acct 620 chapter 6

CHAPTER 6

FINANCIAL MODELING FOR SHORT-TERM DECISION MAKING

Questions, Exercises, Problems, and Cases: Answers and Solutions

6.1 See text or glossary at the end of the book.

6.2 Operating profit = Sales revenue – Variable cost – Fixed cost

6.3 The unit contribution margin is the excess of the unit price over the unit variable costs. The total contribution margin is the excess of total revenue over total variable costs.

6.4 Assumptions:

1. Revenues change proportionately with volume.

2. Variable costs change proportionately with volume.

3. Fixed costs do not change at all with volume.

(Other assumptions may include constant product mix and/or all CVP costs are expensed.)

6-1 Solutions

6.5 Question Breakeven Point Unit Contribution Expected Margin Total Profit

a. Raises. No Effect. Decreases.The contribution More of

the margin (denom- contributioninator) is fixed margin while fixed costs must be (numerator) are used to increased. cover

fixed costs.

b. Lowers. Increases. Increases.A decrease invariable costsper unit in-creases contri-bution margin

per unit. c. Lowers. Increases. Increases.

Increasing sales price increasescontribution

margin. d. No Effect. No Effect. Increases.

e. Raises. No Effect. Decreases.Increasing fixed More of thecosts increases contributionbreakeven point. margin

must be used to cover fixed costs.

6.6 Total contribution margin: Selling price – variable manufacturing costs – variable nonmanufacturing costs = Total contribution margin.

Gross margin: Selling price – variable manufacturing costs – fixed manufacturing costs = Gross margin.

6.7 Profit-volume analysis plots only the profit/loss line against volume, while cost-volume-profit analysis plots total revenue and total costs against volume. Profit-volume analysis is a simpler, but less complete, method of presentation.

6.8 Spreadsheets make sensitivity analysis easier. Spreadsheets enable us to see a range of possible outcomes given different values of the variables used in the financial model.

Solutions 6-2

6.9 Both unit prices and unit variable costs (and resulting unit contribution margin) are expressed on a per product basis as:

Operating Profit = (Product 1 unit contribution margin X Product 1 sales volume) + (Product 2 unit contribution margin X Product 2 sales volume) – Fixed costs

6.10 There are two ways to change the breakeven point for any company: increase contribution or decrease fixed costs. A company can increase contribution margin per unit by raising prices or reducing variable costs per unit. However, price increases may decrease total contribution because of lost sales. This is the situation faced by many companies that have to lower variable costs to increase contribution margins and/or lower total fixed costs in order to lower their breakeven points.

6.11 Costs that are "fixed in the short run" are usually not fixed in the long run. In fact few, if any, costs are fixed (i.e., remain unchanged) over a very long time horizon.

6.12 The accountant makes use of a linear representation to simplify the analysis of costs and revenues. Generally, the accounting models which record costs and form the basis for accounting reports are designed to incorporate considerations of fixed and variable costs as well as a constant sales price. These simplifying assumptions are generally reasonable within a relevant range of activity. Within this range, it is generally believed that the additional costs required to employ nonlinear analysis cannot be justified in terms of the benefits obtained. Thus, within this range, the linear model is considered the "best" in a cost benefit sense.

6.13 a. (2) e. (4) i. (4)b. (1) f. (5) j. (5)*c. (1) g. (2) k. (1)d. (1)* h. (1)

*Assuming: Fixed costs > 0 andFixed costs < Total contribution margin before the change.

6.14 A company operating at "breakeven" 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 do not take a salary as large as the opportunity cost of foregoing alternative employment.

6.15 A constant product mix is assumed to simplify the analysis. Otherwise, there may be nearly an infinite number of solutions.

6-3 Solutions

6.16 The sum of the breakeven quantities would not be the breakeven point for the company if there are common fixed costs which have not been allocated to the products.

6.17 A negative contribution margin arises when variable cost exceeds the unit’s selling price—a common occurrence with the marketing procedure known as a loss leader. With a loss leader, the retailer may intentionally take a loss on selected products in hopes of generating additional store traffic and customers. The goal is for an increase in sales of other items (e.g., tennis racquets, golf clubs, athletic wear) and profits.

6.18 (Breakeven and target profits.)

a. Contribution Margin (per Unit) = Unit Selling Price – Unit Variable Cost= $16 – $8= $8.

