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# Topic A10: Cost-Volume-Profit Analysis Topic Overview P.1

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1

### Cost-Volume-Profit Analysis

Technology Education Section Curriculum Development Institute

Education Bureau, HKSARG April 2009

Introduction

This session will explore the relationship between costs, revenue, output levels and the resulting profit on situations where the changes in the activity level is relatively small and short run. Students are asked to calculate the sales volumes and profits earned under different scenarios.

Duration

Two 40-minute lessons

Content

Lesson 1 – Cost-Volume-Profit Analysis (i) Lesson 2 – Cost-Volume-Profit Analysis (ii)

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2 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Cost-Volume-Profit Analysis (i)

Lesson 1

Teacher begins lesson by reviewing the CVP analysis. Teacher informs students that a case study about the acquisition of a cake shop will be reviewed to gain a thorough understanding to analyse situations and make decisions.

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3 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### CVP Analysis

The CVP analysis is a key in decision making, including choice of product lines, pricing of products, marketing strategies and utilisation of production facilities.

The CVP analysis is sometimes referred to as a break-even analysis. A break-even analysis shows the relationship among costs, volume, contribution and profits at various levels of activity. The sales volume which equates total revenue with related costs and results in neither profit nor loss is called the break-even point (BEP).

The CVP analysis uses the principles of marginal costing and is best suited for short run issues. It explores the relationship among costs, revenue, output levels and resulting profits and is more relevant where the proposed changes in the levels of activity are relatively small.

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4 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

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### Volume for a target profit

Teacher briefly introduces the terms commonly used in CVP analysis and explains their relationships, for example,

1.Sales – Variable costs – Fixed costs = Profit 2.Contribution = Sales – Variable costs 3.Contribution – Fixed costs = Profit 4.Contribution = Fixed costs + Profit

5.Unit contribution = Unit selling price – Unit variable costs 6.Sales volume * Unit contribution = Fixed costs + Profit

7.Volume to earn a target profit = (Fixed costs + Profit) / Unit contribution 8.Break-even sales volume would results in neither a profit nor loss, i.e.

Profit = 0

9.Break-even point = Fixed costs / Unit contribution

10.Margin of safety = Existing sales volume – Break-even sales volume 11.Rate of return = Profit / Investment

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5 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

### 3. Fixed costs are costs, that in total, remain constant for a specified time period.

It is important to emphasise the basic assumptions as the analysis would be meaningless if the basic assumptions are not sustained.

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6 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

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### Activity 1 : Please help Eric to figure out the annual profit and rate of return of the cake shop.

Brief description of the case:

Your friend Eric Chan has been approached by his best friend Mary Wong, and asked whether he is interested in buying her cake shop. It is a small cake shop selling one very special cake imported from Japan.

Mary is asking for \$600,000 and she says that the annual profit and the rate of return on this investment are \$120,000 and 20% respectively. Eric considers that the profit and the rate of return very attractive but he is weak in accounting. He asks you to show him how the figures of profit and rate of return are arrived at.

This is a typical case in which CVP analysis can be applied. Teacher asks students to follow the steps on the next slide in answering the questions from Eric.

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7 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### 4. Calculate the investment rate of return.

Students can refer to student worksheets pp.1-2 for details and divide into groups to complete the case study

Unit contribution is the revenue remaining after deducting variable costs.

Unit contribution measures the contribution made by each product unit sold to cover the fixed costs and generate business profits. Calculating unit contributions is the first step in most CVP analyses.

Usually, we use the contribution approach in calculating profit.

Refer to the footnote in slide #4 for the formulae in calculating the above figures.

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8 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### 2. Rate of return calculation

One important factor to be considered in making an investment is its rate of return. But before calculating the rate of return, we have to calculate the profit and the amount of investment.

Rate of return = Profit / Investment

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9 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

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### Contribution = Fixed costs

Teacher explains the concept of break-even again before proceeding to Activity 2.

Break-even point is when total revenue equals total costs incurred. It identifies activities required to cover costs but not generating any profits.

The break-even point in units is calculated by dividing total fixed costs by the contribution per unit.

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10 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### Activity 2 : Please advise Eric whether he should buy the cake shop based on the rate of return and the margin of safety.

Teacher tells students that besides the rate of return, another important factor that must be considered is the investment risk.

