C.1. Cost-Volume-Profit (CVP) Analysis

Question 1

What is Cost-Volume-Profit (CVP) analysis primarily used for?

Answer 1

Short-term decision-making.

CVP analysis helps determine the level of production and sales required to break even or achieve a specific profit level by examining the relationship among revenue, costs, and profits.

Question 2

What assumptions are made in CVP analysis?

Answer 2

• All costs are either variable or fixed.
• Total costs and revenues are predictable and linear within the relevant range.
• Changes in revenues and costs arise only from changes in units produced and sold.
• Fixed costs remain constant over the relevant range.
• Unit variable costs remain constant over the relevant range.
• Inventory levels do not change.
• The unit selling price remains constant.
• A constant sales mix is assumed.
• The time value of money is ignored.

These assumptions simplify the analysis by excluding variations such as discounts for bulk purchases or changes in selling prices.

Question 3

What is the contribution margin?

Answer 3

The amount of revenues minus variable costs available to cover fixed costs.

Once fixed costs are covered, further increases in the contribution margin from increased sales volume flow straight to operating income.

Question 4

How is the unit contribution margin calculated?

Answer 4

Selling price per unit minus variable cost per unit

The unit contribution margin represents the contribution to covering fixed costs and generating operating income from each unit sold.

Question 5

What is the contribution margin ratio?

Answer 5

Unit Contribution Margin divided by Unit Selling Price

This ratio indicates the percentage of sales revenue that contributes to covering fixed costs and generating operating income.

Question 6

How is the breakeven volume in units calculated?

Answer 6

Total Fixed Costs / Unit Contribution Margin

This calculation determines the number of units that must be sold to cover fixed costs and break even.

Question 7

How is the breakeven sales revenue calculated?

Answer 7

Total Fixed Costs / Contribution Margin Ratio

This calculation determines the amount of revenue required to cover fixed costs and break even.

Question 8

What is the significance of the relevant range for an activity?

Answer 8

It is a level between a designated minimum and maximum within which a specific related amount of revenue or cost expectations are valid.

Within the relevant range, fixed costs are expected to remain constant, but outside this range, they may change.

Question 9

True or False:

In CVP analysis, all costs are considered variable in the long term.

Answer 9

True

Over the long term, all costs can be adjusted, making them variable.

Question 10

What is the meaning of the breakeven point in terms of operating income?

Answer 10

The number of units or the sales revenue level where operating income is zero.

At the breakeven level, taxable operating income is assumed to be zero, so no income tax is due on operating income.

Question 11

How is the required sales volume in units that is needed to achieve a target pretax operating income calculated?

Answer 11

(Total Fixed Cost + Target Pretax Operating Income) / Contribution Margin Per Unit

Question 12

How is the required sales revenue for a target pretax income calculated?

Answer 12

(Total Fixed Cost + Target Pretax Income) / Contribution Margin Ratio

Question 13

What is the formula for the unit contribution margin ratio?

Answer 13

Unit Contribution Margin / Selling Price per Unit

Question 14

How is the target pretax operating income equivalent to a target after-tax operating income calculated?

Answer 14

Target After-Tax Operating Income / (1 – Tax Rate)

Question 15

What is the formula for the adjusted contribution margin per unit, used in calculating the sales volume (units) and sales revenue required to achieve a target operating income as a percentage of revenue?

Answer 15

Adjusted contribution margin per unit = Selling Price Per Unit − Variable Cost Per Unit − Target Pretax Operating Income Per Unit

Question 16

How is the sales volume required to achieve a target pretax operating income as a percentage of sales revenue calculated?

Answer 16

1. Target Pretax Operating Income Per Unit = Target Pretax Operating Income % of Revenue × Selling Price Per Unit
2. Adjusted Contribution Margin Per Unit = Selling Price Per Unit – Variable Cost Per Unit – Target Pretax Operating Income Per Unit
3. Sales Volume Required to Achieve the Target Percentage of Revenue as Pretax Operating Income = Total Fixed Cost / Adjusted Contribution Margin per Unit

Question 17

How is the sales revenue required to achieve a target pretax operating income as a percentage of sales revenue calculated?

Answer 17

1. Target Pretax Operating Income Per Unit = Target Pretax Operating Income % of Revenue × Selling Price Per Unit
2. Adjusted Contribution Margin Per Unit = Selling Price Per Unit – Variable Cost Per Unit – Target Pretax Operating Income Per Unit
3. Adjusted Contribution Margin Ratio = Adjusted Contribution Margin per Unit / Selling Price
4. Revenue Required to Achieve the Target Percentage of Revenue as Pretax Operating Income = Total Fixed Cost / Adjusted Contribution Margin Ratio

Question 18

How is the required sales volume (units) for an after-tax operating income as a target percentage of revenue calculated?