Profit = (Contribution Margin per Unit X Units) – Fixed Costs$0 = ($8 X Units) – $200,000

Units = 25,000.

b. $280,000 = ($8 X Units) – $200,000$480,000 = $8 X Units

60,000 = Units.

c. Profit = (.5* X $2,000,000) – $200,000= $800,000.

*Contribution Margin Ratio:

=

= = = 0.5 = 50%.

6.19 (Cost-volume-profit; volume defined in sales dollars.)

Solutions 6-4

a. $2,100,000 – $660,000 = $1,440,000

$1,440,000/$3,000,000 = 0.48 = 48%.

b. Breakeven Revenue =

Contribution Margin Ratio = ($3,000,000 - $1,440,000)/$3,000,000

= .52

Breakeven Revenue = $660,000/.52

= $1,269,231.

c.

$ of Revenue and Costs

300,000 900,000 1,500,000 600,000 1,200,000 1,800,000

$ of Revenue

1,500,000– 1,200,000– 900,000–

300,000– 0–

Breakeven Point

$1,269,231

Revenue

Total Cost

660,000–600,000–

d. Profit = (.52 X $2,500,000) – $660,000 = $640,000.

e. Sales = $1,660,000/.52 = $3,192,308.

6.20 (Cost-volume-profit graph.)

6-5 Solutions

Breakeven Point

Breakeven Point

Total Costs Line

Loss Area

Total Fixed Costs Area

Total Variable Costs Area

Total Revenue Line

Profit Area

Loss Volume

Profit Volume

Slope = Variable Cost per Unit

ad

f

gh

c

b

h

g

e

6.21 (Profit-volume graph.)

a. Total fixed costs.

b. Breakeven point.

c. Slope = contribution margin per unit.

d. Profit line.

e. Net income area.

f. Net loss area.

g. Zero net income line.

Solutions 6-6

6.22 (Cost--volume-profit analysis.)

a. $5,000,000 ÷ 1,000,000 Units = $5 per Unit.

b. $3,000,000 ÷ 1,000,000 Units = $3 per Unit.

c. $5 – $3 = $2 per Unit.

d. Operating Profit = [(Sales Price per Unit – Variable Cost per Unit) X Unit Sales] – Fixed Cost

0 = [($5 – $3) X Unit Sales] – $1,000,000

Unit Sales = $1,000,000/$2 = 500,000 Units.

e. After Tax Profit/(1 – t) = Before Tax Profit

$1,200,000/(1 – .4) = Before Tax Profit

$2,000,000 = Before Tax Profit

Then, go back to equation shown in Part d. above and set operating profit to $2,000,000 as follows:

$2,000,000 = [($5 – $3) X Unit Sales] – $1,000,000

Unit Sales = $3,000,000/$2 = 1,500,000 Units.

6.23 (Breakeven and target profits; volume defined in sales dollars.)

6-7 Solutions

a. Sales = $300,000/.40 = $750,000.

b. Sales = $300,000/.25 = $1,200,000.

c. Sales = ($300,000 + $100,000)/.4

= $1,000,000.

Solutions 6-8

6.24 (CVP—Sensitivity analysis.)

a. Breakeven Point in Units =

= $400,000/($200- $120)

= $400,000/$80 = 5,000 Students.

b. Target Profit Point in Units =

= ($400,000 + $200,000)/$80

= 7,500 Students.

c. (1) Profit = [($200 – $120) X 8,000] – $400,000

= $240,000.

(2) 10% price decrease. Now price = $180

Profit = [($180 – $120) X 8,000] – $400,000

= $80,000.

Profit decreases by $160,000 (67%).

20% price increase. Now price = $240

Profit = [($240 – $120) X 8,000] – $400,000

= $560,000.

Profit increases by $320,000 (133%).

(3) 10% variable cost decrease. Now variable cost = $108

Profit = [($200 – $108) X 8,000] – $400,000

= $336,000.

Profit increases by $96,000 (40%).

6-9 Solutions

6.24 c. continued.

20% variable cost increase. Now variable cost = $144

Profit = [($200 – $144) X 8,000] – $400,000

= $48,000.


(4) Profit = [($200 – $132) X 8,000] – $360,000

= $184,000.


6.25 (Multiple product profit analysis.)

