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Atkinson, Solutions Manual t/a Management Accounting, 6E

Chapter 3 Using Costs in Decision Making

QUESTIONS 3-1

Cost information is used in pricing, product planning, budgeting, performance evaluation, and contracting. Examples of specific uses of cost information include deciding whether to introduce a new product or discontinue an existing product (given the price structure), assessing the efficiency of a particular operation, and assessing the cost of serving customer segments.

3-2

Variable costs are costs that increase proportionally with changes in the activity level of some variable. Fixed costs are costs that in the short run do not vary with a specified activity. Fixed costs depend on how much of the resource (capacity) is acquired, rather than on how much is used.

3-3

Contribution margin per unit, which is the difference between revenue per unit and variable cost per unit, is the contribution that each unit makes to covering fixed costs and generating a profit. The contribution margin is therefore an important component of the equation to determine the breakeven point and to understand the effect on profit of proposed changes, such as changes in sales volume in response to changes in advertising or sales prices.

3-4

Contribution margin per unit is the difference between revenue per unit and variable cost per unit. The contribution margin per unit indicates how much the total contribution margin will increase with an additional unit of sales. The contribution margin ratio expresses similar ideas, but as a percentage of sales dollars. Specifically, the contribution margin ratio is the total contribution margin divided by total sales dollars (or contribution margin per unit divided by sales price per unit), and indicates how much the total contribution margin increases with an additional dollar of sales revenue.

3-5

In evaluating whether a business venture will be profitable, the breakeven point is the volume at which the profit equals zero, that is, revenues equal total costs. – 52 –

Atkinson, Solutions Manual t/a Management Accounting, 6E

3-6

A mixed cost is a cost that has a fixed component and a variable component. For example, utilities bills may include a fixed component per month plus a variable component that depends on the amount of energy used. A step variable cost increases in steps as quantity increases. For example, one supervisor may be hired for every 20 factory workers. Mixed costs and step variable costs both have elements of fixed and variable costs. However, mixed costs have distinct fixed and variable components, with fixed costs that are constant over a fairly wide range of activity (for a given time period) and variable costs that vary in proportion to activity. Step variable costs are fixed for a fairly narrow range of activity and increase only when the next step is reached.

3-7

Step variable costs are fixed for a fairly narrow range of activity and increase when the next step is reached. For example, one supervisor may be hired for every 20 factory workers. Fixed costs are costs that in the short run do not vary with a specified activity for a wide range of activity. For example, factory rent per month would likely remain unchanged as production increased or decreased, even if by large amounts.

3-8

Incremental cost is the cost of the next unit of production and is similar to the economist’s notion of marginal cost. In a manufacturing setting, incremental cost is often defined as a constant variable cost of a unit of production. However, in some situations, the variable cost of a unit of production may be more complicated. For example, the variable cost of labor per unit may decrease over time if workers become more efficient (a learning effect. Alternatively, the variable cost of labor per unit will change during overtime hours if workers receive an overtime premium (commonly 50%). Finally, some costs exhibit stepvariable behavior, as when one supervisor can supervise a quantity of employees but an additional supervisor is needed beyond a certain number of employees.

3-9

In evaluating the different alternatives from which managers can choose, it is better to focus only on the relevant costs that differ across different alternatives because it does not divert the manager’s attention with irrelevant facts. If some costs remain the same regardless of what alternative is chosen, then those costs are not useful for the manager’s decisions, as they are not affected by the decision. Therefore, it is better to omit them from the cost analysis used to support the decision. Moreover, resources are not expended to find or prepare irrelevant information.

3-10 Sunk costs are costs that are based on a previous commitment and cannot be recovered. For example, depreciation on a building reflects the historical cost of the building, which is a sunk cost. Therefore, they are not relevant costs for the decision. – 53 –

