations.)
   

   Break-even point in dollar sales	300,000

   Explanation

   \(\begin{align*}
   \text{Dollar sales to break even} &= \frac{\text{Fixed expenses}}{\text{CM ratio}} \\[6pt] &= \frac{$180{,}000}{0.60} = $300{,}000
   \end{align*}\)
3. Assume this year’s unit sales and total sales increase by 3,750 units and $75,000, respectively. If the fixed expenses do not change, how much will net operating income increase?
   

   Net operating income	increases	by	45,000

   Explanation

   $75,000 increased sales × 0.60 CM ratio = $45,000 increased contribution margin. Because the fixed costs will not change, net operating income should also increase by $45,000.
   
4. 1. What is the degree of operating leverage based on last year’s sales?

      Degree of operating leverage	4

      Explanation

      The degree of operating leverage is calculated as follows:

      \(\begin{align*}
      \text{Degree of operating leverage} &= \frac{\text{Contribution margin}}{\text{Net operating income}} \\[6pt] &= \frac{$240{,}000}{$60{,}000} \\[6pt] &= 4
      \end{align*}\)
   2. Assume the president expects this year’s unit sales to increase by 20%. Using the degree of operating leverage from last year, what percentage increase in net operating income will the company realize this year?

      Net operating income increases by	80	%

      Explanation

      4 × 20% = 80% increase in net operating income. In dollars, this increase would be 80% × $60,000 = $48,000.

5. The sales manager is convinced that a 10% reduction in the selling price, combined with a $30,000 increase in advertising, would increase this year’s unit sales by 25%.
   1. If the sales manager is right, what would be this year’s net operating income if his ideas are implemented?

      Net operating income (loss)	40,000

      Explanation

      Sales (25,000 units × $18 per unit) = $450,000

      Variable expenses (25,000 units × $8 per unit) = $200,000

      Fixed expenses ($180,000 + $30,000) = $210,000

      Net operating income $450,000 – $200,000 – $210,000 = $40,000

   2. If the sales manager’s ideas are implemented, how much will net operating income increase or decrease over last year?

      Increase (decrease) to net operating income	(20,000)

      Explanation

      The sales manager’s suggestions should not be implemented because they will lower net operating income by $20,000 (= $60,000 – $40,000).

6. The president does not want to change the selling price. Instead, he wants to increase the sales commission by $1 per unit. He thinks that this move, combined with some increase in advertising, would increase this year’s unit sales by 25%. How much could the president increase this year’s advertising expense and still earn the same $60,000 net operating income as last year?

   The amount by which advertising can be increased is	35,000

   Expected total contribution margin:
   20,000 units × 1.25 × $11.00 per unit*	275,000
   Present total contribution margin	240,000
   Incremental contribution margin, and the amount by which advertising can be increased with net operating income remaining unchanged	35,000

   *$20.00 – ($8.00 + $1.00) = $11.00