ACCT 5337-Chapter 16 Problem Shells
There are five variables in the Contribution Income Statement
P
V
Q
F
Z
=
=
=
=
=
Selling Price per unit
Variable Cost per unit
Quantity or Number of Units Sold
Total Fixed Costs
Target or Expected Before Tax Profit
Contribution Margin per Unit (P - V) is the amount that each unit of sales contributes to cover total fixed
costs and to provide a profit.
Contribution Margin in Total (PQ(Sales revenue) - VQ) is the amount of money contributed to cover
fixed costs and to provide a profit.
Contribution Margin Ratio or Contribution Margin Percentage (P - V / P) or
(PQ - VQ / PQ) indicates the portion of each sales dollar that is available to cover fixed costs and to
provide a profit.
Formulas:
-
Contribution Margin = (P – V)
-
Contribution Margin Ratio (CM%) = (P – V)/ P
-
CVP Formula: (P - V) Q - F = Z
o Breakeven in units > find out the Q
o Breakeven in sales > PQ = (Z+F) / CM%
 Since Z is 0 (cuz it is breakeven), then PQ = F / CM%
-
Sales Commission per unit = Selling Price/unit x Sales Comm %
-
Z ( 1 - T) = N
o
o
|
Z =
N
1 - T
T = Tax Rate
N = After-Tax Profit
-
Net income = Sales Revenue – Variable expense – Fixed expense – Income tax
= PQ – VQ – F – T
-
Degree of Operating Leverage = Contribution Margin
Net Income
-
Margin of Safety in Units = Actual Sales Units - Breakeven Sales Units
-
Margin of Safety in Sales = Actual Sales $ - Breakeven Sales $
E16-1, page Part 1
a.
Direct Materials
+ Direct Labor
+ Variable Overhead
= Variable Product Cost/Unit
5.75
1.25
0.6
7.60
b.
Direct Materials
+ Direct Labor
+ Variable Overhead
+ Variable Selling
= Variable Cost/Unit
5.75
1.25
0.6
0.8
8.4
Selling Price/Unit
-Variable Cost/Unit
= Contribution Margin/Unit
16
(8.40)
7.6
c.
d.
Contribution Margin Ratio
= P
P
V
CM% = (16 – 8.4)/16 = 0.475
e.
Fixed Overhead
+ Fixed Sell & Administrative
= Total Fixed Expenses
43,000
19,000
62,000
Part 2
Contribution-Margin/Variable Costing Income Statement
Sales Revenue ( 12,000 x 16 )
- Variable Expenses
Direct Materials ( 12,000 x 5.75 )
Direct Labor ( 12,000 x 1.25 )
Variable O/H ( 12,000 x 0.6 )
Var Selling & Admin Exp ( 12,000 x 0.8 )
= Contribution Margin
- Fixed Expenses
Fixed O/H
Fixed Selling & Admin Exp
= Net Income
192,000
69,000
15,000
7,200
9,600
(100,800)
192,000-100,800
= 91,200
43,000
19,000
Part 3
a.
Direct Materials
+ Direct Labor
+ Variable Overhead
= Variable Product Cost/Unit
IT WONT change because it doesn’t have the variable selling expense
(62,000)
29,200
b.
Direct Materials
+ Direct Labor
+ Variable Overhead
+ Variable Selling
= Variable Cost/Unit
c.
Selling Price/Unit
-Variable Cost/Unit
= Contribution Margin/Unit
d. Contribution Margin Ratio
= P
P
-
V
e.
Fixed Overhead
+ Fixed Sell & Administrative
= Total Fixed Expenses
IT WONT change because it doesn’t have the variable selling expense
Using the five variables above to prepare a Contribution Income Statement, you have
=
=
Sales Revenue
Variable Costs
Contribution Margin
Fixed Costs
Net Income Before Taxes=
$ PQ
- VQ
= CM
- F
Z
Writing this formula from left to right, instead of from top to bottom
PQ - VQ - F = Z
which becomes
(P - V) Q - F = Z which is the basic CVP formula
E16-2, page
Part 1 Sales Commission per unit = Selling Price/unit x Sales Comm %
= 320 * 0.05 = 16
320
Selling Price/Unit
(136)
-Variable Cost/Unit
(DL+DM+DV+Selling Comm)
184
= Contribution Margin/Unit
Part 2
P
V
Q
F
Z
( P
-
=
=
=
=
=
320
136
??
500,000 +116,400 = 616,400
0 at breakeven
V )Q
-
F
=
Z
(320-136)Q – 616,400 = 0
Q = 616,400/184 = 3,350 Units
Part 3.
P
V
Q
F
Z
( P
=
=
=
=
=
320
136
???
616,400
333,408
- V )Q F
=
Z
(320-136)Q – 616,400 =333,408
Q = 949,808/184 = 5,162 Units
For breakeven in Sales Dollars, this formula becomes
PQ
Z + F
P-V
P
=
Z + F
CM %
Since Z is zero at breakeven, then
PQ =
F
CM %
E16-3, page
P
V
Q
F
Z
=
=
=
=
=
90
75.6
??
321,000
0 at breakeven
Part 1.
Selling Price/Unit
-Variable Cost/Unit
= Contribution Margin/Unit
Contribution Margin Ratio
= P
- V
P
= (90-75.6)/90 = 16%
$ 90
75.6
14.4
Part 2 -- For breakeven in Sales Dollars,
PQ
Z + F
Z + F
P-V
Contribution Margin
P
= (0 + 321,000)/0.16 = $ 2,006,250
=
Part 3 -- Sales Dollars needed for a target profit of $100,000,
PQ
Z + F
Z + F
P-V
CM %
P
= (100,000 + 321,000) / 0.16 = $2,631,250
=
After-Tax Profit CVP Analysis
We have two new variables, when looking at AFTER-TAX profit.