Margin of safety tells us the “cushion” of losing sales before incurring a loss if the expected sales fails to materialise. If the Margin of safety is low, say below 10%, Eric should not buy the business as the business will incur a loss when there is a drop of sales volume by 10% or more, which is quite risky.

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11 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### 3. Recommendation.

Students stay with their groups and finish student worksheets p.2-3.

Margin of safety indicates by how much sales may decrease before a loss occurs. It represents the difference between the level of sales and the break-even point. It can be expressed in units, sales revenue and percentages. It is the “cushion” before incurring a loss if the expected sales fails to materialise.

Break-even point = Fixed costs / Unit contribution

Margin of safety = Expected sales volume – Break-even sales volume (in units)

Margin of safety = (Expected sales volume – Break-even sales volume) / Expected sales volume (in %)

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12 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### 20%

In this case, The company has a margin of safety of 25%, which means the business will incur a loss if the sales volume decrease by 25% or more.

As Mary states there are many loyal customers, there is a low possibility that the sales volume will drop by this substantial amount and the margin is comfortable.

As the risk of this investment is low and the rate of return is high, students should suggest Eric to acquire the business.

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13 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### Margin of safety as a measure of the risk of incurring a loss.

Return and risk are two important factors in making any investment decisions.

If the return is high but the corresponding risk is very high, most people will not make such an investment. Most investors would like to invest in a business of reasonable return and acceptable risk. There are many risk factors and one important factor is the decrease in sales. Margin of safety measures the risk in this aspect.

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14 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Activity 3 – Another Situation

There is a 20% chance that the supplier will increase the price of each cake from \$6 to

\$7.5, but in Mary’s opinion, the selling price can only be increased by \$1 to maintain the existing sales volume.

Should I buy the cake shop in view of the new information?

Eric is now thinking of another situation. Students are required to follow the similar approach used in Activity 1 and 2 to make recommendations to Eric whether he should buy the cake shop or not.

There are changes in variable costs and the selling price, which leads to a change in unit contribution. Change in unit contribution will then lead to change in break-even point, monthly profit, margin of safety and the rate of return. Students are required to make recommendation based on the figures arrived at in student worksheets p.5-6.

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15 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### 6. Determine the risk of the business and the reasonableness of the return in the new situation.

Teacher asks students to follow the steps on this slide in their calculations.

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16 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### Recommendation

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If the supplier does not increase the price, which is high at an 80% chance, the rate of return and the margin of safety is 20% and 25% respectively.

This is a very good investment with high rate of return and the risk involved is low.

Even if the supplier does increase the price, which is low at a 20% chance, the rate of return and the margin of safety is 10% and 14.29% respectively.

This is still a good investment as the return is reasonable and the risk involved is acceptable with 14% on margin of safety.

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17 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### CVP Analysis when there is a change in selling price and variable cost.

This part shows how selling price and variable cost changes affect the unit contribution, break-even point, profit, rate of return and margin of safety.

This is the fundamental knowledge that students must know in performing a CVP analysis.

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18 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Eric receives a proposal from Mary and you are required to analyse the proposal to determine whether to accept it or not.

Mary

Teacher introduces some information in this case for students to discuss.

Students can refer to student worksheets p.7-8 for details.

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19 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### Should the proposal be implemented ?

Students are required to read the details in student worksheets p.7-8 to see what Eric did.

They detemine problems with Eric’s calculation and help him decide whether he should implement the proposal or not.

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20 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### A fixed cost is a cost that, in total, remains constant for a specified time period.

This is a common mistake made by students.

The relevant cost is the variable cost which will increase as the sales volume increases. Fixed costs are period costs and will not increase when sales volume increases.

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21 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Activity 4 - Correct approach

z The fixed cost \$30,000 per month will not increase even if the sales volume is increased by 10,000 units.

z Correct approach

z Incremental profit

z = 10,000 units * \$4 - \$10,000 = \$30,000 z Recommendation : Implement the proposal

A fixed cost is a cost, that in total, remains constant for a specified time period and will not be affected by the change in sales volume. Here the shopkeepers’ salary, the monthly rental and other fixed costs will remain the same when the sales volume increases by 10,000 units.

