https://saylordotorg.github.io/text_managerial-accounting/s10-how-is-cost-volume-profit-anal.html
Chapter 6
How Is Cost-Volume-Profit Analysis Used for
Decision Making?
Recilia Vera is vice president of sales at Snowboard Company, a manufacturer of one
model of snowboard. Lisa Donley is the company accountant. Recilia and Lisa are in
their weekly meeting.
Recilia:
Lisa, I’m in the process of setting up an incentive system for my sales staff, and I’d like to get
a better handle on our financial information.
Lisa:
No problem. How can I help?
I’ve reviewed our financial results for the past 12 months. It looks like we made a profit in
some months, and had losses in other months. From what I can tell, we sell each snowboard
Recilia: for $250, our variable cost is $150 per unit, and our fixed cost is $75 per unit. It seems to me
that if we sell just one snowboard each month, we should still show a profit of $25, and any
additional units sold should increase total profit.
Lisa:
Your unit sales price of $250 and unit variable cost of $150 look accurate to me, but I’m not
sure about your unit fixed cost of $75. Fixed costs total $50,000 a month regardless of the
number of units we produce. Trying to express fixed costs on a per unit basis can be
misleading because it depends on the number of units being produced and sold, which
changes each month. I can tell you that each snowboard produced and sold provides $100
toward covering fixed costs—that is, $250, the sales price of one snowboard, minus $150 in
variable cost.
The $75 per unit for fixed costs was my estimate based on last year’s sales, but I get your
point. As you know, I’d like to avoid having losses. Is it possible to determine how many units
Recilia:
we have to sell each month to at least cover our expenses? I’d also like to discuss what it will
take to make a decent profit.
Lisa:
We can certainly calculate how many units have to be sold to cover expenses, and I’d be glad
to discuss how many units must be sold to make a decent profit.
Recilia: Excellent! Let’s meet again next week to go through this in detail.
Answering questions regarding break-even and target profit points requires an
understanding of the relationship among costs, volume, and profit (often called CVP).
This chapter discusses cost-volume-profit analysis, which identifies how changes in key
assumptions (for example, assumptions related to cost, volume, or profit) may impact
financial projections. We address Recilia’s questions in the next section.
6.1 Cost-Volume-Profit Analysis for Single-Product
Companies
L EA RNING O B JEC T IV E
1. Perform cost-volume-profit analysis for single-product companies.
Question: The profit equation shows that profit equals total revenues minus total
variable costs and total fixed costs. This profit equation is used extensively in costvolume-profit (CVP) analysis, and the information in the profit equation is typically
presented in the form of a contribution margin income statement (first introduced
in Chapter 5 "How Do Organizations Identify Cost Behavior Patterns?"). What is the
relationship between the profit equation and the contribution margin income
statement?
Answer: Recall that the contribution margin income statement starts with sales, deducts
variable costs to determine the contribution margin, and deducts fixed costs to arrive at
profit. We use the term “variable cost” because it describes a cost that varies in
total with changes in volume of activity. We use the term “fixed cost” because it
describes a cost that is fixed (does not change) in total with changes in volume of
activity.
To allow for a mathematical approach to performing CVP analysis, the contribution
margin income statement is converted to an equation using the following variables:
Key Equation
S = Selling price per unitV = Variable cost per unitF = Total fixed costsQ = Quantity of
units produced and sold
Thus
Figure 6.1 "Comparison of Contribution Margin Income Statement with Profit
Equation" clarifies the link between the contribution margin income statement
presented in Chapter 5 "How Do Organizations Identify Cost Behavior Patterns?" and
the profit equation stated previously. Study this figure carefully because you will
encounter these concepts throughout the chapter.
Figure 6.1 Comparison of Contribution Margin Income Statement with Profit Equation
Recall that when identifying cost behavior patterns, we assume that management is
using the cost information to make short-term decisions. Variable and fixed cost
concepts are useful for short-term decision making. The short-term period varies,
depending on a company’s current production capacity and the time required to change
capacity. In the long term, all cost behavior patterns are likely to change.
Break-Even and Target Profit
Question: Companies such as Snowboard Company often want to know the sales
required to break even, which is called the break-even point. What is meant by the
term break-even point?
Answer: The break-even point can be described either in units or in sales dollars.
The break-even point in units is the number of units that must be sold to achieve zero
profit. The break-even point in sales dollars is the total sales measured in dollars
required to achieve zero profit. If a company sells products or services easily measured
in units (e.g., cars, computers, or mountain bikes), then the formula for break-even
point in units is used. If a company sells products or services not easily measured in
units (e.g., restaurants, law firms, or electricians), then the formula for break-even point
in sales dollars is used.
Break-Even Point in Units
Question: How is the break-even point in units calculated, and what is the break-even
point for Snowboard Company?
Answer: The break-even point in units is found by setting profit to zero using the profit
equation. Once profit is set to zero, fill in the appropriate information for selling price
per unit (S), variable cost per unit (V), and total fixed costs (F), and solve for the
quantity of units produced and sold (Q).
Let’s calculate the break-even point in units for Snowboard Company. Recall that each
snowboard sells for $250. Unit variable costs total $150, and total monthly fixed costs
are $50,000. To find the break-even point in units for Snowboard Company, set the
profit to zero, insert the unit sales price (S), insert the unit variable cost (V), insert the
total fixed costs (F), and solve for the quantity of units produced and sold (Q):
Thus Snowboard Company must produce and sell 500 snowboards to break even. This
answer is confirmed in the following contribution margin income statement.
Target Profit in Units
Question: Although it is helpful for companies to know the break-even point, most
organizations are more interested in determining the sales required to make a
targeted amount of profit. How does finding the target profit in units help companies
like Snowboard Company?
Answer: Finding a target profit in units simply means that a company would like to
know how many units of product must be sold to achieve a certain profit. At Snowboard
Company, Recilia (the vice president of sales) and Lisa (the accountant) are in their next
weekly meeting.
Lisa:
Recilia, last week you asked how many units we have to sell to cover our expenses. This is
called the break-even point. If each unit produced and sold provides $100 toward covering
fixed costs, and if total monthly fixed costs are $50,000, we would have to sell 500 units to
break even—that is, $50,000 divided by $100.
Recilia: What happens once we sell enough units to cover all of our fixed costs for the month?
Lisa:
Good question! Once all fixed costs are covered for the month, each unit sold contributes
$100 toward profit.
I think I’m getting the hang of this. It will take 500 units in sales to break even, and each unit
Recilia: sold above 500 results in a $100 increase in profit. So if we sell 503 units for a month, profit
will total $300?
Lisa:
You’ve got it!
Recilia:
So if our goal is to make a profit of $30,000 per month (target profit), how many units must be
sold?
Lisa:
It takes 500 units to break even. We also know each unit sold above and beyond 500 units
contributes $100 toward profit. Thus we would have to sell an additional 300 units above the
break-even point to earn a profit of $30,000. This means we would have to sell 800 units in
total to make $30,000 in profit.
Recilia:
Wow, I’m not sure selling 800 units is realistic, but at least we have a better sense of what
needs to be done to make a decent profit. Thanks for your help!
Profit Equation
Question: Let’s formalize this discussion by using the profit equation. How is the profit
equation used to find a target profit amount in units?
Answer: Finding the target profit in units is similar to finding the break-even point in
units except that profit is no longer set to zero. Instead, set the profit to the target profit
the company would like to achieve. Then fill in the information for selling price per unit
(S), variable cost per unit (V), and total fixed costs (F), and solve for the quantity of
units produced and sold (Q):
Thus Snowboard Company must produce and sell 800 snowboards to achieve $30,000
in profit. This answer is confirmed in the following contribution margin income
statement:
Shortcut Formula
Question: Although using the profit equation to solve for the break-even point or target
profit in units tends to be the easiest approach, we can also use a shortcut formula
derived from this equation. What is the shortcut formula, and how is it used to find the
target profit in units for Snowboard Company?
Answer: The shortcut formula is as follows:
Key Equation
Q = (F + Target Profit) ÷ (S − V)
If you want to find the break-even point in units, set “Target Profit” in the equation to
zero. If you want to find a target profit in units, set “Target Profit” in the equation to the
appropriate amount. To confirm that this works, use the formula for Snowboard
Company by finding the number of units produced and sold to achieve a target profit of
$30,000:
The result is the same as when we used the profit equation.
Break-Even Point in Sales Dollars
Question: Finding the break-even point in units works well for companies that have
products easily measured in units, such as snowboard or bike manufacturers, but not
so well for companies that have a variety of products not easily measured in units,
such as law firms and restaurants. How do companies find the break-even point if they
cannot easily measure sales in units?
Answer: For these types of companies, the break-even point is measured in sales dollars.
That is, we determine the total revenue (total sales dollars) required to achieve zero
profit for companies that cannot easily measure sales in units.
Finding the break-even point in sales dollars requires the introduction of two new
terms: contribution margin per unit and contribution margin ratio.
Contribution Margin per Unit
The contribution margin per unit is the amount each unit sold contributes to (1)
covering fixed costs and (2) increasing profit. We calculate it by subtracting variable
costs per unit (V) from the selling price per unit (S).
Key Equation
Contribution margin per unit = S − V
For Snowboard Company the contribution margin is $100:
Thus each unit sold contributes $100 to covering fixed costs and increasing profit.
Contribution Margin Ratio
The contribution margin ratio (often called contribution margin percent) is the
contribution margin as a percentage of sales. It measures the amount each sales
dollar contributes to (1) covering fixed costs and (2) increasing profit. The contribution
margin ratio is the contribution margin per unit divided by the selling price per unit.
(Note that the contribution margin ratio can also be calculated using
the total contribution margin and total sales; the result is the same.)
Key Equation
Contribution margin ratio = (S − V) ÷ S
For Snowboard Company the contribution margin ratio is 40 percent:
Thus each dollar in sales contributes 40 cents ($0.40) to covering fixed costs and
increasing profit.
Question: With an understanding of the contribution margin and contribution margin
ratio, we can now calculate the break-even point in sales dollars. How do we calculate
the break-even point in sales dollars for Snowboard Company?
Answer: The formula to find the break-even point in sales dollars is as follows.
Key Equation
For Snowboard Company the break-even point in sales dollars is $125,000 per month:
Thus Snowboard Company must achieve $125,000 in total sales to break even. The
following contribution margin income statement confirms this answer:
Target Profit in Sales Dollars
Key Equation
Question: Finding a target profit in sales dollars simply means that a company would
like to know total sales measured in dollars required to achieve a certain profit.
