Exercises 3134

CHAPTER 7: COST-VOLUME-PROFIT ANALYSIS

QUESTIONS

7-1 The underlying relationship in cost-volume-profit analysis is that costs, revenues, and profits all change in a predictable way as the volume of activity changes.

7-2 It is more practical to find the breakeven point in sales dollars for companies having thousands of individual items. Finding the breakeven point for each item would be laborious and meaningless.

7-3 The contribution margin ratio is: price - variable costs price

The contribution margin ratio (CMR) represents the net contribution per sales dollar. The CMR tells us the change in profit associated with a given change in sales dollars. It is a useful measure of the relative contribution to profit of different products, divisions, or sales units. The use of this ratio can give a retail store a good approximation of the sales dollars necessary for the store to break even. A higher CMR is associated with higher risk. A higher CMR can have a more favorable impact on profit. However, if sales fall below breakeven, then a high CMR will yield a relatively more negative impact on profits.

7-4 The basic assumption of the CVP model is that the behavior of revenues and total costs is assumed to be linear over the relevant range of activity. Managers must be careful to remember that the calculations done within the context of a given CVP model cannot be interpreted safely outside of the relevant range of output for that particular model. Other assumptions include: fixed costs are measured by all fixed costs if a long-term perspective (i.e., breakeven over a longer period of time) is to be taken, while only incremental fixed costs for the project or activity are included if a short- term perspective (i.e., to determine when the firm will achieve breakeven on a new product) is taken. Also, allocated fixed costs are not included if a short-term perspective is taken, since these costs will not change in the short term.

7-5 If part of the costs are fixed, they will remain constant even when the activity level declines. Therefore, the variable costs will need to fall by the entire amount of the budget cut. Fixed costs are sticky; the expected savings from reducing activity levels will be less than the effect on the activity itself.

7-6 Only include fixed costs that are relevant for a short-term analysis to determine when the new product will reach breakeven. Relevant costs are those additional, new, or incremental fixed costs which will influence the profitability of the new venture. If a new product does not require any new fixed cost, then the

Solutions Manual 7-1

breakeven point is zero.7-7 CVP is used in profit planning, revenue planning and in cost planning. It is a

widely applicable tool for analyzing the relationship between volume and profits, costs, or revenues.

7-8 The issue of taxes does not affect the calculation of the breakeven point because the breakeven point is determined at the level of zero profit.

7-9 Technologically advanced firms usually have high fixed costs. Therefore, profits are strongly affected by the level of activity. High profits are earned beyond the breakeven point, but high losses can result from falling below breakeven.

7-10 Sensitivity analysis deals with the risk that sales may fall short of expectations or that costs will be higher than expected.

7-11 The breakeven point can be calculated using:1. The equation method for sales in units2. The equation method for sales dollars3. The contribution margin method for sales in units4. The contribution margin method for sales dollars

7-12 Margin of safety = expected sales - breakeven sales

The margin of safety is measured in either dollars or units. It measures the potential effect of the risk that sales will fall short of planned levels.

7-13 Operating leverage = contribution margin net income

Operating leverage uses the percentage change in sales to predict the percentage change in profits. The contribution margin ratio uses the dollar change in sales to predict the dollar change in profits.

7-14 Step costs cause a difficulty in the calculation of breakeven because of the discontinuities in the cost line. This usually requires some trial and error to identify the one unique breakeven point. Exhibit 7-9 illustrates how the breakeven point is determined when there are step costs.

7-15 One over one minus the tax rate.

(1/(1-t))

7-16 In order to use the CVP model to find the breakeven point for multiple products, one must assume that the sales of the products will continue at the present sales mix. (Each product will continue to comprise the same proportion of total sales.) The constant sales mix permits two or more products to be treated as one, by

Blocher,Chen,Cokins,Lin: Cost Management 3e 7-2 ©The McGraw-Hill Companies, Inc., 2005

computing a weighted-average price, unit variable cost, and contribution margin.7-17 Sensitivity analysis is used for two important purposes:

1. To determine which factors have the greatest influence on profit, and to assess the magnitude of that influence

2. To examine the sensitivity of profit to a given forecast or estimate for any one of the factors


EXERCISES

7-18 Make or Buy; Two Machines (20 min)

1. S = number of switches Machine X Machine Y$2S = $.65S + $135,000 $2S = $.3S + $204,000 S = 100,000 S = 120,000

2. cost when purchasing from outside supplier:$2 x 200,000 = $400,000

cost when using machine X: $135,000 + $.65 (200,000) = $265,000

cost when using machine Y: $204,000 + $.30 (200,000) = $264,000

When 200,000 switches are needed, it is most profitable to produce them with machine Y, though the difference is only $1,000.

3. cost of using X = cost of using Y$.65S + $135,000 = $.30S + $204,000

$.35S = $69,000 S = 197,143 units

When 197,143 switches are needed, the Calista Company is indifferent as to which machine to use.

Summary of (1), (2) and (3): If output is less than 100,000, buy the switches; if output is less than 197,143 units but greater than 100,000, buy and use machine X; if output is greater than 197,143 units, then buy and use machine Y.


7-19 Operating Leverage (20 min)

1. operating leverage = contribution margin net income

A's operating leverage = $40,000/$25,000 = 1.6

B's operating leverage = $70,000/$30,000 = 2.3333

If sales increase, company B will benefit more. Company B has a higher proportion of fixed costs in relation to variable costs; therefore it has a higher operating leverage than does Company A. The degree of operating leverage is a measure, at a specific level of sales, of how a percentage change in sales volume will affect profits. The higher the operating leverage, the more sensitive profits are to changes in sales volume.