Solutions 6-10

a. Chicken SteakBurritos Burritos Total

(200,000)($4) + (300,000)($6) = $ 2,600,000(200,000)($2) + (300,000)($3) = 1,300,000 (200,000)($2) + (300,000)($3) $1,300,000

200,000 $ 1,100,000

b. Weighted Average Unit Contribution Margin

= (0.4)($2) + (0.6)($3)

= $0.80 + $1.80

= $2.60,

where 0.4 = 200,000 chicken/(200,000 chicken + 300,000 steak)

and 0.6 = 300,000 chicken/(200,000 chicken + 300,000 steak)

Breakeven Point in Units =

= 200,000/$2.60

= 76,923 total units

Chicken Burritos: (0.4)(76,923) = 30,769 Units.Steak Burritos: (0.6)(76,923) = 46,154 Units.

6-11 Solutions

6.25 continued.

c. Weighted Average Unit Contribution Margin (answers are rounded)

()($2) + ()($3)

= (0.8)($2) + (0.2)($3)

= $1.60 + $0.60

= $2.20.Breakeven Point in Units =

= $200,000/$2.20

= 90,910 Total Units

Chicken Burritos: (0.8)(90,190) = 72,728 Units.Steak Burritos: (0.2)(90,190) = 18,182 Units.

6.26 (Multiple product profit analysis.)

Slope = $27

Slope = $1748,000

a.TR = $27X

TC = $48,000 + $17X

$

Units

A Unit = production of one product R, two product Q's, andthree product P's.

Variable Cost per Unit = (3 X $2) + (2 X $3) + (1 X $5) = $17.Revenue per Unit = (3 X $3) + (2 X $5) + (1 X $8) = $27.

Solutions 6-12

6.26 continued.

b. 0 = Total Revenue – Total Cost

0 = $27X – ($17X + $48,000)

$10X = $48,000

X = 4,800 Units.

Not Required:Total Revenue at Break-even Level = 4,800 Units X $27 = $129,600.

c.A Unit = two product P's,

two product Q's, andone product R.

Variable Cost per Unit = (2 X $2) + (2 X $3) + (1 X $5) = $15.Revenue per Unit = (2 X $3) + (2 X $5) + (1 X $8) = $24.

0 = Total Revenue – Total Cost

0 = $24X – ($15X + $48,000)

$9X = $48,000

X = 5,333.33 Units.

Not Required:Total Revenue at Break-even Level = 5,333.33 Units X $24 = $128,000.

6-13 Solutions

6.27 (Solving for cost-based selling price.)

Cost-based Price = $15 X 1.5

= $22.50

a. At 10,000 units: ($22.50 - $15 - $2) 10,000 units – ($50,000 + $75,000)

= $(70,000).

b. At 20,000 units: ($22.50 - $15 - $2) 20,000 units – ($50,000 + $75,000)

= $(15,000).

c. The company shows losses at both volumes. The loss is lower at 20,000 units, but there is still a loss. A break-even analysis shows that the break even point is:

Break even quantity = $125,000/$5.50 = 22,727 units.

Of course, we assume that fixed costs do not increase as volume increases and that the price and variable costs per unit are linear with respect to volume.

Solutions 6-14

6.28 (Explaining sales and cost changes.)

Dear Uncle Y:

The contribution increased by $25,000 between years 1 and 2. Here are the analyses of revenue and variable costs:

Revenue Increase:

Ride hours in Year 1 = $750,000/$10 = 75,000.

Ride hours in Year 2 = $840,000/$12 = 70,000.

In Year 2, ride hours decreased by 5,000 but the admission price increased by $2 per person per hour, resulting in a net increase of $90,000 in revenue. The decline in number of hours is a bit troubling, but we more than made up for the decline in hours with the price increase. The analysis below shows that the variable costs increased per hour:

Increase in Variable Costs of Operations:

Costs in Year 1 $495,000/75,000 = $6.60 per ride hour.

Costs in Year 2 $560,000/70,000 = $8.00 per ride hour.

So, in Year 2, volume decreased by 5,000 hours but variable costs increased by $1.40 per ride hour, resulting in a net increase of $65,000 in costs.

Overall, the company is performing well. Thanks again for the loan.

Your loving nephew,

X

6-15 Solutions

6.29 (CVP Analysis and Financial Modeling.)

a. Breakeven Point (in Units) =

$600,000/[$16 – ($10 + $2)] = 150,000 Units.

b. Net Income Based on 240,000 Units (200,000 X 1.2):

Sales (at $16 per Unit)....................................................... $3,840,000Less Variable Costs (at $12 per Unit)................................. 2,880,000 Contribution Margin........................................................... $ 960,000Less Fixed Costs................................................................ 600,000 Operating Profit................................................................. $ 360,000

c. Number of Units =

= ($600,000 + $200,000)/[$16 – ({$10 X 1.3} + $2)]

= 800,000 Units

Revenue = 800,000 X $16

= $12,800,000

d. Yes. Paralleling the requirements of Parts b. and c., a model integrates a company’s financial relationships through a series of equations, allowing a user to study the interaction of variations in economic variables. The user can thus assess the outcome of numerous what-if scenarios without ever having to implement what could be a disastrous business decision.

