# Chapter 4: Cost-Volume-Profit Relationships

Latest Version

Published 3 years ago

Latest Version

Published 3 years ago

### 1) Explain how changes in activity affect contribution margin and operating income.

**Cost-volume-profit (CFP) **analysis helps managers understand the relationships among cost, volume, and profit and how profits are affected by five elements:

- Prices of products
- Volume or level of activity
- Per unit variable costs
- Total fixed costs
- Mix of products sold for multi-product companies.

#### The Basics of CVP Analysis

- Examine changes in activity levels, selling prices, variable costs per units, or fixed costs, and how they affect profits.
**Contribution Income Statement**emphasizes the behaviour of costs and therefore helpful in judging the impact on profits of changes in selling price, cost, or volume.- Used by managers, and
*operating income is*the measure of profit.

#### Contribution Margin

- CM is used to cover fixed expenses, then the remaining is allocated for profits.
- Total Contribution Margin = Sales – Variable cost
- CM per unit = Price – Variable Cost per unit
**Break-even Point –**The level of sales at which profit is zero.- Could be defined as the point where total sales equals total expenses, or as the point where total contribution margin = total fixed expenses.
**Equation Method -**X * Sales per unit – X * VC per unit – FC = 0**Contribution Margin Method -**BEP in units = fixed expense / contribution margin per unit.

### 2) Prepare and interpret a cost-volume-profit graph.

**CVP Graph** – Highlights relationships between revenues, costs, and level of activity presented in graphic form.

#### Preparing the CVP Graph

- The CVP Graph (or Break-even chart) represents unit volume over the x axis and dollars on the vertical y-axis.
- Steps
- Plot the line parallel to the volume axis that represents fixed expenses.
- Plot the line representing total expenses (fixed + variable) at various activity levels.
- Plot the line representing total sales revenues in dollars at various activity levels.

**Interpretation**- Profit/Loss is measured by the vertical distance between the total revenue line (sales) and the total expenses line.
- Break-even point at the intersection of total revenue and total expenses

**Profit graph –**simpler linear form of the CVP graph that plots:- Profit = Unit CM x Q – Fixed Expenses
- Where Q = quantity of items sold.
- Volume on x-axis and profit in dollars on y-axis.
- Break even point at point in which profit = 0.

### 3) Use the contribution margin ratio to compute changes in contribution margin and operating income resulting from changes in sales volume.

#### Contribution Margin Ratio

- CM Ratio – The contribution margin as a percentage of total sales.
**CM RATIO = CONTRIBUTION MARGIN / SALES**- CM ratio = Contribution margin per unit / sales per unit
- The effect on operating income of any dollar change in total sales can be computed by applying the CM ratio to the dollar change.
**Change in CM = CM Ratio x Change in Sales**- The CM ratio is useful when trade-offs must be made between more dollar sales of one product and more dollar sales of another.
- Emphasize products that yield the greatest amount of CM per dollar of sales.

### 4) Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume.

#### Applications of CVP Concepts

**Variable Expense Ratio –**Ratio of variable expenses to sales.*VE Ratio = Variable Expenses / Sales*- Relation of ratios – CM Ratio = 1 – Variable Expense Ratio

#### Important Formulas for Contribution Format Income Statements

**Operating Income =**Unit CM x Q – Fixed Expenses**CM =**Sales – Variable Expenses**CM per unit =**Per unit sales – Per unit variable expenses**CM Ratio =**Total CM / Total Sales or CM Ratio = Per unit CM / Per Unit Sales**Variable Expense Ratio =**Variable Expenses / Sales

#### Changes in Fixed Cost and Sales Volume

- Analysis 1 - Expected Total Contribution Margin = New projected Sales x CM Ratio
**Current Total Contribution Margin**= Current Sales x CM Ratio**Incremental Contribution**Margin = Subtract Current from expected**Change in Fixed Cost:**Less incremental new expense (The amount of money needed to pay for this increase in sales)**Increased Operating Income**= Incremental CM – change in fixed cost.- Analysis 2 -
**Incremental Contribution Margin =**Increase in total sales x CM Ratio **Less Incremental Expense =**change in fixed cost.**Increased Operating Income =**Incremental CM – change in fixed cost.**Incremental Analysis –**an analytical approach that focuses only on those items of revenue, cost, and volume that will change as a result of a decision.- Both methods use IA, which is simpler.

