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Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
CHAPTER 9
SHORT-TERM PROFIT PLANNING:
COST-VOLUME-PROFIT (CVP) ANALYSIS
QUESTIONS
9-1 The underlying relationship depicted in a cost-volume-profit (CVP) analysis is
that costs, revenues, and operating profits (Y) all change in a predictable way as
9-2 The contribution margin ratio (CMR) is: (selling price per unit − variable cost per
unit) ÷ (selling price per unit) = p ÷ (p – v)
The contribution margin ratio (CMR) is a measure of profitability. The CMR tells
us the change in operating profit associated with a given change in sales dollars.
It is a useful measure of the relative contribution to profit of different products,
9-3 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
CVP model is deterministic, not stochastic), and a single cost driver: volume.
9-4 Sensitivity analysis is used to deal with uncertainties in profit planning, in two
major respects:
1. To determine which factors have the greatest influence on profit, and to assess
9-5 Sensitivity analysis deals with the risk that sales may fall short of expectations or
9-6 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 and income taxes are
9-1
Education.
9-7 Margin of safety (MOS) = sales − breakeven sales, where “sales” can be either
9-8 The concept of operating leverage refers to the extent to which fixed (rather than
variable) costs characterize an organization’s cost structure. The higher the
9-9 The degree of operating leverage (DOL) is a measure, at any volume (X), of the
sensitivity of operating profit to a change in sales volume. It is measured as the
percentage change in operating profit for each percentage change in sales.
9-10 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
9-2
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
BRIEF EXERCISES
9-11Contribution margin per unit = selling price per unit − variable cost per unit
9-12 Total Contribution Margin = (selling price per unit − variable cost per unit) × #units
sold
9-13 Breakeven Point—Units:
Q × p = F + (v × Q)
Q × $20 = $175,000/quarter + ($10 × Q)
9-14 Breakeven Point—Dollars:
p × Q = F + (v × Q)
Q = 500 patient-visits/month
9-15 Breakeven in Dollars: Y = [(v/p) × Y] + F
Y = [($500,000/$750,000) × Y] + $75,000/quarter
Y = [2/3 × Y] + $75,000/quarter
9-16 Unit Sales Q = (F + πB) ÷ (p - v)
Q = ($400,000 + $200,000)/quarter ÷ ($1 − $0.50)
Q = 1,200,000 bottles/quarter
9-3
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
9-17 With a contribution margin (p – v) of $8 per battery, operating profit will increase
9-18 Q = F + π A/(1− t )
(p – v)
Q = $200/week + [$400/(1− 0.2)]/week
($10 − $5)/unit
9-19 Margin of Safety (MOS), in units = Planned Sales – Breakeven Sales
= 20,000 units/quarter
MOS, in $ = Planned Sales ($) − Breakeven Sales ($)
= $40,000
9-20 Degree of Operating Leverage (DOL) = Contribution Margin ÷ operating income
= [($40 − $20)/unit × 400,000 units] ÷ $2,500,000
9-4
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
EXERCISES
9-21 Breakeven Planning; Profit Planning (30-40 minutes)
1. πB= Sales − variable costs − fixed cost
= (30,000 units × $67/unit) − (30,000 units × $34/unit) − $480,500
2. BE units: $67Q = $34Q + $480,500
3. πB = Sales – variable costs – fixed costs
(Operating profit falls by $35,000 = ($33 × 5,000) − $200,000, from
4. BE units: Q = F ÷ cm per unit
(Operating profit is lower, per part 3 above, and breakeven is higher.)
Contribution Income Statement:
9-5
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
9-21 (Continued)
(the slight difference between the indicated operating profit,
$26, and zero is due to rounding up the breakeven point to the
nearest whole number, 20,622 units)
5. Operating profit = Sales – variable costs – fixed costs
9-6
Education.
Slight diference in the above answers is due to
rounding on sales volume, Q. The primary point,
however, is that a given percentage change in ixed cost
leads to an equivalent percentage change in the
breakeven point. (This can be conirmed precisely if the
above breakeven volumes were not rounded.)
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
9-7
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
9-22 Cost Planning; Machine Replacement (30-40 minutes)
1. Breakeven volumes (total external cost/year = $2Q):
For Machine A For Machine B
2. Cost indifference point, Q:
Cost, using Machine A = Cost, using Machine B
When 197,143 switches are needed, the Vista Company is indifferent
as to which machine to use: the total cost under each of the two
decision alternatives is the same at this volume.
An alternative way to determine the indifference point is:
Fixed cost of Machine B − Fixed Cost of Machine A
Unit variable cost of A − Unit variable cost of B
Summary of (1) and (2): If output is less than 100,000, buy the
2. Total cost if volume = 200,000 units/year:
Cost when purchasing from outside supplier:
9-7
Education.
Chapter 09 - Short-Term Profit Planning: Cost-Volume-Profit (CVP) Analysis
9-22 (Continued-1)
Cost when using machine B:
4. Recommendation to management:
Considerations regarding outsourcing (rather than making
internally): what is the reliability of the existing supplier? Likely price
increases in the future from this supplier? What is the reliability of the
external supplier (delivery time, etc.)? As we’ve seen with supply
Considerations regarding insourcing (rather than purchasing
externally from the current supplier): is sufficient capital (to purchase
and install machinery) available? Are there any training-related costs
to be borne? The decision to insource increases the operating
leverage of the company, which in turn increases the business (or
operating) risk of the company. Therefore, what is the long-term
The basic point to make to students is that choice of cost structure
both reflects and influences a company’s strategy. This elevates the
9-8
Education.
9-23 Structuring Sales Commissions (15-20 min)
1. Omega--because it has the higher selling price and therefore the larger
2. From the standpoint of the company, profits may be higher if customers
purchase more units of Alpha (relative to Omega). This is because Alpha
has the higher contribution margin per unit.
To eliminate such a conflict (i.e., the goal-congruency issue), Questar
could revise its compensation plan to motivate greater sales of Alpha. It
could do this by basing sales commissions on contribution margin
generated by sales rather than sales dollars generated. If fixed costs are
not affected by the resulting shift in sales mix (toward increased sales of
Alpha), maximizing contribution margin will also maximize operating
Addendum: Bazerman, M., and A. E. Tenbrunsel. 2011. Ethical
breakdowns. Harvard Business Review (April), pp. 58-65.
Ill-Conceived Goals (p. 60)
In the above-reference article, the authors state: "In our teaching, we
often deal with sales executives. By far the most common problem they
report is that their sales forces maximize sales rather than profits. We
ask them what incentives they give their salespeople, and they confess
to actually rewarding sales rather than profits. The lesson is clear: When
employees behave in undesirable ways, it's a good idea to look at what
you're encouraging them to do."
9-9
Education.