Solutions 6-16

6.30 (CVP—missing data.)

a. Let P = unit selling price that will yield a projected $300,000 profit.

Total sales – total costs = projected profit

200,000P – $1,260,000 = $300,000

200,000P = $1,560,000

P = $7.80 per unit.

b. Let PX = total dollar sales that will yield a projected 20% profit on sales.

Total sales – variable costs – fixed costs = projected profit:

PX – 0.6PX – $420,000 = 0.2PX0.4PX – 0.2PX = $420,000

PX = $2,100,000 sales.

6.31 (CVP Analysis.)

6-17 Solutions

a. The Deluxe system would be more profitable, as shown below.

Basic DeluxeSales......................................................... $ 4,800,000 $ 5,700,000 Less Variable Costs:

150,000 Units X $8.00............................ $1,200,000150,000 Units X $6.40............................ $ 960,000Commissions.......................................... 480,000 570,000

Total Variable Cost..................................... $ 1,680,000 $ 1,530,000 Contribution Margin................................... $3,120,000 $4,170,000Less Fixed Costs........................................ 520,000 672,000 Net Income................................................ $ 2,600,000 $ 3,498,000

b. Breakeven Point in Units =

= $672,000/[$38 – ($6.40 + {$38 X 0.10})]

= 24,173 Units.

c. Straight-line depreciation associated with the new equipment would increase fixed costs by $22,400 (= $224,000/10 years). Thus,

Number of Units =

= ($520,000 + $22,400 + $40,000)/{$32 – [$8 + ($32 x .10)]}

= $582,400/($32 - $11.20)

= 28,000 units.

d. The point of indifference will produce equal levels of profitability. On the basis of the information presented in Part a., the Basic system has a unit contribution margin of $20.80 (= $3,120,000/150,000 units), and the Deluxe system has a unit contribution margin of $27.80 (= $4,170,000/150,000 units). Thus, if X = the required quantity at which you are indifferent:

$20.80X – $520,000= $27.80X – $672,000$7.00X = $152,000

X = 21,714 Units.

6.32 (CVP with taxes.)

a. Sales ........................................ $1,000,000 (= $40 X 25,000)Variable Costs............................ 412,500 (= $16.50 X 25,000)

Solutions 6-18

Contribution Margin................... $ 587,500Fixed Costs................................ 150,000 Before-Tax Profit........................ $ 437,500Taxes (35% Rate)...................... 153,125 After-Tax Profit.......................... $ 284,375

b. Breakeven in Units =

=

= $97,500/$15.275

= 6,383 Units (Rounded)

c. Sales ......................................... $1,120,000 (= $40 X 28,000)Variable Costs............................. 462,000 (= $16.50 X 28,000)Contribution Margin.................... $ 658,000Fixed Costs................................. 190,000 (= $150,000 + $40,000)Before-Tax Profit......................... $ 468,000Taxes (35% Rate)....................... 163,800 After-Tax Profit........................... $ 304,200

d. Breakeven in Units =

= [$190,000 (1 – 0.35)]/[($40 – $16.50)(1-0.35)]

= $123,500/$15.275


Breakeven in Sales Dollars = Sales Units X Sales Price

= 8,085 X $40

= $323,400

6-19 Solutions

e. Target Profit in Units =

= [($190,000 + $437,500)(1 – 0.35)]/$15.275

= $407,875/$15.275


Target Profit in Sales Dollars = Sales Units X Sales Price

= 26,702 X $40

= $1,068,080

f. Sales ........................................... $1,120,000 (= $40 X 28,000)Variable Costs............................... 462,000 (= $16.50 X 28,000)Contribution Margin....................... $ 658,000Advertising Costs.......................... ?Other Fixed Costs.......................... 150,000 Before-Tax Profit........................... $ 115,385 [= $75,000/(1 – .35)]Taxes (35% Rate).......................... 40,385 After-Tax Profit.............................. $ 75,000

To find the maximum advertising cost to maintain after-tax profit of $75,000, solve as follows:

Contribution Margin ($658,000) – Advertising Costs – Other Fixed Costs ($150,000) = Before-Tax Profits ($115,385)

$658,000 – $150,000 – $115,385 = Advertising Costs

Maximum Advertising Costs = $392,615.

