Solution manual cost management measuring monitoring and motivating performance 1st by wolcott ch03

QUESTIONS 3.1 A mixed cost function includes both fixed and variable costs.. If there are fixed costs in the cost function, then total costs will increase at a smaller rate than the inc

Chapter 3 Cost-Volume-Profit Analysis

LEARNING OBJECTIVES

Chapter 3 addresses the following questions:

Q1 What is cost-volume-profit (CVP) analysis, and how is it used for decision making? Q2 How are CVP calculations performed for a single product?

Q3 How are CVP calculations performed for multiple products?

Q4 What is the breakeven point?

Q5 What assumptions and limitations should managers consider when using CVP analysis? Q6 How are margin of safety and operating leverage used to assess operational risk?

These learning questions (Q1 through Q6) are cross-referenced in the textbook to individual exercises and problems

COMPLEXITY SYMBOLS

The textbook uses a coding system to identify the complexity of individual requirements in the exercises and problems

Questions Having a Single Correct Answer:

No Symbol This question requires students to recall or apply knowledge as shown in the

textbook

e This question requires students to extend knowledge beyond the applications

shown in the textbook

Open-ended questions are coded according to the skills described in Steps for Better Thinking (Exhibit 1.10):

 Step 1 skills (Identifying)

 Step 2 skills (Exploring)

 Step 3 skills (Prioritizing)

 Step 4 skills (Envisioning)

QUESTIONS

3.1 A mixed cost function includes both fixed and variable costs If there are fixed costs in

the cost function, then total costs will increase at a smaller rate than the increase in total sales volume If there are variable costs in the cost function, then total costs will increase with total sales volume When there is a combination of fixed and variable costs, a 10% volume increase will increase total costs by less than 10% because only the increase in variable cost is proportionate to volume; the fixed cost does not change with volume

3.2 The weighted average contribution margin per unit is calculated only when performing

CVP analysis for multiple products There are two ways to calculate it:

(1) Calculate the total contribution of all products by subtracting total variable costs from total revenues Then calculate the weighted average contribution margin per unit by dividing the total contribution margin by the total number of units (the sum of units for all products)

(2) Calculate the sales mix for each product by dividing the number of units sold for that product by the total number of units sold for all products Calculate the contribution margin per unit for each product by subtracting that product’s variable cost from its revenues and dividing the result by that product’s number of units sold Then

calculate the weighted average contribution margin per unit by summing the

following computation for all products: Each product’s sales mix percentage times its contribution margin per unit

3.3 The firm has only variable costs and no fixed costs If there were fixed costs, income

would increase by more than 20% when sales increase by 20%

3.4 None The firm does not pay income taxes at the breakeven point

3.5 Assumptions: Fixed costs remain fixed, variable costs per unit or as a percentage of

revenue remain constant, selling prices per unit remain constant, the sales mix remains constant, and operations are within a relevant range where all of these assumptions are met These are very strong assumptions There is always some variation in fixed costs because they include costs such as electricity that varies with weather In addition, organizations often get or give volume discounts, so variable costs and prices per unit may change at high volumes However, results using these assumptions are accurate enough for general planning and decision making purposes

3.6 The margin of safety percentage and degree of operating leverage are related as follows

LeverageOperating

ofDegree

1Percentage

Safety of

Margin

PercentageSafety

ofMargin

1Leverage

Operatingof

Degree

As the degree of operating leverage gets larger (a higher proportion of fixed costs), the margin of safety percentage gets smaller, and vice versa

3.7 The cost function is assumed to be linear over a relevant range If there are volume

discounts, the cost function becomes piece-wise linear and the range of operations within which the organization is performing must be taken into account in CVP analysis The level of operations must be matched with the appropriate part of the function Each piece can be considered as a separate relevant range, and the estimated level of activity needs to

be matched with the appropriate relevant range Otherwise, the analysis will either understate or overstate variable costs

3.8 Sales mix is the specific proportion of total sales of each type of good or service that is

sold A simple example was presented in the chapter for an ice cream store Usually about 15% of revenue was from beverages and the rest from ice cream products As the proportion of specific products sold changes, the contribution margin ratio changes because the contribution per unit is different for the different products in the sales mix