2. COMPANY A COMPANY B Amount % Amount %

Sales $110,000 100 $110,000 100Less variable costs 66,000 60 33,000 30Contribution margin $ 44,000 40 $ 77,000 70Less fixed costs 15,000 40,000Net income $ 29,000 $ 37,000

A’s change in profits = ($29-25)/$25 = 16% = 10% x 1.6

B’s change in profits = ($37-30)/$30 = 23.333% = 10% x 2.333

Yes, these results are what we expected. Operating leverage indicates what change in net income can be expected from a change in sales volume. An operating leverage of 1.6 implies that the change in net income will be 1.6 times as large as the change in sales volume. Therefore, if sales increased by 10%, net income should increase by 16%. This is precisely what happened. The same logic applies to Company B.


7-20 CVP Analysis (25 min)

1. Sales = variable cost + fixed cost + target income/(1-tax rate)30,000($65) = 30,000($32) + $429,000 + N N = $561,000

2. BE units: $65Q = $32Q + $429,000 Q = 13,000 units

3. Net Income: 35,000($65) -35,000($32) - $429,000 - $200,000= NN = $526,000(net income falls by $35,000, from $561,000 to $526,000 as a

result of the plan to increase sales with increased advertising)

4. BE units: $65Q = $32Q + $629,000Q = 19,061 units(and breakeven is higher)

5. $65Q = $32Q + $629,000 + $561,000Q = 36,061 units(to justify the advertising plan, sales would have to rise to at

least 36,061 units, somewhat above the projected 35,000 units)


7-21 Multiple Product CVP Analysis (20 min)

1. Hardbound: .5 x $12.00 = $6.00Paperback: . 6 x $ 2.40 = $1.44Magazines: .6 x $ 1.90 = $1.14

2. Rent $19,200Utilities 7,800Salaries 56,000Overhead 11,500Advertising 900Prof. Services 2,400Total $97,800

Fixed costs are not expected to change, and are therefore the same as last year.

3. Weighted Average contribution ratio, since sales mix is constant in dollars:

Hardbound: .7 x (.5 x $12)/(1.5 x $12) = .2333Paperback: .2 x (.6 x $2.40)/1.6 x $2.40) = .0750Magazines: .1 x (.6 x $1.90)/(1.6 x $1.90) = .0375Weighted Average CMR .3458

Breakeven = $97,800/.3458 = $282,822 of books and magazines

Hardbound: .7 x $282,822 = $197,976Paperback: .2 x $282,822 = $ 56,564Magazines: .1 x $282,822 = $ 28,282

4. Desired before tax profit = $40,000/ (1-.33) = $59,701Cost-Volume-Profit Point = ($97,800 + $59,701)/ .3458 = $455,470 books and magazines


7-22 The Role of Income Taxes (20 min)

1. operating income = $70,000 / (1-.3) = $100,000

2. contribution margin - fixed cost = before tax profitcontribution margin - $200,000 = $100,000

CM = $300,000

3. total sales - total variable cost = total contribution margintotal sales - variable cost ratio x sales = $300,000total sales - .80 x sales = $300,000

.2 x sales = $300,000sales = $1,500,000

4. Contribution margin ration (CMR) = $300,000/$1,500,000 = .2

breakeven point = fixed costs = $200,000 = $1,000,000CMR .2


7-23 CVP with Taxes (20 min)

1. BE units = f + N = $75,000 + 0 = 37,500 units p - v $5 - $3

2. BE dollars = f + N = $75,000 + 0 = 75,000 = $187,500 p-v $5-$3 .4 p $5

OR: 37,500 x $5 = $187,500

3. Q = f + N = $ 75,000 + $10,000 = 42,500 units p - v $5 - $3

4. pQ = f + N = $75,000 + $8,000 = 83,000 = $207,500 p-v $5 -$3 .4 p $5

5. Q = f + N/(1 - t) p - v

Q = $75,000 + $12,000/(1-.4) = $75,000 + $20,000 = 47,500 units

$5 - $3 $2

Using the contribution margin ratio:

pQ = f+N/(1-t) = $75,000+[$12,000/(1-.4)] = $75,000 + $20,000 = $237,500 p - v $5 - $3 .4 p $5

OR: 47,500 x $5 = $237,500


7-24 Margin of Safety (20 min)

1. First, note that the gross margin in this problem is also the contribution margin, since all operating costs are fixed and all merchandise cost is variable with sales dollars.

calculate the breakeven point, using the contribution margin ratio:

CMR = $227,500/$650,000 = .35 Breakeven = $105,000/.35 = $300,000And

Margin of safety = $650,000 - $300,000 = $350,000

Margin of safety ratio = $350,000/$650,000 = 53.85%

2. If sales fall to $500,000, the breakeven point will remain the same, but the margin of safety will change:

Margin of Safety = $500,000 - $300,000 = $200,000

Operating income can be determined in a variety of ways:

Contribution margin = $500,000 x .35 = $175,000Less fixed costs 105,000 Operating Income $ 70,000

Or, using the relationship between the margin of safety and operating income:

Operating Income = Margin of Safety $ x CMR$70,000 = $200,000 x .35

Why this works:Margin of Safety x CMR = operating income

(Expected Sales – Breakeven)xCMR = Expected Sales x CMR – Breakeven x CMR= Contribution margin – fixed costs = operating income

(Note that breakeven sales x CMR = fixed costs)


7-25 Budget Cuts (10 min)

If the budget is reduced by 20%, services will have to decrease by more than 20% because the fixed costs will not change in the short term. Since fixed costs do not change, variable costs will have to decrease by $40,000 ($200,000 x 20%).

decrease in variable costs $ 40,000 = 33.33%last year's variable cost budget $120,000

Although the budget was cut by only 20%, the Pharmacy will have to reduce its services by 33.33%


7-26 Multiple Products CVP (20 min)

The sales revenues for Brighter and Smarter are $150,000(200 x $750) and $300,000 ($1,000 x 300), respectively. The proportion of sales dollars for each product is as follows:

Brighter: $150,000/($150,000 + $300,000) = 33.33%Smarter: $300,000/($150,000 + $300,000) = 66.67

The contribution margin ratio for the two products is 70% and 55%, respectively.

