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Solutions Manual, Chapter 6 255
Chapter 6
Cost-Volume-Profit Relationships
Solutions to Questions
6-1 The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety of ways. For example, the change in total contribu- tion margin from a given change in total sales revenue can be estimated by multiplying the change in total sales revenue by the CM ratio. If fixed costs do not change, then a dollar increase in contribution margin will result in a dollar in- crease in net operating income. The CM ratio can also be used in break-even analysis. There- fore, knowledge of a product’s CM ratio is ex- tremely helpful in forecasting contribution mar- gin and net operating income.
6-2 Incremental analysis focuses on the changes in revenues and costs that will result from a particular action.
6-3 All 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.
6-4 Operating leverage measures the impact on net operating income of a given percentage change in sales. The degree of operating lever- age at a given level of sales is computed by di- viding the contribution margin at that level of sales by the net operating income at that level of sales.
6-5 The break-even point is the level of sales at which profits are zero. It can also be defined as the point where total revenue equals total cost or as the point where total contribu- tion margin equals total fixed cost.
6-6 Three approaches to break-even analy- sis are (a) the graphical method, (b) the equa-
tion method, and (c) the contribution margin method. In the graphical method, total cost and total revenue data are plotted on a graph. The inter- section of the total cost and the total revenue lines indicates the break-even point. The graph shows the break-even point in both units and dollars of sales. The equation method uses some variation of the equation Sales = Variable expenses + Fixed expenses + Profits, where profits are zero at the break-even point. The equation is solved to de- termine the break-even point in units or dollar sales. In the contribution margin method, total fixed cost is divided by the contribution margin per unit to obtain the break-even point in units. Al- ternatively, total fixed cost can be divided by the contribution margin ratio to obtain the break- even point in sales dollars. 6-7 (a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a high- er 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. 6-8 The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It states the amount by which sales can drop before losses begin to be in- curred. 6-9 The 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.
256 Managerial Accounting, 12th Edition
6-10 A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin prod- ucts to low contribution margin products. Such a shift would cause the average contribution mar- gin ratio in the company to decline, resulting in
less total contribution margin for a given amount of sales. Thus, net operating income would de- cline. 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.
258 Managerial Accounting, 12th Edition
Exercise 6-1 (continued)
- The new income statement would be:
Total Per Unit Sales (7,000 units) ....... $182,000 $26. Variable expenses ........ 126,000 18. Contribution margin...... 56,000 $ 8. Fixed expenses ............ 56, Net operating income ... $ 0 Note: This is the company's break-even point.
Solutions Manual, Chapter 6 259
Exercise 6-2 (20 minutes)
- 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 select- ed. We’ll use the sales level of 2,000 units. Fixed expense ..................................................... $12, Variable expense (2,000 units × $24 per unit) ...... 48, Total expense ..................................................... $60,
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,
- 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 by solving for the break-even point in unit sales, Q, using the equation method as follows: Sales = Variable expenses + Fixed expenses + Profits $36Q = $24Q + $12,000 + $ $12Q = $12, Q = $12,000 ÷ $12 per unit Q = 1,000 units
Solutions Manual, Chapter 6 261
Exercise 6-3 (10 minutes)
- The company’s contribution margin (CM) ratio is:
Total sales ............................ $300, Total variable expenses ......... 240, = Total contribution margin ... 60, ÷ Total sales ......................... $300, = CM ratio ............................ 20%
- 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, × CM ratio ..................................... 20% = Estimated change in net operat- ing income .................................. $ 300 This computation can be verified as follows: Total sales ................... $300, ÷ Total units sold ......... 40,000 units = Selling price per unit. $7.50 per unit