Solutions 6-20

6.33 (CVP—missing data; assumptions.)

a. Year 8 Year 9Revenues = $4,704,000 $4,725,000Net Income X9 = .02 X $4,725,000 = $94,500.

Net Income X8 = Net Income X9 + $129,500

= $94,500 + $129,500 = $224,000.

Year 8 Year 9Average Total Cost $2.20 $2.205Total Cost = $2.2 X Units Sold $2.205 X Units SoldUnits Produced $224,000 = $4,704,000 – $2.2X8 $94,500 = $4,725,000 – $2.205X9

X8 = $4,480,000/$2.2 X9 = $4,630,500/$2.205

X8 = 2,036,364 Units X9 = 2,100,000 Units

$4,704,000/2,036,364 units $4,725,000/2,100,000 units= $2.31 = $2.25

b. The total fixed and variable cost per unit cannot be determined for Year 9. The number of units produced and sold decreased while total cost increased. Assuming the total cost function is linear, this suggests that the total cost function shifted upward in Year 9. We cannot determine whether this increase resulted from an increase in fixed cost, an increase in variable cost per unit, or a combination of the two. The possibilities are illustrated in the graph.

$4,630,000

$4,480,000

210,000

224,000

•

Year 9bTotal Cost

Units Sold

• Year 9a

Year 8

a

a

Year 9a: Represents the cost curve if only fixed costs had increased.Year 9b: Represents the cost curve if variable cost per unit

increased.

If costs increased by some combination of the two, the new cost curve would lie between the lines Year 9a and 9b.

aTotal costs = total revenue – profits.

6-21 Solutions

6.34 (Alternatives to reduce breakeven sales.)

a. Variable Costs = Revenues – Fixed Costs

= $2,250,000 – $1,000,000

= $1,250,000.

Total Contribution Margin = Revenues – Variable Costs

= $2,250,000 – $1,250,000

= $1,000,000.

OR

Breakeven point is where the total contribution margin equals total fixed costs. Thus, if fixed costs equal $1,000,000, then the total contribution margin must equal $1,000,000 at the breakeven point.

b. Alternative A

Sales [$2,250,000 – ($2,250,000 X 10%)]........................... $2,025,000Variable Costs.................................................................... 1,250,000 Total Contribution Margin.................................................. $ 775,000

Contribution Margin Ratio =

= $775,000/$2,025,000

= .38

Breakeven Point in Dollars =

= =800,000*/.38

= $2,105,263.

*$800,000 = $1,000,000 – $200,000.

Solutions 6-22

6.34 continued.

c. Alternative B

Sales .............................................................................. $2,250,000Variable Costs (.95)($1,250,000)....................................... 1,187,500 Total Contribution Margin.................................................. $ 1,062,500

Contribution Margin Ratio = $1,062,500/$2,250,000 = .47

Breakeven Point in Dollars = $1,300,000*/.47

= $2,765,957.

*$1,300,000 = $1,000,000 + $300,000.

d. The company should choose the alternative that yields the greatest profit in the projected relevant range, probably Alternative A.

6.35 (CVP analysis with semifixed [step] costs.)

a. Breakeven points:

Breakeven Unit Sales =

Breakeven Units (Level 1) = $40,000/($20 - $12) = 5,000 Units



Levels 2 and 3 provide a profit for the entirerange of activity, hence, there is no breakevenpoint for either of these levels.

b. Profit:

Level 1 (10,000 units):(10,000 X $8) – $40,000 = $40,000

Level 2 (25,000 units):(25,000 X $8) – $80,000 = $120,000

Level 3 (40,000 units):(40,000 X $8) – $100,000 = $220,000

Profit is optimal at Level 3.

6-23 Solutions

6.36 (CVP analysis with semifixed costs and changing unit variable costs.)

a. First find the unit contribution margin last year:

Profit = Total Sales – Total Variable Cost – Fixed Cost

$200,000= ($50)(15,000 units) – V(15,000 units) – $100,000 (Level 1)

where V = Variable Cost per Unit

$200,000= $750,000 – V(15,000 units) – $100,000

V(15,000 units) = $750,000 – $100,000 – $200,000

V = $450,000/15,000 units

= $30 per unit

UnitContribution = $50 – $30 = $20 per unit.

