14e_GNB_CH05_SM

Chapter 5

Cost-Volume-Profit Relationships Solutions to Questions

5-1The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It is used in target profit and break-even analysis and can be used to quickly estimate the effect on profits of a change in sales revenue.

5-2Incremental analysis focuses on the changes in revenues and costs that will result from a particular action.

5-3All other things equal, Company B, with its higher fixed costs and lower variable costs, will have a higher contribution margin ratio than Company A. Therefore, it will tend to realize a larger increase in contribution margin and in profits when sales increase.

5-4Operating leverage measures the impact on net operating income of a given percentage change in sales. The degree of operating leverage at a given level of sales is computed by dividing the contribution margin at that level of sales by the net operating income at that level of sales.

5-5The break-even point is the level of sales at which profits are zero.

5-6(a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a higher unit volume. (b) If the fixed cost increased, then both the fixed cost line and the total cost line would shift upward and the break-even point would occur at a higher unit volume.

(c) If the variable cost increased, then the total cost line would rise more steeply and the break-even point would occur at a higher unit volume. 5-7The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It is the amount by which sales can drop before losses begin to be incurred.

5-8The sales mix is the relative proportions in which a company’s products are sold. The usual assumption in cost-volume-profit analysis is that the sales mix will not change.

5-9 A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin products to low contribution margin products. Such a shift would cause the average contribution margin ratio in the company to decline, resulting in less total contribution margin for a given amount of sales. Thus, net operating income would decline. With a lower contribution margin ratio, the break-even point would be higher because more sales would be required to cover the same amount of fixed costs.

1. The new income statement would be:

Total Per Unit

Sales (8,050 units) ..... $209,300 $26.00

Variable expenses ...... 144,900 18.00

Contribution margin .... 64,400 $ 8.00

Fixed expenses .......... 56,000

Net operating income . $ 8,400

You can get the same net operating income using the following approach.

Original net operating income .. $8,000

Change in contribution margin

(50 units × $8.00 per unit) (400)

New net operating income ....... $8,400

2. The new income statement would be:

Total Per Unit

Sales (7,950 units) ............ $206,700 $26.00

Variable expenses ............. 143,100 18.00

Contribution margin ........... 63,600 $ 8.00

Fixed expenses ................. 56,000

Net operating income ........ $ 7,600

You can get the same net operating income using the following approach.

Original net operating income ............. $8,000

Change in contribution margin

(-50 units × $8.00 per unit) (400)

New net operating income .................. $7,600

3. The new income statement would be:

Total Per Unit Sales (7,000 units) ....... $182,000 $26.00 Variable expenses ........ 126,000 18.00 Contribution margin ...... 56,000 $ 8.00 Fixed expenses ............ 56,000

Net operating income ... $ 0

Note: This is the company's break-even point.

1. The CVP graph can be plotted using the three steps outlined in the text.

The graph appears on the next page.

Step 1. Draw a line parallel to the volume axis to represent the total fixed expense. For this company, the total fixed expense is $12,000.

Step 2. Choose some volume of sales and plot the point representing total expenses (fixed and variable) at the activity level you have

selected. We’ll use the sales level of 2,000 units.

Fixed expenses ................................................... $12,000

Variable expenses (2,000 units × $24 per unit) ..... 48,000

Total expense ..................................................... $60,000

Step 3. Choose some volume of sales and plot the point representing total sales dollars at the activity level you have selected. We’ll use the sales level of 2,000 units again.

Total sales revenue (2,000 units × $36 per unit) ... $72,000

2. The break-even point is the point where the total sales revenue and the

total expense lines intersect. This occurs at sales of 1,000 units. This can be verified as follows:

Profit = Unit CM × Q – Fixed expenses

= ($36 ? $24) × 1,000 ? $12,000

= $12 × 1,000 ? $12,000

= $12,000 ? $12,000

= $0

1. The profit graph is based on the following simple equation:

Profit = Unit CM × Q ? Fixed expenses

Profit = ($19 ? $15) × Q ? $12,000

Profit = $4 × Q ? $12,000

To plot the graph, select two different levels of sales such as Q=0 and Q=4,000. The profit at these two levels of sales are -$12,000 (= $4 × 0 ? $12,000) and $4,000 (= $4 × 4,000 ? $12,000).