Answer 18

1. Target After-tax Operating Income per unit = Target After-Tax Operating Income % of Revenue × Selling Price Per Unit
2. Pretax Operating Income Per Unit Equivalent to Target After-tax Operating Income Per Unit = Target After-Tax Operating Income Per Unit / ( 1 – tax rate)
3. Adjusted Contribution Margin Per Unit Required = Selling Price Per Unit – Variable Cost Per Unit – Target Pretax Operating Income Per Unit
4. Sales Volume (Units) Required to Achieve the Target After-tax Operating Income as a Percentage of Revenue = Total Fixed Cost / Adjusted Contribution Margin Per Unit

Question 19

What is the formula to calculate the target after-tax operating income per unit, used in calculating the required sales volume (units) for an after-tax operating income as a target percentage of revenue?

Answer 19

Target After-Tax Operating Income % of Revenue × Selling Price Per Unit

Question 20

How does increasing marketing costs affect the required sales volume?

Answer 20

Increasing marketing costs increases fixed costs, which will in turn increase the number of units required to earn the required operating income.

Question 21

What is the formula to calculate the revised sales volume required to achieve the target operating income with a proposed new marketing program that will increase fixed costs?

Answer 21

(Present Fixed Costs + Proposed Marketing FC + Target Pretax Operating Income) / Contribution Margin per Unit

Question 22

What is the impact on the contribution margin per unit of reducing the selling price?

Answer 22

Reducing the selling price decreases the contribution margin per unit.

Question 23

What must a company consider when deciding whether to reduce prices to increase sales?

Answer 23

• Whether the increased sales volume will outweigh the decreased revenue per unit.
• Potential changes in fixed costs due to increased volume.
• Possibility of obtaining quantity discounts on materials.
• Ability to raise prices again in the future.

Question 24

What is the sales mix in CVP analysis?

Answer 24

The percentage of sales that each product or service represents of total sales.

Question 25

How is the breakeven volume for a company selling multiple products calculated?

Answer 25

Fixed Costs / Weighted Average Unit Contribution Margin ## Footnote Use as weights the total units sold of each product as a percentage of the total units sold of all products.

Question 26

What assumption is made about the sales mix in breakeven analysis for multiple products?

Answer 26

A constant sales mix is assumed, leading to only one breakeven point.

Question 27

How is the weighted average contribution margin per unit calculated when calculating the breakeven volume when more than one item is sold?

Answer 27

Weighted average contribution margin per unit = (Percentage of Product A × Contribution Margin of A) + (Percentage of Product B × Contribution Margin of B) ) . . . + (Percentage of Product K × Contribution Margin of K)

Question 28

How is the breakeven volume calculated for a multiple-product company when using baskets of goods to do the calculation?

Answer 28

Imagine a basket of goods containing both (or all) products in the given proportions. 1. Calculate the total contribution margin per basket by summing the contribution margins of each product in the basket. 2. Breakeven Number of Baskets = Fixed Costs / Total Contribution Margin Per Basket 3. Multiply the number of units of each product in one basket by the number of breakeven baskets to find the breakeven number of units of each product.

Question 29

What is a "**composite unit**" in breakeven analysis for a multiple-product company?

Answer 29

Another way of expressing the number of "baskets of sales" required to break even.

Question 30

How is the total contribution margin for one composite unit calculated?

Answer 30

Sum the contribution margins of each product in the composite unit.

Question 31

How is the breakeven sales revenue for each product in a multi-product company calculated?

Answer 31

1. Calculate the contribution margin and contribution margin ratios for each of the products. 2. Calculate the weighted average contribution margin ratio per unit for the product mix: (Percentage of Total Revenue for A × Contribution Margin Ratio of A) + (Percentage of Total Revenue for B × Contribution Margin Ratio of B) . . . + (Percentage of Total Revenue for K × Contribution Margin Ratio of K) 3. Calculate the total breakeven revenue: Fixed Costs / Weighted Average Contribution Margin Ratio Per Unit for the Product Mix 4. Apply each product’s percentage of the total revenue to the total breakeven revenue.

Question 32

What is the effect of a change in sales mix on operating income?

Answer 32

Operating income can change even if total revenue does not change, depending on the contribution margins of each product in the mix.

Question 33

In a multiple-product firm, how does an increase in the proportion of higher contribution margin per unit items affect breakeven sales volume?

Answer 33

The weighted average contribution margin per unit will also increase, causing the breakeven sales volume to decrease.

Question 34

In a multiple-product firm, how does a decrease in the proportion of higher contribution margin ratio items affect breakeven sales revenue?