Increase in total sales ... $1, ÷ 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, Sales ........................... $300,000 $301, Variable expenses ........ 240,000 241, Contribution margin...... 60,000 60, Fixed expenses ............ 45,000 45, Net operating income ... $ 15,000 $ 15,
262 Managerial Accounting, 12th Edition
Exercise 6-4 (20 minutes)
- 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, Variable expenses ........ 135,000 144,000 9, Contribution margin...... 90,000 96,000 6, Fixed expenses ............ 75,000 83,000 8, 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 since 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, Present total contribution margin: $225,000 × 40% CM ratio .................. 90, Incremental contribution margin ........... 6, Change in fixed expenses: Less incremental advertising expense. 8, Change in net operating income ............ $(2,000)
Alternative Solution 2 Incremental contribution margin: $15,000 × 40% CM ratio................... $ 6, Less incremental advertising expense .... 8, Change in net operating income ............ $(2,000)
264 Managerial Accounting, 12th Edition
Exercise 6-5 (20 minutes)
- The equation method yields the break-even point in unit sales, Q, as fol- lows: Sales = Variable expenses + Fixed expenses + Profits $8Q = $6Q + $5,500 + $ $2Q = $5, Q = $5,500 ÷ $2 per basket Q = 2,750 baskets
- The equation method can be used to compute the break-even point in sales dollars, X, as follows: Per Unit
Percent of Sales Sales price ...................... $8 100% Variable expenses ........... 6 75% Contribution margin......... $2 25% Sales = Variable expenses + Fixed expenses + Profits X = 0.75X + $5,500 + $ 0.25X = $5, X = $5,500 ÷ 0. X = $22,
- The contribution margin method gives an answer that is identical to the equation method for the break-even point in unit sales: Break-even point in units sold = Fixed expenses ÷ Unit CM = $5,500 ÷ $2 per basket = 2,750 baskets
- The contribution margin method also gives an answer that is identical to the equation method for the break-even point in dollar sales: Break-even point in sales dollars = Fixed expenses ÷ CM ratio = $5,500 ÷ 0. =$22,
Solutions Manual, Chapter 6 265
Exercise 6-6 (10 minutes)
- The equation method yields the required unit sales, Q, as follows:
Sales = Variable expenses + Fixed expenses + Profits $140Q = $60Q + $40,000+ $6, $80Q = $46, Q = $46,000 ÷ $80 per unit Q = 575 units
- The contribution margin yields the required unit sales as follows:
Units sold to attain Fixed expenses + Target profit the target profit = Unit contribution margin
$40,000 + $8,
$80 per unit
$48,
$80 per unit
= 600 units
Solutions Manual, Chapter 6 267
Exercise 6-8 (20 minutes)
- The company’s degree of operating leverage would be computed as fol- lows: Contribution margin............... $36, ÷ Net operating income ......... $12, Degree of operating leverage. 3.
- A 10% increase in sales should result in a 30% increase in net operating income, computed as follows: Degree of operating leverage ................................... 3. × Percent increase in sales ...................................... 10% Estimated percent increase in net operating income .. 30%
- The new income statement reflecting the change in sales would be:
Amount
Percent of Sales Sales ........................... $132,000 100% Variable expenses ........ 92,400 70% Contribution margin...... 39,600 30% Fixed expenses ............ 24, Net operating income ... $ 15, Net operating income reflecting change in sales ...... $15, Original net operating income ................................ $12, Percent change in net operating income ................. 30%
268 Managerial Accounting, 12th Edition
Exercise 6-9 (20 minutes)
- The overall contribution margin ratio can be computed as follows:
Total contribution margin Overall CM ratio = Total sales
$120, = = 80% $150,
- The overall break-even point in sales dollars can be computed as fol- lows: Total fixed expenses Overall break-even = Overall CM ratio
$90, = = $112, 80%
- 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, Percent of total ............ 67% 33% 100% Sales at break-even ...... $75,000 $37,500 $112,
Predator Runway Total Sales ........................... $75,000 $37,500 $112, Variable expenses*....... 18,750 3,750 22, Contribution margin...... $56,250 $33,750 90, Fixed expenses ............ 90, Net operating income ... $ 0
*Predator variable expenses: ($75,000/$100,000) × $25,000 = $18, Runway variable expenses: ($37,500/$50,000) × $5,000 = $3,
270 Managerial Accounting, 12th Edition
Exercise 6-10 (continued)
- Margin of safety in dollar terms:
Margin of safety = Total sales - Break-even sales in dollars
= $600,000 - $500,000 = $100, Margin of safety in percentage terms:
Margin of safety^ Margin of safety in dollars percentage = Total sales
$100, = = 16.7% (rounded) $600,
- The CM ratio is 30%.