Margin

Level 1 UnitContribution = $50 – $30 = $20 per unit.

Margin

Level 2 UnitContribution = $50 – 1.4($30) = $50 – $42 = $8 per unit.

Margin

b. Breakeven Point in Sales Units Level 1: = $100,000/($50 - $30)

= 5,000 units.

Breakeven Point in Sales Units Level 2: The company is profitable at 20,001 units. [(20,000 units X $20 contribution margin) + (1 unit X $8 contribution margin) – $164,000 fixed costs = $236,008.]

c. Compute the profits at the maximum volume for each level.

Level 1:Profit = (Unit Contribution Margin)(Unit Sales) – Fixed Cost

= ($50 – $30)20,000 units – $100,000 = $300,000.

Solutions 6-24

6.36 c. continued.

Level 2:Profit = ($50 – $30)20,000 units + ($50 – $42)16,000 units –

$164,000 = $364,000.

The company is more profitable at Level 2 with 36,000 units.

6.37 (CVP analysis with semifixed costs.)

a. Operating Profit = [($380 – $80)30 students] – [$1,200 X 6 teachers]– $900

= $9,000 – $7,200 – $900

= $900.

b. Operating Profit = ($380 – $80)X – $1,200Q – $900where X = number of students and Q = number of teachers.

(Note: An incorrect but common method is to substitute the ratio X/6 for Q and solve for X. This gives 9 students, but it assumes 1 1/2 teachers are employed.)

This part demonstrates the impact of step costs on cost-volume-profit analysis.

0 - 6 students: Operating Profit = $300X – ($1,200 X 1) – $900

X = = 7 students, which is not feasible.


X = = 11 students.


X = = 15 students.

The Center shows a profit at 12 students, but a loss at 13 or 14 students, then breaking even again at 15 students.


X = = 19 students.

The Center breaks even at 19 students.

6-25 Solutions

6.37 continued.

c. Operating Profit = $300X – $1,200Q – $900where X = number of students and Q = number of teachers.


X = = 7 students.


X = = 11 students.

At 10 students, the Center would show a profit of $900 [i.e., ($300 X 10) – $1,200 – $900], but at 11 students it would just break even.

d. Yes. The Center would increase profit by $1,800.

Two methods are presented here:

1. Total MethodStatus quo: Operating Profit = $900. (From Part a.)Alternative: Operating Profit = ($300 X 36 students) – ($1,200 X

6 teachers) – $900

= $10,800 – $7,200 – $900= $2,700.

Therefore, the increase is $1,800 (= $2,700 – $900).

2. Differential MethodIncrease in total contribution = $300 X 6 = $1,800.No change in fixed or step costs.

e. Profit would decrease by $900. Although the contribution margin would increase by $300, another teacher would be hired at a cost of $1,200 if the maximum 6:1 student-teacher ratio is to be maintained.

6.38 (Break-even analysis for management education.)

The analysis classifies the costs associated with the executive program into their variable, step and fixed components. Furthermore, it identifies the opportunity cost of administrative personnel who will be unable to fulfill their duties elsewhere. These numbers appear to be accurate given the assumptions associated with cost-volume-profit analysis such as price stability and current activity level.

Solutions 6-26

6.38 continued.

However, all the numbers presented in the analysis are estimates and therefore not exact. A useful addition to this analysis would be a sensitivity analysis where the parameters are changed to produce a best case and a worst case scenario.

Cost-volume-profit analysis includes many assumptions including that costs remain the same throughout the relevant range of activity. If the number of students attending is vastly different from those expected, the cost numbers may be inaccurate. Depending on the possibility of this outcome, it can be modeled using sensitivity analysis to broaden the scope of this analysis.

6.39 (Cost cutting to break even.)

a. The breakeven point in units is,

X = F/(P – V)where:

X = number of units(P – V) = average contribution margin per unit.

Plugging in the numbers for Auto, Inc.,

1,100,000 = $3,100,000,000/(P – V)(P – V) = $2,818.18.

b. Management correctly realized the increasing level of competition in the automobile industry. This meant that sales levels for individual companies would probably fall as would prices on individual sales. Faced with falling volume and contribution margin, the only alternative to lower the breakeven point is to reduce fixed costs.

c. Cost cutting can significantly increase profits in the short run. However, cutting costs can lead to reduced profits in the long run. For example, if the company chooses to reduce advertising, this may increase short run profits at the expense of lost sales in the long run. Many companies cut costs during economic recessions, but are faced with inadequate capacity when the economy improves. As a shareholder, I would be concerned that the company not cut costs so drastically as to jeopardize its long-run profitability.