Answer 34

The weighted average contribution margin ratio per unit will decrease, causing the breakeven sales revenue to increase.

Question 35

In a multiple-product firm, what happens to the breakeven points in sales volume and sales revenue if the sales mix changes?

Answer 35

The breakeven points in sales volume and sales revenue will also change.

Question 36

In a multiple-product firm, what happens to the breakeven point in total sales revenue if a product with a higher contribution margin ratio increases in proportion to those with lower contribution margin ratios?

Answer 36

The weighted average contribution margin ratio per unit will increase, causing the breakeven point in total sales revenue to decrease.

Question 37

In a multiple-product firm, what are the effects on breakeven volume and breakeven sales if a product with a higher contribution margin ratio but a lower contribution margin per unit increases in proportion to the other products?

Answer 37

The breakeven revenue will decrease but the breakeven volume will increase.

Question 38

Define **risk** in the context of CVP analysis.

Answer 38

Risk relates to the probability that an outcome has been predicted correctly. As the probability of an event’s occurring nears 100%, the amount of risk decreases, and vice versa.

Question 39

What is **uncertainty** in CVP analysis?

Answer 39

It occurs when there is no basis to draw a conclusion about an outcome one way or another.

Question 40

What is **sensitivity analysis** in CVP analysis?

Answer 40

A method of dealing with uncertainty. One assumption at a time is changed, leaving the other assumptions unchanged, and the resulting change in income is evaluated.

Question 41

What is the margin of safety?

Answer 41

The excess amount of actual or planned sales over the breakeven level of sales.

Question 42

How is the margin of safety ratio calculated?

Answer 42

Margin of Safety Ratio = Margin of Safety / Actual or Planned Sales

Question 43

What is expected value in decision models?

Answer 43

A weighted average of possible outcomes using the probabilities of the outcomes as weights.

Question 44

What is the deterministic approach to determining the outcome to use in a decision model when there are several possible outcomes?

Answer 44

The deterministic approach involves using the single most likely outcome in the decision model.

Question 45

What is the process for choosing between two cost options by finding the variable amount at which the two options are equal?

Answer 45

Create two cost functions, one for each option, with the same variables and using the same variable on the right side of both functions. Set the left sides of the equations equal to each other, and solve for the unknown that is common to both. The solution is the variable amount at which the two options are equal.

Question 46

What is the purpose of CVP analysis in choosing between two production options?

Answer 46

CVP analysis helps determine the level of revenue or units of output at which a company will be indifferent to available options, meaning the operating income under each choice is the same.

Question 47

What is the process for solving for the single level of sales revenue where operating incomes are the same for two products?

Answer 47

Create an equation representing one product’s operating income on one side of the equals sign and the other product’s operating income on the other side of the equals sign. Use the same variable (R) for Revenue on both sides of the equation. Multiply the contribution margin ratios of each product by the product’s revenue and subtract its fixed costs. Solve for R, the unknown quantity that is the same for both products and that equates the operating incomes on the two sides of the equation.

Question 48

What is the process for solving for the single sales volume (units) where operating incomes are the same for two products?

Answer 48

Create an equation representing one product’s operating income on one side of the equals sign and the other product’s operating income on the other side of the equals sign. Use the same variable for the quantity sold (V) on both sides of the equation. Multiply the contribution margin per unit for each product by its volume and subtract its fixed costs. Solve for the unknown quantity (V) that is the same for both products and that equates the operating incomes on the two sides of the equation.

Question 49

Breakeven analysis can be used when determining whether to use fixed versus variable inputs in production. What is the meaning of the "**indifference point**" when choosing between using higher fixed costs and lower variable costs, or lower fixed costs and higher variable costs?

Answer 49

It is the volume at which the two given options are equally favorable.

Question 50

How is the indifference point determined between two machines that can do the same job, but one machine costs more while requiring less labor, and the other machine costs less and is more labor intensive?

Answer 50

Use two cost functions and set the left sides equal to one another. Quantity is the variable, because the objective is to identify the production quantity that will fulfill both equations and make them result in the same amount of total cost. Solve for the variable used for the quantity.

Question 51

In making product mix decisions under resource constraints, when one or more factors of production are limited in some way, how should a company operating at full capacity maximize operating income?

Answer 51

By maximizing the contribution margin per unit of the constrained resource. Assuming the company can sell all the products it manufactures, that is accomplished by giving priority in manufacturing to the product or products with the highest contribution margin per unit of the constrained resource.

Question 52

What should a company consider when deciding which product to produce under a machine hour constraint?

Answer 52

The company should give priority to producing the product that provides the highest contribution margin per machine hour required, assuming the company can sell all the products it manufactures.