Chapter 8 - Cost-volume-profit relationships

Question 1

1. Distinguish between the general case and a special case of CVP

Answer 1

The general case: many revenue drivers, many cost drivers, various time spans for decisions (short run, long run, product life cycles). The most detailed way of predicting total revenues and total costs, requires extensive analysis, hence it is very time-consuming.

Special case: we assume a single revenue driver (output units) and a single cost driver (output units). Short-run decisions (time span, typically less than one year, in which fixed costs do not change within the relevant range)

Question 2

2. Explain the relationship between operating profit and net profit

Answer 2

Operating profit = total revenues - total costs (variable + fixed costs)

Net profit: is operating profit plus non-operating revenues (such as interest revenue) minus non-operating costs (such as interest cost) minus income taxes. For simplicity, throughout this chapter non-operating revenues and non-operating costs are assumed to be zero.
Hence, net profit = operating profit - income taxes

Question 3

3. Describe the assumptions underlying CVP

Answer 3

1. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.
2. The behaviour of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range.
3. The unit selling price, unit variable costs and fixed costs are known and are constant. (This assumption is discussed later in the chapter and in the appendix to this chapter.)
4. The analysis either covers a single product or assumes that the proportion of different products when multiple products are sold will remain constant as the level of total units sold changes. (This assumption is also discussed later in the chapter.)
5. All revenues and costs can be added and compared without taking into account the time value of money. (Chapter 13 relaxes this assumption.)
6. Changes in the level of revenues and costs arise only because of changes in the number of products (or service) units produced and sold. The number of output units is the only revenue and cost driver.

Question 4

Explain the equation method for determining the breakeven point and target operating profit

Answer 4

Equation method: The income statement can be expressed in equation form as follows:
Revenues – Variable costs – Fixed costs = Operating profit

(USP × Q) – (UVC × Q) – FC = OP
This equation provides the most general and easy-to-remember approach to any CVP situation. Setting operating profit equal to zero in the preceding equation, we obtain the breakeven point.

The equation method can also be used to determine the number of units that has to be sold in order to reach the target profit

revenues-variable costs-fixed costs=target operating profit

Question 5

Explain the contribution margin method for determining the breakeven point and target operating profit

Answer 5

Contribution margin method: an algebraic manipulation of the equation method. Contribution margin is equal to revenues minus all costs of the output (a product or service) that vary with respect to the units of output. This method uses the fact that:
(USP × Q) – (UVC × Q) – FC = OP

Which means that
Q=(FC+OP)/UCM

At the breakeven point, operating profit is, by definition, zero. Setting OP = 0, we obtain:

Breakeven nr.of units=(fixed costs)/(unit contribution margin)=FC/UCM

The calculations in the equation method and the contribution margin method appear similar because one is merely a restatement of the other

A contribution income statement groups line items by cost behaviour pattern to highlight the contribution margin

The contribution method can also be used to determine the number of units that has to be sold in order to reach the target profit

QT=(fixed costs+target operating profit)/(unit contribution margin)=(FC+TOP)/UCM

Question 6

Explain the graph method for determining the breakeven point

Answer 6

In the graph method, we plot the total costs line and the total revenues line. Their point of intersection is the breakeven point

A PV (profit-volume) graph shows the impact on operating profit of changes in the output level
One convenient point (X) is the level of fixed costs at zero output

A second convenient point (Y) is the breakeven point

The PV line is drawn by connecting points X and Y and extending the line beyond Y

A comparison of PV charts representing different what-if possibilities can highlight their effects on operating profit

Question 7

8.9 How can a company with multiple products calculate its breakeven point?

Answer 7

When CVP is applied to a multiple-product firm, it is assumed that there is a constant sales mix of products as the total quantity of units sold changes.

Question 8

8.10 How does an increase in the income tax rate affect the breakeven point?

Answer 8

The presence of income taxes will not change the breakeven point - at the breakeven point profit is zero, i.e. there are no income taxes to be paid
However, other types of tax may affect the breakeven point, e.g. a sales tax paid by the seller that is a fixed percentage of revenues can be treated as a variable cost and hence will increase the breakeven point

Question 9

How do we account for income taxes when determining the target operating profit?