#### Change in Variable Costs and Sales Volume

- For a variable cost change, incremental analysis may be used.
- Analysis -
**Expected Total Contribution Margin with change in variable costs =**(Increased sales x New CM) **Current Total Contribution Margin =**(current sales x old unit CM)**Increase in Total Contribution Margin =**Expected CM – Current CM.

#### Change in Fixed Costs, Selling Price, and Sales Volume

- Analysis -
**Expected Total Contribution Margin with Lower Selling Price =**New Sales number x New unit CM **Current Total Contribution Margin =**Old sales number x old unit CM**Incremental Contribution Margin =**Expected CM – Current CM**Change in Fixed Costs =**Less the incremental expense that has to be paid.**Addition (or Reduction) in Operating Income =**Incremental CM – incremental expense.- If the change in income is negative, the changes should not be made.

#### Change in Variable Costs, Fixed Cost, and Sales Volume

- Variable Cost Analysis -
**Expected Total Contribution Margin with Changes =**New sales x new CM **Current Total Contribution Margin =**Old sales x old CM**Increase/Decrease in Total Contribution Margin =**expected CM – old CM.- Fixed Cost Analysis
**Change in fixed costs -**Add cost avoided.**Increase/Decrease in Operating Income =**Sum of increase/decrease in CM and change in fixed cost.

#### Importance of the Contribution Margin

- CVP analysis seeks the most profitable combination of variable costs, fixed costs, selling price, and sales volume.
- The best way to improve profits – increase total CM by reducing selling price (increases volume) and sometimes by trading off variable and fixed costs with changes in volume.

#### Cost-Volume-Profit Analysis

- Changes affecting:
- Selling price per unit
- Variable Unit Costs
- Fixed Cost
- Volume
- Decision Rule
*Make Change if:*Increase in CM > increase in fixed cost.- Decrease in CM < decrease in fixed costs.
*Don’t Make Change if:*Increase in CM < increased in fixed cost.- Decrease in CM > Decrease in fixed costs.

**Unit CM** and CM ratio are significant towards the actions a company is willing to take to improve profits.

### 5) Compute the break-even point in unit sales and sales dollars.

#### Break-Even Computations

- Designed to answer questions of “safety nets,” how far sales could drop, etc.
*Derivation -*Contribution Format Income Statement in equation form- Profits = (Sales – Variable Expenses) – Fixed expenses
- Or -
**Profits [P x Q] – [VC x Q] – Fixed Expenses** - Where P = selling price per unit, Q = number of units sold; VC = variable costs per unit.
- Further simplified:
**Profits = [CM x Q] – Fixed Expenses** - At break-even, profits are zero. Therefore, total contribution margin must equal total fixed expenses.
**Break-even point in units sold = Fixed Expenses / Unit Contribution Margin**- Variation:
*Break-even point in total sales dollars = Fixed Expenses / CM Ratio* - You can get break-even point in sales dollars by multiplying the break-even level of unit sales by selling price per unit.

### 6) Determine the level of sales needed to achieve a desired target profit.

#### Target Operating Profit Analysis

- CVP formulas can be used to determine sales volume needed to achieve a
**target operating profit.** **Derivation**- Utilize the simplified profit equation: Profits [P x Q] – [VC x Q] – Fixed Expenses but include the target operating profit.**Rearranged**-**Units sold to attain target = (Fixed expenses + target operating profit) / Unit contribution margin****Check**- Substitute the computed amount of units into the profit equation.**Dollar Sales to attain target profit = (Fixed Expenses + target Operating Profit) / CM Ratio**- Alternative Solution: Number of products required to achieve target x selling price

#### After-Tax Analysis

- Operating profit after taxes can be computed as a fixed percentage of income before taxes.
**Income Taxes -**tax rate (t) x operating profit before taxes (B)- Derivation of After-Tax Profit - Profit after taxes = Before-tax profit – Taxes
- Profit after taxes
**=**B – t(B) **Profit after taxes = B(1-t)****Income Before Taxes: B = Profit after taxes / (1-t)**- For target profit with tax rate incorporated:
**(Fixed Expenses + [Target after-tax profit / 1 – Tax rate]) / Unit Contribution Margin**

