9-37 CVP Analysis; Strategy
1. BE units = F ÷ (p − v) = $225,000 ÷ ($45 − $30)/unit = 15,000 units
BE $ = F ÷ CMR = F ÷ [(p − v) ÷ p]
= $225,000 ÷ [($45 − $30) ÷ $45]
= $225,000 ÷ 0.33333 = $675,000
2. πB= Sales − variable costs − fixed costs
= [Q × (unit contribution margin)] − F
= [20,000 units × ($45 − $30)/unit] − $225,000
= $300,000 − $225,000 = $75,000
Contribution Income Statement:
Sales (20,000 units × $45.00/unit) =
Less: Variable costs (20,000 units × $30.00/unit) =
Contribution Margin =
Less: Fixed costs =
Operating income =
$900,000
$600,000
$300,000
$225,000
$75,000
3. Margin of safety (MOS) = 32,000 − 15,000 = 17,000 hats
MOS ratio = 17,000 ÷ 32,000 = 53.125%
Both the MOS and the MOS ratio refer to the extent to which sales could
fall before losses are realized. In this sense, they are rough measures of
operating risk and are therefore helpful in addressing inherent
uncertainty in the profit-planning process.
4. BE units = F ÷ contribution margin per unit
= ($225,000 + $106,500) ÷ ($45 − $25.50)
= $331,500 ÷ $19.50/unit = 17,000 units
πB= Sales − variable costs − fixed costs
= [Q × (unit contribution margin)] − F
= [20,000 units × ($45.00 − $25.50*)/unit] − ($225,000 + $106,500)
= $390,000 − $331,500 = $58,500
*$30.00 − $4.50
5. A key strategic issue is that Hank’s sales staff is a critical success factor
for the business, especially in the growing and competitive environment
of Hank’s 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. Hank 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 commission plan. The
decision can also be viewed as an ethical issue: what responsibility does
Hank have to his staff? Is he properly considering what is due their
loyalty to him in prior years, and how the decision will affect their families,
for better or worse?
Finally, there is the issue of operating risk associated with moving to a
cost structure characterized by relatively higher fixed costs (traded-off
against lower variable costs).
• Possible benefits:
o If variable costs (such as variable labor costs) are high, this
strategy may minimize total costs.
o Upside potential: once the breakeven point is reached,
percentage changes in sales volumes are magnified in terms of
their effect on operating income.
• Possible costs/disadvantages:
o Increased operating (business) risk (e.g., generally speaking,
there will be a higher breakeven point)
o If sales volume recedes, these reductions are magnified in terms
of decreasing operating income (that is, there will likely be
greater losses when times are not so good)
o In combination with a high level of financial leverage, total
(combined or composite) leverage, and therefore total risk, can
be magnified
o Locking into a high level of fixed costs (e.g., a certain
technology) may reduce future flexibility (e.g., ability to embrace
new technologies or ability to react to short-term fluctuations in
demand)
o Increased fixed costs on top of an existing high level of fixed
costs can dramatically increase operating risk.
o Increased fixed costs (e.g., those associated with insourcing)
may expose the company to increased risk or exposure to
production slow-downs or stoppages, as experienced in 2011 in
Japan as a consequence of the earthquake/tsunami that hit the
country).
9-38 Profit Planning: Multiple Products
1. Break-even in units: weighted-average contribution margin approach
a. Overall breakeven point = F ÷ weighted-average contribution
margin/unit
Weighted-average unit contribution per unit
= ($15 × 80%) + ($40 × 20%) = $20 per unit
Break-even point = $400,000 ÷ $20/unit = 20,000 units
b. Breakdown of breakeven units:
Product A: 20,000 × 80% = 16,000
Product B: 20,000 × 20% = 4,000
2. Use Goal Seek (in Excel) to calculate the breakeven point, in terms of
total units:
Step One: Set Up the Equation for Operating Income
Step Two: Run Goal Seek
Step Three: Results (after running Goal Seek)
3. Breakeven point in units: “Sales basket” approach (assume that each
basket consists of 4 units of Product A and 1 unit of Product B).
a. Overall breakeven point (in baskets) = F ÷ contribution margin/basket
Contribution margin per sales basket = (4 × $15) + (1 × $40)
= $60 + $40 = $100 per “basket”
Number of “baskets” needed to breakeven =
= $400,000 ÷ $100/basket = 4,000 “baskets,” or 4,000
baskets × 5 units per basket = 20,000 units
b. Breakdown of breakeven units:
Product A: 4,000 “baskets” × 4 units/basket = 16,000 units
Product B: 4,000 “baskets” × 1 unit/basket = 4,000 units
4. Distribution of breakeven point in terms of sales dollars (based on
weighted-average contribution margin ratio, where the individual product
weights are based on relative sales dollars, not physical unit, of each
product in the standard sales mix).
