CMA311S – NOTES 2010. UNIT 1: COST-VOLUME-PROFIT ANALYSIS
Example 1: Tokio Ltd manufactures and sells only one product. The product is sold at N$10 per unit. Other
details are as follows:
Variable cost per unit
N$5
Fixed cost per month
N$20 000
Normal sales per month
6 000 units
Required:
1.
2.
3.
4.
5.
6.
7.
8.
8.1
8.2
Calculate the contribution per unit.
Calculate the contribution ratio (P/V ratio).
Calculate the break-even point in units.
Calculate the break-even point in sales value (N$).
Calculate the margin of safety and the margin of safety ratio.
Draw a break-even graph which clearly indicates the break-even point.
Calculate the net profit per month if 5 000 units are sold.
Suppose the variable cost increases to N$6 per unit and the fixed cost decreases to N$18 000.
Calculate how many more units have to be sold in order to break-even.
Calculate the number of units to be sold in order to earn a net profit of N$7 500 per month.
Solution to Example 1
1.
Contribution per unit = Selling price per unit – variable cost per unit
= N$10 – N$5
= N$5
2.
Contribution ratio = Contribution per unit ÷ Selling price per unit
= N$5 ÷ N$10
= 0,5 (or 50%)
3.
Break-even point (in units) = Fixed cost ÷ Contribution per unit
= N$20 000 ÷ N$5
= 4 000 units
4.
Break-even point (in sales value) = Fixed cost ÷ Contribution ratio
= N$20 000 ÷ 0,5
= N$40 000
OR
Break-even point (in sales value) = Break-even units x Selling price per unit
= 4 000 x N$10
= N$40 000
5.
Margin of safety (in units) = Sales – Break-even sales
= 6 000 – 4 000
= 2 000 units
OR
Margin of safety (in sales value) = Sales – Break-even sales
= N$60 000¹ – N$40 000
= N$20 000
¹ Normal sales = 6 000 units x N$10
Margin of safety ratio = (Margin of safety ÷ Sales) x 100%
= (2 000 ÷ 6 000) x 100%
1
= 33,3%
OR
Margin of safety ratio = (Margin of safety ÷ Sales) x 100%
= (N$20 000 ÷ N$60 000) x 100%
= 33,3%
6.
Graphical presentation of break-even point (break-even graph, break-even chart):
Costs and revenue (N$’000)
Y
Profit area
60
Sales revenue
Break-even point
40
Total cost line
Margin of
Safety
Loss area
Variable cost
20
Fixed cost
0
1
2
3
4
5
6
X
Units of Production and Sales (‘000)
7.
Sales revenue (5 000 units x N$10)
– Variable cost (5 000 units x N$5)
= Contribution
– Fixed cost
= Net profit (net income)
N$50 000
N$25 000
N$25 000
N$20 000
N$ 5 000
8.1
Break-even sales (in units) = Fixed cost ÷ Contribution per unit
= N$18 000 ÷ N$4
= 4 500 units
New break-even point (4 500 units) less Previous break-even point (4 000 units)
= Difference (500 units)
Thus: the company will have to sell 500 more units in order to break even.
8.2
If the company sells 4 500 units, the profit is zero (break-even point). However, for every additional
unit in excess of 4 500, the profit is N$4. Therefore, in order to show a profit of N$7 500, the
company will have to sell an additional 1 875 units per month (N$7 500 ÷ N$4).
Contribution chart
This is an alternative presentation of the break-even point. In this case the variable cost line is drawn first.
The fixed costs are represented by the difference between the total cost line and the variable cost line, with
2
the result that the total cost line is parallel to the variable cost line. The advantage of this form of
presentation is that the total contribution is emphasised in the graph, and is represented by the difference
between the total sales revenue line and the total variable cost line.
Profit area
Y
Costs and Revenue (N$’000)
60
Sales revenue
Break-even point
Total cost
40
Loss area
Fixed cost
Margin of
Safety
20
1
0
2
3
4
Variable cost
5
6
X
Units of Production and Sales (‘000)
Profit-volume graph
The break-even and contribution charts above do not highlight the profit or loss at different volume levels.