Finding the target profit in sales dollars is similar to finding the break-even point in
sales dollars except that “target profit” is no longer set to zero. Instead, target profit is
set to the profit the company would like to achieve. Recall that management of
Snowboard Company asked the following question: What is the amount of total sales
dollars required to earn a target profit of $30,000?
Answer: Use the break-even formula described in the previous section. Instead of
setting the target profit to $0, set it to $30,000. This results in an answer of $200,000
in monthly sales:
Thus Snowboard Company must achieve $200,000 in sales to make $30,000 in
monthly profit. The following contribution margin income statement confirms this
answer:
Business in Action 6.1
Measuring the Break-Even Point for Airlines
During the month of September 2001, United Airlines was losing $15 million per day.
With $2.7 billion in cash, United had six months to return to profitability before facing
a significant cash shortage. Many analysts believed United’s troubles resulted in part
from a relatively high break-even point.
Airlines measure break-even points, also called load factors, in terms of the percentage
of seats filled. At the end of 2001, one firm estimated that United had to fill 96 percent
of its seats just to break even. This is well above the figure for other major airlines, as
you can see in the list that follows:
•
American Airlines: 85 percent
•
Delta Airlines: 85 percent
•
Southwest Airlines: 65 percent
•
Alaska Airlines:75 percent
United Airlines filed for bankruptcy at the end of 2002 and emerged from bankruptcy
in 2006 after reducing costs by $7 billion a year. Other airlines continue to work on
reducing their break-even points and maximizing the percentage of seats filled.
Source: Lisa DiCarlo, “Can This Airline Be Saved?” Forbes magazine’s Web site
(http://www.forbes.com), November 2001; “United Airlines Emerges from
Bankruptcy,” Reuters (http://www.foxnews.com), February 1, 2005.
CVP Graph
Question: The relationship of costs, volume, and profit can be displayed in the form of
a graph. What does this graph look like for Snowboard Company, and how does it help
management evaluate financial information related to the production of snowboards?
Answer: Figure 6.2 "CVP Graph for Snowboard Company" shows in graph form the
relationship between cost, volume, and profit for Snowboard Company. The vertical axis
represents dollar amounts for revenues, costs, and profits. The horizontal axis
represents the volume of activity for a period, measured as units produced and sold for
Snowboard.
There are three lines in the graph:
•
Total revenue
•
Total cost
•
Profit
The total revenue line shows total revenue based on the number of units produced and
sold. For example, if Snowboard produces and sells one unit, total revenue is $250 (= 1
× $250). If it produces and sells 2,000 units, total revenue is $500,000 (= 2,000 ×
$250).
The total cost line shows total cost based on the number of units produced and sold. For
example, if Snowboard produces and sells one unit, total cost is $50,150 [= $50,000 + (1
× $150)]. If it produces and sells 2,000 units, total cost is $350,000 [= $50,000 +
(2,000 × $150)].
The profit line shows profit or loss based on the number of units produced and sold. It is
simply the difference between the total revenue and total cost lines. For example, if
Snowboard produces and sells 2,000 units, the profit is $150,000 (= $500,000 −
$350,000). If no units are sold, a loss is incurred equal to total fixed costs of $50,000.
Figure 6.2 CVP Graph for Snowboard Company
Margin of Safety
Question: Managers often like to know how close projected sales are to the break-even
point. How is this information calculated and used by management?
Answer: The excess of projected sales over the break-even point is called the margin of
safety. The margin of safety represents the amount by which sales can fall before the
company incurs a loss.
Key Equation
Margin of safety (in units) = Projected sales (in units) − Break-even sales (in units)
Assume Snowboard Company expects to sell 700 snowboards and that its break-even
point is 500 units; the margin of safety is 200 units. The calculation is
Thus sales can drop by 200 units per month before the company begins to incur a loss.
The margin of safety can also be stated in sales dollars.
Key Equation
Margin of safety (in sales $) = Projected sales (in sales $) − Break-even sales (in sales
$)
For Snowboard the margin of safety in sales dollars is $50,000:
Thus sales revenue can drop by $50,000 per month before the company begins to incur
a loss.
KE Y TA KEA WAY
•
Cost-volume-profit analysis involves finding the break-even and target profit
point in units and in sales dollars. The key formulas for an organization with a
single product are summarized in the following list. Set the target profit to $0 for
break-even calculations, or to the appropriate profit dollar amount for target
profit calculations. The margin of safety formula is also shown:
o
Break-even or target profit point measured in units:
(The denominator is also called “contribution margin per unit.”)
o
Break-even or target profit point measured in sales dollars:
o
Margin of safety in units or sales dollars:
Projected sales − Break-even sales
RE V IE W P ROB LEM 6.1
Star Symphony would like to perform for a neighboring city. Fixed costs for the
performance total $5,000. Tickets will sell for $15 per person, and an outside
organization responsible for processing ticket orders charges the symphony a fee of $2
per ticket. Star Symphony expects to sell 500 tickets.
1. How many tickets must Star Symphony sell to break even?
2. How many tickets must the symphony sell to earn a profit of $7,000?
3. How much must Star Symphony have in sales dollars to break even?
4. How much must Star Symphony have in sales dollars to earn a profit of $7,000?
5. What is the symphony’s margin of safety in units and in sales dollars?
Solution to Review Problem 6.1
Note: All solutions are rounded.
1. The symphony must sell 385 tickets to break even:
2. The symphony must sell 923 tickets to make a profit of $7,000:
3. The symphony must make $5,769 in sales to break even:
4. The symphony must make $13,846 in sales to earn a profit of $7,000:
5. The symphony’s margin of safety is 115 units or $1,725 in sales:
6.2 Cost-Volume-Profit Analysis for Multiple-Product
and Service Companies
L EA RNING O B JEC T IV E
1. Perform cost-volume-profit analysis for multiple-product and service companies.
Question: Although the previous section illustrated cost-volume-profit (CVP) analysis
for companies with a single product easily measured in units, most companies have
more than one product or perhaps offer services not easily measured in units. Suppose
you are the manager of a company called Kayaks-For-Fun that produces two kayak
models, River and Sea. What information is needed to calculate the break-even point
for this company?
Answer: The following information is required to find the break-even point:
•
Monthly fixed costs total $24,000.
•
The River model represents 60 percent of total sales volume and the Sea model
accounts for 40 percent of total sales volume.
•
The unit selling price and variable cost information for the two products follow:
Finding the Break-Even Point and Target Profit in Units for MultipleProduct Companies
Question: Given the information provided for Kayaks-For-Fun, how will the company
calculate the break-even point?
Answer: First, we must expand the profit equation presented earlier to include multiple
products. The following terms are used once again. However, subscript r identifies the
River model, and subscript s identifies the Sea model (e.g., Sr stands for the River
model’s selling price per unit). CM is new to this section and represents the contribution
margin.
Key Equation
S = Selling price per unitV = Variable cost per unitF = Total fixed costsQ = Quantity of
units produced and soldCM = Contribution margin
Thus
Without going through a detailed derivation, this equation can be restated in a
simplified manner for Kayaks-For-Fun, as follows:
One manager at Kayaks-For-Fun believes the break-even point should be 60 units in
total, and another manager believes the break-even point should be 160 units in total.
Which manager is correct? The answer is both might be correct. If only the River kayak
is produced and sold, 60 units is the break-even point. If only the Sea kayak is produced
and sold, 160 units is the break-even point. There actually are many different breakeven points, because the profit equation has two unknown variables, Qr and Qs.
Further evidence of multiple break-even points is provided as follows (allow for
rounding to the nearest unit), and shown graphically in Figure 6.3 "Multiple Break-Even
Points for Kayaks-For-Fun":
Profit ($0) = ($400 × 30 units of River) + ($150 × 80 units of Sea) − $24,000Profit ($0)
= ($400 × 35 units of River) + ($150 × 67 units of Sea) − $24,000Profit ($0) = ($400
× 40 units of River) + ($150 × 53 units of Sea) − $24,000
Figure 6.3 Multiple Break-Even Points for Kayaks-For-Fun
Break-Even Point in Units and the Weighted Average Contribution Margin per
Unit
Question: Because most companies sell multiple products that have different selling
prices and different variable costs, the break-even or target profit point depends on the
sales mix. What is the sales mix, and how is it used to calculate the break-even point?
Answer: The sales mix is the proportion of one product’s sales to total sales. In the case
of Kayaks-For-Fun, the River model accounts for 60 percent of total unit sales and the
Sea model accounts for 40 percent of total unit sales.
In calculating the break-even point for Kayaks-For-Fun, we must assume the sales mix
for the River and Sea models will remain at 60 percent and 40 percent, respectively, at
all different sales levels. The formula used to solve for the break-even point in units for
multiple-product companies is similar to the one used for a single-product company,
with one change. Instead of using the contribution margin per unit in the denominator,
multiple-product companies use a weighted average contribution margin per unit. The
formula to find the break-even point in units is as follows.
Key Equation
When a company assumes a constant sales mix, a weighted average contribution margin
per unit can be calculated by multiplying each product’s unit contribution margin by its
proportion of total sales. The resulting weighted unit contribution margins for all
products are then added together.
At Kayaks-For-Fun, the weighted average contribution margin per unit of $300 is
$300 = ($400 × 60 percent) + ($150 × 40 percent)
We can now determine the break-even point in units by using the following formula:
Kayaks-For-Fun must sell 48 River models (= 60 percent × 80 units) and 32 Sea models
(= 40 percent × 80 units) to break even. Again, this assumes the sales mix remains the
same at different levels of sales volume.
Target Profit in Units
Question: We now know how to calculate the break-even point in units for a company
with multiple products. How do we extend this process to find the target profit in units
for a company with multiple products?
Answer: Finding the target profit in units for a company with multiple products is
similar to finding the break-even point in units except that profit is no longer set to zero.
Instead, profit is set to the target profit the company would like to achieve.
Key Equation
For example, assume Kayaks-For-Fun would like to know how many units it must sell to
make a monthly profit of $96,000. Simply set the target profit to $96,000 and run the
calculation:
Kayaks-For-Fun must sell 240 River models (= 60 percent × 400) and 160 Sea models
(= 40 percent × 400) to make a profit of $96,000.
RE V IE W P ROB LEM 6.2
International Printer Machines (IPM) builds three computer printer models: Inkjet, Laser,
and Color Laser. Information for these three products is as follows:
Inkjet
Laser
Color Laser Total
Selling price per unit
$250
$400
$1,600
Variable cost per unit
$100
$150
$ 800
6,000
2,000
Expected unit sales (annual) 12,000
Sales mix
60 percent 30 percent 10 percent
20,000
100 percent
Total annual fixed costs are $5,000,000. Assume the sales mix remains the same at all
levels of sales.