Answer 9

The only change in the equation method of CVP analysis is to modify the target operating profit to allow for income taxes

Target net profit = (Operating profit) – [(Operating profit) × (Tax rate)]
Target net profit = (Operating profit) × (1 – Tax rate)
Operating profit=(target net profit)/(1-tax rate)

So, taking income taxes into account, the equation method yields:

Revenues-variable costs-fixed costs=(target net profit)/(1-tax rate)

Question 10

5. Explain how sensitivity analysis can help managers cope with uncertainty

Answer 10

Sensitivity analysis is 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 profit be if the output level decreases by 5% from the original prediction? What will operating profit be if variable costs per unit increase by 10%? The sensitivity to various possible outcomes broadens managers’ perspectives as to what might actually occur despite their well-laid plans.

Question 11

Explain the margin of safety

Answer 11

Margin of safety: the excess of budgeted revenues over the breakeven revenues. The margin of safety is the answer to the what-if question: If budgeted revenues are above breakeven and drop, how far can they fall below budget before the breakeven point is reached? Such a fall could be due to a competitor having a better product, poorly executed marketing, and so on

We are often interested in the margin of safety as a percentage (Turnover – Turnover at BE)/Turnover = 25%

Question 12

6. Illustrate how CVP can assist cost planning

Answer 12

Sensitivity analysis highlights the risks that an existing cost structure poses for an organisation. This may lead managers to consider alternative cost structures. CVP helps managers in this task.

The risk–return trade-off across alternative cost structures is usefully summarised in a measure called operating leverage. Operating leverage describes the effects that fixed costs have on changes in operating profit as changes occur in units sold and hence in contribution margin.

Organisations with a high proportion of fixed costs in their cost structures, as is the case under option 1 in our example, have high operating leverage. As a result, small changes in sales lead to large changes in operating profits.

Consequently, if sales increase, operating profits increase even more, yielding higher returns. If sales decrease, however, operating profits decline yet more, leading to a greater risk of losses. At any given level of sales, the degree of operating leverage equals contribution margin divided by operating profit.

Question 13

Describe the effect of time horizon on CVP

Answer 13

Effect of time horizon: A critical assumption of CVP analysis is that costs can be classified as either variable or fixed. This classification can be affected by the time period being considered. The shorter the time horizon we consider, the higher the percentage of total costs we may view as fixed.

Question 14

7. Describe the effect of revenue mix on operating profit

Answer 14

Revenue mix: (or sales mix) is the relative combination of quantities of products or services that constitutes total revenues. If the mix changes, overall revenue targets may still be achieved. However, the effects on operating profit depend on how the original proportions of lower or higher contribution margin products have shifted.

Unlike the single product (or service) situation, there is not a unique number of units for a multiple-product situation. This number instead depends on the revenue mix.

Other things being equal, for any given total quantity of units sold, if the mix shifts towards units with higher contribution margins, operating profit will be higher.

Question 15

8.5 Define contribution margin, gross margin, gross margin percentage, contribution margin percentage and variable-cost percentage.

Answer 15

Contribution margin = revenues - all variable costs
Gross margin = revenues - cost of goods sold

Service-sector companies cannot calculate a gross margin as they do not have COGS

Contribution margin percentage = the total contribution margin divided by revenues
Variable cost percentage = total variable costs divided by revenues
Gross margin percentage = the gross margin divided by revenues

Question 16

Explain the differences in contribution margin and gross margin for merchandising sector companies and manufacturing sector companies

Answer 16

The two areas of difference between contribution margin and gross margin for companies in the merchandising sector are fixed cost of goods sold (such as a fixed annual payment to a supplier to guarantee an exclusive option to purchase merchandise) and variable non-cost of goods sold items (such as a salesperson’s commission that is a percentage of sales euros). Contribution margin is calculated after all variable costs have been deducted, whereas gross margin is calculated by deducting only cost of goods sold from revenues.

The two areas of difference between contribution margin and gross margin for companies in the manufacturing sector are fixed manufacturing costs and variable non-manufacturing costs. Fixed manufacturing costs are not deducted from revenues when computing contribution margin but are deducted when computing gross margin. Cost of goods sold in a manufacturing company includes entirely manufacturing costs. Variable non-manufacturing costs are deducted from revenues when computing contribution margins but are not deducted when computing gross margins.

Question 17

8.8 ‘There is no such thing as a fixed cost. All costs can be “unfixed” given sufficient time.’ Do you agree? What is the implication of your answer for CVP analysis?

Answer 17

A critical assumption of CVP analysis is that costs can be classified as either variable or fixed. This classification can be affected by the time period being considered. The shorter the time horizon we consider, the higher the percentage of total costs we may view as fixed. Hence, it is important to acknowledge how the time horizon of a decision affects the analysis of cost behaviour. In brief, whether costs really are fixed depends heavily on the relevant range, the length of the time horizon in question, and the specific decision situation.