Chapter 3: Using Costs in Decision Making

3-11 The general principal is that sunk costs are not relevant costs. But, some managers may consider sunk costs to be relevant because they may be concerned about how others will perceive their original decision to incur these costs, and may want to cover up their initial poor judgment. Managers may also feel that they do not want to waste the sunk costs by giving up on the possibility of some benefit from the invested funds, or may continue to believe in potential success despite overwhelming evidence to the contrary. Also, managers may be embarrassed and unwilling to admit they made a mistake. 3-12 No, fixed cost are not always irrelevant. For example, in comparing the status quo and a proposal to substantially increase the quantity of goods or services provided, additional fixed costs (that is, costs not proportional to volume) may be incurred to provide the increased quantity. Such costs might include a large expenditure for more equipment or expanded factory facilities. 3-13 An opportunity cost is the maximum value forgone when a course of action is chosen. 3-14 Yes, avoidable costs are relevant because they can be eliminated when, for example, a part, product, product line, or business segment is discontinued. 3-15 In the context of a make or buy decision, fixed costs such as production engineering staff salaries are relevant if these costs can be eliminated by assigning the staff to other tasks, or by laying off the engineers not required when a part is outsourced. If it is possible to find an alternative use for the facilities made available because of the elimination of a product or a component, the associated fixed costs also are relevant. Conversely, fixed costs that cannot be eliminated or used for other productive purposes are not relevant for the decision. For example, if factory facilities would remain idle if the company buys from outside, then the associated costs are not relevant for the decision. 3-16 There are several qualitative considerations that must be evaluated in a make-orbuy decision. For example, one must question whether the outside supplier has quoted a lower price to obtain the order, and plans to increase the price. Also, the reliability of the supplier in meeting the required quality standards and in making deliveries on time is important. 3-17 When a decision to outsource frees up space to produce an alternative product, then the contribution margin on the alternative product is a relevant opportunity cost for the “make” alternative in a make-or-buy decision. – 54 –

Atkinson, Solutions Manual t/a Management Accounting, 6E

3-18 A difficulty that arises with respect to revenue when analyzing whether to drop a product or department is whether sales by one organizational unit can affect sales in another organizational unit. A difficulty that arises with respect to cost analysis is that many product costs, such as machine and factory depreciation, are the result of sunk costs that often remain in whole or in part after the product is discontinued. The analysis of what costs are avoided when a product is dropped can be difficult due to the closing of plants, severance pay and environmental cleanup costs. 3-19 The answer depends on the time frame and context considered. For example, a one-time order that covers variable production (and selling costs) is advantageous if capacity cannot be changed in the short run and excess capacity exists. Also, for given capacity with one scare resource, maximizing contribution margin per unit of scarce resource will maximize profit. In the long run, prices must cover all their costs, both fixed and variable, in order for the firm to survive. 3-20 No. Products should be ranked by the contribution margin per unit of the constrained resource rather than by the contribution margin per unit of the product. 3-21 Yes. When capacity is fixed in the short run, the firm may need to sacrifice the production of some profitable products to make capacity available for a new order. The contribution margin on the production of profitable products sacrificed for a new order is an opportunity cost that must be considered to evaluate the profitability of the new order. 3-22 The three components of a linear program are the objective function, the decision variables, and the constraints.

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Chapter 3: Using Costs in Decision Making

EXERCISES 3-23 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 3-24 (a) (b) (c) (d) (e) (f) (g) (h)

Fixed Variable Variable Fixed Fixed Variable Variable Fixed or variable (if number of production workers can vary in the short run); Fixed Variable Fixed Variable Variable Fixed Fixed or variable (if number of billing clerks can vary in the short run) Fixed Fixed Variable Fixed Fixed (with respect to a unit of product, as stated in the problem. However, gasoline costs will vary with miles driven.)

3-25 Burger ingredients

Variable

Cooks’ wages

Fixed

Server’s wages

Fixed

Janitor’s wages

Fixed

Depreciation on cooking equipment

Fixed

Paper supplies (wrapping, napkins, and supplies)

Variable

Rent

Fixed

Advertisement in local newspaper

Fixed

– 56 –

Atkinson, Solutions Manual t/a Management Accounting, 6E

3-26 (a)

Contribution margin per unit = $1,000 – $500 – $100 = $400 Contribution margin ratio = (Contribution margin)/Sales = $400/$1,000 = 0.40

(b)

Let X = the number of units sold to break even Sales revenue – Costs = Income (Price × Quantity) – Variable costs – Fixed costs = Income $1,000X – $600X – $3,500,000 = $0 $400X – $3,500,000 = 0 X = 8,750 units

(c)

Because the variable cost per unit will decrease, the contribution margin per unit will increase. The breakeven point equals (fixed costs)/ (contribution margin), so the breakeven point will decrease. Specifically, the new contribution margin per unit is $1,000 – $450 – $100 = $450 and the new breakeven point is $3,500,000/$450 = 7,778 units (rounded).