(750-225)/750 = .7; (1,000 – 450)/1,000 = .55

Weighted average CM Ratio = .333 x .7 + .667 x .55 = .60Breakeven Point: $132,000/.6 = $220,000


PROBLEMS

7-27 CVP Analysis; Strategy (20 min)

1. BE units = f + N = $150,000 = 15,000 hats p - v $30 - $20

BE $ = fixed costs = fixed costs = $150,000 = $450,000

CMR p - v $30-$20 p $30

2. 20,000= $150,000 + N $30 - $20

$200,000= $150,000 + N net income = $50,000

3. Margin of safety = 25,000 – 15,000 = 10,000 hats Margin of safety ratio = 10,000/25,000 = 40%

4. BE units = f = $150,000 + $82,000 = 16,000 p - v $30 - $15.50

20,000 = $232,000 + N $30 - $15.50

N = net income = $58,000

5. A key strategic issue is that Frank’s sales staff is a critical success factor for the business. His knowledgeable and courteous staff help to bring in and retain customers. If the salary/commissions plan would alienate his sales staff, the plan could be a big mistake. Frank should proceed with caution, and be sure that his sales staff will be as highly motivated under the salary plan as they were under the commissions plan.


7-28 Contribution Income Statements (Excel; 25 min)

1. A variety of possible spreadsheets could satisfy this requirement. Once example is shown below. The sensitivity analysis shows sales levels from 20% to 200% of expected sales of 2,400 units, and the related effect on operating profit. HFI’s operating leverage is 2 2/3, so that profits change much faster (2.667 times faster) than a given change in the sales level.


Problem 7-28 (continued)

2. The Goal Seek tool is available under the Tools menu in Excel. An example of how it is used is show below. The price would have to increase to $101.67 in order for HFI to make a $100,000 before tax profit.


7-29 Breakeven Analysis for Multiple Products (25 min)

1. Weighted-average unit contribution = ($20 x 80%) + ($45 x 20%) = $25

The break-even point = $200,000 = 8,000 units $25

Break-even sales in units:

Product A 8,000 x 80% = 6,400Product B 8,000 x 20% = 1,600

The following income calculation verifies the break-even point:

Sale revenues:Product A: 6,400 x $90 $576,000Product B: 1,600 x $ 140 224,000Total sales 800,000

Less variable cost:Product A: 6,400 x $ 70 448,000Product B: 1,600 x $95 152,000Total variable costs 600,000

Fixed costs 200,000Total costs 800,000Operating profit -0-

2.The management of the company plans $40,000 target-net-profit:

Fixed expenses + Target net profit Contribution margin

$200,000 + $40,000 =9,600 units $25

Product A = 9,600 x 80% = 7,680 unitsProduct B = 9,600 x 20% = 1,920Total 9,600



So to achieve the target-net-profit Hycel has to sell 7,680 units of Product A and 1,920 units of Product B.

Income Statement to verify the Target-net-profit calculation:

Sale revenues:Product A: 7,680 x $90 $ 691,200Product B: 1,920 x $140 268,800Total sales 960,000

Variable costs:Product A: 7,680 x $70 537,600Product B: 1,920 x $95 182,400Total variable costs 720,000

Fixed costs 200,000Total costs 920,000Net Income $ 40,000


7-30 Multiple Product CVP Analysis (25 min)

1. Contribution analysis based on actual sales:

Small Standard Super Total

Sales $400,000 100% $225,000 100% $200,000 100% $825,000Variable costs 276,000 69 56,250 25 100,000 50 432,250Contribution 124,000 31 168,750 75 100,000 50 392,750Fixed costs 425,000Net Income ($32,250)

2. Breakeven based on actual sales mix:

BE = fixed costs = $425,000 = $892,744 average CM ($392,750/$825,000)

Breakeven based on budgeted sales:

Small Standard Super Total

Sales $175,000 100% $400,000 100% $250,000 100% $825,000Variable costs 120,750 69 100,000 25 125,000 50 345,750Contribution 54,250 31 300,000 75 125,000 50 479,250Fixed costs 425,000Net Income $ 54,250

BE = $425,000 = $731,612 ($479,250/$825,000)

3. Although total sales dollars remained constant ($825,000), the breakeven point changed because the sales mix changed. Sales shifted from products with a higher contribution margin (standard and super) to a product with a lower contribution margin (small). More sales were necessary to cover the same amount of fixed costs.


Therefore, the breakeven point increased from $731,612 to $892,744. Also, since the actual sales level fell below $892,744, there was an actual net loss of $32,250.


7-31 CVP Analysis; Taxes (25 min)

1. BE units = f + N = $350,000 + 0 = 14,000 units p - v $60 - $35

BE sales dollars = f + n = $350,000 + 0 = $350,000 = $840,000

p-v $60 -$35 .417 p $60

OR: 14,000 x $60 = $840,000

2. BE units = $350,000 + $150,000 = 20,000 units $60 - $35

3. 40,000 = $350,000 + N $60 - $35

N = $650,000

4. X = f + N/(1-t) = $ 350,000 + $150,000/(1-.4) = 24,000 units p - v $60 - $35

5. Original = New $200,000 + $30Q = $150,000 + $35Q

Q = 10,000

6. The CVP Graph appears below:


7-32 CVP Analysis in a Professional Service Firm (25 min)

1. If net income is to increase the contribution margin of the new business must be positive.

Y = Variable cost + Fixed cost + Income

Y + $50(800) = $5(800 + 900) + $45,000 + 0

Y = $13,500

where Y is the minimum revenue that must be earned from the county work in order to insure that net income of the firm does not decrease. Revenue above this level will result in incremental profit. The average billing rate at the breakeven rate of $13,500 would be $13,500/900 = $15 per hour. Clearly, the key to the bidding strategy is the desirability of bringing in 800 hours of new business at the going billing rate.