To ascertain the profit or loss figures from a break-even chart, it is necessary to determine the difference
between the total-cost and total-revenue lines. The profit-volume graph is a more convenient method of
showing the impact of changes in volume on profit. The horisontal axis represents the various levels of sales
volume, and the profits and losses for the period are recorded on the vertical scale.
Y
20
Break-even point
Profit
(N$’000)
Loss area
Profit area
10
0
1
2
3
4
10
5
Units of Production and Sales
Loss
(N$’000)
20
Y1
3
6
X
Expected profit after tax: Example 2
Easysteam Ltd manufactures and sells steam irons. The irons sell at N$190 per unit and the variable costs
amount to N$81,70 per unit. The company’s fixed costs are N$108 000 per year and the current tax rate is
35%.
Required:
Calculate what the company’s sales value (N$) must be if management expects a net income of N$125 000
after income tax.
Solution to Example 2
Required sales value =
Fixed costs + [Expected after-tax profit ÷ (1 – Tax rate)]
Marginal income ratio
=
N$108 000 + [N$125 000 ÷ (1 – 0,35)]
N$108,30 ÷ N$190
=
N$108 000 + (N$97 500 ÷ 0,65)
0,57
N$108 000 + N$192 308
=
0,57
N$300 308
= 0,57
= N$526 856
Activity 1:
A summary of a manufacturing company’s budgeted profit statement for its next financial year, when it
expects to be operating at 75% of capacity, is given below:
(N$)
Sales 9 000 units at N$32
Less: Direct materials
Direct wages
Production overhead:
Fixed
Variable
Gross Profit
Less: Administration, selling
And distribution costs
Fixed
Varying with sales volume
Net profit
(N$)
288 000
54 000
72 000
42 000
18 000
186 000
102 000
36 000
27 000
63 000
39 000
Required:
1.1
1.2
Calculate the break-even point in units and in N$-value
Draw a contribution (profit-volume) graph which indicates what profit could be expected if the
company operated at full capacity.
1.3
1.3.1
It has been estimated that:
if the selling price per unit were reduced to N$28, the increased demand would utilise 90% of the
company’s capacity without any additional advertising expenditure; and
4
1.3.2
to attract sufficient demand to utilize full capacity would require a 15% reduction in the current
selling price and a N$5 000 special advertising campaign.
You are required to present a statement showing the effect of the two alternatives compared with the
original budget and to advise management which of the three possible plans should be adopted, i.e.
the original budget plan or 10.4.1 above or 10.4.2 above.
1.4
An independent market research study shows that by spending N$15 000 on a special advertising
campaign, the company could operate at full capacity and maintain the selling price at N$32 per unit.
You are required to:
10.4.1 advise management whether this proposal should be adopted; and
10.4.2 state any reservations you might have.
Solution to Activity 1
1.1
Variable costs = N$54 000 + N$72 000 + N$18 000 + N$27 000
= N$171 000
Variable cost per unit = N$171 000 ÷ 9 000 units
= N$19 per unit
Fixed costs = N$42 000 + N$36 000
= N$78 000
Break-even point (in units) = Fixed cost ÷ Contribution per unit
= N$78 000 ÷ (N$32 – N$19)
= N$78 000 ÷ N$13
= 6 000 units
1.2
Break-even point (in sales value) = B/E point in units x Selling price per unit
= 6 000 x N$32
= N$192 000
Profit-volume graph
75% Capacity = Sales of N$288 000 (9 000 units) → This was given in the question
N$288 000 (9 000 units) 100
Therefore, 100% Capacity =
1
X 75
= N$384 000 (12 000 units)
X-axis: Volume (Sales)
Y-axis: Net income
0
N$78 000 (Fixed costs)
5
N$192 000
0 (B/E point)
N$384 000
N$ 78 000
Y
120
Break-even point
At sales of N$192 000
Profit
(N$’000)
80
Profit area
Loss area
40
0
3 000
6 000
9 000
12 000
X
Units of Production and Sales
40
Loss
(N$’000)
80
Fixed cost = N$78 000
120
Y1
1.3.1
1.3.2
Proposal 1: Total contribution = (90% x 12 000 units x N$9)
Less fixed overheads
Net income
Proposal 2: Total contribution = (12 000 units x N$8,20)
Less fixed overheads = (N$78 000 + N$5 000)
Net income
Recommendation:
= N$97 200
= N$78 000
= N$19 200
= N$98 400
= N$83 000
= N$15 400
Based on the above information management should adopt the original budget plan as this yields the
largest profit.
