Solution manual managerial accounting by cabrera 2010 chapter 13 answer

The degree of operating leverage at agiven level of sales is computed by dividing the contribution margin atthat level of sales by the net operating income.. A higher break-even point an

CHAPTER 13 COST-VOLUME-PROFIT RELATIONSHIPS

I Questions

1 The total “contribution margin” is the excess of total revenue over totalvariable costs The unit contribution margin is the excess of the unitprice over the unit variable costs

2 Total contribution margin:

Selling price manufacturing variable costs expensed nonmanufacturing variable costs expensed = Total contribution margin

4 In the short-run, without considering asset replacement, net operatingcash flows would be expected to exceed net income, because the latterincludes depreciation expense, while the former does not Thus, thecash basis break-even would be lower than the accrual break-even ifasset replacement is ignored However, if asset replacement costs aretaken into account, (i.e., on a “cradle to grave” basis), the long-run netcash flows equal long-run accrual net income, and the long-run break-even points are the same

5 Both unit price and unit variable costs are expressed on a per productbasis, as:

 = (P1 - V1) X1 + (P2 - V2) X2 +  + (Pn - Vn) Xn - F,for all products 1 to n where:

 = operating profit,

P = average unit selling price,

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V = average unit variable cost,

X = quantity of units,

F = total fixed costs for the period

6 If the relative proportions of products (i.e., the product “mix”) is notheld constant, products may be substituted for each other Thus, theremay be almost an infinite number of ways to achieve a target operatingprofit As shown from the multiple product profit equation, there areseveral unknowns for one equation:

 = (P1 - V1) X1 + (P2 - V2) X2 +  + (Pn - Vn) Xn - F,for all products 1 to n

7 A constant product mix is assumed to simplify the analysis Otherwise,there may be no unique solution

8 Operating leverage measures the impact on net operating income of agiven percentage change in sales The degree of operating leverage at agiven level of sales is computed by dividing the contribution margin atthat level of sales by the net operating income

9 Three approaches to break-even analysis are (a) the equation method,(b) the contribution margin method, and (c) the graphical method Inthe equation method, the equation is: Sales = Variable expenses + Fixedexpenses + Profits, where profits are zero at the break-even point Theequation is solved to determine the break-even point in units or pesosales

10 The margin of safety is the excess of budgeted (or actual) sales over thebreak-even volume of sales It states the amount by which sales candrop before losses begin to be incurred

11 The sales mix is the relative proportions in which a company’sproducts are sold The usual assumption in cost-volume-profit analysis

is that the sales mix will not change

12 A higher break-even point and a lower net operating income couldresult if the sales mix shifted from high contribution margin products tolow contribution margin products Such a shift would cause theaverage contribution margin ratio in the company to decline, resulting

in less total contribution margin for a given amount of sales Thus, netoperating income would decline With a lower contribution marginratio, the break-even point would be higher since it would require moresales to cover the same amount of fixed costs

II Exercises

Exercise 1 (Using a Contribution Format Income Statement)

Requirement 1

Sales (30,000 units × 1.15 = 34,500 units) P172,500 P5.00Less variable expenses 103,500 3.00Contribution margin 69,000 P2.00Less fixed expenses 50,000Net operating income P  19,000

Requirement 2

Sales (30,000 units × 1.20 = 36,000 units) P162,000 P4.50Less variable expenses 108,000 3.00Contribution margin 54,000 P1.50Less fixed expenses 50,000Net operating income P   4,000

Requirement 3

Sales (30,000 units × 0.95 = 28,500 units) P156,750 P5.50Less variable expenses 85,500 3.00Contribution margin 71,250 P2.50Less fixed expenses (P50,000 + P10,000) 60,000Net operating income P  11,250

Requirement 4

Sales (30,000 units × 0.90 = 27,000 units) P151,200 P5.60Less variable expenses 86,400 3.20Contribution margin 64,800 P2.40Less fixed expenses 50,000Net operating income P  14,800

Exercise 2 (Break-even Analysis and CVP Graphing)

Requirement 1

The contribution margin per person would be:

Price per ticket P30

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Less variable expenses:

Dinner P7Favors and program 3 10Contribution margin per person P20The fixed expenses of the Extravaganza total P8,000; therefore, the break-even point would be computed as follows:

Sales = Variable expenses + Fixed expense + Profits

or at P900 per lantern, P4,500,000 in sales

Requirement 2

An increase in the variable expenses as a percentage of the selling pricewould result in a higher break-even point The reason is that if variableexpenses increase as a percentage of sales, then the contribution marginwill decrease as a percentage of sales A lower CM ratio would mean thatmore lanterns would have to be sold to generate enough contributionmargin to cover the fixed costs

