Chapter 10 CVP ANALYSIS

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

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

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 ?

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

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.

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

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

Cost-Volume-Profit Graph (CVP Chart)

Profit -Volume Graph (PV Chart)

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)

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

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

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

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

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

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

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

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)

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