# MGAB03H3 Chapter Notes -Variable Cost, Operational Risk, Zirconium

Chapter 3 Cost-Volume-Profit Analysis Notes

Cost-Volume-Profit Analysis

x cost-volume-profit (CVP) analysis Æ technique that examines changes in profits in response to changes in sales volumes, costs,

and prices; ;used to identify the levels of operating activity needed to avoid losses, achieve targeted profits, plan future

operations, and monitor organizational performance

x accountants often perform CVP analysis to plan future levels of operating activity and provide information about the following—

(1) which products or services to emphasize, (2) the volume of sales needed to achieve a targeted level of profit, (3) the amount

of revenue required to avoid losses, (4) whether to increase fixed costs, (5) how much to budget for discretionary expenditures,

and (6) whether fixed costs expose the organization to an unacceptable level of risk

Profit Equation and Contribution Margin

x CVP analysis begins with the basic profit equation: Profit = Total revenue – Total costs

x separating costs into variable and fixed categories: Profit = Total revenue – Total variable costs – Total fixed costs

x contribution margin (CM) Æ total revenues minus total variable costs

x contribution margin per unit (CMU) Æ selling price per unit minus variable cost per unit

x both contribution margin and CMU are valuable tools when considering the effects of volume on profit

x CMU tells how much revenue from each unit sold can be applied towards FC or contributed to cover FC

x once enough units have been sold to cover all FC, the CMU from all remaining sales becomes profit

x if the selling price and variable cost per unit are assumed to be constant, then total revenue is equal to price times quantity, and

total variable cost is equal to variable cost per unit times quantity

x the profit equation can then be rewritten in terms of the CMU:

EBT = S × Q – V × Q – F = (S – V) × Q – F

where EBT = Earnings before taxes

S = Selling price per unit

V = Variable cost per unit

(S – V) = Contribution margin per unit (CMU)

Q = Quantity of product sold (units of goods or services)

F = Total fixed costs

x CVP analysis can be performed using either: units (quantity) of product sold or revenues (in dollars)

CVP Analysis in Units

x assuming that FC remain constant, solve for expected quantity of product that must be sold to achieve a target level of profit:

Earnings (profit) equation: EBT = S × Q – V × Q – F = (S – V) × Q – F

Solving for Q: (F + EBT) / (S – V) or CMU = Quantity (units) required to obtain target profit

CVP Analysis in Revenues

x contribution margin ratio (CMR) Æ percent by which the selling price (or revenue) per unit exceeds the variable cost unit, or

contribution margin as a percent of revenue; for a single product, it is: CMR = (S – V) / S

x to analyze CVP in terms of total revenue instead of units, substitute the CMR for the CMU:

Sales revenue = (F + EBT) / ((S – V) / S) = (F + EBT) / CMR

x the CMR can also be written in terms of total sales revenue (TS) and total variable costs (TVC)

x that is, for a single product, the CMR is the same whether computing it using per-unit selling price and VC or using TR and TVC

x thus, the following mathematical formula is the equivalent version of the CVP formula:

Sales revenue = (F + EBT) / ((TS – TVC) / TS)

Breakeven Point

x managers often want to know the level of activity required to break even, which can be determined by a CVP analysis

x breakeven point Æ level of operating activity at which revenues cover all fixed and variable costs and there is no profit

x depending on which formula is being used, the breakeven point can be calculated either in number of units or in total revenues

x set EBT to $0 and input all other data to find the breakeven point either in number of units or in total revenues

Cost-Volume-Profit Graph

x cost-volume-profit (CVP) graph Æ diagram of the relationship between total revenues and total costs; illustrates expected

changes in an organization’s profits under different volumes of activity

CVP with Income Taxes

x an organization’s after-tax earnings are calculated by subtracting income tax from pre-tax earnings

x the tax is usually calculated as a percentage of pre-tax earnings

Earnings after taxes (EAT) = EBT – Taxes = EBT – (Tax rate × EBT) = EBT × (1 – Tax rate)

x to know pre-tax earnings needed to achieve a target level of after-tax earnings, the preceding formula is solved:

EBT = EAT / (1 – Tax rate)

Performing CVP Analyses with a Spreadsheet

x spreadsheets are often used for CVP computations, particularly when an organization has multiple products; and they simplify

basic computations and can be designed to show how changes in volumes, selling prices, costs, or sales mix alter the results

CVP for Multiple Products

x sales mix Æ proportion of different products or services that an organization sells

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## Document Summary

Profit = total revenue total variable costs total fixed costs. N cvp analysis begins with the basic profit equation: N separating costs into variable and fixed categories: N contribution margin (cm) total revenues minus total variable costs. N contribution margin per unit (cmu) selling price per unit minus variable cost per unit. N both contribution margin and cmu are valuable tools when considering the effects of volume on profit. N cmu tells how much revenue from each unit sold can be applied towards fc or contributed to cover fc. V = variable cost per unit (s v) = contribution margin per unit (cmu) Q = quantity of product sold (units of goods or services) Ebt = s q v q f = (s v) q f. N cvp analysis can be performed using either: units (quantity) of product sold or revenues (in dollars)