Solution manual managerial accounting concept and applications by cabrera 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:

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

π = operating profit,

P = average unit selling price,

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:

π = (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

13 The contribution margin (CM) ratio is the ratio of the total contributionmargin to total sales revenue It can be used in a variety of ways Forexample, the change in total contribution margin from a given change

in total sales revenue can be estimated by multiplying the change intotal sales revenue by the CM ratio If fixed costs do not change, then apeso increase in contribution margin will result in a peso increase in netoperating income The CM ratio can also be used in break-evenanalysis Therefore, knowledge of a product’s CM ratio is extremelyhelpful in forecasting contribution margin and net operating income

14 Incremental analysis focuses on the changes in revenues and costs thatwill result from a particular action

15 All other things equal, Company B, with its higher fixed costs andlower variable costs, will have a higher contribution margin ratio thanCompany A Therefore, it will tend to realize a larger increase incontribution margin and in profits when sales increase

16 (a) If the selling price decreased, then the total revenue line would riseless steeply, and the break-even point would occur at a higher unitvolume (b) If the fixed cost increased, then both the fixed cost line andthe total cost line would shift upward and the break-even point wouldoccur at a higher unit volume (c) If the variable cost increased, thenthe total cost line would rise more steeply and the break-even pointwould occur at a higher unit volume

II Exercises

Exercise 1 (Using a Contribution Format Income Statement)

Requirement 1

Total Per Unit

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 P1.50

Less 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 P30Less variable expenses:

Dinner P7Favors and program 3 10Contribution margin per person P20

The fixed expenses of the Extravaganza total P8,000; therefore, the even point would be computed as follows:

break-Sales = Variable expenses + Fixed expense + Profits

P30Q = P10Q + P8,000 + P0

P20Q = P8,000

Q = P8,000 ÷ P20 per person

Q = 400 persons; or, at P30 per person, P12,000

Total Sales

Break-even point: 400 persons,

or P12,000 in sales

Break-even point

in unit sales

= Unit contribution marginFixed expenses

= P1,350,000P270 per

lantern

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*

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)

Requirement 1

Unit sales to attain target profit

= Fixed expenses + Target profitUnit contribution margin

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)

or, at P40 per unit, P500,000.

Requirement 4

Margin of safety in peso terms:

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

= P600,000 – P500,000 = P100,000

Break-even point

Margin 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

Exercise 7 (Changes in Variable Costs, Fixed Costs, Selling Price, and Volume)

Requirement (1)

The following table shows the effect of the proposed change in monthly advertising budget:

Sales With Additional Current Advertising

Sales P225,000 P240,000 P15,000Variable expenses 135,000 144,000 9,000Contribution margin 90,000 96,000 6,000Fixed expenses 75,000 83,000 8,000

Net operating income P 15,000 P 13,000 P(2,000)Assuming that there are no other important factors to be considered, theincrease in the advertising budget should not be approved since it wouldlead to a decrease in net operating income of P2,000.

Alternative Solution 1

Expected total contribution margin:

P240,000 × 40% CM ratio P96,000Present total contribution margin:

P225,000 × 40% CM ratio 90,000Incremental contribution margin 6,000Change in fixed expenses:

Less incremental advertising expense 8,000Change in net operating income P(2,000)Alternative Solution 2

Incremental contribution margin:

P15,000 × 40% CM ratio P 6,000Less incremental advertising expense 8,000Change in net operating income P(2,000)

Requirement (2)

The P3 increase in variable costs will cause the unit contribution margin todecrease from P30 to P27 with the following impact on net operatingincome:

Expected total contribution margin with the higher-quality

Exercise 8 (Compute the Margin of Safety)

Requirement (1)

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

Sales = Variable expenses + Fixed expenses + Profits

Requirement (2)

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

Margin of safety (in pesos) P3,750

÷ Sales P25,000Margin of safety as a percentage of sales 15.0%

Exercise 9 (Compute and Use the Degree of Operating Leverage)

Requirement (1)

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

follows:

Contribution margin P36,000

÷ Net operating income P12,000

Degree of operating leverage 3.0

Requirement (2)

A 10% increase in sales should result in a 30% increase in net operatingincome, computed as follows:

Degree of operating leverage 3.0

× Percent increase in sales 10%Estimated percent increase in net operating income 30%

Requirement (3)

The new income statement reflecting the change in sales would be:

Amount

Percent of Sales

Sales P132,000 100%

Variable expenses 92,400 70%

Contribution margin 39,600 30%

Fixed expenses 24,000

Net operating income P 15,600

Net operating income reflecting change in sales P15,600Original net operating income P12,000Percent change in net operating income 30%

Exercise 10 (Compute the Break-Even Point for a Multiproduct Company)

Requirement (3)

To construct the required income statement, we must first determine the relative sales mix for the two products:

Original peso sales P100,000 P50,000 P150,000Percent of total 67% 33% 100%Sales at break-even P75,000 P37,500 P112,500

Sales P75,000 P37,500 P112,500Variable expenses* 18,750 3,750 22,500Contribution margin P56,250 P33,750 90,000Fixed expenses 90,000Net operating income P 0

*Ping variable expenses: (P75,000/P100,000) × P25,000 = P18,750

Pong variable expenses: (P37,500/P50,000) × P5,000 = P3,750

Exercise 11 (Break-Even and Target Profit Analysis)

Let Q = Break-even point in units

Sales = Variable expenses + Fixed expenses + Profits

Let X = Break-even point in sales pesos.

X = 0.60X + P360,000 + P00.40X = P360,000

X = P450,000 ÷ 0.40

X = P1,125,000

In units: P1,125,000 ÷ P60 per unit = 18,750 units

c The company’s new cost/revenue relationships will be:

Selling price P60 100%Variable expenses (P36 – P3) 33 55%Contribution margin P27 45%P60Q = P33Q + P360,000 + P0

X = P360,000 ÷ 0.45

X = P800,000

In units: P800,000 ÷ P60 per unit = 13,333 units (rounded)

in unit sales = Unit contribution marginFixed expenses

= P360,000 ÷ P24 per unit = 15,000 units

= P360,000 ÷ P27 per unit

In sales pesos: 13,333 units × P60 per unit = P800,000 (rounded)

Alternative solution:

In units: P800,000 ÷ P60 per unit = 13,333 (rounded)

Exercise 12 (Operating Leverage)

Requirement (1)

Sales (30,000 doors) P1,800,000 P60Variable expenses 1,260,000 42Contribution margin 540,000 P18Fixed expenses 450,000

Net operating income P 90,000

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 operatingleverage 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 90,000Expected increase in net operating income next year

= P540,000 ÷ P90,000 = 6

Total expected net operating income P225,000

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

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:

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:

Fixed expenses + Target profit

Contribution margin per unit =

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

Degree of operating leverage =Contribution margin

Net operating income

= P300,000P60,000 = 5