1.
1. How many printers in total must be sold to break even?
2. How many units of each printer must be sold to break even?
2.
1. How many printers in total must be sold to earn an annual profit of $1,000,000?
2. How many units of each printer must be sold to earn an annual profit of
$1,000,000?
Solution to Review Problem 6.2
Note: All solutions are rounded.
1.
1. IPM must sell 20,408 printers to break even:
2. As calculated previously, 20,408 printers must be sold to break even. Using
the sales mix provided, the following number of units of each printer must
be sold to break even:
1.
2.
3.
2.
1. IPM must sell 24,490 printers to earn $1,000,000 in profit:
2. As calculated previously, 24,490 printers must be sold to earn $1,000,000
in profit. Using the sales mix provided, the following number of units for
each printer must be sold to earn $1,000,000 in profit:
0.
1.
2.
Finding the Break-Even Point and Target Profit in Sales Dollars for
Multiple-Product and Service Companies
A restaurant like Applebee’s, which serves chicken, steak, seafood, appetizers, and
beverages, would find it difficult to measure a “unit” of product. Such companies need a
different approach to finding the break-even point. Figure 6.4 "Type of Good or Service
Determines Whether to Calculate Break-Even Point and Target Profit Points in Units or
Sales Dollars" illustrates this point by contrasting a company that has similar products
easily measured in units (kayaks) with a company that has unique products (meals at a
restaurant) not easily measured in units.
Break-Even Point in Sales Dollars and the Weighted Average Contribution
Margin Ratio
Question: For companies that have unique products not easily measured in units, how
do we find the break-even point?
Answer: Rather than measuring the break-even point in units, a more practical
approach for these types of companies is to find the break-even point in sales dollars.
We can use the formula that follows to find the break-even point in sales dollars for
organizations with multiple products or services. Note that this formula is similar to the
one used to find the break-even point in sales dollars for an organization with one
product, except that the contribution margin ratio now becomes the weighted
average contribution margin ratio.
Key Equation
For example, suppose Amy’s Accounting Service has three departments—tax, audit, and
consulting—that provide services to the company’s clients. Figure 6.5 "Income
Statement for Amy’s Accounting Service" shows the company’s income statement for the
year. Amy, the owner, would like to know what sales are required to break even. Note
that fixed costs are known in total, but Amy does not allocate fixed costs to each
department.
Figure 6.5 Income Statement for Amy’s Accounting Service
The contribution margin ratio differs for each department:
Tax
70 percent (= $70,000 ÷ $100,000)
Audit
20 percent (= $30,000 ÷ $150,000)
Consulting 50 percent (= $125,000 ÷ $250,000)
Question: We have the contribution margin ratio for each department, but we need it
for the company as a whole. How do we find the contribution margin ratio for all of
the departments in the company combined?
Answer: The contribution margin ratio for the company as a whole is the weighted
average contribution margin ratio. We calculate it by dividing the total contribution
margin by total sales. For Amy’s Accounting Service, the weighted average contribution
margin ratio is 45 percent (= $225,000 ÷ $500,000). For every dollar increase in sales,
the company will generate an additional 45 cents ($0.45) in profit. This assumes that
the sales mix remains the same at all levels of sales. (The sales mix here is measured in
sales dollars for each department as a proportion of total sales dollars.)
Now that you know the weighted average contribution margin ratio for Amy’s
Accounting Service, it is possible to calculate the break-even point in sales dollars:
Amy’s Accounting Service must achieve $266,667 in sales to break even.The weighted
average contribution margin ratio can also be found by multiplying each department’s
contribution margin ratio by its proportion of total sales. The resulting weighted average
contribution margin ratios for all departments are then added. The calculation for Amy’s
Accounting Service is as follows:45 percent weighted average contribution margin ratio
= (tax has 20 percent of total sales × 70 percent contribution margin ratio) + (audit has
30 percent of total sales × 20 percent contribution margin ratio) + (consulting has 50
percent of total sales × 50 percent contribution margin ratio)Thus 45 percent = 14
percent + 6 percent + 25 percent.
Target Profit in Sales Dollars
Question: How do we find the target profit in sales dollars for companies with
products not easily measured in units?
Answer: Finding the target profit in sales dollars for a company with multiple products
or services is similar to finding the break-even point in sales dollars except that profit is
no longer set to zero. Instead, profit is set to the target profit the company would like to
achieve.
Key Equation
For example, assume Amy’s Accounting Service would like to know sales dollars
required to make $250,000 in annual profit. Simply set the target profit to $250,000
and run the calculation:
Amy’s Accounting Service must achieve $822,222 in sales to earn $250,000 in profit.
Important Assumptions
Question: Several assumptions are required to perform break-even and target profit
calculations for companies with multiple products or services. What are these
important assumptions?
Answer: These assumptions are as follows:
•
Costs can be separated into fixed and variable components.
•
Contribution margin ratio remains constant for each product, segment, or
department.
•
Sales mix remains constant with changes in total sales.
These assumptions simplify the CVP model and enable accountants to perform CVP
analysis quickly and easily. However, these assumptions may not be realistic,
particularly if significant changes are made to the organization’s operations. When
performing CVP analysis, it is important to consider the accuracy of these simplifying
assumptions. It is always possible to design a more accurate and complex CVP model.
But the benefits of obtaining more accurate data from a complex CVP model must
outweigh the costs of developing such a model.
Margin of Safety
Question: Managers often like to know how close expected sales are to the break-even
point. As defined earlier, the excess of projected sales over the break-even point is
called the margin of safety. How is the margin of safety calculated for multipleproduct and service organizations?
Answer: Let’s return to Amy’s Accounting Service and assume that Amy expects annual
sales of $822,222, which results in expected profit of $250,000. Given a break-even
point of $266,667, the margin of safety in sales dollars is calculated as follows:
Thus sales revenue can drop by $555,555 per year before the company begins to incur a
loss.
KE Y TA KEA WAYS
•
The key formula used to calculate the break-even or target profit point in
units for a company with multiple products is as follows. Simply set the target
profit to $0 for break-even calculations, or to the appropriate profit dollar
amount for target profit calculations.
•
The formula used to find the break-even point or target profit in sales dollars for
companies with multiple products or service is as follows. Simply set the “Target
Profit” to $0 for break-even calculations, or to the appropriate profit dollar
amount for target profit calculations:
RE V IE W P ROB LEM 6.3
Ott Landscape Incorporated provides landscape maintenance services for three types of
clients: commercial, residential, and sports fields. Financial projections for this coming
year for the three segments are as follows:
Assume the sales mix remains the same at all levels of sales.
1. How much must Ott Landscape have in total sales dollars to break even?
2. How much must Ott Landscape have in total sales dollars to earn an annual profit of
$1,500,000?
3. What is the margin of safety, assuming projected sales are $5,000,000 as shown
previously?
Solution to Review Problem 6.3
1. Sales of $1,000,000 are required to break even:
*Weighted average contribution margin ratio = $1,000,000 ÷ $5,000,000 = 20
percent or 0.20.
2. Sales of $8,500,000 are required to make a profit of $1,500,000:
3. The margin of safety is $4,000,000 in sales:
6.3 Using Cost-Volume-Profit Models for Sensitivity
Analysis
L EA RNING O B JEC T IV E
1. Use sensitivity analysis to determine how changes in the cost-volume-profit equation
affect profit.
Question: We can use the cost-volume-profit (CVP) financial model described in this
chapter for single-product, multiple-product, and service organizations to perform
sensitivity analysis, also called what-if analysis. How is sensitivity analysis used to
help managers make decisions?
Answer: Sensitivity analysis shows how the CVP model will change with changes in any
of its variables (e.g., changes in fixed costs, variable costs, sales price, or sales mix). The
focus is typically on how changes in variables will alter profit.
Sensitivity Analysis: An Example
To illustrate sensitivity analysis, let’s go back to Snowboard Company, a company that
produces one snowboard model. The assumptions for Snowboard were as follows:
Sales price per unit
$
250
Variable cost per unit
150
Fixed costs per month
50,000
Target profit
30,000
Recall from earlier calculations that the break-even point is 500 units, and Snowboard
must sell 800 units to achieve a target profit of $30,000. Management believes a goal of
800 units is overly optimistic and settles on a best guess of 700 units in monthly sales.
This is called the “base case.” The base case is summarized as follows in contribution
margin income statement format:
Question: Although management believes the base case is reasonably accurate, it is
concerned about what will happen if certain variables change. As a result, you are
asked to address the following questions from management (you are now performing
sensitivity analysis!). Each scenario is independent of the others. Unless told
otherwise, assume that the variables used in the base case remain the same. How do
you answer the following questions for management?
1. How will profit change if the sales price increases by $25 per unit (10 percent)?
2. How will profit change if sales volume decreases by 70 units (10 percent)?
3. How will profit change if fixed costs decrease by $15,000 (30 percent) and
variable cost increases $15 per unit (10 percent)?
Answer: The CVP model shown in Figure 6.6 "Sensitivity Analysis for Snowboard
Company" answers these questions. Each column represents a different scenario, with
the first column showing the base case and the remaining columns providing answers to
the three questions posed by management. The top part of Figure 6.6 "Sensitivity
Analysis for Snowboard Company" shows the value of each variable based on the
scenarios presented previously, and the bottom part presents the results in contribution
margin income statement format.
Figure 6.6 Sensitivity Analysis for Snowboard Company
a
$17,500 = $37,500 − $20,000.
b
87.5 percent = $17,500 ÷ $20,000.
Carefully review Figure 6.6 "Sensitivity Analysis for Snowboard Company". The column
labeled Scenario 1 shows that increasing the price by 10 percent will increase profit 87.5
percent ($17,500). Thus profit is highly sensitive to changes in sales price. Another way
to look at this is that for every one percent increase in sales price, profit will increase by
8.75 percent, or for every one percent decrease in sales price, profit will decrease by
8.75 percent.
The column labeled Scenario 2 shows that decreasing sales volume 10 percent will
decrease profit 35 percent ($7,000). Thus profit is also highly sensitive to changes in
sales volume. Stated another way, every one percent decrease in sales volume
will decrease profit by 3.5 percent; or every one percent increase in sales volume
will increase profit by 3.5 percent.
When comparing Scenario 1 with Scenario 2, we see that Snowboard Company’s profit is
more sensitive to changes in sales price than to changes in sales volume, although
changes in either will significantly affect profit.
The column labeled Scenario 3 shows that decreasing fixed costs by 30 percent and
increasing variable cost by 10 percent will increase profit 22.5 percent ($4,500).
(Perhaps Snowboard Company is considering moving toward less automation and more
direct labor!)