2. $20,000 + $50(X) = $5(900 + X)+$45,000 + 0

X = 656

The managing partner's estimate of 800 hours of new business leaves a margin of safety of 800 - 656 = 144 hours.



1. Break-even in units = Fixed cost/Unit Contribution Margin

CM = $36,000,000 - $22,500,000 = $3,000 - $1,875 = $1,125/unit

12,000 12,000

B/E = $7,500,000/1,125 = 6,667 units

2. Contribution margin ratio = Unit contribution margin Unit sales price

Thus, CM ratio = $1,125 = .375 $3,000

Fixed Cost = B/E in dollars CM ratio

$7,500,000 = $20,000,000 = $3,000 * 6,667 .375

3. Fixed Cost + Target profit = $7,500,000 + $7,250,000 = $39,333,333 CM ratio .375

4. New CM = $3,000 - ($22,500,000 x 1.10) = $937.50 per unit 12,000

B/E = Fixed cost = $7,500,000 = 8,000 units CM $937.50/unit


7-34 CVP Analysis; Activity-based costing; Taxes (30 min)

1. Total fixed manufacturing expense = 12 x $60,000 = $720,000

$300X = $10X + ($720,000 + $100,000 + $50,000)X= $870,000/$290X= 3,000 units per year

2. 20 unit batch means 6,000/20 = 300 batches per yearBatch level costs = $720,000 x .2 = $144,000Non-batch costs = $720,000 - $144,000 = $576,000Cost per batch = $144,000/300 = $480Cost per unit = $480/20 = $24

Breakeven:$300X = $10X + 24X + ($576,000 + $100,000 + $50,000)X= $726,000/$266X= 2,729 units per year, or 136.5 batches (137 batches,

rounded)

Exact Breakeven$300X = $10X + ($576,000 + 137 x $480 + $100,000 +

$50,000)X= $791,760/$290X= 2,730 units per year

Note that the breakeven for the ABC approach is somewhat smaller than that of the volume based analysis, because batch level costs of $480 per batch can be saved if production falls below the budgeted level of 6,000 units.

3. Total fixed expenses: $720,000 + ($100,000 x 2) + $50,000 = $970,000

Target profit per year = $12,000 x 12 = $144,000Target before tax profit: $144,000/(1 - .4) = $240,000

Q = ($970,000 + $240,000)/$290 = 4,173 units.


7-35 CVP Analysis (25 min)1. Pro-rated per year fixed cost of blood gas machine = $750,000/10

= $75,000

Savings per sample in direct costs if a gas analysis machine is purchased : $85 - $40 = $45

Indifference point:$75,000/$45 = 1,667 samples (tests) per year.

Alternatively (where X is the breakeven number of tests):

$85 X = $40 X + $75,000 X = 1,667 tests

2. Current number of patients needing analysis = 5,000 patients5,000 x 30% needing blood gas analysis = 1,500The difference 1,667 – 1,500 = 167

167 is the additional number of blood gas samples needed to break even at the $85 charge. To generate 167 additional charges, we need 167/.3 = 557 additional patients.

3. The amount the diagnostic screening center would have to charge clients at the current patient levels:

p x 1,500 = $40 x 1,500 + $75,000p = $90


7-36 CVP Analysis; Sensitivity Analysis; Strategy

1. GoGo Juice’s profit (loss) before tax, from implementing the promotional coupon with no change in sales volume is ($8,000)

Gasoline Food and beverage

Other Total

Sales Revenue $100,000 $60,000 $40,000 $200,000Coupons redeemed(note 1)

(16,000) (16,000)

Cost of Sales (note 2)

75,000 36,000 20,000 131,000

Contribution Margin

$9,000 $24,000 $20,000 53,000

Fixed costs (note 3)

61,000

Loss before tax $(8,000)

Note 1: Coupons redeemed: total sales of $200,000 x 80% x 10% ($1 per $10) = $16,000Note 2: Gasoline cost of sales: $100,000/$1.129 price per gallon = 88,574 gallons

88,574 x $.84675 = $75,000Note 3: Fixed costs

Labor$9,000 + $2,500 $11,500Rent, power, supplies, etc 46,500Depreciation 2,500Coupon printing cost 500 Total fixed costs $61,000

2. The breakeven for GoGo:

Contribution margin ratio = $53,000/$200,000 = 26.5%

Breakeven in dollars = $61,000/.265 = $230,189



3. Sales revenue ($200,000 x 1.2) $240,000

Contribution margin ($240,000 x 30%) 72,000Less fixed costs 61,000Profit before tax $11,000

4. Sensitivity analysis is used to deal more effectively with uncertainty or risk. Sensitivity analysis is a "what-if' type of analysis used to determine the outcomes if any parameters change from the initial assumptions. For example, revenues or costs could be changed from the initial assumptions and a new break-even sales volume calculated. At least three factors that make sensitivity analysis prevalent in decision making including the following. The availability of computers and spreadsheet software has made it very

quick and easy to compute the impact of changing one or more assumptions in a financial model.

As the business environment is becoming more dynamic and competitive, sensitivity analysis provides management with an understanding of the impact of changes in the environment. The increased emphasis on productivity , competitive marketplace, changing consumer demand, shorter product life cycle times, and faster obsolescence of technology makes sensitivity analysis more widely used.

Sensitivity analysis aids management in identifying the key variables and assumptions, so the variables can be monitored or a decision made to obtain additional information on them.