P =
V =
Q =
F =
Z =
T = Tax Rate
N = After-Tax Profit
Z - ZT = N
Z ( 1 - T) = N
Z
=
N
1 - T
We want to substitute this value for Z in our basic CVP formula
E16-4, page
P = 275
V = 185
Q
F = 730,000
Z
Part 1 -- Convert After-Tax Profit to Before-Tax Profit.
T = Tax Rate
N = After-Tax Profit
Z
=
N
1 - T
Z = 420,000 / (1 – 0.4) = 700,000
Part 2 Solve for Q to achieve a given After-Tax Profit of $420,000
( P - V )Q F
=
(175 – 185)Q – 730 = 700,000
Q = 15,888.88
Z
Contribution-Margin/Variable Costing Income Statement
Sales Revenue (
x
- Variable Expenses
Direct Materials (
x
Direct Labor (
x
Variable O/H (
x
= Contribution Margin
- Fixed Expenses
Fixed O/H
= Net Income Before Taxes
Income Taxes
= Net Income
)
)
)
)
Operating Leverage is a measure of the extent to which fixed costs are being used in a company. If a
company has a high operating leverage, then profits will be very sensitive to a change in sales.
Degree of Operating Leverage is a measure at a given level of sales of how a % change in sales volume
will affect profits.
Degree of Operating Leverage = Contribution Margin
Net Income
Margin of Safety ( MOS or M/S or MS) is the excess of budgeted (or actual) sales over and above the
breakeven volume of sales. It may be expressed in sales units or sales dollars or as a Percentage.
Margin of Safety = Actual Sales - Breakeven Sales
or
MOS %
= Budgeted Sales - Breakeven Sales
=
Margin of Safety in Dollars (or in Units)
Total Sales Dollars (or Units)
If there is NO change in Costs, then
Change in Net Income = Change in Sales dollars x CM %
Or
= Change in Sales Units x CM / unit
% Change in Net Income = Deg of Oper Leverage x % Change in Sales
E16-6, page
P
V
Q
F
Z
=
=
=
=
=
Part 1 -- Solve for Q
( P - V )Q -
F
=
Z
Part 2 -- Solve for PQ, breakeven in Sales Dollars,
PQ
=
Z + F
P-V
P
Z + F
CM %
Part 3 -- Margin of Safety in Units
Margin of Safety = Actual Sales Units - Breakeven Sales Units
Part 4 -- Margin of Safety in Sales Dollars
Margin of Safety = Actual Sales $ - Breakeven Sales $
E16-8, page
P
V
Q
F
Z
=
=
=
=
=
Part 1
Selling Price/Unit
-Variable Cost/Unit
= Contribution Margin/Unit
Part 2 Breakeven in Sales Units, Q
( P - V )Q F
=
Z
Part 3 Solve for Z, given Q
( P - V )Q F
=
Z
Part 4
MOS in Units = Actual Sales Units - Breakeven Sales Units
MOS in Sales Dollars = Actual Sales $ - Breakeven Sales $
E16-10, page
P
V
Q
F
Z
=
=
=
=
=
Part 1
Selling Price/Unit
-Variable Cost/Unit
= Contribution Margin/Unit
Contribution Margin Ratio
= P
- V
P
Part 2 – Solve for Breakeven in PQ
For breakeven in Sales Dollars, this formula becomes
PQ
=
Z + F
P-V
P
Z + F
CM %
Part 3 – Solve for PQ given a Target Profit of $245,000
Z + F
Z + F
PQ
=
P-V
P
CM %
E16-14, page
P
V
Q
F
Z
=
=
=
=
=
Part 1
Contribution Margin Ratio
= P
- V
P
For breakeven in Sales Dollars/Revenue
PQ
Z + F
P-V
P
=
Z + F
CM %
Part 2
Margin of Safety = Actual Sales - Breakeven Sales
or
= Budgeted Sales - Breakeven Sales
To perform CVP analysis in a multi-product company, one must assume either a constant product sales mix
or an average contribution margin ratio. Sales mix is the relative combination of products being sold by a firm.
Use of an assumed constant mix allows the computation of a weighted average contribution margin ratio for
the package of products being sold. (A package would contain X# units of prod A and Y# units of prod B.)
This weighting process means that the contribution margin ratio of the product making up the largest
proportion of the group has the greatest impact on the average contribution margin of the product mix.
To apply CVP to a multi-product firm, treat the package as a single product. You will need to compute the
package selling price and the variable cost per package. Below is an example of how this is applied.
E16-5
Part 1:
Sales Mix = Ratio of Product 1 to Product 2
Ceiling Fan
Table Fan
Product
Ceiling Fan
Table Fan
Package total
Price/U
nit
$60
$15
Var Cost
/Unit
$12
$7
CM
/Unit
*Sales
Mix
**Pkg Unit
Contrib Mar
*Ratio of Product 1 to Product 2
** CM/unit x Sales Mix
Breakeven in Pkgs =
Total Fixed Costs
Package Total CM
Breakeven in Ceiling Fans = Sales Mix of Ceiling x Breakeven in Pkgs
Breakeven in Table Fans = Sales Mix of Table x Breakeven in Pkgs
Contribution-Margin/Variable Costing Income Statement
Ceiling Fans
Sales Revenue
- Variable Expenses
= Contribution Margin
- Direct Fixed Expenses
= Product Margin
- Common Fixed Expenses
= Operating Income
Table Fans
TOTAL