1.4.1
Contribution = 12 000 units x N$13
Less fixed costs (N$78 000 + N$15 000)
Net income
= N$156 000
= N$ 93 000
= N$ 63 000
Recommendation:
This proposal yields the largest profit and therefore should be accepted.
1.4.2
However, there is a risk that the estimated sales demand will not be obtained and this could result in a
reduced profit since the N$15 000 will be a committed cost irrespective of the outcome.
Management would need some assurance that the market research company is reliable and has a good
track record.
6
Cost-volume-profit analysis: Multi-products
In today’s complex production times no company produces a single product only. In other words, the
previous discussions based on a single product were too simplistic. Often companies produce and sell more
than one product. Breakeven analysis under these circumstances is somewhat more complex than discussed
earlier in this chapter. The reason is that different products will have different selling prices, different costs,
and different contribution margins. Consequently the breakeven point will depend on the mix in which the
different products are sold.
Businesses try to achieve the combination (or mix) that will yield the greatest amount of profits. Most
companies produce several products and often these products are not equally profitable. Where this is true,
profits will depend to some extent on the company’s sales mix. Profits will be greater if high-margin rather
than low-margin items make up a relatively large proportion of total sales.
Changes in sales mix can cause interesting variations in a company’s profits. A shift in the sales mix from
high margin items to low margin items can cause total profits to decrease even though total sales may
increase. Conversely, a shift in the sales mix from low margin items to high margin items can cause total
profits to increase even though total sales may decrease. It is one thing to achieve a particular sales volume;
it is quite a different thing to sell the most profitable mix of products!
Calculation of break-even point in units
You will recall from the previous paragraphs above that the break-even point in units is calculated as
follows:
Total fixed costs
Break-even point in units = Contribution per unit
When there is more than one product, the formula is adjusted as follows:
Total fixed costs
Break-even point in units = Average contribution per unit
Example 3
Hangana Ltd supplied the following information regarding its three products:
Product A
Sales in units
2 000
Selling price per unit
N$20
Variable cost per unit
N$16
Total fixed cost = N$77 000
Product B
3 000
N$50
N$36
Required:
Compute the company’s break-even point in units.
7
Product C
5 000
N$40
N$28
Solution to Example 3
Compute the average contribution per unit. This can be done in one of the following two ways:
Method 1:
Sales price – Variable cost = Contribution
Product
per unit
per unit
per unit
A
N$20
N$16
N$ 4
B
N$50
N$36
N$14
C
N$40
N$28
N$12
Totals
Average contribution per unit (N$110 000 ÷ 10 000 units)
x Number
of units
2 000
3 000
5 000
10 000
= Total
contribution
N$ 8 000
N$ 42 000
N$ 60 000
N$110 000
N$11,00
Method 2:
Product Contribution per unit
A
N$ 4
B
N$14
C
N$12
Average contribution per unit
x Sales mix¹
0,20 (2 000 ÷ 10 000)
0,30 (3 000 ÷ 10 000)
0,50 (5 000 ÷ 10 000)
= Weighted contribution²
N$ 0,80
N$ 4,20
N$ 6,00
N$11,00
¹ The sales mix is the proportion of each product’s sales in units to total sales in units.
² Each product has a different contribution, and it is necessary to reduce the separate contributions to a
weighted average contribution of all products.