Requirement 3

Present:

8,000 Lanterns

Proposed: 10,000 Lanterns* Total Per Unit Total Per Unit

Less variable expenses 5,040,000 630 6,300,000 630Contribution margin 2,160,000 P270 1,800,000 P180Less fixed expenses 1,350,000 1,350,000

Net operating income P  810,000 P  450,000

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

** P900 per lantern × 0.9 = P810 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

Alternative solution:

Exercise 4 (Operating Leverage)

Requirement 1

Sales (30,000 doors) P18,000,000 P600Less variable expenses 12,600,000 420Contribution margin 5,400,000 P180Less fixed expenses 4,500,000Net operating income P 900,000

Requirement 2

a Sales of 37,500 doors represents an increase of 7,500 doors, or 25%,

over present sales of 30,000 doors Since the degree of operating

leverage is 6, net operating income should increase by 6 times as much,

or by 150% (6 × 25%)

b Expected total peso net operating income for the next year is:

Present net operating income P 900,000Expected increase in net operating income next year

(150% × P900,000) 1,350,000Total expected net operating income P2,250,000

Exercise 5 (Multiproduct Break-even Analysis)

Model E700 Model J1500 Total Company

Less variable expenses

280,000 40 90,000 30 370,000 37Contribution margin P420,000 60 P210,000 70 630,000 63 *

Net operating income P 31,500

Exercise 6 (Break-even Analysis; Target Profit; Margin of Safety)

Requirement 4

Margin of safety in peso terms:

Margin of safety in pesos = Total sales – Break-even sales

= P600,000 – P500,000 = P100,000Margin of safety in percentage terms:

Requirement 5

The CM ratio is 30%

Expected total contribution margin: P680,000 × 30% P204,000Present total contribution margin: P600,000 × 30% 180,000Increased contribution margin P  24,000Alternative solution:

P80,000 incremental sales × 30% CM ratio = P24,000

Since in this case the company’s fixed expenses will not change, monthlynet operating income will increase by the amount of the increasedcontribution margin, P24,000

Sales = Variable expenses + Fixed expenses + Profits

Multiply by the CM ratio x 25%

Expected increase in contribution margin P100,000

Since the fixed expenses are not expected to change, net operating incomewill increase by the entire P100,000 increase in contribution margincomputed above

Fixed expenses + Target profit

Contribution margin per unit =

P240,000 + P90,000P15 per unit = 22,000 units

Requirement 6

a

b Expected increase in sales 8%

Degree of operating leverage x 5 Expected increase in net operating income 40%

c If sales increase by 8%, then 21,600 units (20,000 x 1.08 = 21,600) will be sold next year The new income statement will be as follows:

Total Per Unit Percent of Sales

Sales (21,600 units) P1,296,000 P60 100%Less variable expenses 972,000 45 75%Contribution margin 324,000 P15 25%Less fixed expenses 240,000

Net operating income P 84,000

Thus, the P84,000 expected net operating income for next yearrepresents a 40% increase over the P60,000 net operating incomeearned during the current year:

Note from the income statement above that the increase in sales from20,000 to 21,600 units has resulted in increases in both total sales andtotal variable expenses It is a common error to overlook the increase

in variable expense when preparing a projected income statement

Margin of safety

percentage = Margin of safety in pesosTotal sales =

P240,000P1,200,000 = 20%

Degree of operating leverage =Contribution margin

Net operating income

= P300,000P60,000 = 5

P84,000 – P60,000

P24,000P60,000 = 40% increase

Contribution margin 288,000 P12 20%Less fixed expenses 210,000†

Net operating income P 78,000

Margin of safety in pesos = Total sales – Break-even sales

= P1,440,000 – P1,050,000 = P390,000

As shown in requirement (5) above, the company’s present margin ofsafety is only P240,000 Thus, several benefits will result from theproposed changes

Problem 2 (Basics of CVP Analysis; Cost Structure)

in peso sales = Fixed expensesCM ratio

= P210,0000.20

= P1,050,000

Total Per Unit Percentage

Less variable expenses 189,000 14 70

Contribution margin P  81,000 P  6 30 %The break-even point is:

Sales = Variable expenses + Fixed expenses + Profits

Incremental contribution margin:

P70,000 increased sales × 30% CM ratio P21,000Less increased fixed costs:

Increased advertising cost 8,000

Break-even point

in unit sales =

Fixed expensesContribution margin per unit

Increase in monthly net operating income P13,000Since the company presently has a loss of P9,000 per month, if the changesare adopted, the loss will turn into a profit of P4,000 per month.

a The new CM ratio would be:

The new break-even point would be:

b Comparative income statements follow:

Total Per Unit % Total Per Unit %

Sales (20,000 units) P400,000 P20 100 P400,000 P20 100Less variable expenses 280,000 14 70 140,000 7 35Contribution margin 120,000 6P 30 260,000 P13 65Less fixed expenses 90,000 208,000

Net operating income P  30,000 P  52,000

c Whether or not one would recommend that the company automate itsoperations depends on how much risk he or she is willing to take, anddepends heavily on prospects for future sales The proposed changeswould increase the company’s fixed costs and its break-even point.However, the changes would also increase the company’s CM ratio(from 30% to 65%) The higher CM ratio means that once the break-even point is reached, profits will increase more rapidly than at present

If 20,000 units are sold next month, for example, the higher CM ratiowill generate P22,000 more in profits than if no changes are made

The greatest risk of automating is that future sales may drop back down

to present levels (only 13,500 units per month), and as a result, losseswill be even larger than at present due to the company’s greater fixedcosts (Note the problem states that sales are erratic from month tomonth.) In sum, the proposed changes will help the company if salescontinue to trend upward in future months; the changes will hurt thecompany if sales drop back down to or near present levels

Note to the Instructor: Although it is not asked for in the problem, if

time permits you may want to compute the point of indifferencebetween the two alternatives in terms of units sold; i.e., the pointwhere profits will be the same under either alternative At this point,total revenue will be the same; hence, we include only costs in ourequation:

Let Q = Point of indifference in units soldP14Q + P90,000 = P7Q + P208,000

Problem 3 (Sales Mix; Multiproduct Break-even Analysis)

Requirement 1

Products

Percentage of total sales 32% 40% 28% 100%

Sales P160,000 100 % P200,000 100 % P140,000 100 % P500,000 100% Less variable expenses 48,000 30 160,000 80 77,000 55 285,000 57 Contribution margin P112,000 70 % P 40,000 20 % P 63,000 45 % 215,000 43%* Less fixed expenses 223,600

Net operating income (loss)

P ( 8,600)

Requirement 3

Memo to the president:

Although the company met its sales budget of P500,000 for the month, themix of products sold changed substantially from that budgeted This is thereason the budgeted net operating income was not met, and the reason thebreak-even sales were greater than budgeted The company’s sales mixwas planned at 48% Sinks, 20% Mirrors, and 32% Vanities The actualsales mix was 32% Sinks, 40% Mirrors, and 28% Vanities

As shown by these data, sales shifted away from Sinks, which provides ourgreatest contribution per peso of sales, and shifted strongly toward Mirrors,which provides our least contribution per peso of sales Consequently,although the company met its budgeted level of sales, these sales providedconsiderably less contribution margin than we had planned, with a resultingdecrease in net operating income Notice from the attached statements thatthe company’s overall CM ratio was only 43%, as compared to a planned

CM ratio of 52% This also explains why the break-even point was higherthan planned With less average contribution margin per peso of sales, agreater level of sales had to be achieved to provide sufficient contributionmargin to cover fixed costs

Problem 4 (Basic CVP Analysis)

28,000 units 42,000 units* Proposed:

Less variable expenses

1,680,000 60.00 2,520,000 60.00Contribution margin 2,520,000 P  90.00 3,150,000 P 75.00

Less fixed expenses 1,800,000 2,500,000

Net operating income P  720,000 P  650,000

* 28,000 units × 1.5 = 42,000 units

** P150 per unit × 0.90 = P135.00 per unit

No, the changes should not be made

Requirement 6

Expected total contribution margin:

28,000 units × 200% × P70 per unit* P3,920,000Present total contribution margin: 2,520,000

= P2,160,000P360,000 = 6

28,000 units × P90 per unit Incremental contribution margin, and the amount by which

advertising can be increased with net operating income

Purchase cost of the patches P15Commissions to the student salespersons 6 21Contribution margin P  9Since there are no fixed costs, the number of unit sales needed to yield thedesired P7,200 in profits can be obtained by dividing the target profit bythe unit contribution margin:

Requirement 2

Since an order has been placed, there is now a “fixed” cost associated withthe purchase price of the patches (i.e., the patches can’t be returned) Forexample, an order of 200 patches requires a “fixed” cost (investment) ofP3,000 (200 patches × P15 per patch = P3,000) The variable costs drop toonly P6 per patch, and the new contribution margin per patch becomes:

Selling price P30Less variable expenses (commissions only) 6Contribution margin P24Since the “fixed” cost of P3,000 must be recovered before Ms Moralesshows any profit, the break-even computation would be:

Target profitUnit contribution margin =

P7,200P9 per patch = 800 patches

=

800 patches x P30 per patch P24,000 in total sales