3.9 CVP refers to changes in income over the relevant range of activity; as such, it includes

the notion of breakeven Breakeven is more narrowly constructed; it focuses on only one outcome—the single point at which total revenue equals total cost

3.10 By definition, the margin of safety is the difference between expected unit sales and

breakeven unit sales If expected unit sales are below breakeven unit sales, the margin of safety will be negative

3.11 CVP analysis can be used for planning purposes such as budgets, product emphasis,

setting prices, setting activity levels, setting work schedules, purchasing raw materials, setting levels for discretionary costs such as advertising and research and development It can also help with monitoring operations, and analyzing the operating leverage of an

organization

3.12 To make decisions about advertising costs, accountants predict the amount of cost to be

incurred and predict the increase in sales CVP analysis is then used to determine

whether the increase in cost is equal to or greater than the increase in contribution margin

from additional units sold

3.13 Good managers are likely to always ask for sensitivity analysis because uncertainty about

sales volumes and other factors always exists However, when unanticipated changes in the business environment or consumer preferences arise, managers will be even more interested in sensitivity analysis By analyzing a variety of scenarios, managers can

respond more quickly to unanticipated changes

EXERCISES

3.14 Target Profit, Not-For-Profit Breakeven

A Information is given on a per unit basis, so use the following equation:

profit = (p-v)q – F

$1,000 = ($7 per gift basket – $2 per gift basket)*Q - $5,000

$6,000 = ($5 per gift basket)*Q

Q = $6,000/$5 per gift basket = 1,200 gift baskets

B This problem is about a not-for-profit organization Many not-for-profit organizations provide services or sell products at a loss and use donations or grants to cover the losses

As students approach problems in this textbook, they should think briefly about the type

of organization in the problem to help them solve it This problem is a breakeven

problem with a unit cost of $7.64 and unit revenue of $4.64, or a unit contribution margin (loss) of $(3.00) In a for-profit organization, these numbers would indicate that the company loses money on each unit it sells In a not-for-profit, it may be appropriate to sell services at a loss, as long as another source of funds covers the loss In this problem, the clinic receives a grant from the city, so there is ―fixed‖ revenue in addition to the fees collected

Taking the grant into account, the breakeven is:

0 = ($4.64 - $7.64)*Q + $460,000 grant - $236,000 fixed cost

0 = $-3*Q +$224,000 Solving for Q:

3Q = $224,000

Q = 74,667 patients

The revenue line is $7 times number of baskets and represents total revenue from units sold The cost line intersects the intercept at $5,000 reflecting the fixed cost The slope

is 2, which represents the variable cost The breakeven occurs at 1,000 gift baskets Total revenues exceed total costs by $1,000 at 1,200 gift baskets

Total revenue is the sum of the grant plus patient fees Unlike most CVP graphs, the

breakeven point is the maximum volume before the clinic incurs a loss The grant

exceeds fixed costs, so the clinic has a surplus up the breakeven point Because the clinic’s contribution margin is negative, the surplus decreases by $3 per patient visit After the breakeven point of 74,667 patient visits, the clinic incurs losses

3.16 Cost Function, Breakeven

A This problem gives information in units, so use the formula TC = v*q + F to determine variable cost The average cost must first be turned into total cost:

Total cost for 1,200 units is $234*1,200 = $280,800 Total cost for 1,400 units is $205*1,400 = $287,000

Use the two-point method (change in cost divided by change in volume) to determine the variable cost:

Variable cost = (287,000 – 280,800)/(1,400 – 1,200)

V = $31

Notice that the information about profit is not used because it is irrelevant for this

problem Recognizing and discarding irrelevant information is an important skill

B Turn sales into units and use profit = (P-V)*Q – F

Calculate the number of units sold:

Revenue / Selling price per unit = Number of units

$10,600/$0.25 per unit =42,400 units Variable cost is $0.12 plus selling costs of $0.02 = $0.14 per unit

Use the breakeven equation, and then solve for the unknown amount of fixed costs:

0 = ($0.25 - $0.14)*42,400 – F

0 = $4,664 – F

F = $4,664

C There can only be one breakeven point within the relevant range, so the breakeven point

is first calculated for the first range If the result is within that range, no additional calculations are needed However, if the breakeven point is not in the first range, then calculations must be made for the next range

