Solution manual managerial accounting concept and applications by cabrera chapter 13 answer

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1111111CHAPTER 13
COST-VOLUME-PROFIT RELATIONSHIPS
I.
Questions
1.
The total “contribution margin” is the excess of total revenue over total variable
costs. The unit contribution margin is the excess of the unit price over the unit variable
costs.
2.
Total contribution margin:
Selling price - manufacturing variable costs expensed - nonmanufacturing
variable costs expensed = Total contribution margin.
Gross margin:
Selling price - variable manufacturing costs expensed - fixed manufacturing
costs expensed = Gross margin.
3.
A company operating at “break-even” is probably not covering costs which are
not recorded in the accounting records. An example of such a cost is the opportunity cost
of owner-invested capital. In some small businesses, owner-managers may not take a
salary as large as the opportunity cost of forgone alternative employment. Hence, the
opportunity cost of owner labor may be excluded.
4.
In the short-run, without considering asset replacement, net operating cash flows

would be expected to exceed net income, because the latter includes depreciation
expense, while the former does not. Thus, the cash basis break-even would be lower than
the accrual break-even if asset replacement is ignored. However, if asset replacement
costs are taken into account, (i.e., on a “cradle to grave” basis), the long-run net cash
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 product basis, 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,
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 not held
constant, products may be substituted for each other. Thus, there may be almost an

infinite number of ways to achieve a target operating profit. As shown from the multiple
product profit equation, there are several 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 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.
9.
Three approaches to break-even analysis are (a) the equation method, (b) the
contribution margin method, and (c) the graphical method. In the equation method, the
equation is: Sales = Variable expenses + Fixed expenses + Profits, where profits are zero
at the break-even point. The equation is solved to determine the break-even point in units
or peso sales.
10.
The margin of safety is the excess of budgeted (or actual) sales over the breakeven volume of sales. It states the amount by which sales can drop before losses begin to
be incurred.
11.
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.
12.
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 breakeven point would be higher since it would require more sales to cover the same amount of

fixed costs.
13.
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
contribution 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 peso increase in contribution margin will result in a peso increase in net
operating income. The CM ratio can also be used in break-even analysis. Therefore,
knowledge of a product’s CM ratio is extremely helpful in forecasting contribution
margin and net operating income.
14.
Incremental analysis focuses on the changes in revenues and costs that will
result from a particular action.
15.
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.
16.
(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.
II.

Exercises

Exercise 1 (Using a Contribution Format Income Statement)
Requirement 1
TotalPer UnitSales (30,000 units × 1.15 = 34,500 units)
P172,500P5.00Less
variable expenses 103,500 3.00Contribution margin
69,000P2.00Less fixed
expenses
50,000Net operating income
P33333333 1393,30303033333333
3R3e3q3u3i3r3e3m3e3n3t3 323
3
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3
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3
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3
The contribution margin per person would be:


Price per ticket P30Less variable expenses:Dinner P7Favors and program
10Contribution margin per person P20

3

The fixed expenses of the Extravaganza total P8,000; therefore, the
break-even point would be computed as follows:
Sales =Variable expenses + Fixed expense + ProfitsP30Q=P10Q + P8,000 +
P0P20Q=P8,000Q=P8,000 ÷ P20 per personQ=400 persons; or, at P30 per person,
P12,000
Alternative solution:

or, at P30 per person, P12,000.
Requirement 2
Variable cost per person (P7 + P3) P10Fixed cost per person (P8,000 ÷ 250 persons)
32Ticket price per person to break even
P42

