Chapter 9
Cost Volume Profit
Variable definitions (notation)
X – number of units
USP – Unit Selling Price
UVC – Unit Variable Cost
UCM – Unit Contribution Margin
FC – Fixed Cost
TR – Total Revenue = USP * X
TC – Total Costs
VC – Total Variable Costs = UVC * X
CMR – Contribution Margin Ratio (a.k.a. Contribution Margin
Percentage)
BEP – Break Even Point
TOI – Target Operating Income
TNI – Target Net Income
t – tax rate
Basic assumptions:
1)
2)
3)
TC = FC + UVC * X
TC and TR are linear in X
Single product assumption
Definitions
CM
CMR
UCM
Break-Even Point
Target Net Income and taxes
Miscellaneous other CVP issues
Decision making
Operating leverage
Margin of safety
Sales Mix
Contribution Margin versus Gross Margin
Appendix – CVP under uncertainty
Example 1
ECAT manufactures printed circuit boards, which sell for $4 per board. They have
variable costs of $2 for each board produced (including materials and variable overhead
costs) and fixed costs of $100,000 per month. Currently they are selling 60,000 boards
per month.
a.
b.
c.
d.
e.
What is ECAT’s break-even in units? What is their break-even in dollars?
What is their current operating income (before taxes)?
How many boards must they sell in order to earn $100,000 before taxes?
How many boards must they sell in order to earn $90,000 after taxes?
Suppose ECAT is selling 60,000 units and that the selling price is fixed at $4.
What unit variable cost must they achieve in order to earn operating income of
$35,000?
Example 2
Suppose ECAT can spend $10,000 on advertising and increase sales by 10% (above the
60,000 level).
a. Should ECAT purchase the advertising?
b. What is the minimum increase in sales to make this investment worthwhile?
Example 3
Suppose that ECAT can reduce the selling price by 10% and increase sales by 10,000
units. Should they reduce the selling price?
Example 4
Suppose ECAT can choose from the following two operating cost structures:
UVC1 = $1 FC1 = $100,000
UVC2 = $3 FC2 = $30,000
If the USP is $4, what is the optimal structure at various levels of activity and sales?
Example 5
Suppose that ECAT makes two products PB1 and PB2. They have selling prices of $4
and $6 per board respectively and unit variable costs of $1 and $2 respectively. For
every 10 units of PB1 that ECAT sells, they sell 6 units of PB2. How many units of PB1
and PB2 must ECAT sell in order to break-even?
Example 6
Watco sells electric motors. The unit variable cost of each motor is $45. The unit selling
price of each motor is $70. The fixed costs are $450,000. Watco is currently selling
20,000 electric motors.
What is their break-even point in units? In dollar sales?
FC
450,000
=
= 18,000
UCM
25
= 18, 000 * 70 = $1, 260, 000
X BE =
TRBE
Should they buy advertising for $100,000 in order to increase sales by 10%?
Increase in sales is 2,000 units. That has a CM of 2,000 * 25 = $50,000. Since this is
less than the cost of $100,000, they should not buy the advertising.
What is the minimum percentage increase in sales that would be required in order
to make the advertising worthwhile?
Increase in sales is D units (I just made up the D) which provides D*25 in contribution
margin. That must at least cover $100,000, so D must be at least 4,000 units.
4,000
= 20% .
20,000
Suppose that Watco can buy a machine that costs $200,000 and decrease unit
variable costs to $30. What is the minimum number of units that Watco must sell in
order to make this investment worthwhile?
Current profit is $50,000. New UCM = $40. New FC = $650,000.
$40 * X − $650, 000 = $50, 000
$700, 000
X=
= 17, 500 units
$40
Suppose Watco can decrease selling price by 10% and increase unit sales by 20%,
should they reduce their selling price?
New USP = $63. New UCM = 18. New X is 24,000.
18*24,000 - $450,000 = ( $18,000 ) , so clearly they should not do so.