2. Looking at the graph, the break-even point appears to be 3,000 units.

This can be verified as follows:

Profit = Unit CM × Q ? Fixed expenses

= $4 × Q ? $12,000

= $4 × 3,000 ? $12,000

= $12,000 ? $12,000 = $0

1. The company’s contribution margin (CM) ratio is:

Total sales ............................ $300,000

Total variable expenses ......... 240,000

= Total contribution margin ... $ 60,000

÷ Total sales ......................... $300,000

= CM ratio ............................ 20%

2. The change in net operating income from an increase in total sales of

$1,500 can be estimated by using the CM ratio as follows:

Change in total sales ...................... $1,500

× CM ratio ..................................... 20%

= Estimated change in net

operating income ......................... $ 300

This computation can be verified as follows:

Total sales ................... $300,000

÷ Total units sold ......... 40,000 units

= Selling price per unit . $7.50 per unit

Increase in total sales ... $1,500

÷ Selling price per unit . $7.50 per unit

= Increase in unit sales 200 units

Original total unit sales . 40,000 units

New total unit sales ...... 40,200 units

Original New

Total unit sales............. 40,000 40,200

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

Variable expenses ........ 240,000 241,200

Contribution margin ...... 60,000 60,300

Fixed expenses ............ 45,000 45,000

Net operating income ... $ 15,000 $ 15,300

1. The following table shows the effect of the proposed change in monthly

advertising budget:

Sales With

Additional

Current Advertising

Sales Budget Difference

Sales ........................... $225,000 $240,000 $15,000

Variable expenses ........ 135,000 144,000 9,000

Contribution margin ...... 90,000 96,000 6,000

Fixed expenses ............ 75,000 83,000 8,000

Net operating income ... $ 15,000 $ 13,000 $(2,000)

Assuming that there are no other important factors to be considered, the increase in the advertising budget should not be approved because it would lead to a decrease in net operating income of $2,000.

Alternative Solution 1

Expected total contribution margin:

$240,000 × 40% CM ratio .................. $96,000

Present total contribution margin:

$225,000 × 40% CM ratio .................. 90,000

Incremental contribution margin ........... 6,000

Change in fixed expenses:

Less incremental advertising expense . 8,000

Change in net operating income ............ $(2,000)

Alternative Solution 2

Incremental contribution margin:

$15,000 × 40% CM ratio ................... $6,000

Less incremental advertising expense .... 8,000

Change in net operating income ............ $(2,000)

2. The $3 increase in variable expenses will cause the unit contribution

margin to decrease from $30 to $27 with the following impact on net operating income:

Expected total contribution margin with the

higher-quality components:

3,450 units × $27 per unit .............................. $93,150

Present total contribution margin:

3,000 units × $30 per unit .............................. 90,000

Change in total contribution margin .................... $ 3,150

Assuming no change in fixed expenses and all other factors remain the same, the higher-quality components should be used.

1. The equation method yields the required unit sales, Q, as follows:

Profit = Unit CM × Q ? Fixed expenses

$6,000 = ($140 ? $60) × Q ? $40,000

$6,000 = ($80) × Q ? $40,000

$80 × Q = $6,000 + $40,000

Q = $46,000 ÷ $80

Q = 575 units

2. The formula approach yields the required unit sales as follows:

Target profit + Fixed expenses Units sold to attain =

the target profit Unit contribution margin

$8,000 + $40,000

=

$48,000

=

$80 per unit

= 600 units

1. The equation method yields the break-even point in unit sales, Q, as

follows:

Profit = Unit CM × Q ? Fixed expenses

$0 = ($8 ? $6) × Q ? $5,500

$0 = ($2) × Q ? $5,500

$2Q = $5,500

Q = $5,500 ÷ $2

Q = 2,750 baskets

2. The equation method can be used to compute the break-even point in

sales dollars as follows:

Unit contribution margin

CM ratio =

Unit selling price

$2

= = 0.25

$8

Profit = CM ratio × Sales ? Fixed expenses

$0 = 0.25 × Sales ? $5,500

0.25 × Sales = $5,500

Sales = $5,500 ÷ 0.25

Sales = $22,000

3. The formula method gives an answer that is identical to the equation

method for the break-even point in unit sales:

Fixed expenses

Unit sales to break even =

Unit CM

$5,500

= = 2,750 baskets

$2 per basket

4. The formula method also gives an answer that is identical to the

equation method for the break-even point in dollar sales:

Fixed expenses

Dollar sales to break even =

CM ratio

$5,500

= = $22,000

0.25

1. To compute the margin of safety, we must first compute the break-even

unit sales.

Profit = Unit CM × Q ? Fixed expenses

$0 = ($25 ? $15) × Q ? $8,500

$0 = ($10) × Q ? $8,500

$10Q = $8,500

Q = $8,500 ÷ $10

Q = 850 units

Sales (at the budgeted volume of 1,000 units) .. $25,000

Break-even sales (at 850 units) ........................ 21,250

Margin of safety (in dollars) ............................. $ 3,750

2. The margin of safety as a percentage of sales is as follows:

Margin of safety (in dollars) ...................... $3,750

÷ Sales .................................................... $25,000

Margin of safety percentage ...................... 15%

1. The company’s degree of operating leverage would be computed as

follows:

Contribution margin ............... $36,000

÷ Net operating income ......... $12,000

Degree of operating leverage . 3.0

2. A 10% increase in sales should result in a 30% increase in net operating

income, computed as follows:

Degree of operating leverage ................................... 3.0

× Percent increase in sales ...................................... 10%

Estimated percent increase in net operating income .. 30%

3. The new income statement reflecting the change in sales is:

Amount Percent of Sales

Sales ........................... $132,000 100%

Variable expenses ........ 92,400 70%

Contribution margin ...... 39,600 30%

Fixed expenses ............ 24,000

Net operating income ... $ 15,600

Net operating income reflecting change in sales ...... $15,600 Original net operating income (a) ........................... 12,000 Change in net operating income (b) ....................... $ 3,600 Percent change in net operating income (b ÷ a) .....