Requirement 3
Cost-volume-profit graph:
EMBED MSGraph.Chart.8 \s ﾵ ﾵ Exercise 3 (Break-even and Target Profit Analysis)
Requirement 1
Sales=Variable expenses + Fixed expenses + ProfitsP900Q=P630Q + P1,350,000 +
P0P270Q=P1,350,000Q=P1,350,000 ÷ P270 per lanternQ=5,000 lanterns, or at P900 per
lantern, P4,500,000 in sales
Alternative solution:


or at P900 per lantern, P4,500,000 in sales
Requirement 2
An increase in the variable expenses as a percentage of the selling price would result in a
higher break-even point. The reason is that if variable expenses increase as a percentage
of sales, then the contribution margin will decrease as a percentage of sales. A lower CM
ratio would mean that more lanterns would have to be sold to generate enough
contribution margin to cover the fixed costs.
Requirement 3
Present:
8,000 Lanterns Proposed:
10,000 Lanterns*TotalPer UnitTotalPer UnitSales
P7,200,000P900P8,100,000P810**Less variable expenses
5,040,000 630

6,300,000 630Contribution margin
2,160,000P2701,800,000P180 Less fixed
expenses
1,350,000 1,350,000Net operating income
P
555555555555555555555555555555555555555555555555555555555555555555555555
555555555555555555555555555555555555555555555555555555555555555555555555
5555555555555 851505,505050555P5 455505,50505055555 5
5
5*5
585,5050505 5l5a5n5t5e5r5n5s5 5×5 515.52555 5=5 51505,5050505
5l5a5n5t5e5r5n5s5
5*5*5 5P5950505 5p5e5r5 5l5a5n5t5e5r5n5 5×5 505.595 5=5 5P5851505 5p5e5r5
5l5a5n5t5e5r5n5
5
5
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Requirement 4
Sales=Variable expenses + Fixed expenses + ProfitsP810Q=P630Q + P1,350,000 +
P720,000P180Q=P2,070,000Q=P2,070,000 ÷ P180 per lanternQ=11,500 lanterns
Alternative solution:


Exercise 4 (Operating Leverage)
Requirement 1

Sales (30,000 doors)
P18,000,000P600Less variable expenses
12,600,000
420Contribution margin 5,400,000P180Less 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
Model E700Model J1500Total CompanyAmount%Amount%Amount%Sales
P700,000100P300,000100P1,000,000100Less variable expenses
280,000 40 90,000 30 370,000 37Contribution margin
P420,000 60P210,000 70630,000 63*Less fixed expenses
598,500Net
operating income P 31,500
* 630,000 ÷ P1,000,000 = 63%.
Requirement 2
The break-even point for the company as a whole would be:

Requirement 3
The additional contribution margin from the additional sales can be computed as follows:
P50,000 × 63% CM ratio = P31,500
Assuming no change in fixed expenses, all of this additional contribution margin should
drop to the bottom line as increased net operating income.
This answer assumes no change in selling prices, variable costs per unit, fixed expenses,
or sales mix.
Exercise 6 (Break-even Analysis; Target Profit; Margin of Safety)
Requirement 1
Sales=Variable expenses + Fixed expenses + ProfitsP40Q=P28Q + P150,000 +
P0P12Q=P150,000Q=P150,000 ÷ P12 per unitQ=12,500 units, or at P40 per unit,
P500,000
Alternatively:

or, at P40 per unit, P500,000.
Requirement 2
The contribution margin at the break-even point is P150,000 since at that point it must
equal the fixed expenses.
Requirement 3

TotalUnitSales (14,000 units × P40 per unit)

P560,000P40Less variable expenses

(14,000 units × P28 per unit)
392,000 28Contribution margin
(14,000 units × P12 per unit)
168,000P12Less fixed expenses7 77 7