In the relevant range 0 < Q < 200, the breakeven point is calculated as:

0 = ($300 - $200)*Q - $24,000

Q = 240 units This result is outside of the relevant range, so it is not a feasible solution

In the relevant range 200 < Q, the breakeven point is calculated as:

0 = $100*Q - $36,000

Q = 360 units

This result is in the relevant range, so it is the breakeven point

3.17 The Martell Company

A Profit (loss) before taxes is:

Hair dresser salaries $18,000

Salaries: The amount of salaries in May is used to predict the next month because there

was a cost-of-living increase

Supplies: An examination of the pattern in supplies costs reveals that for April and May

supply cost was $0.50 per appointment The cost was higher in March, but it is best to use the most current information Students may have averaged the three months for

$0.52 per month, or they could have used the high-low method which gives $0.50 with no fixed costs

Utilities: Because weather probably drives most of utilities cost for this business, this

solution uses the prior month’s utilities to predict next month’s cost

Miscellaneous: An examination of miscellaneous costs reveals that while it increases as

volumes increase, it does not do so proportionately (as did supplies) For this solution the high-low method is used Variable cost = $0.325 [($3,580 - $3,450)/(1,900 – 1,500)] Using TC = F +VC*Q and solving for F gives a fixed cost of $2,963 [$3,450 = F +

B Variable costs are $12.50 per unit/$50.00 per unit = 25% of revenue

Breakeven in sales, where TR = total revenue:

TR - 0.25*TR - $3,000,000 = $4,500,000 0.75*TR= $7,500,000

TR = $10,000,000

C Target after-tax profit

0.10*$36,000,000 = $3,600,000 After-tax income = (1-0.40)*before tax income

Combining these calculations:

$3,600,000 = 0.60*before tax income Before-tax income = $6,000,000 CVP calculation:

TR- 0.25*TR - $3,000,000 = $6,000,000 0.75*TR = $9,000,000

$25*Q – $15*Q - $150,000 = $0

Q = 15,000 units

B Adjust the after-tax income target to a before-tax income target

Income before tax*(1 - 45) = $77,000 Income before tax*0.55 = $77,000 Income before tax = $140,000 Then solve for units at target profit:

$25Q- 15Q - 150,000 = $140,000

Q = 29,000 units

Less old component (2.50) Plus depreciation on

Plus new component 4.50 new machine $18,000/6 3,000

Solve for breakeven where

$25*Q – $17*Q - $153,000 = $0

Q = 19,125 units

D Solve for target profit where:

π - [0.15 x $40,000 + 0.40*(π - $40,000)] = $150,000

π - (6,000 + 0.4 π - 16,000) = $150,000 0.6 π + 10,000 = $150,000

π = $233,333.33 Now total revenue (TR) can be calculated:

TR - 0.60*TR - $250,000 = $233,333.33 0.40*TR = $483,333.33

TR = $1,208,333.33

3.22 All-Day Candy Company

A $4*Q - $2.40*Q - $440,000 = $0

Q = 275,000 boxes to break even

B Current contribution margin ratio = ($4.00-$2.40)/$4.00 = 40%

Estimated variable costs next period (only the candy costs increase)

$2.00 x 1.15 + $0.40 = $2.70 Selling price needed to maintain 40% contribution margin ratio:

P - $2.70 = 0.40*P 0.60*P = $2.70

P = $4.50

C Current pretax income = $4.00*390,000 units - $2.40*390,000 units - $440,000

3.23 Junior Achievement Group

A Breakeven for option 1:

$5,600/($20 – $6) = 400 sets Breakeven for option 2:

New variable cost = 0.10*$20 = $2

$5,600/($20 - $6 - $2) = 317 sets Breakeven for option 3:

There are no fixed costs, so the breakeven point = 0 sets; if no units are sold, no

fee is paid

B The cost function for option 1 has the highest proportion of fixed cost, so it has the highest operating leverage

C Lowest operating risk is option 3 because no fees are paid unless there are sales

D To find the indifference point, the two cost equations are set equal to each other as

follows:

$5,600 = $3,800 + 10%TR

$1,800 = 10%TR

TR = $18,000

When total revenues are below $18,000, option 2 is more profitable Above

$18,000, option 1 is more profitable

Marketing and Administration 110,000 50,000

Variable cost per unit = $700,000/100,000 units = $7.00 per unit

Price per unit = $1,000,000/100,000 units = $10.00 per unit

Target pretax income = $120,000/(1-.40) = $200,000

100,000 units – 70,000 units = 30,000 units

Margin of safety in revenues

3.26 Pike Street Taffy

A It is first necessary to determine the cost function:

Assuming that the cost of ingredients varies with the amount of taffy produced, the

variable cost per pound is:

$3,200/2,000 lbs = $1.60/lb

The rent is assumed to be fixed The wages are also fixed because employees work standard shifts Total fixed costs are:

$800+$4800 = $5,600 Breakeven point in pounds:

($5,600 + $3,750)/($4.80 per lb -$1.60 per lb.) = 2,922 lbs

Revenues needed to earn a pretax income of $3,750:

2,922 lbs * $4.80 per lb = $14,026

Check calculation using contribution margin ratio formula:

Contribution margin ratio = ($4.80-$1.60)/$4.80 = 66.6667%

($5,600 + $3,750)/66.6667% = $14,025 (difference due to rounding)

C The margin of safety is current total sales less total sales at breakeven:

=$9,600 - $8,400 = $1,200 The margin of safety percentage = $1,204/$9,600 = 0.125 = 12.5%

(Revenues are 12.5% above the breakeven point)

D Degree of operating leverage = contribution margin/pretax income

= ($9,600 - $3,200)/$800 = 8.0

An alternative calculation for degree of operating leverage is:

1/margin of safety percentage

= 1/0.125 = 8.0

3.27 Vines and Daughter

A Estimated sales in number of swimsuits = $2,000,000/$40 = 50,000 swimsuits

Variable cost per unit = $1,100,000/50,000 swimsuits = $22 per swimsuit

Contribution margin = $40-$22 = $18 per swimsuit

Breakeven in units:

$765,000/$18 = 42,500 swimsuits

B Margin of safety is 50,000 – 42,500 = 7,500 swimsuits

C If the margin of safety was 5,000 swimsuits in 2004 and increases to 7,500 swimsuits in

2005 (calculated in Part B), then operations will be less risky in 2005 A larger margin of safety means that the company is operating further beyond the breakeven point; swimsuit sales can drop by a larger amount before the company incurs a loss

D Contribution margin ratio = $18/$40 = 0.45

Breakeven in revenues:

$765,000/0.45 = $1,700,000

E Margin of safety in revenue = $2,000,000 - $1,700,000 = $300,000

F An increase in revenues of $200,000 is expected to increase pretax profits by $90,000 in profits ($200,000 x 0.45 contribution margin ratio) because fixed costs have been covered

at this point Total pretax is estimated to be:

$135,000 + $90,000 = $225,000

G Pretax profit = $180,000/(1-.30) = $257,143

CVP calculation:

($765,000+$257,143)/$18 = 56,786 swimsuits

PROBLEMS

3.28 Oysters Away

[Note about problem complexity: Item A is coded as Extend instead of Step 2 because judgment

is minimal and students can use chapter examples for help.]

A

Rent and Insurance $25,000

Variable cost per case: $120,000/2,000 cases = $60

In the absence of information about a change, the quality of the income estimate in Part C

is probably low In addition, any change in operations major enough to increase sales by 50% might change the cost function (see Part E) So, even if the manager anticipates expanding the size of operations, the quality of the income estimate is low

E It is possible that the costs for workers or packing materials would change above 2,000 cases If the company does not have enough space to handle all of the oysters, rent would need to increase The company might have to pay workers overtime or hire additional

workers at a higher or lower rate than current workers (depending on skill levels and supply of workers) With the additional volume, the company might get a discount on packing materials, so that cost might be smaller Administrative costs might or might not increase with the volume of operations A 50% increase in volume is very significant, which might require additional administrative costs such as staff, supplies, or fixed assets

3.29 Francesca

A

Quantitative information

Cart lease $800 per month: This is relevant because this is a cost that will be

incurred if Francesca leases the cart, but will not be incurred otherwise City license $20 per month: This is relevant for the same reason as the cart

lease

Lessor records showing average gross revenues of $32 per hour: This

information is relevant if Francesca thinks she will sell about the same amount as the lessor However, the lessor’s records might not be reliable