1. The overall contribution margin ratio can be computed as follows:

Total contribution margin

Overall CM ratio =

Total sales

$120,000

= = 80%

$150,000

2. T he overall break-even point in sales dollars can be computed as follows:

Total fixed expenses

Overall break-even =

Overall CM ratio

$90,000

= = $112,500

80%

3. To construct the required income statement, we must first determine

the relative sales mix for the two products:

Predator Runway Total

Original dollar sales ...... $100,000 $50,000 $150,000

Percent of total ............ 67% 33% 100%

Sales at break-even ...... $75,000 $37,500 $112,500

Predator Runway Total

Sales ........................... $75,000 $37,500 $112,500

Variable expenses* ....... 18,750 3,750 22,500

Contribution margin ...... $56,250 $33,750 90,000

Fixed expenses ............ 90,000

Net operating income ... $ 0

*Predator variable expenses: ($75,000/$100,000) × $25,000 = $18,750 Runway variable expenses: ($37,500/$50,000) × $5,000 = $3,750

1. Profit = Unit CM × Q ? Fixed expenses

$0 = ($40 ? $28) × Q ? $150,000

$0 = ($12) × Q ? $150,000

$12Q = $150,000

Q = $150,000 ÷ $12 per unit

Q = 12,500 units, or at $40 per unit, $500,000

Alternatively:

Fixed expenses

Unit sales=

to break even Unit contribution margin

$150,000

==12,500 units

$12 per unit

or, at $40 per unit, $500,000.

2. The contribution margin at the break-even point is $150,000 because at

that point it must equal the fixed expenses.

3. Target profit + Fixed expenses

Units sold to attain=

target profit Unit contribution margin

$18,000+ $150,000

==14,000 units

$12 per unit

Total Unit Sales (14,000 units × $40 per unit) .............. $560,000 $40 Variable expenses

(14,000 units × $28 per unit) .................... 392,000 28 Contribution margin

(14,000 units × $12 per unit) .................... 168,000 $12 Fixed expenses ........................................... 150,000

Net operating income .................................. $ 18,000

4. Margin of safety in dollar terms:

Margin of safety = Total sales - Break-even sales

in dollars

= $600,000 - $500,000 = $100,000 Margin of safety in percentage terms:

Margin of safety in dollars

Margin of safety =

percentage Total sales

$100,000

= = 16.7% (rounded)

$600,000

5. The CM ratio is 30%.

Expected total contribution margin: $680,000 × 30% .... $204,000 Present total contribution margin: $600,000 × 30% ...... 180,000 Increased contribution margin ...................................... $ 24,000

Alternative solution:

$80,000 incremental sales × 30% CM ratio = $24,000

Given that the company’s fixed expenses will not change, monthly net operating income will increase by the amount of the increased

contribution margin, $24,000.

1. Profit = Unit CM × Q ? Fixed expenses

$0 = ($90 ? $63) × Q ? $135,000

$0 = ($27) × Q ? $135,000

$27Q = $135,000

Q = $135,000 ÷ $27 per lantern

Q = 5,000 lanterns, or at $90 per lantern, $450,000 in sales Alternative solution:

Fixed expenses

Unit sales =

to break even Unit contribution margin

$135,000

= = 5,000 lanterns,

$27 per lantern

or at $90 per lantern, $450,000 in sales

2. An increase in variable expenses as a percentage of the selling price

would result in a higher break-even point. If variable expenses increase as a percentage of sales, then the contribution margin will decrease as a percentage of sales. With a lower CM ratio, more lanterns would have to be sold to generate enough contribution margin to cover the fixed costs.

3.

Present:

8,000 Lanterns

Proposed:

10,000 Lanterns*

Sales .............................. $720,000 $90 $810,000 $81 ** Variable expenses ........... 504,000 63 630,000 63 Contribution margin ......... 216,000 $27 180,000 $18 Fixed expenses ............... 135,000 135,000

Net operating income ...... $ 81,000 $ 45,000

* 8,000 lanterns × 1.25 = 10,000 lanterns

** $90 per lantern × 0.9 = $81 per lantern

As shown above, a 25% increase in volume is not enough to offset a 10% reduction in the selling price; thus, net operating income decreases.

4. Profit = Unit CM × Q ? Fixed expenses

$72,000 = ($81 ? $63) × Q ? $135,000

$72,000 = ($18) × Q ? $135,000

$18Q = $207,000

Q = $207,000 ÷ $18 per lantern

Q = 11,500 lanterns

Alternative solution:

Target profit + Fixed expenses Unit sales to attain =

target profit Unit contribution margin

$72,000+ $135,000

= = 11,500 lanterns

$18 per lantern