7175707,7070707777N7e7t7 7o7p7e7r7a7t7i7n7g7 7i7n7c7o7m7e7 77P7
1787,7070707777


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8
8
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88P8280848,808080888P8r8e8s8e8n8t8
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= P24,000
Since in this case the company’s fixed expenses will not change, monthly net operating
income will increase by the amount of the increased contribution 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 WithAdditionalCurrentAdvertisingSalesBudgetDifferenceSales
P225,000P240,000P15,000Variable expenses
135,000 144,000 9,000Contribution margin
90,00096,0006,000Fixed
expenses
75,000 83,000 8,000Net operating income
P 15,000P 13,000P(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 P2,000.
Alternative Solution 1
Expected total contribution margin:
P240,000 × 40% CM ratioP96,000Present 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
to decrease from P30 to P27 with the following impact on net operating income:
Expected total contribution margin with the higher-quality components:
3,450 units × P27 per unit P93,150Present total contribution margin:
3,000 units × P30 per unit 90,000Change in total contribution margin P 3,150
Assuming no change in fixed costs and all other factors remain the
same, the higher-quality components should be used.
Exercise 8 (Compute the Margin of Safety)
Requirement (1)
To compute the margin of safety, we must first compute the break-even
unit sales.
Sales= Variable expenses + Fixed expenses + ProfitsP25Q= P15Q + P8,500 + P0P10Q=
P8,500Q= P8,500 ÷ P10 per unitQ= 850 units
Sales (at the budgeted volume of 1,000 units)
P25,000Break-even sales (at 850
units)
21,250Margin of safety (in pesos) P 3,750
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
operating leverage
Requirement (2)

P36,000÷ Net operating income
3.0

P12,000Degree of

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
percent increase in net operating income
30%
Requirement (3)

10%Estimated

The new income statement reflecting the change in sales would be:
AmountPercent of SalesSales
P132,000100%Variable expenses
92,400 70%Contribution margin 39,600 30%Fixed expenses
24,000Net
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 (1)
The overall contribution margin ratio can be computed as follows:


Requirement (2)
The overall break-even point in sales pesos can be computed as follows:

Requirement (3)
To construct the required income statement, we must first determine the
relative sales mix for the two products:
PingPongTotalOriginal peso sales P100,000P50,000P150,000Percent of total
67%33%100%Sales at break-even
P75,000P37,500P112,500PingPongTotalSales
P75,000P37,500P112,500Variable expenses*
18,750 3,750 22,500Contribution margin P56,250P33,75090,000Fixed
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)
Requirement (1)
Variable expenses: P60 × (100% – 40%) = P36.
Requirement (2)
a.Selling price P60100%Variable expenses
36 60%Contribution margin
P24 40%

Let Q = Break-even point in units.
Sales=Variable expenses + Fixed expenses + ProfitsP60Q=P36Q + P360,000 +
P0P24Q=P360,000Q=P360,000 ÷ P24 per unitQ=15,000 units
In sales pesos: 15,000 units × P60 per unit = P900,000
Alternative solution:
Let X=Break-even point in sales pesos.X=0.60X + P360,000 +
P00.40X=P360,000X=P360,000 ÷ 0.40X=P900,000


In units: P900,000 ÷ P60 per unit = 15,000 units
b.P60Q=P36Q + P360,000 + P90,000P24Q=P450,000Q=P450,000 ÷ P24 per
unitQ=18,750 units
In sales pesos: 18,750 units × P60 per unit = P1,125,000
Alternative solution:
X=0.60X + P360,000 + P90,0000.40X=P450,000X=P450,000 ÷ 0.40X=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
P60100%Variable expenses (P36 – P3)
33 55%Contribution
margin P27 45%
P60Q=P33Q + P360,000 + P0P27Q=P360,000Q=P360,000 ÷ P27 per unitQ=13,333
units (rounded).
In sales pesos: 13,333 units × P60 per unit = P800,000
(rounded)
Alternative solution:
X=0.55X + P360,000 + P00.45X=P360,000X=P360,000 ÷ 0.45X=P800,000

In units: P800,000 ÷ P60 per unit = 13,333 units (rounded)
Requirement (3)
a.

In sales pesos: 15,000 units × P60 per unit = P900,000
Alternative solution:

In units: P900,000 ÷ P60 per unit = 15,000
units
b.


In sales pesos: 18,750 units × P60 per unit = P1,125,000
Alternative solution:

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

c.