1. Weekly: $.60 per issue x 52 = $ 31.20 per subscription $ 3.00 per subscription

$ 1.50 per subscriptionTotal variable cost $35.70

Selling Price ($47.00) - Total Variable Cost ($35.70) = $11.30 Contribution Margin Per Unit

Monthly: $.60 per issues x 12 = $ 7.20 per subscription $ 3.00 per subscription $ 1.50 per subscription

Total Variable Cost $11.70

Selling Price ($19.00) - Total Variable Cost ($11.70) = $7.30 Contribution Margin Per Unit

2. Contribution Margin Ratio Weekly: $11.30 / $47.00 = 24% Monthly: $ 7.30 / $19.00 = 38.4%

3. $11.30 X .20 = $2.26 HPC-Weekly $ 7.30 X .80 = $5.84 HPC-Monthly

$8.10 weighted average Contribution Margin

$306,000 / $8.10 = 37,778 subscriptions (7,556 for HPC-weekly; 30,222 for HPC-monthly)

4. Breakeven Point for Target Before Tax Profit of $ 75,000

$306,000 + $75,000 = $381,000 $381,000 / $8.10 = 47,037 (9,407 for HPC-weekly; 37,630 HPC-

monthly)



5. The point of this question is to get the students started thinking about the competitive context in which the firm operates. There are many different relevant points that could be made. If the discussion is slow to start, ask them to think about what a firm like HPC must do to be competitive.

There are a number of critical success factors that are likely to be important for both domestic and foreign subscriptions. These would include quality of presentation and timeliness and accuracy of information, as well as competitive price. However, other factors will differ across countries. For example, in some countries the cost of distribution including selling and handling costs are quite high, so that it is critical in these countries to devise new ways to deliver the subscriptions profitably. Other factors include changes in literacy rates, the business climate, and investment opportunities in different countries.


7-38 CVP Analysis; Commissions; Ethics (50 min)

1. Breakeven dollars (dollars in thousands)Y = Variable cost of goods sold + current

fixed costs + fixed cost of hiring + commissions

Y = .45Y + $6,120 + $1,890 + .10Y Y = $17,800

Supporting CalculationsVariable cost of goods sold rate:(dollars in thousands) $11,700/$26,000 = 45%

Current fixed costs ($ thousands) Fixed cost of goods sold $2,870 Fixed advertising cost 750 Fixed administrative cost 1,850 Fixed interest expense 650 Total $6,120

Fixed cost of hiring ($ thousands) Sales people (8 x $80) $ 640 Travel & entertainment 600 Manager/secretary 150 Additional advertising 500 Total $1,890

2. Breakeven formula set equal to net income: (dollars in thousands)

Y - .45Y - $6,120 - .23Y = $3,500Y = $30,063

This is $30,063 - $26,000 = $ 4,063 greater than budgeted sales



3. The general assumptions underlying breakeven analysis that limit its usefulness include the following:

All costs can be divided into fixed and variable elements.Variable costs vary proportionally to volume.Selling prices remain unchanged.The analysis is done within the relevant range of the cost and

revenue variables

4. Let sales at the indifference point be Y (in 000s).

Total Cost for Current Agents = Total cost for Our Agents

.45Y + .23Y + $6,120 = .45Y + $6,120 + $1,890 + .10Y .13Y = $1,890 Y = $14,538 (rounded)

Since the point of indifference, $14,538 is less than current sales of $26,000, the firm would be better off hiring their own agents, because the relatively low variable cost offsets the relatively high fixed costs of the new agents when sales are higher than the indifference point.

5. Total compensation under the new plan:Salary $ 640,000Commission: 26,000,000 x 0.1 = 2,600,000Total $3,240,000

This does not compare favorably (from the sales agents’ point of view) to the previous plan, for which the total compensation was

.23 x $26,000,000 = $5,980,000.Thus, there is no basis for an increase in commission rates under the existing plan.



6. Markowitz should consider the firm’s ethical responsibility to its shareholders, employees and agents. The new plan would be a savings for the firm and thus would have an upward effect on stock price and thus benefit the shareholders. However, the plan would be a blow to the sales agents, many of whom may be depend on Marston Corporation for a significant portion (or perhaps all of) their income. The agents are likely to have alternative job prospects if Marston lets them go, but there will also be a difficult transition time. Marston needs to think carefully about the nature and extent of its responsibility to the sales agents, as part of its overall responsibility to its constituencies. What is our responsibility to these sales agents who are not our employees. The shareholders are a prime concern, but employees and others such as the sales agents must also be given consideration.


7-39 CVP Analysis; Different Production Plans (35 min)

1. The annual breakeven point in units at the Peoria plant is 73,500 units and at the Moline plant is 47,200 units, calculated as follows.

Unit contribution calculation:

Peoria MolineSelling price $150.00 $150.00Less variable costs: Manufacturing 72.00 88.00 Commissions 7.50 7.50 G & A 6.50 6.50

Unit contribution $ 64.00 $ 48.00

Fixed costs calculation:

Total fixed costs = (Fixed manufacturing cost + Fixed G & A) x Production rate/day x Normal working days.

Peoria = {$30.00 + ($25.50 - $6.50)}x 400 x 240 = $4,704,000

Moline = {$15.00 + ($21.00 - $6.50)}x 320 x 240 = $2,265,600

Breakeven calculation:Breakeven units = Fixed costs / Unit contribution

Peoria = $4,704,000/$64 = 73,500 units

Moline = $2,265,600/$48 = 47,200 units

2. The operating income that would result from the division production manager's plan to produce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is 96,000 units (400 x 240); however, the normal capacity at the Moline plant is 76,800 units (320 x 240). Therefore, 19,200 units (96,000 - 76,800) will be manufactured at Moline at a reduced contribution of $40.00 per unit ($48 - $8).



Contribution per plant:Peoria (96,000 x $64) $ 6,144,000Moline (76,800 x $48) 3,686,400Moline (19,200 x $40) 768,000

Total contribution $10,598,400Less total fixed costs ($4,704,000 + $2,265,600) 6,969,600 Operating income $ 3,628,800

3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units x 300 days), should be utilized as the contribution from these units is higher at all levels of production than the contribution from units produced at the Moline plant.

