Chapter 5: Cost-volume-profit relations

assumptions to simplify CVP

1) selling price is constant and will not change with volume. 2) costs are linear and can be divided into variable and fixed elements. VC per unit is constant. 3) for multiproduct companies the mix of products sold remains constant.

factors of CVP analysis

1) selling prices. 2) sales volume. 3) unit variable costs. 4) total fixed costs. 5) mix of products sold

CM ratio and variable expense

CM/sales. [s - variable expenses]/sales CM Ratio = 1 - variable expense ratio

change in variable costs and sales: 1

Expected Total Contribution Margin post change: New Units x New Contribution Margin per unit. Present Total Contribution Margin: Present Units x Present CM per unit Change in Total Contribution Margin: xxxx Assumes no change in fixed costs.

changes in fixed selling price and sales: 1

Expected Total Contribution Margin with Changed Price: New Units x New Contribution margin per unit. Present Total Contribution Margin: Current Units x current contribution margin per unit. Incremental Contribution Margin: the difference of above. Change in Fixed Expenses: Less: incremental expense Total Change in Net operating Income

change in variable, fixed and selling volume

Expected total CM with proposed change: New Units x New CM per unit. Present Total Contribution Margin: Current Units x current CM per unit. Change in Total Contribution Margin. Change in Fixed Expenses: Add/Less change in expenses. Net change in net operating income.

changes in Fixed costs and volume: 1

Expected total contribution Margin: New sales x CM Ratio = New Contribution margin. Present Total Contribution margin: Present sales x CM ratio= xxx. Change in Total CM: the difference of above.

changes in fixed costs and volume: 2

Incremental Contribution Margin: Change in sales x CM ratio = change in CM. Less: added expenses (plus less expenses) . Changed Net operating income

target profit and sales: equation method

Profit = CM Ratio x Sales - Fixed Expenses. set profit to desired level and solve for sales.

target profit analysis: equation method

Profit = Unit CM x Q - FE. set the profit to the desired level.

profit equation with contribution margin

Unit Cm = selling price per unit - variable expense per unit = P -V . Profit = {[price x quantity] - [v x q]} - fixed expenses. Profit = [p - v] x q - fixed expenses. Profit = Unit CM x Q - Fixed Expenses.

determining a price to quote

Variable Cost per unit. Desired profit per unit (profit divided by quantity). Quoted Price: The sum of above. This is used for bulk sales mostly. so the fixed expenses to not come into play.

basic profit equation

[sales - variable expenses] - fixed expenses. Sales = selling price x quantity. Variable Expenses = expenses per unit x quantity. profit = {[price x quantity] - [v x q]} - fixed expenses

structure and profit stability

a higher contribution margin means a more rapid response of profits to sales. lower CM means a greater margin of safety and less volatile.

break even analysis

again break even is the level at which the companies profits are zero. use equation or formula format

break even dollars: equation method

again use the Profit = CM ratio x Sales - Fixed Expenses. Set the profit to zero and find sales.

costs and leverage

all else being held constant a higher relative proportion of fixed costs will mean a higher operating leverage

contribution margin ratio: expanded

allows cost volume profit calculations not visualizations. another column under contribution margin approach. it is the contribution margin divided by the sales. will work even it total or per unit basis.

incremental analysis

an analytical approach that focuses only on those costs and revenues that change as a result of a decision

interpreting the CVP graph

below the intersect point is a loss. above the intersect is a profit.

structuring sales commissions

commissions based on sales dollars can lead to lower profits as it means workers push the higher margin goods which end up selling less. commissions based on contribution margin might encourage a more balanced sales.

percentage change in net operating income

degree of operating leverage x the percentage change in sales

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target profit and sales: formula method

dollar sales to attain a target profit. [Target profit + fixed expenses] / CM ratio.

target profit analysis

estimated sales volume needed to hit a target profit.

margin of safety

excess of budgeted or actual dollar sales over the break even dollar sales.

break even dollars: formula method

fixed expenses divided by the CM ratio

effects of contribution margin ratio

for each dollar change in sales the contribution margin will change parallel to that rate. assuming all else is constant

break even: equation method

goes back to the basic profit equation. either [P-v] x Q - FE or Unit CM x Q - FE. the only trick is to set Profit to zero and solve for the quantity.

margin of safety: expanded

how much we have over the break even. amount sales can drop before we start to see losses. an increase means less risk of incurring a loss.