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)
P1,800,000P60Variable expenses 1,260,000 42Contribution

margin 540,000P18Fixed expenses
450,000Net 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 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
P1
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14R14e14q14u14i14r14e14m14e14n14t14 14214
14
14S14a14l14e14s1414=1414V14a14r14i14a14b14l14e14 14e14x14p14e14n14s14e14s14
14+14 14F14i14x14e14d14 14expenses + ProfitsP60Q=P45Q + P240,000 +


P0P15Q=P240,000Q=P240,000 ÷ P15 per unitQ=16,000 units, or at P60 per unit,
P960,000
Alternative solution:
X=0.75X + P240,000 + P00.25X =P240,000 X=P240,000 ÷ 0.25X=P960,000; or at P60
per unit, 16,000 units
Requirement 3
Increase in sales
P400,000
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 income will increase

by the entire P100,000 increase in contribution margin computed above.
Requirement 4
Sales=Variable expenses + Fixed expenses + ProfitsP60Q=P45Q + P240,000 +
P90,000P15Q=P330,000Q=P330,000 ÷ P15 per unitQ=22,000 units
Contribution margin method:

Requirement 5
Margin of safety in pesos =

Total sales

–

P240,000

–

Break-even sales
=

P960,000

=

P1,200,000

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 UnitPercent of SalesSales (21,600 units)
P1,296,000P60100%Less variable
expenses
972,000 45 75%Contribution margin 324,000P15 25%Less
fixed expenses
240,000Net operating income P 84,000
Thus, the P84,000 expected net operating income for next year represents a 40%
increase over the P60,000 net operating income earned during the current year:

Note from the income statement above that the increase in sales from 20,000 to
21,600 units has resulted in increases in both total sales and total variable expenses. It is
a common error to overlook the increase in variable expense when preparing a projected
income statement.
Requirement 7
a.
A 20% increase in sales would result in 24,000 units being sold next year:
20,000 units x 1.20 = 24,000 units.

Total
Per UnitPercent of SalesSales (24,000 units)
P1,440,000P60100%Less variable
expenses
1,152,000 48* 80%Contribution margin 288,000P12 20%Less
fixed expenses
210,000†Net operating income P 78,000
* P45 + P3 = P48;
P48 ( P60 = 80%.
† P240,000 – P30,000 = P210,000.
Note that the change in per unit variable expenses results in a change in both the
per unit contribution margin and the CM ratio.

b.


c.
Yes, based on these data the changes should be made. The changes will increase
the company’s net operating income from the present P60,000 to P78,000 per year.
Although the changes will also result in a higher break-even point (17,500 units as
compared to the present 16,000 units), the company’s margin of safety will actually be
wider than before:
Margin of safety in pesos =
=

P1,440,000

Total sales
–

–

P1,050,000

Break-even sales
= P390,000

As shown in requirement (5) above, the company’s present margin of safety is only
P240,000. Thus, several benefits will result from the proposed changes.
Problem 2 (Basics of CVP Analysis; Cost Structure)
Requirement 1
The CM ratio is 30%.
TotalPer UnitPercentageSales (13,500 units)
P270,000P20100%Less variable
expenses
189,000 14 70Contribution margin
P1
717171717171717171717171717171717171717171717171717171717171717171717171
717171717171717171717171717171717171717171717171717171717171717171717171
717171717171717171717171717171717171717171717171717171717171717171717171
717171717171717171717171717171717171717171717171717171717171717171717171
717171717171717171717171717171717171717171717171717171717171717171717171
717171717171717171717171717171717171717171717171717171717171717171717171
7171717171717171717171717171717171717171717171717171717171717
817117,1701701701717P17 61717 1731701717%171717
17
17
17
17
17

17T17h17e17 17b17r17e17a17k17-17e17v17e17n17
17p17o17i17n17t17 17i17s17:17
17
17S17a17l17e17s1717=1717V17a17r17i17a17b17l17e17 17e17x17p17e17n17s17e17s17
17+17 17F17i17x17e17d17 17e17x17p17e17n17s17e17s17 17+17
17P17r17o17f17i17t17s171717P17217017Q1717=1717P17117417Q17 17+17
17P17917017,17017017017 17+17 17P170171717P17 17
17617Q1717=1717P17917017,170170170171717Q1717=1717P17917017,17017017017