Computer Application
Using Excel to Perform Sensitivity Analysis
The accountants at Snowboard Company would likely use a spreadsheet program, such
as Excel, to develop a CVP model for the sensitivity analysis shown in Figure 6.6
"Sensitivity Analysis for Snowboard Company". An example of how to use Excel to
prepare the CVP model shown in Figure 6.6 "Sensitivity Analysis for Snowboard
Company" is presented as follows. Notice that the basic data are entered at the top of the
spreadsheet (data entry section), and the rest of the information is driven by formulas.
This allows for quick sensitivity analysis of different scenarios.
Using the base case as an example, sales of $175,000 (cell D14) are calculated by
multiplying the $250 sales price per unit (cell D5) by 700 units (cell D8). Variable costs
of $105,000 (cell D15) are calculated by multiplying the $150 variable cost per unit (cell
D6) by 700 units (cell D8). Fixed costs of $50,000 come from the top section (cell D7).
The contribution margin of $70,000 is calculated by subtracting variable costs from
sales, and profit of $20,000 is calculated by subtracting fixed costs from the
contribution margin.
Expanding the Use of Sensitivity Analysis
Question: Although the focus of sensitivity analysis is typically on how changes in
variables will affect profit (as shown in Figure 6.6 "Sensitivity Analysis for Snowboard
Company"), accountants also use sensitivity analysis to determine the impact of
changes in variables on the break-even point and target profit. How is sensitivity
analysis used to evaluate the impact changes in variables will have on break-even and
target profit points?
Answer: Let’s look at an example for Snowboard Company. Assume the company is able
to charge $275 per unit, instead of $250 per unit. How many units must Snowboard
Company sell to break even? The following calculation is based on the shortcut formula
presented earlier in the chapter:
Thus if the sales price per unit increases from $250 to $275, the break-even point
decreases from 500 units (calculated earlier) to 400 units, which is a decrease of 100
units.
How would this same increase in sales price change the required number of units sold to
achieve a profit of $30,000? We apply the same shortcut formula:
Thus if the sales price per unit increases from $250 to $275, the number of units sold to
achieve a profit of $30,000 decreases from 800 units (calculated earlier) to 640 units,
which is a decrease of 160 units.
Business in Action 6.2
Performing Sensitivity Analysis for a Brewpub
Three entrepreneurs in California were looking for investors and banks to finance a new
brewpub. Brewpubs focus on two segments: food from the restaurant segment, and
freshly brewed beer from the beer production segment. All parties involved in the
process of raising money—potential investors and banks, as well as the three
entrepreneurs (i.e., the owners)—wanted to know what the new business’s projected
profits would be. After months of research, the owners created a financial model that
provided this information. Projected profits were slightly more than $300,000 for the
first year (from sales of $1.95 million) and were expected to increase in each of the next
four years.
One of the owners asked, “What if our projected revenues are too high? What will
happen to profits if sales are lower than we expect? After all, we will have debt of well
over $1 million, and I don’t want anyone coming after my personal assets if the business
doesn’t have the money to pay!” Although all three owners felt the financial model was
reasonably accurate, they decided to find the break-even point and the resulting margin
of safety.
Because a brewpub does not sell “units” of a specific product, the owners found the
break-even point in sales dollars. The owners knew the contribution margin ratio and all
fixed costs from the financial model. With this information, they were able to calculate
the break-even point and margin of safety. The worried owner was relieved to discover
that sales could drop over 35 percent from initial projections before the brewpub
incurred an operating loss.
KE Y TA KEA WAY
•
Sensitivity analysis shows how the cost-volume-profit model will change with changes in
any of its variables. Although the focus is typically on how changes in variables affect
profit, accountants often analyze the impact on the break-even point and target profit as
well.
RE V IE W P ROB LEM 6.4
This problem is an extension of Note 6.28 "Review Problem 6.2". Recall that
International Printer Machines (IPM) builds three computer printer models: Inkjet, Laser,
and Color Laser. Base case information for these three products is as follows:
Inkjet
Laser
Color Laser Total
Selling price per unit
$250
$400
$1,600
Variable cost per unit
$100
$150
$ 800
6,000
2,000
Expected unit sales (annual) 12,000
Sales mix
60 percent 30 percent 10 percent
20,000
100 percent
Total annual fixed costs are $5,000,000. Assume that each scenario that follows is
independent of the others. Unless stated otherwise, the variables are the same as in the
base case.
1. Prepare a contribution margin income statement for the base case. Use the format
shown in Figure 6.5 "Income Statement for Amy’s Accounting Service".
2. How will total profit change if the Laser sales price increases by 10 percent? (Hint: Use
the format shown in Figure 6.5 "Income Statement for Amy’s Accounting Service", and
compare your result with requirement 1.)
3. How will total profit change if the Inkjet sales volume decreases by 4,000 units and the
sales volume of other products remains the same?
4. How will total profit change if fixed costs decrease by 20 percent?
Solution to Review Problem 6.4
1. Base Case:
2. Laser sales price increases 10 percent:
Total profit would increase $240,000 (from loss of $100,000 in base case
to profit of $140,000 in this scenario).
3. Inkjet sales volume decreases 4,000 units:
Total profit would decrease $600,000 (from loss of $100,000 in base case
to loss of $700,000 in this scenario).
4. Fixed costs decrease 20 percent:
Total profit would increase $1,000,000 (from loss of $100,000 in base case to
profit of $900,000 in this scenario).
6.4 Impact of Cost Structure on Cost-Volume-Profit
Analysis
L EA RNING O B JEC T IV E
1. Understand how cost structure affects cost-volume-profit sensitivity analysis.
Question: Describing an organization’s cost structure helps us to understand the
amount of fixed and variable costs within the organization. What is meant by the term
cost structure?
Answer: Cost structure is the term used to describe the proportion of fixed and variable
costs to total costs. For example, if a company has $80,000 in fixed costs and $20,000
in variable costs, the cost structure is described as 80 percent fixed costs and 20 percent
variable costs.
Question: Operating leverage refers to the level of fixed costs within an
organization. How do we determine if a company has high operating leverage?
Answer: Companies with a relatively high proportion of fixed costs have high operating
leverage. For example, companies that produce computer processors, such
as NEC and Intel, tend to make large investments in production facilities and
equipment and therefore have a cost structure with high fixed costs. Businesses that rely
on direct labor and direct materials, such as auto repair shops, tend to have higher
variable costs than fixed costs.
Operating leverage is an important concept because it affects how sensitive profits are to
changes in sales volume. This is best illustrated by comparing two companies with
identical sales and profits but with different cost structures, as we do in Figure 6.7
"Operating Leverage Example". High Operating Leverage Company (HOLC) has
relatively high fixed costs, and Low Operating Leverage Company (LOLC) has relatively
low fixed costs.
Figure 6.7 Operating Leverage Example
One way to observe the importance of operating leverage is to compare the break-even
point in sales dollars for each company. HOLC needs sales of $375,000 to break even (=
$300,000 ÷ 0.80), whereas LOLC needs sales of $166,667 to break even (= $50,000 ÷
0.30).
Question: Why don’t all companies strive for low operating leverage to lower the
break-even point?
Answer: In Figure 6.7 "Operating Leverage Example", LOLC looks better up to the sales
point of $500,000 and profit of $100,000. However, once sales exceed $500,000,
HOLC will have higher profit than LOLC. This is because every additional dollar in sales
will provide $0.80 in profit for HOLC (80 percent contribution margin ratio), and only
$0.30 in profit for LOLC (30 percent contribution margin ratio). If a company is
relatively certain of increasing sales, then it makes sense to have higher operating
leverage.
Financial advisers often say, “the higher the risk, the higher the potential profit,” which
can also be stated as “the higher the risk, the higher the potential loss.” The same applies
to operating leverage. Higher operating leverage can lead to higher profit. However,
high operating leverage companies that encounter declining sales tend to feel the
negative impact more than companies with low operating leverage.
To prove this point, let’s assume both companies in Figure 6.7 "Operating Leverage
Example" experience a 30 percent decrease in sales. HOLC’s profit would decrease by
$120,000 (= 30 percent × $400,000 contribution margin) and LOLC’s profit would
decrease by $45,000 (= 30 percent × $150,000 contribution margin). HOLC would
certainly feel the pain more than LOLC.
Now assume both companies in Figure 6.7 "Operating Leverage Example" experience a
30 percent increase in sales. HOLC’s profit would increase by $120,000 (= 30 percent ×
$400,000 contribution margin) and LOLC’s profit would increase by $45,000 (= 30
percent × $150,000 contribution margin). HOLC benefits more from increased sales
than LOLC.
KE Y TA KEA WAY
•
The cost structure of a firm describes the proportion of fixed and variable costs to total
costs. Operating leverage refers to the level of fixed costs within an organization. The
term “high operating leverage” is used to describe companies with relatively high fixed
costs. Firms with high operating leverage tend to profit more from increasing sales, and
lose more from decreasing sales than a similar firm with low operating leverage.
RE V IE W P ROB LEM 6.5
What are the characteristics of a company with high operating leverage, and how do
these characteristics differ from those of a company with low operating leverage?
Solution to Review Problem 6.5
Companies with high operating leverage have a relatively high proportion of fixed costs
to total costs, and their profits tend to be much more sensitive to changes in sales than
their low operating leverage counterparts. Companies with low operating leverage have
a relatively low proportion of fixed costs to total costs, and their profits tend to be much
less sensitive to changes in sales than their high operating leverage counterparts.
6.5 Using a Contribution Margin When Faced with
Resource Constraints
L EA RNING O B JEC T IV E
1. Use an alternative form of contribution margin when faced with a resource constraint.
Question: Many companies have limited resources in such areas as labor hours,
machine hours, facilities, and materials. These constraints will likely affect a
company’s ability to produce goods or provide services. When a company that
produces multiple products faces a constraint, managers often calculate the
contribution margin per unit of constraint in addition to the contribution margin per
unit. The contribution margin per unit of constraint is the contribution margin per unit
divided by the units of constrained resource required to produce one unit of
product. How is this measure used by managers to make decisions when faced with
resource constraints?
Answer: Let’s examine the Kayaks-For-Fun example introduced earlier in the chapter.
The company produces two kayak models, River and Sea. Based on the information
shown, Kayaks-For-Fun would prefer to sell more of the River model because it has the
highest contribution margin per unit.
Kayaks-For-Fun has a total of 320 labor hours available each month. The specialized
skills required to build the kayaks makes it difficult for management to find additional
workers. Assume the River model requires 4 labor hours per unit and the Sea model
requires 1 labor hour per unit (most of the variable cost for the Sea model is related to
expensive materials required for production). Kayaks-For-Fun sells everything it
produces. Given its labor hours constraint, the company would prefer to maximize the
contribution margin per labor hour.