3-27 (a)

Let P

charges per patient-day.

(5,400 P) (5,400 $500) $2,000,000) = 0 5,400 (P $500) = $2,000,000 P

$500 = $2,000,000/5,400 = $370.37

P = $870.37 (b)

Let X = the average number of patient days per month necessary to generate a target profit of $45,000 per month Revenue – Costs = Income (Price × Quantity) – Variable costs – Fixed costs = Income $2,000X – $500X – $2,000,000 = $45,000 $1,500X = $2,000,000 + $45,000 = $2,045,000 X = 1,363 patient days (rounded)

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Chapter 3: Using Costs in Decision Making

3-28 (a)

Contribution margin per unit = $30 – $19.50 = $10.50 Contribution margin ratio = (Contribution margin)/Sales = $10.50/$30 = 0.35

(b)

Let X = the number of units sold to break even Sales revenue – Costs = Income (Price × Quantity) – Variable costs – Fixed costs = Income $30X – $19.50X – $147,000 = $0 $10.50X – $147,000 = 0 X = 14,000 units

(c)

Let X = the number of units sold to generate revenue necessary to earn pretax income of 20% of revenue Sales revenue – Costs = Income (Price × Quantity) – Variable costs – Fixed costs = Income $30X – $19.50X – $147,000 = 0.2 × $30X $10.50X – $147,000 = $6X X = 32,667 units (rounded) Desired revenue = $30X = $30 × 32,667 = $980,010 Alternatively, let R = sales revenue necessary to earn pretax income of 20% of revenue Sales revenue – Variable costs – Fixed costs = Income R – 0.65R – $147,000 = 0.2R R = $147,000/0.15 = $980,000

(d)

Let X = the number of units sold to generate after-tax profit of $109,200 (Before-tax income) (1 – 0.35) = $109,200 Before-tax income = $109,200/0.65 = $168,000 $30X – $19.50X – $147,000 = $168,000 $10.50X = $315,000 X = $315,000/$10.50 = 30,000 units

(e)

Let Y = necessary increase in sales units Incremental sales revenue – Incremental variable costs – Incremental fixed costs = $0 $30Y – $19.50Y – $38,500 = $0 Y = 3,667 units (rounded) – 58 –

Atkinson, Solutions Manual t/a Management Accounting, 6E

3-29 (a)

Let R = sales dollars necessary for a before-tax target profit of $250,000 The contribution margin ratio = ($1,260,000 – $570,000)/$1,260,000 = 0.547619 (rounded). Sales revenue – Variable costs – Fixed costs = Income Contribution margin – Fixed costs = Income 0.547619 R – $480,500 = $250,000 R = ($250,000 + $480,500)/0.547619 R = $1,333,956.60

(c) Let R = sales dollars necessary to break even Contribution margin – Fixed costs = 0 0.547619 R – $480,500 = $0 R = $480,500/0.547619 R = $877,434.85 3-30 The sales mix in units is 3/5 Domestic and 2/5 International. The Domestic CM = $50 – $30 = $20; the International CM = $40 – $16 = $24 Let X = total number of units that must be sold in the International market to earn $200,000 before taxes, assuming the stated sales mix Total CM – Fixed costs = $200,000 ($20 1.5X) + $24X − $5,000,000 − $1,280,000= $200,000 $54X = $6,480,000 X = $6,480,000/$54 = 120,000 units in the International market 1.5 X = 180,000 units in the Domestic market Equivalently, one can compute a weighted average unit CM: (3/5) × ($20) + (2/5) × ($24) = $21.60 Let Y = total number of units that must be sold to earn $200,000 before taxes, assuming the stated sales mix Total CM – Fixed costs = $200,000 $21.60Y − $5,000,000 − $1,280,000= $200,000 $21.60Y = $6,480,000 Y = 300,000 units, which consists of 3/5 or 180,000 units in the Domestic market and 2/5 or 120,000 units in the International market

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Chapter 3: Using Costs in Decision Making