18÷18 18P18618 18p18e18r18 18u18n18i18t181818Q1818=1818118518,18018018018
18u18n18i18t18s181818
18
18
18
18118518,18018018018 18u18n18i18t18s18 18×18
18P18218018 18p18e18r18 18u18n18i18t18 18=18 18P18318018018,18018018018
18i18n18 18s18a18l18e18s18
18
18
18
18
18
18
18
18
18A18lternative solution:

Requirement 2
Incremental contribution margin:P70,000 increased sales × 30% CM ratio

P21,000Less increased fixed costs:Increased advertising cost 8,000Increase in
monthly net operating income
P13,000
Since the company presently has a loss of P9,000 per month, if the
changes are adopted, the loss will turn into a profit of P4,000 per month.
Requirement 3
Sales (27,000 units × P18 per unit*)
P486,000Less variable expenses
(27,000 units × P14 per unit)
378,000Contribution margin
108,000Less fixed
expenses (P90,000 + P35,000)
125,000Net operating loss
P(17,000)
*P20 – (P20 × 0.10) = P18

Requirement 4


Sales=Variable expenses + Fixed expenses + ProfitsP 20Q=P14.60Q* + P90,000 +
P4,500P5.40Q=P94,500Q=P94,500 ÷ P5.40 per unitQ=17,500 units
* P14.00 + P0.60 = P14.60.
Alternative solution:

** P6.00 – P0.60 = P5.40.
Requirement 5
a.
The new CM ratio would be:
Per UnitPercentageSales P20100%Less variable expenses
7 35 Contribution margin

P13 65%
The new break-even point would be:

b.

Comparative income statements follow:

Not AutomatedAutomatedTotalPer Unit%TotalPer Unit%Sales (20,000 units)
P400,000P20100P400,000P20100Less variable expenses
280,000 14 70
140,000 7 35Contribution margin
120,000P 6 30260,000P13 65Less fixed
expenses
90,000 208,000Net operating income
P1919191919191919191919191919191919191919191919191919191919
319019,19019019019191919P19 519219,1901901901919191919


20c20.20
20W20h20e20t20h20e20r20 20o20r20 20n20o20t20 20o20n20e20
20w20o20u20l20d20 20r20e20c20o20m20m20e20n20d20 20t20h20a20t20 20t20h20e20
20c20o20m20p20a20n20y20 20a20u20t20o20m20a20t20e20 20i20t20s20
20o20p20e20r20a20t20i20o20n20s20 20d20e20p20e20n20d20s20 20o20n20
20h20o20w20 20m20u20c20h20 20r20i20s20k20 20h20e20 20o20r20 20s20h20e20
20i20s20 20w20i20l20l20i20n20g20 20t20o20 20t20a20k20e20,20 20a20n20d20
20d20e20p20e20n20d20s20 20h20e20a20v20i20l20y20 20o20n20
20p20r20o20s20p20e20c20t20s20 20f20o20r20 20f20u20t20u20r20e20
20s20a20l20e20s20.20 20 20T20h20e20 20p20r20o20p20o20s20e20d20
20c20h20a20n20g20e20s20 20w20o20u20l20d20 20i20n20c20r20e20a20s20e20
20t20h20e20 20c20o20m20p20a20n20y20’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 ratio will 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, losses will be even larger
than at present due to the company’s greater fixed costs. (Note the problem states that
sales are erratic from month to month.) In sum, the proposed changes will help the
company if sales continue to trend upward in future months; the changes will hurt the
company 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 indifference between the two alternatives
in terms of units sold; i.e., the point where profits will be the same under either
alternative. At this point, total revenue will be the same; hence, we include only costs in
our equation:
Let Q=Point of indifference in units soldP14Q + P90,000=P7Q +
P208,000P7Q=P118,000Q=P118,000 ÷ P7 per unitQ=16,857 units (rounded)
If more than 16,857 units are sold, the proposed plan will yield the greatest
profit; if less than 16,857 units are sold, the present plan will yield the greatest profit (or
the least loss).
Problem 3 (Sales Mix; Multiproduct Break-even Analysis)
Requirement 1
ProductsSinksMirrorsVanitiesTotalPercentage of total sales 32%40%28%100%Sales
P160,000100%P200,000100%P140,000100%P500,000100%Less variable
expenses
48,000 30 160,000 80 77,000 55 285,000 57Contribution margin
P112,000 70%P 40,000 20%P 63,000 45%215,000 43%*Less fixed expenses
223,600Net operating income (loss)
P ( 8,600)
* P215,000 ÷ P500,000 = 43%.