Contribution per plant:Peoria (96,000 x $64) $ 6,144,000Peoria (24,000 x $61) 1,464,000Moline (72,000 x $48) 3,456,000

Total contribution $11,064,000Less total fixed cost 6,969,600

Operating income $ 4,094,400


7-40 CVP Analysis; Bid Pricing (40 min)This problem (part 2) can be used to introduce the concepts of contribution margin decision making, and the irrelevance of fixed costs for short term pricing decisions. This is covered in Chapter 9.

1. The unit variable cost per blanket is:

The total fixed cost for the order is:800,000 x $8/4 = $1,600,000

The breakeven price using the firm’s full cost system is $26:

p x 800,000 = $24.00 x 800,000 + $1,600,000p = $26

2. The minimum price per blanket that Jason Fibers Inc. could bid without reducing the company's net income is $24.00 since the fixed costs will not change whether or not Jason takes the order. Since the fixed costs will not change, they are irrelevant in the decision.

3. Using the full cost criteria and the maximum allowable return specified, Jason Fibers Inc.'s bid price per blanket would be $29.90 calculated as follows. Relevant costs from Requirement 1 $24.00Plus: Fixed overhead (.25 hrs. @$8.00/hr.) 2.00Subtotal 26.00Allowable return (.15* x $26.00) 3.90

Bid price $ 29.90

* 9% / (1 - 40%)



4. Strategic actors that Jason Fibers Inc. should consider before deciding whether or not to submit a bid at the maximum acceptable price of $27.00 per blanket include the following.

If the order is accepted at $27.00 per blanket, there will be a $3.00 contribution per blanket to fixed costs. However, the company should consider whether or not there are other jobs that would make a greater contribution.

Acceptance of the order at a low price could cause problems with current customers who might demand a similar pricing arrangement.


7-41 CVP Analysis; Probability Analysis (40 min)

1. In order to break even, during the first year of operations, 10,220 clients must visit the law office being considered by Don Masters and his colleagues as calculated below.

Fixed Expenses for First Year of Operations

Advertising $500,000Rent (6,000 x 28) 168,000Property Insurance 22,000Utilities 32,000Malpractice Insurance 180,000Depreciation ($60,000/4) 15,000Wages and Fringe Benefits Regular Wages ($95+$35+$15+$10)x16hrsx360days) $892,800 Overtime Wages (200x$15x1.5 + 200x$10x1.5) 7,500 Total Wages 900,300 Fringe Benefits @40% 360,120 1,260,420

Total Fixed Expenses $ 2,177,420

Breakeven Calculation:Revenues = Variable cost (supplies) + Fixed cost (from above)30Q + ($4,000 x .3 x .2)Q = $4Q + $2,177,420Q= 8,186 clients per year

2. Based on the report of the marketing consultant, the expected number of new clients during the first year is 18,000 as calculated below. Therefore, it is feasible for the law office to break even during the first year of operations as the breakeven point is 8,186 clients.

Expected value = (20 x .10) + (30 x .30) + (55 x .40) + (85 x .20)

= 50 clients per day


Problem 7-41 (continued)Annual number of clients = 50 x 360 days = 18,000 clients per

year, which is well above the breakeven of 8,186 clients per year. Since there is uncertainty in the prediction of the number of clients per year, based on a probability distribution, further sensitivity analysis should be considered, with the objective of determining the potential loss if in fact the number of clients falls short of the forecast.

3. Sensitivity analysis is used to deal more effectively with uncertainty or risk. Sensitivity analysis is a "what-if” type of analysis used to determine the outcomes if any parameters change from the initial assumptions. For example, revenues or costs could be changed from the initial assumptions and a new break-even sales volume calculated.

The availability of spreadsheet software has made it very quick and easy to compute the impact of changing one or more assumptions in a financial model. At least three factors that make sensitivity analysis prevalent in decision making including the following:

As the business environment is becoming more dynamic and competitive, sensitivity analysis provides management with an understanding of the impact of changes in the environment. The increased emphasis on productivity, competitive marketplace, changing consumer demand, shorter product life cycle times, and faster obsolescence of technology makes sensitivity analysis more prevalent.

Sensitivity analysis aids management in identifying the key variables and assumptions, so the variables can be monitored or a decision made to obtain additional information.

The use of probability distributions to determine expected values is an excellent way to conduct a sensitivity analysis. This approach allows Masters to see the distribution of costs and profits, as they are affected by the distribution of potential demand (number of clients). Masters can enhance this analysis by using standard deviations to measure the dispersion of the distributions, as a means to get at the degree of uncertainty – higher standard deviations for greater uncertainty.

Other approaches to sensitivity analysis include Excel-based analysis (see problem 7-43), graphical analysis, the use of operating leverage, and the contribution margin ratio.


7-42 CVP Analysis; Strategy (45 min)

1. a. A total of 480 seminar participants is needed for the joint venture to break even, calculated as follows.

The break-even number of participants equals the fixed costs divided by the contribution margin per participant

Fixed costs (FC) = $318,000 from GSI + $210,000 from Eastern = $528,000

Contribution margin (CM) = $1,200 fee - ($47 + $18 + $35) variable costs = $1,100

Break-even = FC/CM = $528,000/$1,100 = 480 seminar participants

b. A total of 700 seminar participants is needed for the joint venture to earn a net income of $169,400, calculated as follows.

The target number of participants equals the fixed costs plus the desired operating profit, divided by the contribution margin per participant. The desired operating profit equals the net income divided by (1 minus the tax rate).

Operating profit (OF) = $169,400/(1 - .30) = $169,400/ .70 = $242,000

Target participants = (FC + OF)/CM = ($528,000 + $242,000)/$1,100

= $770,000/$1,100 = 700 participants

2. A minimum of 1,055 participants is needed in order for GSI to prefer the 40 percent fee option rather than the flat fee, calculated as follows.