Note that the average contribution is not simply the sum of N$4, N$14 and N$12 divided by 3, because the
products are not sold in equal proportions. The contribution of product C, which constitutes 50% of unit
sales, must be weighted more heavily than the contributions of products A and B. The weighted average
contribution, therefore, represents the contribution of all separate products with a specific sales mix.
The break-even point can now be computed:
Fixed costs
Break-even point in units = Average contribution per unit
N$77 000
= N$11
= 7 000 units
Activity 2
Chem-Sol Ltd produces and sells two chemicals called Solvex and Dysolve. The following data regarding
these two products is available:
Solvex
Selling price per unit
N$10
Variable cost per unit
N$ 7
Sales mix
60%
Total fixed cost = N$29 700
Dysolve
N$20
N$12
40%
Required:
2.1
Compute the company’s break-even point in units.
8
2.2
Calculate how many more (or fewer) units have to be sold if the sales mix is changed to 50% for each
product.
Individual product break-even points
In Example 3 above the break-even point was 7 000 units for all three products combined. However,
production planning and scheduling require break-even data for individual products. The sales mix used to
calculate the weighted average contribution per unit is now used to extract the individual product break-even
points. Total break-even units are multiplied by the individual sales mix percentages to determine the breakeven point for individual products. The calculation is as follows:
Product Total units
A
7 000
B
7 000
C
7 000
x Sales
mix
0,20
0,30
0,50
= Individual
Product B/E
in units
1 400
2 100
3 500
7 000
x Selling
price
N$20
N$50
N$40
= Individual
Product B/E
in N$
N$ 28 000
N$105 000
N$140 000
N$273 000
Example 4
Flupp Ltd produces 3 products and has fixed costs of N$363 000 per year. Other data for the year is as
follows:
Selling price per unit
Variable cost per unit
Relative sales mix
A
N$18
N$12
0,4
B
N$12
N$7
0,3
C
N$36
N$27
0,3
Required:
4.1
4.2
Calculate the break-even point in units for each product individually.
Determine how many units of each product must be sold to earn a net income of
N$99 000.
Solution to Example 4
Product Selling price Variable cost
A
N$18
N$12
B
N$12
N$ 7
C
N$36
N$27
Average contribution per unit
Contribution Sales mix
N$6
0,4
N$5
0,3
N$9
0,3
Weighted
contribution
N$2,40
N$1,50
N$2,70
N$6,60
Break-even point (in units) = Fixed costs ÷ Average contribution per unit
= N$363 000 ÷ N$6,60
= 55 000 units
Individual break-even sales in units:
A
B
C
55 000 x 0,4 = 22 000 units
55 000 x 0,3 = 16 500 units
55 000 x 0,3 = 16 500 units
55 000 units
9
4.2
Required sales = (Fixed costs + Expected profit) ÷ Average contribution per unit
= (N$363 000 + N$99 000) ÷ N$6,60
= 70 000 units
Individual break-even sales in units:
A
B
C
70 000 x 0,4 = 28 000 units
70 000 x 0,3 = 21 000 units
70 000 x 0,3 = 21 000 units
70 000 units
Activity 3
Dynatone Tape Company produces two types of blank recording tapes that it distributes through wholesalers
or sells directly to large retailers. The following data apply to these products:
Product
Sales price Variable costs
Cassette
N$2,00
N$0,60
Cartridge
N$3,00
N$1,10
Total fixed costs = N$3 000
Contribution
N$1,40
N$1,90
Expected %
of units sold
60
40
Required:
3.1
3.2
Calculate the break-even point in units and in N$ for each product individually.
Calculate the number of units and sales value in N$ of each product necessary to achieve a net
income of N$600.
Calculation of break-even point in sales value
In the previous paragraphs above you learned that the break-even point in sales value could be determined in
two different ways:
Break-even point in sales value = Break-even point in units x Selling price per unit
OR
Total fixed costs
Break-even point in sales value = Contribution ratio
In a multi-product situation, the break-even point in sales value can also be calculated in two different ways
by adjusting these two formulas.