Requirement 2
Break-even sales:

Requirement 3
Memo to the president:
Although the company met its sales budget of P500,000 for the month, the mix of
products sold changed substantially from that budgeted. This is the reason the budgeted
net operating income was not met, and the reason the break-even sales were greater than
budgeted. The company’s sales mix was planned at 48% Sinks, 20% Mirrors, and 32%
Vanities. The actual sales mix was 32% Sinks, 40% Mirrors, and 28% Vanities.
As shown by these data, sales shifted away from Sinks, which provides our greatest
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 provided considerably less contribution margin than
we had planned, with a resulting decrease in net operating income. Notice from the
attached statements that the 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 higher than
planned. With less average contribution margin per peso of sales, a greater level of sales
had to be achieved to provide sufficient contribution margin to cover fixed costs.
Problem 4 (Basic CVP Analysis)
Requirement 1
The CM ratio is 60%:
Selling price
P150100%Less variable expenses
P 90 60%Requirement 2

60 40Contribution margin

Requirement 3
P450,000 increased sales × 60% CM ratio = P270,000 increased contribution
margin. Since fixed costs will not change, net operating income should also increase by
P270,000.
Requirement 4
a.
b.

6 × 15% = 90% increase in net operating income.

Requirement 5
Last Year:
28,000 unitsProposed:
42,000 units*TotalPer UnitTotalPer UnitSales
P4,200,000P150.00P5,670,000P135.00**Less variable expenses
1,680,000 60.00 2,520,000 60.00Contribution margin
2,520,000P222222
922022.2202202222322,22122522022,2202202202222P22 22722522.22022022222222L
22e22s22s22 22f22i22x22e22d22 22e22x22p22e22n22s22e22s22
2222
22 22122,22822022022,220220220222222 22
22222,22522022022,2202202202222222222N22e22t22
22o22p22e22r22a22t22i22n22g22 22i22n22c22o22m22e22 2222P22
722222022,220220220222222P22 622522022,2202202202222222222
22*22 22222822,22022022022 22u22n22i22t22s22 22×22 22122.22522 22=22
22422222,22022022022 22u22n22i22t22s22
22*22*22
22 22P22122522022 22p22e22r22 22u22n22i22t22 22×22
22022.22922022 22=22 22P22122322522.22022022 22p22e22r22 22u22n22i22t22

22
22N22o22,22 22t22h22e22 22c22h22a22n22g22e22s22 22s22h22o22u22l22d22
22n22o22t22 22b22e22 22m22a22d22e22.22
22
22R22e22q22u22i22r22e22m22e22n22t22 22622
22


23Expected total contribution margin:
28,000 units × 200% × P70 per unit*
P3,920,000Present total contribution margin:
28,000 units × P90 per unit
2,520,000Incremental contribution margin, and the amount by which advertising can be increased with net operating income
remaining unchanged
P1,400,000
* P150 – (P60 + P20) = P70
Problem 5 (Break-Even and Target Profit Analysis)
Requirement 1
n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added. Note from the income
statements above that this ratio drops from 55% to 49% with the addition of the third product. This product, called HY143, has a CM ratio of only 25%, which
causes the average contribution margin ratio to fall.
This problem shows the somewhat tenuous nature of break-even analysis when more than one product is involved. The manager must be very careful of his or
her assumptions regarding sales mix when making decisions such as adding or deleting products.
It should be pointed out to the president that even though the break-even point is higher with the addition of the third product, the company’s margin of safety is
also greater. Notice that the margin of safety increases from P8,000 to P25,300 or from 6.25% to 15.81%. Thus, the addition of the new product shifts the
company much further from its break-even point, even though the break-even point is higher.