The relevant cost is the variable costs which varies linearly with the change in sales volume. The correct approach is to compare the incremental contribution with incremental expenditure to determine whether there is incremental profit or not.

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22 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

### Different behavior of Variable costs and Fixed costs.

z

Students should be aware that only the variable costs, but not fixed costs, are the relevant costs for decision making in this case.

Most of the time, as the variable cost varies with the change in sales volume, we should compare incremental contributions with incremental expenditures in order to determine the profit or loss for decision making.

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23 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

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### CVP analysis used when there are changes in the selling price and variable costs

Teacher concludes the lesson by reviewing the key points learned.

Key points learned include:

1. CVP analysis concerns with analysis within a relevant range and for short run.

2. Costs can be divided into variable and fixed elements.

3. The unit selling price and unit variable cost remain constant.

4. A fixed cost is a cost, that in total, remains constant for a specified time period.

5. The different cost behavior of variable cost and fixed cost.

6. The formulae in calculating profit and break-even point.

To prepare for the next lesson, students must study the questions and answers distributed in this lesson and ask the teacher to clarify areas they do not understand. The case in lesson 1 will continue in lesson 2 and the thorough understanding of the materials in lesson 1 is vital for them to answer questions in lesson 2.

End of Lesson 1

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24 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Cost-Volume-Profit Analysis (ii)

Lesson 2

Teacher starts the lesson by telling students that following the case in Lesson 1, they are continued to help Eric in solving his business problems.

Inform students to ignore the proposal in Activity 4.

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25 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example BAFS Elective Part Learning and Teaching Example

z

### Eric receives a letter from the landlord informing him that the monthly rent will increase by 20%.

Dear Mr. Eric Chan, The monthly shop rent will be increased by 20% if you wish to renew the rental lease which will expire in six months.

Yours faithfully, Landlord

### Advise Eric how it affects the company’s annual profit, rate of return and the risk of this investment.

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26 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### reasonableness of the return in the new situation

This is a very straight forward question and it serves as a warm up exercise for students.

Teacher should encourage students to complete these questions to evaluate how much they have learned in lesson one.

Fixed cost is changed which leads to a change in break-even point, margin of safety, contribution, profit earned and rate of return.

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27 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

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### Advise Eric whether he should carry out his plan.

This is a complicated CVP analysis with changes in all the elements, i.e.

selling price, sales volume, unit variable costs and monthly fixed costs.

Teacher asks students to follow the steps on the next slide in solving this business problem. Students can also refer to student worksheets p.12-14 for details.

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28 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### 4. Make recommendations to Eric.

For Step 1

Teacher asks students to think whether the chocolate mix, baker’s salary and the cost of flyers are variable costs or fixed costs, and then calculate the unit contribution and the monthly fixed costs.

For Step 3

Teacher asks students that annual profit, rate of return and margin of safety should be compared.

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29 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

### Eric phones you one day and says that he would like to earn the same amount of profit as last year’s (\$120,000) and plans to boost sales more by staying in the cake shop on weekends.

z

Students can refer to student worksheet p.15 for details.

In this situation, to determine the required sales units to maintain a certain profit, students should add the target profits with the fixed costs to determine the total amount. Then, they divide this amount by the unit contribution to find out the sales units.

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30 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

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### Form groups of four or five and discuss the qualitative factors to be considered before making the decision.

This is an open-ended question and there are many possible answers.

Students have to think critically and discuss among themselves whether the points they raise are appropriate or not.

Students are required to present their points in front of the class.

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31 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Present the qualitative factors drawn by your group to the class.

Presentation to the class will lead to more discussions and arguments and students will know more limitations of CVP analysis in making decisions.

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32 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### Will the shop keepers ask for a raise of wages in view of the increase in workload?

Students may have other answers and give them credit if their answers are reasonable.

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33 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

### expenditures after the new product has been launched?

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34 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

z

z

z

### Qualitative factors to be considered before making decisions.

Teacher concludes this lesson by reviewing the key points.

Teacher should emphasise that the CVP analysis uses the principles of marginal costing and is best suited to short run problems; it explores the relationship which exists among costs, revenue, output levels and resulting profit and is more relevant where the proposed changes in the levels of activity are relatively small.

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35 Topic A10

CVP Analysis

BAFS Elective Part Learning and Teaching Example

## The End

End of Lesson 2.

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