•
By using the weighted average selling price per unit
One way of calculating the break-even point in sales value is to compute the weighted average selling price
per unit and then applying the following formula:
Break-even sales value = Break-even quantity x Weighted average selling price per unit
Example 5
Refer to Example 3 above.
Required:
Compute the break-even point in sales value by first computing the weighted average selling price per unit.
10
Solution to Example 5
Product Sales price per unit x Sales mix
A
N$20
0,20
B
N$50
0,30
C
N$40
0,50
Weighted average selling price per unit
= Weighted selling price
N$ 4
N$15
N$20
N$39
Break-even point in sales value
= Break-even point in units x Weighted average selling price per unit
= 7 000 x N$39
= N$273 000
Activity 4
A company manufactures and sells two products, X and Y. Forecast data for a year are:
Sales (units)
Sales price (per unit)
Variable cost (per unit)
Product X
80 000
N$12
N$ 8
Product Y
20 000
N$8
N$3
Annual fixed costs are estimated at N$273 000.
What is the break-even point in sales revenue with the current sales mix?
A N$570 000
B N$606 667
C N$679 467
(Hint: First calculate the break-even point in units).
•
D N$728 000
By using the average contribution ratio
If the average contribution ratio is known, the break-even point in sales value can be computed by means of
the following formula:
Total fixed costs
Break-even point in sales value = Average contribution ratio
Example 6
Refer to Example 3 above
Required:
Calculate the break-even point in sales value by first computing the average contribution ratio.
Solution to Example 6
Average contribution per unit
Average contribution ratio = Average selling price per unit
N$11
= N$39
= N$0,28205
OR
11
Product
A
B
C
Totals
Units
2 000
3 000
5 000
10 000
x Sales price
N$20
N$50
N$40
Average contribution ratio =
= Sales revenue
N$ 40 000
N$150 000
N$200 000
N$390 000
– Variable cost
N$ 32 000
N$108 000
N$140 000
N$280 000
= Contribution
N$ 8 000
N$ 42 000
N$ 60 000
N$110 000
Total contribution
Total sales
N$110 000
= N$390 000
= 0,28205
Fixed costs
Break-even point in sales value = Average contribution ratio
N$77 000
= 0,28205
= N$273 000
Activity 5
Refer to Activity 3 above. Repeat the question without first calculating the break-even point in units.
Activity 6
H Limited manufactures and sells two products, J and K. Annual sales are expected to be in the ratio of J:1
and K:3. Total annual sales are planned to be N$420 000. Product J has a contribution to sales ratio of 40%,
whereas that of product K is 50%. Annual fixed costs are estimated to be N$120 000.
The budgeted break-even sales value (to the nearest N$1 000) is:
A N$196 000;
B N$200 000;
C N$253 000;
E Cannot be determined from the above data.
D N$255 000
Activity 7
Z plc currently sells products Aye, Bee and Cee in equal quantities and at the same selling price per unit.
The contribution to sales ratio for product Aye is 40%; for product Bee it is 50% and the total is 48%. If
fixed costs are unaffected by mix and are currently 20% of sales, the effect of changing the product mix to:
Aye
40%;
Bee
25%;
Cee
35%
is that the total contribution : total sales ratio changes to:
A 27,4%
B 45,3%
C 47,4%
D 48,4%
E 68,4%
Activity 8
PE Limited produces and sells two products, P and E. Budgets prepared for the next six months give the
following information:
12
Product P per unit Product E per unit
Selling price
N$10,00
N$12,00
Variable costs:
Production and selling
N$ 5,00
N$10,00
Common fixed costs:
Production and selling (for six months) N$561 600
You are required in respect of the forthcoming six months to:
8.1
8.2
8.3
state what the break-even point in N$’s will be and the number of each product this figure represents
if the two products are sold in the ration 4P to 3E;
state the break-even point in N$’s and the number of products this figure represents if the sales mix
changes to 4P to 4E (ignore fractions of products);
advise the sales manager as to which product mix should be better, that in 8.1 or that in 8.2 above.