#### Single-Product CVP Analysis

**Break-Even****Units**- Break-even point in units sold = Fixed Expenses / Unit Contribution Margin**Sales Dollars**- Break-even point in total sales dollars = Fixed Expenses / CM Ratio**Target Operating Profit****Units**- Units sold to attain target profit = (Fixed expenses + [Target after-tax profit / 1 – Tax Rate]) / Unit Contribution Margin**Sales Dollars**- Units sold to attain target profit = (Fixed expenses + [Target after-tax profit / 1 – Tax Rate]) / CM Ratio

### 7) Compute the margin of safety and explain its significance.

#### The Margin of Safety

**Margin of Safety –**Excess of budgeted (or actual) sales over the break-even volume of sales.- States the amount by which sales can drop before losses begin to occur.
- Higher margin of safety = lower risk of not breaking even.
**Margin of Safety - Total Budgeted (or Actual) sales – Break-even sales****Margin of safety percentage = Margin of Safety in dollars / total Budgeted (or actual) sales.**

### 8) Explain Cost structure, compute the degree of operating leverage at a particular level of sales, and explain how operating leverage can be used to predict changes in operating income.

#### Cost Structure and Profit Stability

**Cost Structure – **Relative proportion of fixed and variable costs incurred by an organization.

- It has latitude in trading off fixed and variable costs. Different cost structures have advantages and disadvantages.

**Generally:**

*High fixed costs and low variable costs*= wider swings in operating income as sales change – greater profits in good years and greater losses in bad years.*Low fixed costs and higher variable costs*= greater operating income stability and protected from losses during bad years at the cost of lower operating income in good years.

#### Operating Leverage

**Operating Leverage –**A measure of how sensitive operating income is to a given percentage change in sales.**Degree of Operating Leverage –**A measure, at a given level of sales, of how a percentage change in sales volume will affect profits.- Degree of Operating Leverage = contribution margin / operating income
- Operating income grows x times as fast as its sales, where x is degree of OL.
- To find
**percentage change in operating income,**take degree of operating leverage x change in sales. - Greatest at sales levels near break-even point and decreases as sales and profits rise.

#### Indifference Analysis

- CVP Analysis aids in decision-making for comparative profitability of alternatives.
- Relative profitability depends on activity levels.
- Product with
**higher fixed costs requires a higher sales activity level**than a product with low fixed costs and high variable costs. - To calculate the point at which a company is indifferent about two different cost systems, use an indifference analysis.
- Determine the unit CM multiplied by the number of units (Q) minus the total fixed costs of each alternative.
- Unit CM x Q – total cost = Unit CM (alternative) x Q – total cost (alternative)
- Set up an equation with each alternative on opposite sides of the equal sign.
- Solve for Q, the indifference point.
- At sales below the indifference point, profitability is lower for the option with lower CM.
- At sales above the indifference point, profitability is higher for the option with higher CM.

### 9) Compute the break-even point for a multi-product company and explain the effects of changes in the sales mix on the contribution margin and the break-even point.

#### Sales Mix

**Sales Mix –**The relative proportions in which a company’s products are sold.- Sales mix - Sales of each product as a percentage of total sales.
- Managers try to achieve the combination or mix that yields the most profits.
- Profits are
**greater**if**high-margin items**make up a large proportion of sales. - Changes in sales mix causes variation in profits, independent of sales volume.

#### Sales Mix and Break-Even Analysis

- With more than one product, break-even analysis depends on the mix in which the products are sold.
- Analysis can be done in units or sales dollars.
- Calculate Number of Units of product that must be sold to break even.
- Total number of units to break even x Sales Mix percentage
- Calculate Sales in dollars of each product that must be sold to break even.
- Previous answer x cost per unit.
- Sales mix changes - Break even point changes.

#### Assumptions of CVP Analysis

- Assumptions underlie CVP analysis.
- Selling price is
**constant**throughout the entire relevant range. Price of a product/service doesn’t change as volume changes. - Costs are
**linear**throughout the entire relevant range and can be accurately divided into**variable and fixed elements.** - Variable costs per unit are
**constant**and fixed costs are**constant**in total over the entire relevant range. - In multi-product companies, the sales mix is constant.
- In manufacturing companies, inventories
**do not change**. The number of units produced = number of units sold.

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