note on changes of wages

is you see an change from salaries to commissions then both fixed and variables will be affected. again unit contribution margin will change parallel to the change in price per unit or variable cost per unit.

target profit in terms of sales

just as was the case for break even we can find target profit in terms of money as well as quantities. by taking the quantity level times the selling price, equation method, or formula method

verifying CVP analysis

keep in mind that all of these analyses can be verified by making a new IS. sorta like a comparative IS. a reduction in fixed expenses will increase net operating income.

degree of operating leverage

measure at a given level of sales of how a percentage change in sales will effect profits. the degree of operating leverage is the contribution margin divided by net operating income.

operating leverage

measure of sensitivity of the net operating income. sensitivity to a percentage change in dollar sales

variable and fixed costs affects on profits

more FC and less VC means more volatile. Less FC and more VC means stability but less profits in good years.

estimating planned increase on sales and profits

multiply the proposed increase in number of units sold by the contribution margin. say we have zero sales then our total loss is the fixed expenses. each unit sold decreases loss by amount unit CM.

note on change analysis

none of the proposed alternatives need a new income statement to see how the incremental changes affect the relevant terms. only consider what will change. though a new income statement is official required and serves as a good check

note on changes of sales or costs

note that either a decrease in selling price per unit or an increase in variable cost per unit will decrease the contribution margin per unit by the respective amount.

the CM and break even

once the break even quantity has been reached the net operating income will increase by the amount of the unit contribution margin for each additional unit sold.

definition of sales mix

relative proportion products are sold. combo for max profits. want high margin goods to make up relatively large proportion of the mix.

sales mix

relative proportions in which a company's products are sold. found by expressing the sales of each product as a percentage of total sales.

contribution margin

sales minus variable expenses. amount to cover fixed costs and then provide profits. leftovers give profits. if to small we have a loss. when enough units are sold for CM to equal fixed expenses then we break even.

target profit analysis: expanded

sales quantity needed to reach a profit desired. same process as for break even.

operating leverage: expanded

sensitivity of Net income to changes in sales. a bigger leverage means a tiny change in sales has huge effects.

break even: formula method

shortcut of the equation method. idea that each unit sold provides more contribution margin to cover costs. Unit sales to break even = Fixed Expense/ unit contribution margin.

change in profit and CM ratio

the CM ratio times the change in sales minus the change in fixed expenses.

contribution margin ratio

the CM ratio. ratio computed by dividing contribution margin by the dollar sales

cost-volume profit graph

the CVP graph. graph showing relations between revenues, costs, profits on the one hand and sales volume on the other

note on operating leverage

the degree of operating leverage is a measure at any level of sales of a percentage change in sales volume will affect profits

net income and CM ratio

the impact on net operating income of any given dollar change in sales can be completed by applying the CM ratio to the change in dollar sales

break-even point

the level of sales at which profit is zero

margin of safety equation percentage

the margin of safety in dollars divided by total budgeted or actual sales

note on CVP

this analysis is actually quite judgmental. it really only gets you a "good enough" idea of the situation and that is if you are still in the relevant range.

profit graph

this is slightly different then the CVP graph. it only has two lines and is directly based on CM. uses the equation CM x Q - FE is profit. use the equation to find to points on a graph and draw a line back to the origin. then a line parallel to x-axis to signify the quantity of zero profits.

calculating change in CM

this is the CM ratio x the change in sales

use of CM ratio

this ratio is very useful when dollar sales of one product must be weighed against that of another.

estimate profit for X units

to find the estimated profit for any number of units sold above the break even point multiply the number sold in excess of break even by the unit contribution margin. gets you anticipated period profits

margin of safety equation

total budgeted or actual sales minus break even sales.

target profit analysis: formula method

units to attain the target profit is [target profit plus fixed expenses] divided by Unit CM

variable expense ratio

variable expenses divided by the dollar sales

preparing the CVP graph

x-axis is the unit volume. y-axis is the money. 1) draw a line parallel to x-axis to represent total fixed costs. 2) choose a unit sales volume and plot point representing total cost (F + C) at that volume. draw line back to x-o y-fixed 3) choose a new sales volume and plot it. draw line back to origin.

Format of CVP analysis

you always start with a contribution margin format. then you can make it easier on yourself by making new columns to express sales, variable costs and contribution margin on a per unit basis

break even in terms of sales

you can find break even in monetary terms as well. whether by taking the quantity version times the selling price or using the formula and equation method slightly altered.