Graphical presentation for multiple products
In the paragraphs above you learned that the relationship between cost, volume and profit could be presented
by a graph. You also learned that there are three types of graphs namely the break-even chart, the
contribution chart and the profit-volume graph. When the details of more than one product have to be
presented graphically, more lines have to be drawn and this can become very cumbersome as well as
confusing. However, the easiest method is to make use of the Profit-volume graph.
Example 7
An enterprise supplied the following information regarding its three products:
Details
Product A
N$
160 000
80 000
80 000
Sales
Variable cost
Contribution
Total fixed cost
Product B
N$
160 000
120 000
40 000
Product C
N$
80 000
80 000
NIL
N$40 000
Required:
Plot the above information on a Profit-volume graph and indicate the break-even sales clearly.
Solution to Example 7
Step 1:
Calculate the contribution ratio of each product separately and rank them in order from the largest to the
smallest:
Product A
Product B
Product C
Contribution ratio
N$80 000 x 100%
N$160 000
N$40 000 x 100%
N$160 000
N$0 x 100%
N$80 000
= 50% (0,5)
= 25% (0,25)
= 0% (0)
Ranking = A, B, C.
13
Step 2:
Determine the cumulative sales and cumulative profit figures in the order established in Step 1 above:
X-axis (Cumulative sales)
Y-axis (Cumulative profit)
N$0
(N$40 000)
A
N$160 000
N$ 40 000
A+B
N$320 000
N$ 80 000
A+B+C
N$400 000
N$ 80 000
Step 3:
The profit-volume graph can now be plotted as follows:
Net income N$’000
Product C

80

Profit area
70
Product B
60
50

40
30
Product A
20
10
0
50
100
150
200
250
300
350
400
450
-10
-20
Break-even point (N$133 333,33)
-30
Loss area
-40
500
550
600
Volume (sales) units ‘000
Fixed costs N$40 000
-50
14
Example 8
Nerina CC supplied the following information regarding their four products for the year 2005:
1.
Sales, Variable costs and Contributions:
Sales
Variable costs
Contribution
2.
Product A
N$
200 000
205 000
(5 000)
Product B
N$
400 000
350 000
50 000
Product C
N$
200 000
175 000
25 000
Product D
N$
100 000
70 000
30 000
Fixed costs: N$50 000
Required:
8.1
Plot the relevant information on a Profit-volume graph (P/V chart) and indicate the break-even sales
clearly.
8.2
Check the correctness of your answer by calculating the break-even sales with the aid of an
applicable formula.
Solution to Example 8
Step 1: Calculation of individual as well as average contribution ratios:
Calculations
Sales
Less Variable costs
= Contribution
Less Fixed costs
= Net income
Contribution ratio
Product A
N$
200 000
205 000
(5 000)
Product B
N$
400 000
350 000
50 000
Product C
N$
200 000
175 000
25 000
Product D
N$
100 000
70 000
30 000
- 0,025
0,125
0,125
0,30
Total
N$
900 000
800 000
100 000
50 000
50 000
0,111
Ranking = D, B, C, A.
Step 2: Calculation of cumulative sales and cumulative net income:
N$
Sales (X-axis)
Net income (Y-axis)
0
(50 000)
D
N$
100 000
(20 000)
D+B
N$
500 000
30 000
Step 3:
The profit-volume graph can now be plotted as follows:
15
D+B+C
N$
700 000
55 000
D+B+C+A
N$
900 000
50 000
Y
Net income N$’000
80
Profit area
70
60

55
Product A

50
Product C
40

30
Product B
20
10
0
100
200
300
400
500
600
700
800
-10
-20
900

Product D
Break-even point
(N$450 450)
Loss area
-40
Fixed costs N$50 000
-60
8.2
1 100
1 200
Volume (sales) units ‘000
-30
-50
1 000
Break-even sales = Fixed costs ÷ Average contribution ratio
= N$50 000 ÷ 0,111
= N$450 450
16
X
Activity 9
Desert Ltd supplied the following information regarding their three products for the year 2010:
1.
Sales, Variable costs and Contribution:
Sales
Variable costs
Contribution
2.
