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

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.. In the equation method, th

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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

4 In the short-run, without considering asset replacement, net operating cash flowswould 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 thanthe 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

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 since it would require more sales to cover the same amount offixed 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 totalcontribution 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, itwill 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 andthe 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 wouldoccur at a higher unit volume.

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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 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 P900 per lantern, P4,500,000 in salesRequirement 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

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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 incomeP2,250,000

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:

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

(14,000 units × P12 per unit) 168,000P12Less fixed expenses7 77 7

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Alternative Solution 1Expected 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 2Incremental 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)

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

*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 + ProfitsP60Q=P36Q + P360,000 +

P0P24Q=P360,000Q=P360,000 ÷ P24 per unitQ=15,000 units

In sales pesos: 15,000 units × P60 per unit = P900,000Alternative 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 unitsb.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 = P1,125,000Alternative 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)

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

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

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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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:

Degree of operating leverage x 5Expected 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

† 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 increasethe 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 = Total sales – Break-even sales

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

P21,000Less increased fixed costs:Increased advertising cost 8,000Increase inmonthly 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 fixedexpenses (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

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