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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.
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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 step-variable 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
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the building, which is a sunk cost. Therefore, they are not relevant costs for the
decision.
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–
or-buy 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.
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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.
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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EXERCISES
3-23 (a) Fixed
(b) Variable
(c) Variable
(d) Fixed
(e) Fixed
(f) Variable
(g) Variable
(h) Fixed or variable (if number of production workers can vary in the short
run);
(i) Fixed
(j) Variable
(k) Fixed
(l) Variable
3-24 (a) Variable
(b) Fixed
(c) Fixed or variable (if number of billing clerks can vary in the short run)
(d) Fixed
(e) Fixed
(f) Variable
(g) Fixed
(h) 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
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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)
Atkinson, Solutions Manual t/a Management Accounting, 6E
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)