Expected total contribution margin: $680,000 × 30% .... $204, Present total contribution margin: $600,000 × 30% ...... 180, Increased contribution margin ...................................... $ 24,
Alternative solution: $80,000 incremental sales × 30% CM ratio = $24, Since in this case the company’s fixed expenses will not change, month- ly net operating income will increase by the amount of the increased contribution margin, $24,000.
Solutions Manual, Chapter 6 271
Exercise 6-11 (30 minutes)
- The contribution margin per person would be:
Price per ticket .................................................. $ Variable expenses: Dinner ............................................................ $ Favors and program ........................................ 3 10 Contribution margin per person .......................... $ The fixed expenses of the Extravaganza total $8,000; therefore, the break-even point would be computed as follows: Sales = Variable expenses + Fixed expense + Profits $30Q = $10Q + $8,000 + $ $20Q = $8, Q = $8,000 ÷ $20 per person Q = 400 persons; or, at $30 per person, $12,
Alternative solution:
Break-even point^ Fixed expenses
in unit sales (^) Unit contribution margin
$8, = = 400 persons $20 per person or, at $30 per person, $12,000.
- Variable cost per person ($7 + $3) ....................... $ Fixed cost per person ($8,000 ÷ 250 persons) ...... 32 Ticket price per person to break even ................... $
Exercise 6-12 (20 minutes)
- Solutions Manual, Chapter
- Sales (30,000 units × 1.15 = 34,500 units) $172,500 $5. Total Per Unit
- Variable expenses 103,500 3.
- Contribution margin.................................... 69,000 $2.
- Fixed expenses 50,
- Net operating income $ 19,
- Sales (30,000 units × 1.20 = 36,000 units) $162,000 $4.
- Variable expenses 108,000 3.
- Contribution margin.................................... 54,000 $1.
- Fixed expenses 50,
- Net operating income $ 4,
- Sales (30,000 units × 0.95 = 28,500 units) $156,750 $5.
- Variable expenses 85,500 3.
- Contribution margin.................................... 71,250 $2.
- Fixed expenses ($50,000 + $10,000) 60,
- Net operating income $ 11,
- Sales (30,000 units × 0.90 = 27,000 units) $151,200 $5.
- Variable expenses 86,400 3.
- Contribution margin.................................... 64,800 $2.
- Fixed expenses 50,
- Net operating income $ 14,
274 Managerial Accounting, 12th Edition
Exercise 6-13 (20 minutes)
a. Case #1 Case # Number of units sold .... 9,000 * 14, Sales ........................... $270,000 * $30 $350,000 * $ Variable expenses ........ 162,000 * 18 140,000 10 Contribution margin...... 108,000 $12 210,000 $15 * Fixed expenses ............ 90,000 * 170,000 * Net operating income ... $ 18,000 $ 40,000 *
Case #3 Case # Number of units sold .... 20,000 * 5,000 * Sales ........................... $400,000 $20 $160,000 * $ Variable expenses ........ 280,000 * 14 90,000 18 Contribution margin...... 120,000 $ 6 * 70,000 $ Fixed expenses ............ 85,000 82,000 * Net operating income ... $ 35,000 * $(12,000) *
b. Case #1 Case # Sales ........................... $450,000 * 100 % $200,000 * 100 % Variable expenses ........ 270,000 60 130,000 * 65 Contribution margin...... 180,000 40 %* 70,000 35 % Fixed expenses ............ 115,000 60,000 * Net operating income ... $ 65,000 * $ 10,
Case #3 Case # Sales ........................... $700,000 100 % $300,000 * 100 % Variable expenses ........ 140,000 20 90,000 * 30 Contribution margin...... 560,000 80 %* 210,000 70 % Fixed expenses ............ 470,000 * 225, Net operating income ... $ 90,000 * $ (15,000) *
*Given