6-27 Solutions

6.40 (CVP—partial data; special order.)

a. First Quarter Sales =$36,000/$3.60= 10,000 Units.

Total Costs = Fixed Costs (F) + Variable Cost per Unit (V) X Unit Sales (X).

V = ($67,000 – $49,000)/ (17,500 – 10,000 ) = $2.40 per Unit.

F = $67,000 – ($2.40 X 17,500) = $25,000.

Breakeven Point = $25,000/($3.60 - $2.40) = 20,833 Units.

b. University Officials University Officials Contract Accepted Contract Not

AcceptedUnits 25,000 17,500

Revenue $87,000a $63,000Variable Costs:

Materials (15,000)b (10,500)b

Labor (33,000)c (21,000)d

Overhead (15,000) (10,500)

Fixed Costs (28,000)e (25,000)Operating Profit

(Loss) $(4,000) $(4,000)

a$87,000 = $63,000 + ($3.20 X 7,500).

bAmounts = $.60 per meal X number of meals.$.60 per meal = 25% of $2.40 variable cost per meal according to Part a. of the solution.

c$33,000 = $1.20 per meal X 1.1 for cost increase X 25,000 meals.$1.20 per meal = 50% of $2.40 variable cost per meal according to Part a. of the solution.

d$21,000 = $1.20 per meal X 17,500 meals.

e$28,000 = $25,000 + $3,000 cost increase.

No change in Operating Profit (Loss) if the order is accepted.

Solutions 6-28

6.40 continued.

c. V = ($15,000 + $33,000 + $15,000)/25,000 = $2.52 per Unit.

Find X:

$6,800 = $3.60X + $24,000 – $2.52X – $18,900 – $28,000

$6,800 = $1.08X – $22,900

$29,700 = $1.08X

X = $29,700/$1.08

X =27,500 student meals.

6.41 (Financial modeling with multiple cost drivers.)

6-29 Solutions

a. Memorandum

Date: TodayTo: Vice-President for Manufacturing, Radio, Inc.From: I.M. Student, ControllerSubject: Activity-Based Costing

The $150,000 cost that has been characterized as “fixed” will not increase with increases in sales volume. However, as the activity-based costing analysis demonstrates, these costs are not fixed with respect to other important cost drivers. This is the difference between a traditional costing system and an ABC system. The latter recognizes that costs vary with respect to a variety of cost drivers, not just sales volume.

b. New breakeven point if automated equipment is installed:

Sales price......................................................................... $26Costs that are variable (with respect to sales volume):

Unit variable cost [$525,000 – $150,000 = $375,000;($375,000 X 0.8) ÷ 25,000 units]............................... 12

Unit contribution margin.................................................... $ 14

Costs that are fixed (with respect to sales volume):Setup (300 setups at $50 per setup).............................. $ 15,000Engineering (800 hours at $28 per hour)........................ 22,400Inspection (100 inspections at $45 per inspection)......... 4,500General factory overhead............................................... 166,100

Total.......................................................................... $208,000

Fixed selling and administration costs............................... 30,000 Total.......................................................................... $ 238,000

Breakeven Point (in Units): Fixed Cost ÷ Unit Contribution Margin

$238,000 ÷ $14 = 17,000 units.

c. Number of units = (Fixed Cost + Target Profit) ÷ Unit Contribution Margin

($238,000 + $140,000) ÷ $14 = 27,000 units.

d. If Radio, Inc. adopts the new manufacturing technology:

(1) The breakeven point will be higher (17,000 units instead of 15,000 units). The 15,000-unit figure is derived as follows:

Unit variable cost = $15 [= ($525,000 – $150,000) ÷ 25,000 units]

Unit contribution margin = $10 (= $25 – $15)

Solutions 6-30

Breakeven units = 15,000 (= $150,000 ÷ $10)

(2) The number of units sold to show a profit of $140,000 will be lower than before (27,000 units instead of 29,000 units). The 29,000-unit figure is computed as follows: [($150,000 + $140,000) ÷ $10].