Based on this information, Kayaks-For-Fun would prefer to sell the Sea model because it
provides a contribution margin per labor hour of $150 versus $100 for the River model.
The company would prefer only to make the Sea model, which would yield a total
contribution margin of $48,000 (= $150 × 320 hours). If the River model were the only
model produced, the total contribution margin to the company would be $32,000 (=
$100 × 320 hours).
Analysis such as this often leads to further investigation. It may be that Kayaks-For-Fun
can find additional labor to alleviate this resource constraint. Or perhaps the production
process can be modified in a way that reduces the labor required to build the River
model (e.g., through increased automation). Whatever the outcome, companies with
limited resources are wise to calculate the contribution margin per unit of constrained
resource.
KE Y TA KEA WAY
•
Many organizations operate with limited resources in areas such as labor hours, machine
hours, facilities, or materials. The contribution margin per unit of constraint is a helpful
measure in determining how constrained resources should be utilized.
RE V IE W P ROB LEM 6.6
This review problem is based on the information for Kayaks-For-Fun presented
previously. Assume Kayaks-For-Fun found additional labor, thereby eliminating this
resource constraint. However, the company now faces limited available machine hours.
It has a total of 3,000 machine hours available each month. The River model requires 16
machine hours per unit, and the Sea model requires 10 machine hours per unit.
1. Calculate the contribution margin per unit of constrained resource for each model.
2. Which model would Kayaks-For-Fun prefer to sell to maximize overall company profit?
Solution to Review Problem 6.6
1.
2. Kayaks-For-Fun would prefer to sell the River model because it provides a contribution
margin per machine hour of $25 compared to $15 for the Sea model. If only the River
model were sold, the total contribution margin would be $75,000 (= $25 × 3,000
machine hours). If only the Sea model were sold, the total contribution margin would be
$45,000 (= $15 × 3,000 machine hours).
6.6 Income Taxes and Cost-Volume-Profit Analysis
L EA RNING O B JEC T IV E
1. Understand the effect of income taxes on cost-volume-profit analysis.
Question: Some organizations, such as not-for-profit entities and governmental
agencies, are not required to pay income taxes. However, most for-profit
organizations must pay income taxes on their profits. How do we find the target profit
in units or sales dollars for organizations that pay income taxes?
Answer: Three steps are required:
Step 1. Determine the desired target profit after taxes (i.e., after accounting
for income taxes).
Step 2. Convert the desired target profit after taxes to the target profit before
taxes.
Step 3. Use the target profit before taxes in the appropriate formula to
calculate the target profit in units or sales dollars.
Using Snowboard Company as an example, the assumptions are as follows:
Sales price per unit
Variable cost per unit
$
250
150
Fixed costs per month 50,000
Target profit
30,000
Assume also that the $30,000 target profit is the monthly profit desired after taxes and
that Snowboard has a tax rate of 20 percent.
Step 1. Determine the desired target profit after taxes.
Snowboard’s management wants to know how many units must be sold to earn a profit
of $30,000 after taxes. Target profit before taxes will be higher than $30,000, and we
calculate it in the next step.
Step 2. Convert the desired target profit after taxes to the target profit before
taxes.
The formula used to solve for target profit before taxes is as follows.
Key Equation
Target profit before taxes = Target profit after taxes ÷ (1 − tax rate)
Using Snowboard Company’s data, the formula would read as follows:
Step 3. Use the target profit before taxes in the appropriate formula to
calculate the target profit in units or sales dollars.
The formula used to solve for target profit in units is
For Snowboard Company, it would read as follows:
This answer is confirmed in the following contribution margin income statement.
KE Y TA KEA WAY
•
Companies that incur income taxes must follow three steps to find the breakeven point or target profit.
Step 1. Determine the desired target profit after taxes.
Step 2. Convert the desired target profit after taxes to target profit before taxes
using the following formula:
Target profit before taxes = Target profit after taxes ÷ (1 − tax rate)
Step 3. Use the target profit before taxes from step 2 in the appropriate target
profit formula to calculate the target profit in units or in sales dollars.
R E V IE W P ROB LEM 6.7
This review problem is based on the information for Snowboard Company. Assume
Snowboard’s tax rate remains at 20 percent.
1. Use the three steps described in this section to determine how many units Snowboard
Company must sell to earn a monthly profit of $50,000 after taxes.
2. Use the three steps to determine the sales dollars Snowboard needs to earn a monthly
profit of $60,000 after taxes.
Solution to Review Problem 6.7
1. The three steps to determine how many units must be sold to earn a target profit
after taxes are as follows:
Step 1. Determine the desired target profit after taxes.
Management wants a profit of $50,000 after taxes and needs to know how many
units must be sold to earn this profit.
Step 2. Convert the desired target profit after taxes to the target profit before
taxes.
The formula used to solve for target profit before taxes is
Step 3. Use the target profit before taxes in the appropriate formula to calculate
the target profit in units.
The formula to solve for target profit in units is
For Snowboard Company, it would read as follows:
2. The three steps to determine how many sales dollars are required to achieve a
target profit after taxes are as follows:
Step 1. Determine the desired target profit after taxes.
Management wants a profit of $60,000 after taxes and needs to know the sales
dollars required to earn this profit.
Step 2. Convert the desired target profit after taxes to target profit before taxes.
The formula used to solve for target profit before taxes is
Step 3. Use the target profit before taxes in the appropriate formula to calculate
the target profit in sales dollars.
The formula used to solve for target profit in sales dollars is
6.7 Using Variable Costing to Make Decisions
L EA RNING O B JEC T IV E
1. Understand how managers use variable costing to make decisions.
In Chapter 2 "How Is Job Costing Used to Track Production Costs?", we discussed how
to report manufacturing costs and nonmanufacturing costs following U.S. Generally
Accepted Accounting Principles (U.S. GAAP). Under U.S. GAAP, all nonmanufacturing
costs (selling and administrative costs) are treated as period costs because they are
expensed on the income statement in the period in which they are incurred. All costs
associated with production are treated as product costs, including direct materials,
direct labor, and fixed and variable manufacturing overhead. These costs are attached to
inventory as an asset on the balance sheet until the goods are sold, at which point the
costs are transferred to cost of goods sold on the income statement as an expense. This
method of accounting is called absorption costing because all manufacturing overhead
costs (fixed and variable) are absorbed into inventory until the goods are sold. (The
term full costing is also used to describe absorption costing.)
Question: Although absorption costing is used for external reporting, managers often
prefer to use an alternative costing approach for internal reporting purposes called
variable costing. What is variable costing, and how does it compare to absorption
costing?
Answer: Variable costing requires that all variable production costs be included in
inventory, and all fixed production costs (fixed manufacturing overhead) be reported as
period costs. Thus all fixed production costs are expensed as incurred.
The only difference between absorption costing and variable costing is in the treatment
of fixed manufacturing overhead. Using absorption costing, fixed manufacturing
overhead is reported as a product cost. Using variable costing, fixed manufacturing
overhead is reported as a period cost. Figure 6.8 "Absorption Costing Versus Variable
Costing" summarizes the similarities and differences between absorption costing and
variable costing.
Figure 6.8 Absorption Costing Versus Variable Costing
Impact of Absorption Costing and Variable Costing on Profit
Question: If a company uses just-in-time inventory, and therefore has no beginning or
ending inventory, profit will be exactly the same regardless of the costing approach
used. However, most companies have units of product in inventory at the end of the
reporting period. How does the use of absorption costing affect the value of ending
inventory?
Answer: Since absorption costing includes fixed manufacturing overhead as a product
cost, all products that remain in ending inventory (i.e., are unsold at the end of the
period) include a portion of fixed manufacturing overhead costs as an asset on the
balance sheet. Since variable costing treats fixed manufacturing overhead costs as
period costs, all fixed manufacturing overhead costs are expensed on the income
statement when incurred. Thus if the quantity of units produced exceeds the quantity of
units sold, absorption costing will result in higher profit.
We illustrate this concept with an example. The following information is for Bullard
Company, a producer of clock radios:
Assume Bullard has no finished goods inventory at the beginning of month 1. We will
look at absorption costing versus variable costing for three different scenarios:
•
Month 1 scenario: 10,000 units produced equals 10,000 units sold
•
Month 2 scenario: 10,000 units produced is greater than 9,000 units sold
•
Month 3 scenario: 10,000 units produced is less than 11,000 units sold
Month 1: Number of Units Produced Equals Number of Units Sold
Question: During month 1, Bullard Company sells all 10,000 units produced during
the month. How does operating profit compare using absorption costing and variable
costing when the number of units produced equals the number of units sold?
Answer: Figure 6.9 "Number of Units Produced Equals Number of Units Sold" presents
the results for each costing method. Notice that the absorption costing income
statement is called a traditional income statement, and the variable costing income
statement is called a contribution margin income statement.
As you review Figure 6.9 "Number of Units Produced Equals Number of Units Sold",
notice that when the number of units produced equals the number sold, profit totaling
$90,000 is identical for both costing methods. With absorption costing, fixed
manufacturing overhead costs are fully expensed because all units produced are sold
(there is no ending inventory). With variable costing, fixed manufacturing overhead
costs are treated as period costs and therefore are always expensed in the period
incurred. Because all other costs are treated the same regardless of the costing method
used, profit is identical when the number of units produced and sold is the same.
Figure 6.9 Number of Units Produced Equals Number of Units Sold
a
$250,000 = $25 × 10,000 units sold.
b
$110,000 = ($4 per unit fixed production cost × 10,000 units sold) + ($7 per unit variable
production cost × 10,000 units sold).
c
$70,000 = $7 per unit variable production cost × 10,000 units sold.
d
$50,000 = $20,000 fixed selling and admin. cost + ($3 per unit variable selling and admin.
cost × 10,000 units sold).
e
$30,000 = $3 per unit variable selling and admin. cost × 10,000 units sold.
f
Variable costing treats fixed manufacturing overhead as a period cost. Thus all fixed
manufacturing overhead costs are expensed in the period incurred regardless of the level of
sales.
g
Given.
Month 2: Number of Units Produced Is Greater Than Number of Units Sold
Question: During month 2, Bullard Company produces 10,000 units but sells only
9,000 units. How does operating profit compare using absorption costing and
variable costing when the number of units produced is greater than the number of
units sold?