GSI fees for flat fee option = $9,500 per seminar x 40 seminars = $380,000

GSI fees for 40% of Eastern's profit-before-tax option = 40% x [(contribution margin x number of participants) -fixed cost)

= .40 x [($1,100 x N) -$210,000)] = $440 x N -$84,000



GSI fees are equal for the two options at the following number of participants.

$380,000 = $440 x N - $84,000 $464,000 = $440 x N $464,000/$440 = N = 1054.5 participants (1,055 rounded)

Therefore, GSI will earn more revenue and prefer the 40 percent option when the number of participants is 1,055 or higher.

3. Some of the strategic and implementation issues facing GSI in this decision are the following: Are the CVP assumptions satisfied? That is, total costs can be

divided into a fixed component and a component that is variable with respect to volume. Total costs and total revenues have a linear relationship to volumes within the relevant range. Total fixed costs, per unit variable cost, and selling price remain constant within the relevant range. Technology has no impact on cost relationships or selling prices. All costs and revenues are known with certainty.

Alternative uses of capacity? Since the Eastern U seminars would occupy all GSI’s available capacity, GSI should consider whether there might be more profitable uses for that capacity before making this commitment. Would the commitment include an implied or explicit promise to continue the seminars in future years, if successful this year? Can GSI expand its capacity quickly and easily if desired?

Has GSI considered the uncertainty in the situation? What happens if the breakeven level of participants is not met? GSI and Eastern should use various sensitivity analysis methods to assess the potential impact of this uncertainty on future profits.

Does the collaboration make sense strategically? Are Eastern and GSI likely to enhance each other’s reputation and to provide operating synergies and efficiencies that will make the alliance a profitable one. For example, if the Eastern University’s academic reputation might suffer from this alliance, then this should be considered in the decision.


7-43 CVP Analysis; Strategy; ABC Costing; Uncertainty (50 min)

1.Current Plan Proposed Plan

Contribution Margin

$100-$43.50-$10 = $46.50

$100-$58.75-$10=$31.25

Breakeven* ($6,000,000+$1,250,000) /$46.50 = 155,914 units

($3,000,000+$1,250,000) /$31.25 = 136,000 units

* Manufacturing fixed costs are determined from the fixed overhead rates:Current Plan Proposed Plan150,000 units sold x $40 = $6,000,000

150,000 units sold x $20 = $3,000,000

2. To determine the number of sales units at which CG would be indifferent between the current manufacturing plan and the proposed plan:

Solve for X:$43.50 X + $6,000,000 = $58.75 X + $3,000,000X = 196,722 units

(The above calculations show that at the current level of 150,000 units, the firm would prefer the low fixed cost strategy, that is, the new plan)


Problem 7-43 (continued)3. CG’s strategy is best described as differentiation, since the firm has succeeded by innovation in product design. Further, the firm operates in an industry in which innovation and product design are critical to success. An important element of the firm’s strategy is also the fact that the technology, as for many firms in the industry, is not proven. That is, there is a significant level of risk that the firm’s product will fail to meet customer’s expectations. The overall strategy then must both support the firm’s innovative image and also protect against the possibility of loss due to a failure of the technology – that is, simultaneously, the firm must advance and market its technological prowess and develop a plan to deal with the possibility that the technology might fail.

4. a) The calculations in part 2 above support a decision to go to

the new plan; at the current level of 150,000 units, costs are lower for the new plan, and will continue to be lower for the new plan as long as volume stays below 196,722 units.

b) Thinking strategically, the new plan is also preferred since it is an appropriate response to the firm’s risk, as noted in Part 3 above. By reducing operating leverage (that is, by reducing manufacturing fixed costs from $6,000,000 to $3,000,000) the firm is less exposed to a possible failure of the innovation and then drop off in sales. The reduction in fixed costs also helps the firm to manage cash flows. Thus, the new plan is more consistent with the firm’s strategy of developing an innovative product and also dealing with the risk of potential loss because of a possible failure of the technology in the market place.

Also, one could look at the proposal as consistent with the firm’s core strength, which appears to be product innovation. There is no evidence that the firm is particularly innovative or cost-effective in manufacturing. Thus, a strategy which goes to less focus on manufacturing would be consistent with this strategy; more focus should be retained in product design and development.c) Sensitivity analysis. Since uncertainty is important in this case, CG Graphics should use some of the tools as illustrated below. Note that the current method looks good if projected demand rises.




Current Proposed DifferenceMaterials and purchased parts 6.00$ 15.00$ Direct labor 12.50 13.75Variable GS&A 10.00 10.00Variable overhead 25.00 30.00Total Variable cost 53.50$ 68.75$ 15.25$

Price 100 100CM 46.50$ 31.25$

Fixed Cost 7,250,000.00$ 4,250,000.00$ 3,000,000$

Breakeven 155,914 136,000

Demand 150,000 150,000

Profit (275,000)$ 437,500$

Indifference Point 196,721.3

Assumed Levels of Demand Profit- Current Profit - Proposed30,000 (5,855,000)$ (3,312,500)$ 60,000 (4,460,000)$ (2,375,000)$ 90,000 (3,065,000)$ (1,437,500)$

120,000 (1,670,000)$ (500,000)$ 150,000 (275,000)$ 437,500$ 180,000 1,120,000$ 1,375,000$ 210,000 2,515,000$ 2,312,500$ 240,000 3,910,000$ 3,250,000$ 270,000 5,305,000$ 4,187,500$

7-44 CVP Analysis; ABC Costing (30 min)

1. If there are 50 units per batch and setup costs are $300 per setup, then there must be 3,000 batches (150,000/50), and total setup costs must be $900,000 (3,000 x $300). Thus, the total fixed costs for the current manufacturing plan must be $900,000 for setups and $5,100,000 (=$6,000,000 - $900,000) for the remaining fixed costs. The ABC breakeven can be determined as follows, where the unit cost of setup is $300/50 = $6:

Breakeven can be determined as follows:Current Plan Proposed Plan

Contribution Margin

$100-$43.50-$10-$6 = $40.50

$100-$58.75-$10-$6=$25.25

Breakeven ($5,100,000+$1,250,000) /$40.50 = 156,790 units (or, 3,136 batches)

To figure the exact breakeven, total setup costs are 3,136 x $300 = $940,800, and: Q = ($5,100,000 + $940,800 + $1,250,000)/($100-43.50-10) = 156,792 units

($2,100,000+$1,250,000) /$25.25 = 132,673 units (or 2,654 batches)

To figure the exact breakeven, total setup costs are 2,654 x $300 = $796,200, and: Q = ($2,100,000 + 796,200 + $1,250,000)/31.25= 132,679 units

Note as before that the breakeven for the current manufacturing plan is above the current operating level of 150,000 units. Also, since the operating level of 150,000 is based on the assumption of 50 batches of 3,000 each, to achieve breakeven will require more than 3,000 batches. Thus, breakeven analysis under ABC gives a higher breakeven number than the volume-based approach; it recognizes a larger number of setups and therefore larger setup cost ($940,800 versus $900,000).



2. The ABC costing breakeven calculations do not differ much from that for the volume based calculations in problem 7-43, and they both point to the same answer -- at the current volume level of approximately 150,000 units, the proposed manufacturing plan is preferred.


7-45 New Manufacturing Facility; Strategy (20 min)

The plan to build the new plant would be consistent with a cost leadership strategy, and would enable ICL to become more cost competitive. However, it is apparent that ICL’s plant is really following a differentiation strategy – their growing market is for design work, which is potentially more profitable than the manufacturing, and which builds on their core competencies. ICL should consider additional investment in the research and engineering groups that Julius supervises, instead of manufacturing. Rather than to be highly leveraged from large investments in manufacturing capacity and technology, the firm’s strategy should be to maintain their leadership in design and continue to use sub-contractors for the manufacturing work when necessary. ICL should carefully determine: is it a design firm or a manufacturing firm? It may be difficult to accomplish both.


7-46 CVP Analysis

Since fixed costs, except for the cost of the lease, will not be affected by the decision to make or to buy, they are excluded from the analysis:

Cost to Buy = Cost to Make$25 x Q = Q x ($10 + $6 + $3) + $34,000Q = 5,667 brake assemblies

The indifference point is 5,667, meaning that BBC would prefer to make if volume is expected to be above 5,667, and prefer to buy if volume is less than 5,667.

The strategic issues facing BBC will certainly affect this decision. BBC apparently competes on the basis of differentiation because of their emphasis on quality and their distribution through specialty shops. The quest for quality might cause them to stick with the internal manufacturing option, irrespective of the cost differential, to maintain control over quality. On the other hand, it might be that a higher quality brake could be obtained from the outside vendor. Also, BBC should consider the alternative uses of the manufacturing space. Could this be used to manufacture accessories or other parts for their bicycles, and thus improve the overall value to the customer?


7-47 CVP Analysis; ABC Costing (25 min)

In contrast to problem 7-46 which treats inspection, setup and materials handling costs as fixed costs, the following considers them batch related and solves for breakeven using an ABC costing approach.

If there are 1,000 units per batch, then BBC expects 10 batches and batch-level costs are $2,000 ($20,000/10) per batch, and the ABC indifference point can be determined as follows. The cost of the allocated fixed overhead will not be different whether BBC purchases or makes the brakes, so these costs are excluded:

The approximate solution (assuming 10 batches, and batch-level costs are $2/brake assembly)

Cost to Buy = Cost to Make$25 x Q = Q x ($10 + $6 + $3) + $2 x Q + $34,000Q = 8,500 brake assemblies

The exact solution, using 9 batches to manufacture 8,000+ assemblies:

Cost to Buy = Cost to Make$25 x Q = Q x ($10 + $6 + $3) + $2,000 x 9 + $34,000Q = 8,667 brake assemblies

The indifference point is 8,667, meaning that BBC would prefer to make if volume is expected to be above 8,667, and prefer to buy if volume is less than 8,667. The indifference quantity is slightly larger when adjusted for batch level costs because the cost of the 9th and last batch, $2,000 is spread over fewer than 1,000 units.

The indifference point is somewhat higher under ABC costing because the batch level costs are now considered a relevant cost of the “make” strategy, while under the volume-based approach in problem 7-46, these costs were considered as fixed and therefore irrelevant. In this context, the ABC costing approach probably produces a more reliable answer.



1. Based on estimates given, a farmer interested in the production of hemp would need to receive a price of at least $.55/lb to breakeven on farming for hemp, as shown in the following analysis.

First, separate the fixed and variable costs.Variable/400lb Fixed/acre

Seed $80.00Fertilizer 38.15Chemicals 10.00Fuel 11.00Machinery costs 15.00Crop insurance 6.00Other costs 7.50Land taxes 5.50Licensing fee 15.00Sampling and analytical fees

15.00

Drying costs 3.57Cleaning costs 5.00Interest 7.44 Total Cost $147.72 $71.44

From the above:Variable cost per pound = $147.72/400 = $.3693Total Fixed Cost = $71.44 x 180 = $12,859.20

Solving for breakeven price per lb (Q), where Q= 180 x 400 = 72,000 pounds for the average size farm:

Revenue = Total operating cost p x 72,000 = $.3693 x 72,000 + $12,859.20 p = $ .5479

Based on information from: “Industrial Hemp for Manitoba,” http://www.gov.mb.ca/agriculture/crops/hemp/bko04s00.html).


http://www.gov.mb.ca/agriculture/crops/hemp/bko04s00.html


Exercises 3134

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