(3) These results are typical of situations where firms adopt advanced manufacturing equipment and practices. The breakeven point increases because of the increased fixed costs associated with the large investment in equipment. However, at higher levels of sales after fixed costs have been covered, the larger unit contribution margin ($14 instead of $10) earns a profit at a faster rate. (The higher contribution is usually the result of increased operating efficiencies.) The overall outcome is that the firm needs to sell fewer units to reach a given target profit level.

6-31 Solutions

6.42 (Roseville Brewing Company; financial modeling for a brew pub.)

a. Potential investors and bankers were concerned about the accuracy of the income statement projections. They wanted to know what would happen if the projections were overly optimistic. Operating profit was heavily influenced by projected sales dollars and product mix. The concern was over the impact changes in sales and product mix (among other things) might have on operating profit.

b. The first income statement was in the traditional format. In the traditional format, costs are not show according to cost behavior. Thus, it is difficult to predict what will happen with costs as changes are made in sales volume. For example, if sales volume decreases by 10 percent, it is difficult to predict what will happen with cost of sales and marketing and administrative expenses. Will they decrease by the same percentage? (Unlikely unless all costs are variable!)

c. The best way to quickly check for reasonableness is to compare the operating profit as a percentage of sales to other similar businesses. In addition, the dollar amount of operating profit can be compared to other similar businesses. (In fact, the banks and investors who were approached by RBC often looked at these two items as a starting point to ensure the projected income statement was reasonable.)

d. The cost of a pint of beer can range from $0.15 to $1.40 depending on what is included in the cost. Should we include only the materials? Should we include direct labor? Indirect labor? Manufacturing overhead? The point is to understand what is included in the cost of a product, particularly when this information is used for pricing and other forms of decision-making.

e. i. The breakeven point in sales dollars is $1,235,154, calculated as follows:

Breakeven Point = Total Fixed Costs/Contribution Margin Ratio

= $520,000/($822,213/$1,953,000)

= $520,000/.421

= $1,235,154.

ii. The margin of safety is $717,846, calculated as follows:

= $1,953,000 – $1,235,154

= $717,846.

Solutions 6-32

6.42 e. continued.

iii. RBC is selling many different products that change daily. It is difficult if not impossible, to measure units of product for a brew pub. This same argument holds true for most service companies as well. Service companies do not sell “units” of service. Thus, for these types of companies, breakeven points and target profit points are calculated using sales dollars.

iv. The sales dollars required to achieve $200,000 in operating profit is $1,710,214, calculated as follows:

Target Profit =

= ($520,000 + $200,000)/.421

= $720,000/.421

= $1,710,214.

The sales dollars required to achieve $500,000 in operating profit is $2,422,803, calculated as follows:

Target Profit =

= ($520,000 + $500,000)/.421

= $1,020,000/.421

= $2,422,803.

These calculations assume that the product mix is constant. The contribution margin ratio is dependent on the product mix, and will change as the product mix changes.

6-33 Solutions

6.42 continued.

f. The revised income statement given the shift in product mix is as follows:

Sales:Beer Sales (25% of Total Sales).............. $ 488,250Food Sales (70% of Total Sales).............. 1,367,100Other Sales (5% of Total Sales).............. 97,650

Total Sales................................................. $1,953,000Variable Costs:

Cost of Sales:Beer (15% of Beer Sales)..................... $ 73,238Food (35% of Food Sales).................... 478,485Other (33% of Other Sales).................. 32,225

Wages of Employees (25% of Sales)....... 488,250Supplies (1% of Sales)............................ 19,530Utilities (3% of Sales)............................. 58,590Other: Credit Card, Misc. (2% of

Sales).................................................. 39,060 Total Variable Costs................................... 1,189,378 Contribution Margin................................... $ 763,622

Fixed Costs:Salaries: Manager, Chef, Brewer............ $ 140,000Equipment & Building Maintenance........ 30,000Advertising............................................. 20,000Other: Cleaning, Menus, Misc................ 40,000Insurance and Accounting...................... 40,000Property Taxes....................................... 24,000Depreciation.......................................... 94,000Debt Service (Interest on Debt).............. 132,000

Total Fixed Costs....................................... 520,000 Operating Profit......................................... $ 243,622

Thus, operating profits would decrease by $58,590 from the original projection of $302,212. This is a 19.4% decrease (= $58,590/$302,212).

g. Answers will vary. Examples of strategic factors to be considered include competition, economic conditions, and demographics.

Solutions 6-34

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acct 620 chapter 6

Documents

total costs

unit variable costs

total variable costs

analysis of costs

fixed margin

sales volume fixed costs

cvp costs

total contribution margin