Answer: Figure 6.10 "Number of Units Produced Is Greater Than Number of Units
Sold" presents the results for each costing method. Notice that absorption costing
results in higher profit. When absorption costing is used, a portion of fixed
manufacturing overhead costs remains in ending inventory as an asset on the balance
sheet until the goods are sold. However, variable costing requires that all fixed
manufacturing overhead costs be expensed as incurred regardless of the level of sales.
Thus when more units are produced than are sold, variable costing results in higher
costs and lower profit.
The difference in profit between the two methods of $4,000 (= $79,000 − $75,000) is
attributed to the $4 per unit fixed manufacturing overhead cost assigned to the 1,000
units in ending inventory using absorption costing ($4,000 = $4 × 1,000 units).
Figure 6.10 Number of Units Produced Is Greater Than Number of Units Sold
a
$225,000 = $25 × 9,000 units sold.
b
$99,000 = ($4 per unit fixed production cost × 9,000 units sold) + ($7 per unit variable
production cost × 9,000 units sold).
c
$63,000 = $7 per unit variable production cost × 9,000 units sold.
d
$47,000 = $20,000 fixed selling and admin. cost + ($3 per unit variable selling and admin.
cost × 9,000 units sold).
e
$27,000 = $3 per unit variable selling and admin. cost × 9,000 units sold.
f
Variable costing always treats fixed manufacturing overhead as a period cost. Thus all fixed
manufacturing overhead costs are expensed in the period incurred regardless of the level of
sales.
g
Given.
Month 3: Number of Units Produced Is Less Than Number of Units Sold
Question: During month 3, Bullard Company produces 10,000 units but sells 11,000
units (1,000 units were left over from month 2 and therefore were in inventory at the
beginning of month 3). How does operating profit compare using absorption costing
and variable costing when the number of units produced is less than the number of
units sold?
Answer: Figure 6.11 "Number of Units Produced Is Less Than Number of Units
Sold" presents the results for each costing method. Using variable costing, the $40,000
in fixed manufacturing overhead costs continues to be expensed when incurred.
However, using absorption costing, the entire $40,000 is expensed because all 10,000
units produced were sold; an additional $4,000 related to the 1,000 units produced last
month and pulled from inventory this month is also expensed. Thus when fewer units
are produced than are sold, absorption costing results in higher costs and lower profit.
The difference in profit between the two methods of $4,000 (= $105,000 − $101,000) is
attributed to the $4 per unit fixed manufacturing overhead cost assigned to the 1,000
units in inventory on the balance sheet at the end of month 2 and recorded as cost of
goods sold during month 3 using absorption costing ($4,000 = $4 × 1,000 units).
Figure 6.11 Number of Units Produced Is Less Than Number of Units Sold
a
$275,000 = $25 × 11,000 units sold.
b
$121,000 = ($4 per unit fixed production cost × 11,000 units sold) + ($7 per unit variable
production cost × 11,000 units sold).
c
$77,000 = $7 per unit variable production cost × 11,000 units sold.
d
$53,000 = $20,000 fixed selling and admin. cost + ($3 per unit variable selling and admin.
cost × 11,000 units sold).
e
$33,000 = $3 per unit variable selling and admin. cost × 11,000 units sold.
f
Variable costing always treats fixed manufacturing overhead as a period cost. Thus all fixed
manufacturing overhead costs are expensed in the period incurred regardless of the level of
sales.
g
Given.
Advantages of Using Variable Costing
Question: Why do organizations use variable costing?
Answer: Variable costing provides managers with the information necessary to prepare
a contribution margin income statement, which leads to more effective cost-volumeprofit (CVP) analysis. By separating variable and fixed costs, managers are able to
determine contribution margin ratios, break-even points, and target profit points, and
to perform sensitivity analysis. Conversely, absorption costing meets the requirements
of U.S. GAAP, but is not as useful for internal decision-making purposes.
Another advantage of using variable costing internally is that it prevents managers from
increasing production solely for the purpose of inflating profit. For example, assume the
manager at Bullard Company will receive a bonus for reaching a certain profit target but
expects to be $15,000 short of the target. The company uses absorption costing, and the
manager realizes increasing production (and therefore increasing inventory levels) will
increase profit. The manager decides to produce 20,000 units in month 4, even though
only 10,000 units will be sold. Half of the $40,000 in fixed production cost ($20,000)
will be included in inventory at the end of the period, thereby lowering expenses on the
income statement and increasing profit by $20,000. At some point, this will catch up to
the manager because the company will have excess or obsolete inventory in future
months. However, in the short run, the manager will increase profit by increasing
production. This strategy does not work with variable costing because all fixed
manufacturing overhead costs are expensed as incurred, regardless of the level of sales.
KE Y TA KEA WAY
•
As shown in Figure 6.8 "Absorption Costing Versus Variable Costing", the only
difference between absorption costing and variable costing is in the treatment of
fixed manufacturing overhead costs. Absorption costing treats fixed
manufacturing overhead as a product cost (included in inventory on the balance
sheet until sold), while variable costing treats fixed manufacturing overhead as a
period cost (expensed on the income statement as incurred).
When comparing absorption costing with variable costing, the following three
rules apply: (1) When units produced equals units sold, profit is the same for both
costing approaches. (2) When units produced is greater than units sold,
absorption costing yields the highest profit. (3) When units produced is less than
units sold, variable costing yields the highest profit.
RE V IE W P ROB LEM 6.8
Winter Sports, Inc., produces snowboards. The company has no finished goods inventory
at the beginning of year 1. The following information pertains to Winter Sports, Inc.,:
1. All 100,000 units produced during year 1 are sold during year 1.
1. Prepare a traditional income statement assuming the company uses absorption
costing.
2. Prepare a contribution margin income statement assuming the company uses
variable costing.
2. Although 100,000 units are produced during year 2, only 80,000 are sold during
the year. The remaining 20,000 units are in finished goods inventory at the end of
year 2.
1. Prepare a traditional income statement assuming the company uses absorption
costing.
2. Prepare a contribution margin income statement assuming the company uses
variable costing.
Solution to Review Problem 6.8
1.
1. Traditional income statement (absorption costing), year 1:
a
$20,000,000 = $200 × 100,000 units sold.
b
$13,500,000 = ($5 per unit fixed production cost × 100,000 units sold) + ($130 per unit
variable production cost × 100,000 units sold).
c
$1,800,000 = $800,000 fixed selling and admin. cost + ($10 per unit variable selling and
admin. cost × 100,000 units sold).
2. Contribution margin income statement (variable costing), year 1:
a
$20,000,000 = $200 × 100,000 units sold.
b
$13,000,000 = $130 per unit variable production cost × 100,000 units sold.
c
$1,000,000 = $10 per unit variable selling and admin. cost × 100,000 units sold.
d
Variable costing treats fixed manufacturing overhead as a period cost. Thus all fixed
manufacturing overhead costs are expensed in the period incurred regardless of the level of
sales.
e
Given.
2.
1. Traditional income statement (absorption costing), year 2:
a
$16,000,000 = $200 × 80,000 units sold.
b
$10,800,000 = ($5 per unit fixed production cost × 80,000 units sold) + ($130 per unit variable
production cost × 80,000 units sold).
2. Contribution margin income statement (variable costing), year 2:
a
$16,000,000 = $200 × 80,000 units sold.
b
$10,400,000 = $130 per unit variable production cost × 80,000 units sold.
c
$800,000 = $10 per unit variable selling and admin. cost × 80,000 units sold.
d
Variable costing treats fixed manufacturing overhead as a period cost. Thus all fixed
manufacturing overhead costs are expensed in the period incurred regardless of the level of
sales.
e
Given.
E ND -O F - CHAP TER EX E RCISE S
Questions
1. Describe the components of the profit equation.
2. What is the difference between a variable cost and a fixed cost? Provide examples of
each.
3. You are asked to find the break-even point in units and in sales dollars. What does this
mean?
4. You are asked to find the target profit in units and in sales dollars. What does this mean?
5. For a company with one product, describe the equation used to calculate the break-even
point or target profit in (a) units, and (b) sales dollars.
6. Distinguish between contribution margin per unit and contribution margin ratio.
7. What does the term margin of safety mean? How might management use this
information?
8. Review Note 6.16 "Business in Action 6.1" How do airlines measure break-even points?
In 2001, which airline had the lowest break-even point?
9. How does the break-even point equation change for a company with multiple products
or services compared to a single-product company?
10. Describe the assumptions made to simplify the cost-volume-profit analysis described in
the chapter.
11. What is sensitivity analysis and how might it help those performing cost-volume-profit
analysis?
12. Review Note 6.37 "Business in Action 6.2" What were the owners concerned about with
regards to projected profits? What were the results of the calculations made to address
the owners’ concerns?
13. If you are asked to review the cost structure of an organization, what are you being
asked to do?
14. When might the contribution margin per unit of constraint be more effective than the
contribution margin per unit for making decisions?
15. Describe the three steps used to calculate the target profit for companies that incur
income tax costs.
16. Describe the difference between absorption costing and variable costing.
17. Why do some organizations use variable costing?
Brief Exercises
18. Planning at Snowboard Company. Refer to the dialogue at Snowboard Company
presented at the beginning of the chapter. What information is Recilia, vice president of
sales, requesting from Lisa, the company accountant? How does Recilia plan on using
this information?
19. Contribution Margin Calculations. Ace Company sells lawn mowers for $200 per unit.
Variable cost per unit is $40, and fixed costs total $4,000. Find (a) the contribution
margin per unit, and (b) the contribution margin ratio.
20. Weighted Average Contribution Margin Calculation. Radio Control, Inc., sells radio
controlled cars for $300 per unit representing 80 percent of total sales, and radio
controlled boats for $400 per unit representing 20 percent of total sales. Variable cost
per unit is $150 for cars and $300 for boats. Find (a) the contribution margin per unit for
each product, and (b) the weighted average contribution margin per unit.
21. Sensitivity Analysis, Sales Price. Refer to the base case for Snowboard Company
presented in the first column of Figure 6.6 "Sensitivity Analysis for Snowboard
Company". Assume the unit sales price decreases by 10 percent. Calculate (a) the new
projected profit, (b) the dollar change in profit from the base case, and (c) the percent
change in profit from the base case.
22. Sensitivity Analysis, Unit Sales. Refer to the base case for Snowboard Company
presented in the first column of Figure 6.6 "Sensitivity Analysis for Snowboard
Company". Assume the number of units sold increases by 10 percent. Calculate (a) the
new projected profit, (b) the dollar change in profit from the base case, and (c) the
percent change in profit from the base case.
23. Operating Leverage. High operating leverage means:
1. The company has relatively low fixed costs.
2. The company has relatively high fixed costs.
3. The company will have to sell more units than a comparable company with low
operating leverage to break even.
