1. Chapter 10
CVP ANALYSIS

2. Learning Objectives
Distinguish between the general case and a specific case of CVP
Explain the relationship between operating income and net income
Describe the assumptions underlying CVP
Demonstrate three methods for determining the breakeven point and target operating income

3. Learning Objectives
Explain how sensitivity analysis can help managers cope with uncertainty
Illustrate how CVP can assist cost planning
Describe the effect of revenue mix on operating income
Illustrate how CVP can incorporate income taxes

4. Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, operating income as changes occur in the output level, selling prices, variable costs, or fixed costs
How will revenue and costs be affected
If we sell 1,000 more units?
If we raise or lower our selling prices ?
If we expand business into overseas markets ?

5. Basic Relationships Total costs = Fixed costs + Variable costs
= FC + UVC  Q
Operating income = Total revenues - Total costs
= USP  Q - (FC + UVC  Q)
Net income = Operating income - Income taxes
USP = Unit selling price
UVC = Unit variable costs
FC = Total fixed costs
Q = Quantity of output units manufactured and sold
OI = Operating income

6. CVP Assumptions
Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.
The behavior of total revenues and total costs is linear in relation to output units within the relevant range.
The unit selling price, unit variable costs, and fixed costs are known.
The analysis either cover a single product or assumes that a given revenue mix of products will remain constant as the level of total units sold changes.
All revenues and costs can be added and compared without taking into account the time value of money.

7. BREAKEVEN POINT
The breakeven point is that quantity of output where total revenues and total costs are equal, that is , where the operating income is zero
Methods for determining breakeven point
Equation Method
Contribution Margin Method
Graphic Method

8. Contribution Margin Method
Equation Method and
Contribution Margin Method
Operating Income
= Revenues - Variable costs - Fixed costs
OI = (USP  Q) - (UVC  Q) - FC
OI + FC = (USP - UVC)  Q
Q = (OI + FC)/(USP - UVC)
Q* = FC/(USP - UVC)
= Fixed costs/Unit contribution margin

9. Cost-Volume-Profit Graph
(CVP Chart)

10. Profit -Volume Graph (PV Chart)

11. Contribution Margin Contribution Margin(CM)
= Revenues - Variable costs = (USP-UVC)  Q
Unit Contribution Margin(UCM)
= Unit selling price - Unit variable costs
= USP-UVC
Contribution Margin Ratio (C/M Ratio)
= Contribution margin /Revenues
= [(USP-UVC)  Q]/USP  Q
= 1 - (UVC/USP)

12. Target Operating Income
= Revenues - Variable costs - Fixed costs
TOI = (USP  Q) - (UVC  Q) - FC
FC + TOI = (USP - UVC)  Q
Q* = (FC + TOI)/(USP - UVC)
= (Fixed costs + Target Operating Income)
/Unit contribution margin

13. Sensitivity Analysis and Uncertainty
A what-if technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes
In the context of CVP, sensitivity analysis answers such questions as
What will operating income be if the output level
increases by 5% form the original prediction ?
What will operating income be if variable costs per
unit increase by 10% ?
Sensitivity analysis is one approach to recognizing uncertainty

14. Margin of Safety Margin of Safety = Revenues - Breakeven Revenues
How do we increase our M/S ratio ?
Margin of Safety
= Revenues - Breakeven Revenues
= USPQ - { FC/[1 - UVC/USP]}
Margin of Safety (M/S) Ratio
= Margin of Safety/ Revenues
= 1 - { FC/[1 - UVC/USP]}/USPQ

15. Cost Structure and Operating Leverage
= Percentage changes in OI
/Percentage changes in Q
= [OI/OI]/[Q/Q]
= [(USP-UVC)Q]/ [(USP-UVC)Q-FC]
= Contribution Margin/Operating Income

16. Cost Structure and Operating Leverage
DOLX = $40,000/$10,000 = 4
DOLY = $70,000/$10,000 = 7

17. Cost structure determines operating leverage (capital-intensive vs
Cost structure determines operating leverage (capital-intensive vs. labor -intensive production)
R,C
Revenues
Cost-Y
Cost-X Q

18. Effects of Revenue Mix on Income
Revenue mix (sales mix) can be defined as the relative proportion of total units sold(or total sales dollar) which is represented by each of a company’s several product lines
In a multiple-product situation, breakeven point depends on the sales mix
Other thins being equal, for any given total quantity of units sold, if the mix shifts toward units with higher contribution margins, operating income will be higher S2

19. Taxes in CVP Cash BEP EAT = (1-t)[(USP-UVC)Q - FC]
(USP-UVC) Q ={EAT/(1-t)} + FC
Q* = [{EAT/(1-t)} + FC]/(USP-UVC)
Cash BEP
Cash receipts = Cash disbursements
USP Q = FC + UVC Q -Noncash FC
Qcash* = (FC - Noncash FC)/(USP-UVC)

20. 숙 제
10-23
10-27
10-28
10-31