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Chapter 3

# Chapter 3

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Ryerson University

Accounting

ACC 410

Maurizio Di Maio

Summer

Description

Chapter 3 – Cost-Volume-Profit
Analysis
Cost-volume-profit (CVP) analysis: is a technique that examines changes in
profits in response to changes in sales volumes, costs, and prices
CVP analysis begins with the basic profit equation:
PROFIT = TOTAL REVENUE – TOTAL COSTS
or if separating costs into variable and fixed categories, we express profit as:
PROFIT or EARNING =
TOTAL REVENUE – TOTAL VARIABLE COSTS –
TOTAL FIXED COSTS
Contribution Margin
Contribution Margin: is the total revenue minus the total variable costs
Contribution Margin per unit (CMu): is the selling price per unit minus the
variable cost per unit
Contribution margin per unit tells us how much revenue from each unit sold
can be applied toward fixed costs or contributed to cover fixed costs
Once enough units have been sold to cover all fixed costs, the contribution margin
per unit from all remaining sales becomprofit
TP =
S =
V =
(S – V) =
Q =
F =
www.notesolution.com TP = (S x Q) – (V x Q) – F
or TP = [(S – V) x Q] – F
Cost-Volume-Profit Analysis in Units
Example: Suppose that Magik Bicycles wants to produce a new mountain bike
called Magikbike III and has forecasted the following information:
Price per bike = $800
Variable cost per bike = $300
Fixed costs related to bike production = $5,500,000
Target Profit = $200,000
Estimated sales = 12,000 bikes
Input values into formula to determine the quantity of bikes needed to achieve profit of
$200,000
*
Cost-Volume-Profit Analysis in Revenues
Contribution margin ratio (CMR): the percentage by which the selling price (or
revenue) per unit exceeds the variable cost per unit, or contribution margin as a
percentage of revenue
For single product Contribution Margin Ratio (CMR) =
www.notesolution.com CVP in terms of total revenue instead of units, substitute the contribution
margin ratio for the contribution margin per unit
Recall previous example
First: calculate contribution margin ratio = (S – V)/S ($800 – $300)/$800 = 0.625 (62.5%)
then, Input values into formula to determine the sales (revenue) needed to achieve profit of
$200,000
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***Contribution as an Income Statement
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www.notesolution.com Sales revenue
- Variable Cost .
Contribution Margin
- Fixed Cost .
= Profit before taxes
Breakeven Point
A CVP analysis can be used to determine the breakeven point, or level of
operating activity at which revenues cover all fixed and variable costs, resulting in
zero profit
Since TP is set at 0 when trying to find the breakeven point,
the formula for breakeven is simply...
$*
Recall previous Magik Bicycles example,
$*
,,,,,
*
*
$*
Recall previous Magik Bicycles example,
$*
,,, ,
,
+,
$%
CVP with Income Taxes
An organization’s after-tax earnings are calculated by subtracting income tax
from pre-tax earnings
%%&%$%$
'
%%&%$
www.notesolution.com If managers wanted to know the pre-tax earnings needed to achieve a target
level of after-tax earnings, we rearrange the previous formula
%
%$%&
Example: suppose that Magik Bicycle plans for after-tax earnings of $20,000 and its
tax rate is 30%. Then:
%$,
,
Therefore, the company needs earnings before tax of $28,571 to earn earnings after
tax of $20,000
CVP with Variable Amount of Earning
Managers may want to set an earning as a variable amount of sales. This
variable amount of earning should be calculated as an additional variable
cost
Example: Suppose Magik Bicycles plans for before-tax earnings of 7.5% of
sales
o Recall Profit equation: EBT = (S-V)-F
Solving for S
1S – 0.375S – 5,500,000 = 0.075S
0.625S – 0.075S = 5,500,000
S = $10,000,000
CVP for Multiple Products
Sales mix: the proportion of different products or services that an organization
sells.
CVP Calculations for a Sales Mix
If the manager wanted to use CVP results to plan future operations for
individual products, the required revenue for each product needs to be
determined
Sales mix analysis allows managers to achieve the combination of sales that
will yield the greatest amount of earnings
www.notesolution.com When performing CVP computations for sales mix, we assume that the
products a company sells are in a constant ratio
For instance, Magik Bicycle developed three different products, a small bike
for children and youths, a road bike, and a mountain bike.
o Whenever Magik Bicycles sells 5 youth bikes, it sells 9 road bikes and 6
mountain bikes, therefore, the ratio is expressed 5:9:6
Youth Road Mountain
Price per unit $200 $700 $800
Variable cost per unit 75 250 300
Contribution margin $125 $450 $500
per unit
Contribution margin 62.50% 64.29% 62.50%
ratio
Also assuming, fixed costs are $14,700,00

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