4. The company will have to sell fewer units than a comparable company with low
operating leverage to break even.
5. Both (2) and (3) are correct.
6. Both (1) and (4) are correct.
24. Contribution Margin per Unit of Constraint. Paint Toys Company sells paint ball guns for
$100 per unit. Variable cost is $60 per unit. Each paint ball gun requires 1.25 machine
hours and 2.00 direct labor hours to produce. Calculate the contribution margin (a) per
unit, (b) per machine hour, and (c) per direct labor hour.
25. Target Profit with Taxes. Management of Lakewood Company would like to achieve a
target profit after taxes of $300,000. The company’s income tax rate is 40 percent. What
target profit before taxes is required to achieve the $300,000 after-tax profit desired by
management?
26. Absorption Costing Versus Variable Costing. Describe the difference between
absorption costing and variable costing. Which approach yields the highest profit when
the units produced are greater than the units sold? Explain.
Exercises: Set A
27. Break-Even Point and Target Profit Measured in Units (Single Product). Nellie
Company has monthly fixed costs totaling $100,000 and variable costs of $20 per
unit. Each unit of product is sold for $25.
Required:
a. Calculate the contribution margin per unit.
b. Find the break-even point in units.
c. How many units must be sold to earn a monthly profit of $40,000?
28. Break-Even Point and Target Profit Measured in Sales Dollars (Single
Product). Nellie Company has monthly fixed costs totaling $100,000 and variable
costs of $20 per unit. Each unit of product is sold for $25 (these data are the same
as the previous exercise):
Required:
.
Calculate the contribution margin ratio.
a. Find the break-even point in sales dollars.
b. What amount of sales dollars is required to earn a monthly profit of $60,000?
29. Margin of Safety (Single Product). Nellie Company has monthly fixed costs
totaling $100,000 and variable costs of $20 per unit. Each unit of product is sold
for $25 (these data are the same as the previous exercise). Assume Nellie
Company expects to sell 24,000 units of product this coming month.
Required:
.
Find the margin of safety in units.
a. Find the margin of safety in sales dollars.
30. Break-Even Point and Target Profit Measured in Units (Multiple Products). HiTech Incorporated produces two different products with the following monthly
data.
Cell
GPS
Selling price per unit $100
$400
Variable cost per unit $ 40
$240
Expected unit sales
21,000
9,000
Sales mix
70 percent 30 percent 100 percent
Fixed costs
Total
30,000
$1,800,000
31. Assume the sales mix remains the same at all levels of sales.
32. Required:
.
Calculate the weighted average contribution margin per unit.
a. How many units in total must be sold to break even?
b. How many units of each product must be sold to break even?
c. How many units in total must be sold to earn a monthly profit of $180,000?
d. How many units of each product must be sold to earn a monthly profit of
$180,000?
33. Break-Even Point and Target Profit Measured in Sales Dollars (Multiple
Products). Hi-Tech Incorporated produces two different products with the
following monthly data (these data are the same as the previous exercise).
Cell
GPS
Selling price per unit $100
$400
Variable cost per unit $ 40
$240
Expected unit sales
21,000
9,000
Sales mix
70 percent 30 percent 100 percent
Fixed costs
Total
30,000
$1,800,000
34. Assume the sales mix remains the same at all levels of sales.
35. Required:
36. Round your answers to the nearest hundredth of a percent and nearest dollar
where appropriate. (An example for percentage calculations is 0.434532 = 0.4345
= 43.45 percent; an example for dollar calculations is $378.9787 = $379.)
.
Using the information provided, prepare a contribution margin income statement
for the month similar to the one in Figure 6.5 "Income Statement for Amy’s
Accounting Service".
a. Calculate the weighted average contribution margin ratio.
b. Find the break-even point in sales dollars.
c. What amount of sales dollars is required to earn a monthly profit of $540,000?
d. Assume the contribution margin income statement prepared in requirement a is
the company’s base case. What is the margin of safety in sales dollars?
37. Changes in Sales Mix. Hi-Tech Incorporated produces two different products with
the following monthly data (these data are the same as the previous exercise).
Cell
GPS
Selling price per unit $100
$400
Variable cost per unit $ 40
$240
Expected unit sales
21,000
9,000
Sales mix
70 percent 30 percent 100 percent
Fixed costs
Total
30,000
$1,800,000
38. Required:
.
If the sales mix shifts to 50 percent Cell and 50 percent GPS, would the breakeven point in units increase or decrease? Explain. (Detailed calculations are not
necessary but may be helpful in confirming your answer.)
a. Go back to the original projected sales mix. If the sales mix shifts to 80 percent
Cell and 20 percent GPS, would the break-even point in units increase or
decrease? Explain. (Detailed calculations are not necessary but may be helpful in
confirming your answer.)
39. CVP Sensitivity Analysis (Single Product). Bridgeport Company has monthly fixed
costs totaling $200,000 and variable costs of $40 per unit. Each unit of product is
sold for $50. Bridgeport expects to sell 30,000 units each month (this is the base
case).
Required:
For each of the independent situations in requirements b through d, assume that
the number of units sold remains at 30,000.
.
Prepare a contribution margin income statement for the base case.
a. Refer to the base case. What would the operating profit be if the unit sales price
increases 10 percent?
b. Refer to the base case. What would the operating profit be if the unit variable
cost decreases 20 percent?
c. Refer to the base case. What would the operating profit be if total fixed costs
decrease 20 percent?
40. CVP Sensitivity Analysis (Multiple Products). Gonzalez Company produces two
different products that have the following monthly data (this is the base case).
Cruiser
Racer
Total
Selling price per unit $300
$1,200
Variable cost per unit $120
$ 720
Expected unit sales
1,400
600
Sales mix
70 percent 30 percent 100 percent
Fixed costs
2,000
$180,000
41. Required:
42. For each of the independent situations in requirements b through d, assume that
total sales remains at 2,000 units.
.
Prepare a contribution margin income statement.
a. Refer to the base case. What would the operating profit be if the Cruiser sales
price (1) increases 20 percent, or (2) decreases 20 percent?
b. Refer to the base case. What would the operating profit be if the Cruiser sales
volume increases 400 units with a corresponding decrease of 400 units in Racer
sales?
c. Refer to the base case. What would the operating profit be if total fixed costs
increase five percent? Does this increase in fixed costs result in higher operating
leverage or lower operating leverage? Explain.
43. Contribution Margin with Resource Constraints. CyclePath Company produces
two different products that have the following price and cost characteristics.
Bicycle Tricycle
Selling price per unit $200
$100
Variable cost per unit $120
$ 50
44. Management believes that pushing sales of the Bicycle product would maximize
company profits because of the high contribution margin per unit for this
product. However, only 50,000 labor hours are available each year, and the
Bicycle product requires 4 labor hours per unit while the Tricycle model requires 2
labor hours per unit. The company sells everything it produces.
45. Required:
.
Calculate the contribution margin per unit of constrained resource for each
model.
a. Which model would CyclePath prefer to sell to maximize overall company profit?
Explain.
46. Target Profit Measured in Units (with Taxes). Optical Incorporated has annual
fixed costs totaling $6,000,000 and variable costs of $350 per unit. Each unit of
product is sold for $500. Assume a tax rate of 20 percent.
Required:
Use the three steps described in the chapter to determine how many units must
be sold to earn an annual profit of $100,000 after taxes. (Round to the nearest
unit.)
47. Target Profit Measured in Sales Dollars (with Taxes). Optical Incorporated has
annual fixed costs totaling $6,000,000 and variable costs of $350 per unit. Each
unit of product is sold for $500. Assume a tax rate of 20 percent (these data are
the same as the previous exercise).
Required:
Use the three steps described in the chapter to determine the sales dollars
required to earn an annual profit of $150,000 after taxes.
48. Absorption Costing Versus Variable Costing. Technic Company produces portable
CD players. The company has no finished goods inventory at the beginning of year
1. The following information pertains to Technic Company.
Required:
.
All 50,000 units produced during year 1 are sold during year 1.
1. Prepare a traditional income statement assuming the company uses
absorption costing.
2. Prepare a contribution margin income statement assuming the company
uses variable costing.
a. Although 50,000 units are produced during year 2, only 40,000 are sold
during the year. The remaining 10,000 units are in finished goods inventory
at the end of year 2.
1. Prepare a traditional income statement assuming the company uses
absorption costing.
2. Prepare a contribution margin income statement assuming the company
uses variable costing.
Exercises: Set B
39. Break-Even Point and Target Profit Measured in Units (Single Product). Phan
Incorporated has annual fixed costs totaling $6,000,000 and variable costs of
$350 per unit. Each unit of product is sold for $500.
Required:
a. Calculate the contribution margin per unit.
b. Find the break-even point in units.
c. How many units must be sold to earn an annual profit of $750,000?
40. Break-Even Point and Target Profit Measured in Sales Dollars (Single
Product). Phan Incorporated has annual fixed costs totaling $6,000,000 and
variable costs of $350 per unit. Each unit of product is sold for $500 (these data
are the same as the previous exercise).
Required:
.
Calculate the contribution margin ratio.
a. Find the break-even point in sales dollars.
b. What amount of sales dollars is required to earn an annual profit of $300,000?
41. Margin of Safety (Single Product). Phan Incorporated has annual fixed costs
totaling $6,000,000 and variable costs of $350 per unit. Each unit of product is
sold for $500 (these data are the same as the previous exercise). Assume Phan
Incorporated expects to sell 51,000 units of product this coming year.
Required:
.
Find the margin of safety in units.
a. Find the margin of safety in sales dollars.
42. Break-Even Point and Target Profit Measured in Units (Multiple
Products). Advanced Products Company produces three different CDs with the
following annual data.
Music
Data
DVD
Selling price per unit $10
$4
$12
Variable cost per unit $ 3
$1
$ 3
Expected unit sales
8,000
10,000
22,000
Sales mix
20 percent 25 percent 55 percent 100 percent
Fixed costs
Total
40,000
$205,900
43. Assume the sales mix remains the same at all levels of sales.
44. Required:
45. (Round all answers to the nearest cent and nearest unit where appropriate.)
.
Calculate the weighted average contribution margin per unit.
a. How many units in total must be sold to break even?
b. How many units of each product must be sold to break even?
c. How many units in total must be sold to earn an annual profit of $200,000?
d. How many units of each product must be sold to earn an annual profit of
$200,000?
46. Break-Even Point and Target Profit Measured in Sales Dollars (Multiple
Products). Advanced Products Company produces three different CDs with the
following annual data (these data are the same as the previous exercise).