a. Breakeven ($) = F ÷ weighted-average cm ratio
Relative sales dollars (not units), based on standard sales mix:
Product A: 18,000 units × $80/unit = $1,440,000
Product B: 4,500 units × $140/unit = $630,000
Weights:
Product A: $1,440,000 ÷ $2,070,000 = 0.6956522
Product B: $630,000 ÷ $2,070,000 = 0.3043478
Weighted-average contribution margin ratio:
A: 0.69565 × ($15/$80) = 0.6956522 ×0.1875 = 0.13043478
B: 0.30435× ($40/$140)= 0.3043478 ×0.2857 = 0.08695652
0.21739130
Breakeven point in overall dollars ($) = $400,000 ÷ 0.21739130
= $1,840,000
b. breakdown of total breakeven sales dollars, by product:
Product A: mix % x breakeven sales, in $
= 0.6956522 × $1,840,000 = $1,280,000
Product B: mix % x breakeven sales, in $
= 0.3043478 × $1,840,000 =
$560,000
5. For the multiproduct firm, there is no breakeven point independent of the
sales mix assumption. For the multiproduct firm, we typically assume that
the outputs are sold in some standard mix, based either on relative
physical units or relative sales dollars. If the individual products differ in
terms of their contribution margin per unit (or contribution margin ratio),
then the weighted-average contribution margin (and contribution margin
ratio) will vary in response to changes in the sales mix. This, in turn,
affects the breakeven point since that point is defined as the ratio of fixed
costs to the weighted-average contribution margin per unit (or, the
weighted-average contribution margin ratio). Of course, if the unit
contribution margins are the same for each product, then the assumed
mix has no impact on the breakeven calculation. Note, however, that this
is a trivial example.
6. Change in the breakeven point (in total units) in response to a 10%
change in fixed costs:
New level of fixed costs = $400,000 + $40,000 = $440,000
Original level of fixed costs
= $400,000
$ change in fixed costs = $40,000
Percentage change in fixed cost = $40,000 ÷ $400,000 = 10.00%
New breakeven point = $440,000 ÷ $20.00/unit = 22,000 units
Original breakeven point =
20,000 units
Change in breakeven point = 2,000 units
Percentage change in breakeven point = 2,000 ÷ 20,000 = 10.00%
As seen from the above, the percentage change in fixed cost (here 10%)
led to an identical percentage change in the breakeven point. Because of
the linear cost functions assumed in a conventional CVP model, this
finding can be generalized: with everything else held constant, a given
percentage change (+ or -) in the amount of fixed costs leads to an
equivalent percentage change in the breakeven point.
9-39 CVP Analysis/Profit Planning
1. BE in units = F ÷ (p − v) = $324,000 ÷ ($90 − $63) = 12,000 units
Contribution margin ratio = (p – v) ÷ p
= $27 ÷ $90 = 30%
BE sales dollars = 12,000 × $90 = $1,080,000
Alternatively, B/E in dollars = F ÷ cm ratio
= $324,000 ÷ 0.30 = $1,080,000
2. Required sales, in units and in dollars, to achieve pre-tax profit goal of
$30,000:
# units = (F + πB) ÷ cm per unit = ($324,000 + $30,000) ÷ $27/unit
= $354,000 ÷ $27/unit = 13,111.11 units
required sales, in $ = required sales in units × selling price/unit
= 13,111.11 units ÷ $90/unit = $1,180,000
OR,
required sales in $ = (F + πB) ÷ cm ratio
= $354,000 ÷ 0.30 = $1,180,000
3. Required sales to achieve after-tax profit goal:
after-tax profit goal = $25,000
conversion of after-tax profit goal into pre-tax dollar equivalent:
$25,000 ÷ (1 – t), where t = combined income tax rate
\
= $25,000 ÷ (1 – 0.4) = $41,666.67
Required sales (in units) to achieve after-tax profit target
= (F + targeted pre-tax profit) ÷ cm per unit
= ($324,000 + $41,666.67) ÷ $27.00
= $365,666.67 ÷ $27.00 = 13,544 units (rounded up)
Required sales, in $, to achieve after-tax profit target
= required sales volume, in $ × selling price/unit
= 13,544 units × $90/unit = $1,218,960
4. Contribution income statement:
Sales (13,544 units × $90/unit) =
$1,218,960
Less: Variable cost (@ $63/unit) =
$853,272
Contribution margin (@ $27/unit) =
$365,688
Less: Fixed costs
$324,000
Pre-tax (operating) income =
$41,688
Less: Income tax (@40%) =
$16,675
Profit after tax =
$25,013
Note: Difference of $13 is due to rounding up in terms of sales volume in
units.
5. Profits will decrease by $19,500, from -$27,000 to - $46,500
Sales
Variable Costs
$
Contribution Margin
Fixed Costs
Operating Loss
Original
990,000 $
693,000
297,000
324,000
$
$
(27,000) $
135,000
94,500
40,500
60,000
After change
$
1,125,000
$
787,500
$
$
(19,500) $
337,500
384,000
(46,500)
Or,
= Increase in CM – Increase in Fixed Costs
= ($135,000 × 0.3) − $60,000 = ($19,500)
6. Profit will decrease $109,400, from a loss of $27,000 to a loss of $136,400:
Planned reduction in selling price/unit =
Estimated increase in sales volume (units) =
Estimated increase in fixed costs =
Sales
Variable Costs
Contribution Margin
Fixed Costs
Operating Income (Loss)
$
$
$
$
$
Original
990,000
693,000
297,000
324,000
(27,000)
$
$
$
$
$
Change
79,200
138,600
(59,400)
50,000
(109,400)
10%
20%
$50,000
$
$
$
$
$
New
1,069,200
831,600
237,600
374,000
(136,400)
7. The total reduction in variable cost is $5 × 11,000 = $55,000, while the
increase in fixed costs is $30,000, resulting in a net savings of $25,000.