Problem 8 (Break-Even Analysis with Step Fixed Costs)
Requirement (1)
The total annual fixed cost of the Pediatric Ward can be computed as follows:

Annual
Patient-DaysAidesNursesSupervising NursesTotal
PersonnelOther Fixed CostTotal Fixed Cost@ P360,000@ P580,000@ P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00113,750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00013,75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000
Requirement (2)
The “break-even” can be computed for each range of activity by dividing the total fixed cost for that range of activity by the contribution
margin per patient-day, which is P3,000 (=P4,800 revenue
232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323"


n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added. N

The contribution margin per patch would be:
Selling price
P30Less variable expenses:Purchase cost of24 24t24h24e24 24p24a24t24c24h24e24s24
2424P24124524242424C24o24m24m24i24s24s24i24o24n24s24 24t24o24 24t24h24e24 24s24t24u24d24e24n24t24
24s24a24l24e24s24p24e24r24s24o24n24s24
2424 24 24 2462424 24 242241242424C24o24n24t24r24i24b24u24t24i24o24n24 24m24a24r24g24i24n24
242424P24 9242424
24
24S24i24n24c24e24 24t24h24e24r24e24 24a24r24e24 24n24o24 24f24i24x24e24d24 24c24o24s24t24s24,24 24t24h24e24 24n24u24m24b24e24r24
24o24f24 24u24n24i24t24 24s24a24l24e24s24 24n24e24e24d24e24d24 24t24o24 24y24i24e24l24d24 24t24h24e24 24d24e24s24i24r24e24d24
24P24724,24224024024 24i24n24 24p24r24o24f24i24t24s24 24c24a24n24 24b24e24 24o24b24t24a24i24n24e24d24 24b24y24 24d24i24v24i24d24i24n24g24
24t24h24e24 24t24a24r24g24e24t24 24p24r24o24f24i24t24 24b24y24 24t24h24e unit contribution margin:

Requirement 2
Since an order has been placed, there is now a “fixed” cost associated with the purchase price of the patches (i.e., the patches can’t be returned).
For example, an order of 200 patches requires a “fixed” cost (investment) of P3,000 (200 patches × P15 per patch = P3,000). The variable costs drop to only P6
per patch, and the new contribution margin per patch becomes:
Selling price

P30Less variable expenses (commissions only)
6Contribution margin P24
Since the “fixed” cost of P3,000 must be recovered before Ms. Morales shows any profit, the break-even computation would be:

125 patches x P30 per patch = P3,750 in total sales
If a quantity other than 200 patches were ordered, the answer would change accordingly.
Problem 6
Requirement 1: Break-even chart


n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added. Note from the income
statements above that this ratio drops from 55% to 49% with the addition of the third product. This product, called HY143, has a CM ratio of only 25%, which
causes the average contribution margin ratio to fall.
This problem shows the somewhat tenuous nature of break-even analysis when more than one product is involved. The manager must be very careful of his or
her assumptions regarding sales mix when making decisions such as adding or deleting products.
It should be pointed out to the president that even though the break-even point is higher with the addition of the third product, the company’s margin of safety is
also greater. Notice that the margin of safety increases from P8,000 to P25,300 or from 6.25% to 15.81%. Thus, the addition of the new product shifts the
company much further from its break-even point, even though the break-even point is higher.

Problem 8 (Break-Even Analysis with Step Fixed Costs)
Requirement (1)
The total annual fixed cost of the Pediatric Ward can be computed as follows:
Annual
Patient-DaysAidesNursesSupervising NursesTotal
PersonnelOther Fixed CostTotal Fixed Cost@ P360,000@ P580,000@ P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00113,750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00013,75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000
Requirement (2)
The “break-even” can be computed for each range of activity by dividing the total fixed cost for that range of activity by the contribution
margin per patient-day, which is P3,000 (=P4,800 revenue
252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525"