Ingredients 40% of revenue: This is relevant because this cost will be incurred

only if Francesca sells coffee

Last year’s income tax rate of 25%: Assuming that the income tax rate is not

different for operating the coffee cart, the tax rate is irrelevant to Francesca’s decision The income tax rate will reduce earnings for both options

Condo rent of $1,000 per month and 20% of condo cost for garage: This cost is

not relevant because it will be the same under both options; it is unavoidable

Current income $2,400 per month: This is relevant as the opportunity cost if

Francesca decides to operate the coffee cart instead of continuing her current work

B This question calls for calculating the hours Francesca should work to earn a target profit equal to her current earnings of $2,400 per month Before this computation can be performed, the cost function for the coffee cart must be determined:

Target profit calculation (assuming that revenue is $32 per hour):

$2,400 = ($32 - 0.40*$32)*Hours per month - $820

$3,220 = $19.2*Hours per month Hours per month = 168

Assuming that she is willing to work 30 days per month, total hours per month are 168 Then, the average hours that must be worked per day to earn a target profit of $2,400 is:

168 hours per month/30 days per month = 5.6 hours per day

C This problem requires students to perform the same calculation as when determining the selling price needed to achieve a target profit

Total hours per month = 25 days x 4 hours per day = 100 hours per month

Target profit calculation:

$2,400 = (Revenue per hour - 0.40*Revenue per hour)*100 hours - $820

$3,220 = 60*Revenue per hour

Revenue per hour = $53.67

D As mentioned in Part A above, Francesca cannot be certain that the information she received from the lessor is reliable In addition, revenues are likely to fluctuate based on weather, the economy, competition, and consumer preferences

E There are many other types of information to consider Some information might help Francesca evaluate the financial viability of the coffee cart, such as local population trends, competition, and economic outlook Additional information relates to Francesca’s own preferences, such as whether she wants to give up her other occupations and how much she would enjoy running a coffee cart in Vail

D To calculate the overall breakeven, it is easiest to first calculate the weighted average contribution margin ratio using an income statement approach:

E Breakeven for regular boomerangs ignoring corporate fixed costs:

G Corporate fixed costs are not usually under the control of the individual product

managers Therefore, corporate fixed costs generally are not considered when evaluating individual product profitability However, the company as a whole needs to cover all of its fixed costs, so it is important to take corporate fixed costs into account when planning overall operations

H The actual sales mix can differ from plans for many reasons For example, customer preferences can change, altering the number and prices of units Competitor’s prices and products could affect the sales mix Consumer buying patterns change when the

economy changes Sometimes an unforeseen event will greatly alter consumer behavior These changes cannot easily be predicted

I When the sales mix is more uncertain, the quality of information from CVP analysis is lower because the CVP assumptions are more likely to be violated Therefore, the

likelihood that the sales mix will remain constant must be evaluated Sensitivity analysis

should also be performed to examine a larger range of operations that incorporate

possible changes in sales mix The quality of the CVP analysis is negatively affected by higher uncertainty about any of the variables used

3.31 Not-For-Profit After-School Art Program

A

1 Here are several possible costs; students may think of others

Staff people Fixed (fixed schedule according to # of children)

Art supplies Mixed, some that will be used up, and some (easels) that

will be fixed High school help Fixed (fixed schedule according to # of children)

Snack food Variable

2 Snack food is the only completely variable cost and number of snacks served would

be a good cost driver Art supplies have a variable component, and number of

children or number of hours of art would be reasonable cost drivers

B The cost structure likely has a larger proportion of fixed costs because salaries for staff and supervisors would be much higher per hour than the cost of supplies and snacks

C The marginal cost is the variable cost (supplies and snacks) per child for three children

D The opportunity cost is the revenue foregone from a fee-paying child

E CVP analysis offers the neighbor an opportunity to vary assumptions, such as price and volume of children served while he is considering various options such as scholarships

A spreadsheet can be set up with an input area for all of the assumptions such as fixed costs, variable costs, number of children, fees per child, number of fee-paying children, number of scholarships, and so on Then the CVP calculations would be performed in a separate part of the spreadsheet, with cell references to the input cells The neighbor could then modify data in the input cells to analyze the expected financial results under different sets of assumptions