Music
Data
DVD
Selling price per unit $10
$4
$12
Variable cost per unit $ 3
$1
$ 3
Expected unit sales
8,000
10,000
22,000
Sales mix
20 percent 25 percent 55 percent 100 percent
Fixed costs
Total
40,000
$205,900
47. Assume the sales mix remains the same at all levels of sales.
48. Required:
49. Round your answers to the nearest hundredth of a percent and nearest dollar
where appropriate. (An example for percentage calculations is 0.434532 = 0.4345
= 43.45 percent; an example for dollar calculations is $378.9787 = $379.)
.
Using the information provided, prepare a contribution margin income statement
similar to the one in Figure 6.5 "Income Statement for Amy’s Accounting Service".
a. Calculate the weighted average contribution margin ratio.
b. Find the break-even point in sales dollars.
c. What amount of sales dollars is required to earn an annual profit of $200,000?
d. Assume the contribution margin income statement prepared in requirement a is
the company’s base case. What is the margin of safety in sales dollars?
50. Changes in Sales Mix. Advanced Products Company produces three different CDs
with the following annual data (these data are the same as the previous exercise).
Music
Selling price per unit $10
Data
DVD
$4
$12
Total
Variable cost per unit $ 3
$1
$ 3
Expected unit sales
8,000
10,000
22,000
Sales mix
20 percent 25 percent 55 percent 100 percent
Fixed costs
40,000
$205,900
51. Required:
52. If the sales mix shifts more toward the Data product than the other two products,
would the break-even point in units increase or decrease? Explain. (Detail
calculations are not necessary, but may be helpful in confirming your answer.)
53. CVP Sensitivity Analysis (Single Product). Skyler Incorporated has monthly fixed
costs of $1,000,000 and variable costs of $24 per unit. Each unit of product is sold
for $120. Skyler expects to sell 15,000 units each month (this is the base case).
Required:
For each of the independent situations in requirements b through d, assume that
the number of units sold remains at 15,000. (Round to the nearest cent where
appropriate.)
.
Prepare a contribution margin income statement for the base case.
a. Refer to the base case. What would the operating profit be if the unit sales price
decreases 10 percent?
b. Refer to the base case. What would the operating profit be if the unit variable
cost increases 10 percent?
c. Refer to the base case. What would the operating profit be if total fixed costs
decrease 20 percent?
54. CVP Sensitivity Analysis (Multiple Products). CyclePath Company produces two
different products that have the following annual data (this is the base case).
Bicycle
Selling price per unit $200
Tricycle
$100
Total
Variable cost per unit $120
$ 50
Expected unit sales
5,000
20,000
Sales mix
20 percent 80 percent 100 percent
Fixed costs
25,000
$1,000,000
55. Required:
56. For each of the independent situations in requirements b through d, assume that
total sales remains at 25,000 units.
.
Prepare a contribution margin income statement for the base case.
a. Refer to the base case. What would the operating profit be if the Tricycle sales
price (1) increases 10 percent, or (2) decreases 10 percent?
b. Refer to the base case. What would the operating profit be if Bicycle sales volume
decreases 500 units and there is a corresponding increase of 500 units in Tricycle
sales?
c. Refer to the base case. What would the operating profit be if total fixed costs
decrease 10 percent? Does this decrease in fixed costs result in higher operating
leverage or lower operating leverage? Explain.
57. Contribution Margin with Resource Constraints. CyclePath Company produces
two different products that have the following price and cost characteristics.
Bicycle Tricycle
Selling price per unit $200
$100
Variable cost per unit $120
$ 50
58. Management believes that pushing sales of the Bicycle product would maximize
company profits because of the high contribution margin per unit for this
product. However, only 23,000 machine hours are available each year, and the
Bicycle product requires 2 machine hours per unit while the Tricycle model
requires 1 machine hour per unit. The company sells everything it produces.
59. Required:
.
Calculate the contribution margin per unit of constrained resource for each
model.
a. Which model would CyclePath prefer to sell to maximize overall company profit?
Explain.
60. Target Profit Measured in Units (with Taxes). Martis Company has annual fixed
costs totaling $4,000,000 and variable costs of $300 per unit. Each unit of product
is sold for $400. Assume a tax rate of 20 percent.
Required:
Use the three steps described in the chapter to determine how many units must
be sold to earn an annual profit of $500,000 after taxes. (Round to the nearest
unit.)
61. Target Profit Measured in Sales Dollars (with Taxes). Martis Company has annual
fixed costs totaling $4,000,000 and variable costs of $300 per unit. Each unit of
product is sold for $400. Assume a tax rate of 20 percent (these data are the same
as the previous exercise).
Required:
Use the three steps described in the chapter to determine the sales dollars
required to earn an annual profit of $1,000,000 after taxes.
62. Absorption Costing Versus Variable Costing. Photo Company produces digital
cameras. The company has no finished goods inventory at the beginning of year
1. The following information pertains to Photo Company.
Required:
.
All 60,000 units produced during year 1 are sold during year 1.
1. Prepare a traditional income statement assuming the company uses
absorption costing.
2. Prepare a contribution margin income statement assuming the company
uses variable costing.
a. Although 60,000 units are produced during year 2, only 40,000 are sold
during the year. The remaining 20,000 units are in finished goods inventory
at the end of year 2.
1. Prepare a traditional income statement assuming the company uses
absorption costing.
2. Prepare a contribution margin income statement assuming the company
uses variable costing.
Problems
51. CVP and Sensitivity Analysis (Single Product). Madera Company has annual fixed
costs totaling $120,000 and variable costs of $3 per unit. Each unit of product is
sold for $15. Madera expects to sell 12,000 units this year (this is the base case).
Required:
a. Find the break-even point in units.
b. How many units must be sold to earn an annual profit of $50,000? (Round to the
nearest unit.)
c. Find the break-even point in sales dollars.
d. What amount of sales dollars is required to earn an annual profit of $70,000?
e. Find the margin of safety in units and in sales dollars.
f. Prepare a contribution margin income statement for the base case.
g. What will the operating profit (loss) be if the sales price decreases 30 percent?
(Assume total sales remains at 12,000 units, and round to the nearest cent where
appropriate.)
h. Go back to the base case. What will the operating profit (loss) be if the variable
cost per unit increases 10 percent? (Assume total sales remains at 12,000 units,
and round to the nearest cent where appropriate.)
52. CVP Analysis and Cost Structure (Single Product). Riviera Incorporated produces
flat panel televisions. The company has annual fixed costs totaling $10,000,000
and variable costs of $600 per unit. Each unit of product is sold for $1,000. Riviera
expects to sell 70,000 units this year.
Required:
.
Find the break-even point in units.
a. How many units must be sold to earn an annual profit of $2,000,000?
b. Find the break-even point in sales dollars.
c. What amount of sales dollars is required to earn an annual profit of $500,000?
d. Find the margin of safety in units.
e. Find the margin of safety in sales dollars.
f. How much will operating profit change if fixed costs are 15 percent higher than
anticipated? Would this increase in fixed costs result in higher or lower operating
leverage? Explain.
53. CVP Analysis with Taxes (Single Product). Riviera Incorporated produces flat
panel televisions. The company has annual fixed costs totaling $10,000,000 and
variable costs of $600 per unit. Each unit of product is sold for $1,000. Riviera
expects to sell 70,000 units this year (this is the same data as the previous
problem). Assume a tax rate of 30 percent.
Required:
Round all calculations to the nearest dollar and nearest unit where appropriate.
.
How many units must be sold to earn an annual profit of $2,000,000 after taxes?
a. What amount of sales dollars is required to earn an annual profit of $500,000
after taxes?
b. Refer to requirement a. What would happen to the number of units required to
earn $2,000,000 in operating profit if the company were a non-profit organization
that did not incur income taxes? Explain. (Detailed calculations are not necessary
but may be helpful in confirming your answer.)
54. CVP Analysis and Sales Mix (Multiple Products). Sierra Books Incorporated
produces two different products with the following monthly data (this is the base
case).
Text
Lecture Notes Total
Selling price per unit $100
$12
Variable cost per unit $ 60
$ 3
Expected unit sales
21,000
14,000
Sales mix
60 percent 40 percent
Fixed costs
35,000
100 percent
$750,000
55. Assume the sales mix remains the same at all levels of sales except for
requirement i.
56. Required:
57. Round to the nearest unit of product, hundredth of a percent, and nearest cent
where appropriate. (An example for unit calculations is 3,231.15 = 3,231; an
example for percentage calculations is 0.434532 = 0.4345 = 43.45 percent; an
example for dollar calculations is $378.9787 = $378.98.)
.
Calculate the weighted average contribution margin per unit.
a.
1. How many units in total must be sold to break even?
2. How many units of each product must be sold to break even?
b.
1. How many units in total must be sold to earn a monthly profit of
$100,000?
2. How many units of each product must be sold to earn a monthly profit of
$100,000?
c. Using the base case information, prepare a contribution margin income
statement for the month similar to the one in Figure 6.5 "Income Statement for
Amy’s Accounting Service".
d. Calculate the weighted average contribution margin ratio.
e. Find the break-even point in sales dollars.
f. What amount of sales dollars is required to earn a monthly profit of $80,000?
g. Assume the contribution margin income statement prepared in requirement d is
the company’s base case. What is the margin of safety in sales dollars?
h. If the sales mix shifts more toward the Text product than the Lecture Notes
product, would the break-even point in units increase or decrease? Explain.
(Detail calculations are not necessary, but may be helpful in confirming your
answer.)
58. CVP Analysis and Cost Structure (Service Company). Conway Electrical Services
provides services to two types of clients: residential and commercial. The
company’s contribution margin income statement for the year is shown (this is
the base case). Fixed costs are known in total, but Conway does not allocate fixed
costs to each department.
Required:
.
Find the break-even point in sales dollars.
a. What is the margin of safety in sales dollars?
b. What amount of sales dollars is required to earn an annual profit of $750,000?
c. Refer to the base case shown previously. What would the operating profit be if
the Commercial variable costs are 20 percent higher than originally anticipated?
How does this increase in Commercial variable costs impact the operating
leverage of the company?
59. CVP and Sensitivity Analysis, Resource Constraint (Multiple Products). Hobby
Shop Incorporated produces three different models with the following annual
data (this is the base case).
Plane
Car
Boat
Selling price per unit $20
$14
$24
Variable cost per unit $ 5
$ 7
$ 8
Expected unit sales
30,000
50,000
20,000
Sales mix
30 percent 50 percent 20 percent 100 percent
Fixed costs
Total
100,000
$650,000
60. Assume the sales mix remains the same at all levels of sales except for
requ...
Purchase answer to see full
attachment