3-31

(a) Units sold Sales mix percentage*

Alligators 140,000 .7

Dolphins 60,000

Total 200,000

.3 Weighted average**

Weighted average**

Sum of weighted averages

Sales price per unit

$20.00

$14.00

$25.00

$7.50

$21.50

Variable costs per unit

$ 8.00

$ 5.60

$10.00

$3.00

$ 8.60

Unit CM

$12.00

$ 8.40

$15.00

$4.50

$12.90

* 140,000/(140,000 + 60,000) = .7; 60,000/(140,000 + 60,000) = .3 ** $20 × .7 = $14; $8 × .7 = $5.60; $25 × .3 = $7.50; $10 × .3 = $3

Breakeven units = $1,290,000/$12.90 = 100,000 units. Of these, 100,000 × .7 = 70,000 will be alligators and 100,000 × .3 = 30,000 will be dolphins. (b) Units sold Sales mix percentage*

Alligators 60,000 .3

Dolphins 140,000

Total 200,000

.7 Weighted average**

Weighted average**

Sum of weighted averages

Sales price per unit

$20.00

$6.00

$25.00

$17.50

$23.50

Variable costs per unit

$ 8.00

$2.40

$10.00

$ 7.00

$ 9.40

Unit CM

$12.00

$3.60

$15.00

$10.50

$14.10

* 60,000/(140,000 + 60,000) = .3; 140,000/(140,000 + 60,000) = .7 ** $20 × .3 = $6; $8 × .3 = $2.40; $25 × .7 = $17.50; $10 × .7 = $7

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Atkinson, Solutions Manual t/a Management Accounting, 6E

Breakeven units = $1,290,000/$14.10 = 91,489.36, which we round up to 91,490 units. Of these, 91,490 × .3 = 27,447 will be alligators and 91,490 × .7 = 64,043 will be dolphins. (c)

3-32

In part (b), the sales mix percentage for the higher-CM product (dolphins) is greater than in part (a). Consequently, fewer total units are required to break even (91,490 in part (b) versus 100,000 in part (a)).

Total Sales Without Total Sales With Special Promotion Special Promotion Difference Hamburgers $1.09 20,000 $0.69 24,000 ($5,240) $21,800 $16,560 Chicken — — — Sandwiches 1.29 10,000 $12,900 1.29 9,200 $11,868 (1,032) Product

French fries

0.89

20,000

$17,8000.89

22,400

$19,936

2,136 ($4,136)

Product

Hamburgers

Variable Costs Without Special Promotion $0.51 20,000 $10,200

Variable Costs With Special Promotion $0.51 24,000 $12,240

—

—

Chicken

Difference ($2,040) —

Sandwiches

0.63

10,000

$6,300 0.63

9,200

$5,796

504

French fries

0.37

20,000

$7,400 0.37

22,400

$8,288

(888) ($2,424)

Decrease in sales with special promotion Increase in variable costs with special promotion Decrease in contribution margin with special promotion Incremental advertising expenses with special promotion Decrease in profit with special promotion

$4,136 2,424 $6,560 4,500 ($11,060)

Therefore, Andrea should not go ahead with this special promotion. A countervailing argument is the creation of new customers who may stay with the firm and generate additional contribution margin in the future.

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Chapter 3: Using Costs in Decision Making

3-33 (a)

Healthy Hearth has sufficient excess capacity to handle the one-time (short-run) order for 1,000 meals next month. Consequently, the analysis focuses on incremental revenues and costs associated with the order: Incremental revenue per meal Incremental cost per meal Incremental contribution margin per meal Number of meals Increase in contribution margin and operating income

$3.50 3.00 $0.50 × 1,000 $ 500

Healthy Hearth will be better off by $500 with this one-time order. Note that total fixed costs remain unchanged, so it is sufficient to evaluate the change in the contribution margin. If the order had been long-term, Healthy Hearth would need to evaluate whether the price provides the desired profitability considering the fixed costs and whether filling the government order might require giving up higher-priced regular sales. (b)

Healthy Hearth has insufficient excess capacity to handle the one-time order for 1,000 meals next month, and must give up regular sales of 500 meals at $4.50 each, resulting in an opportunity cost. Incremental contribution margin from one-time order Incremental revenue per meal Incremental cost per meal Incremental contribution margin per meal Number of meals Increase in operating income from one-time order

$3.50 3.00 $0.50 1,000 $5...