Product A
N$
600 000
590 000
10 000
Product B
N$
200 000
150 000
50 000
Product C
N$
500 000
460 000
40 000
Fixed costs: N$40 000
Required:
9.1
Plot the relevant information on a Profit-volume graph (P/V chart) and indicate the break-even sales
clearly.
9.2
Check the correctness of your answer by calculating the break-even sales with the aid of an
applicable formula.
Activity 10
Namsa Ltd supplied the following information regarding their three products for the year 2010:
1.
Sales, Variable costs and Contribution:
Sales
Variable costs
Contribution
2.
Product A
N$
100 000
70 000
30 000
Product B
N$
100 000
90 000
10 000
Product C
N$
600 000
560 000
40 000
Fixed costs: N$50 000
Required:
10.1
Plot the relevant information on a Profit graph (P/V chart) and indicate the break-even sales clearly.
10.2
Check the correctness of your answer by calculating the break-even sales with the aid of an
applicable formula.
Cost structure and the operating leverage factor
The concept cost structure refers to the relative relationship between fixed and variable costs in an
enterprise. During recent years the cost structure of manufacturing enterprises has changed in that costs have
become more fixed as a result of automation. More machines and less manual labour are used in production.
Enterprises with a high percentage fixed costs are more sensitive to changes in sales than enterprises with a
low percentage fixed costs. For example, consider a firm with relatively high fixed costs (ie, relatively low
variable costs and consequently a high profit-volume ratio). If sales should increase, profit will increase as a
higher rate than for a firm with relatively low fixed costs, because of the high profit-volume ratio. However,
if sales should drop, profit will also drop at a higher rate because, although variable costs will drop as well,
the fixed costs (rent, salaries, etc) must still be paid.
17
Example 9
The following details regarding two different firms are available:
Company A
N$
%
60 000
100
15 000
25
45 000
75
30 000
15 000
Sales
– Variable cost
= Contribution
– Fixed cost
= Net profit
Company B
N$
%
60 000
100
30 000
50
30 000
50
15 000
15 000
Required:
9.1
9.2
Calculate the increase in profit for each company if sales were to increase by 20%.
Calculate the decrease in profit for each company if sales were to decrease by 20%.
Solution to Example 9
Details
Sales
– Variable cost
= Contribution
– Fixed cost
= Net profit
% increase in Profit
Company A
Presently 20% increase
N$
N$
60 000
72 000
15 000
18 000
45 000
54 000
30 000
30 000
15 000
24 000
60%
Company B
Presently 20% increase
N$
N$
60 000
72 000
30 000
36 000
30 000
36 000
15 000
15 000
15 000
21 000
40%
Conclusion: Company A has relatively high fixed costs. However, because it has a high P/V-ratio, profit
will also increase at a higher rate than that of Company B.
Details
Sales
– Variable cost
= Contribution
– Fixed cost
= Net profit
% decrease in Profit
Company A
Presently 20% decrease
N$
N$
60 000
48 000
15 000
12 000
45 000
36 000
30 000
30 000
15 000
6 000
60%
Company B
Presently 20% decrease
N$
N$
60 000
48 000
30 000
24 000
30 000
24 000
15 000
15 000
15 000
9 000
40%
Conclusion:
Company A has relatively high fixed costs. Therefore, because it has a high P/V-ratio, profit will also
decrease at a higher rate than that of Company B.
The operating leverage factor reflects how much influence a percentage change in sales volume has on net
profit. A specific operating leverage factor is valid for a specific sales volume and changes as the sales
volume changes. The operating leverage factor is calculated as follows:
Contribution
Operating leverage factor = Net profit
18
The operating leverage is a management instrument that shows, relatively easily, the effect of a change in
turnover on net income, without detailed statements having to be prepared.
Example 10
The management of Shilongo Ltd supplied the following details:
Sales
Variable cost
Fixed cost
N$
100 000
20 000
40 000
Required:
10.1
10.2
Calculate the operating leverage factor
Use the operating leverage factor calculated in 10.1 above to compute the increase in net income if
sales were to increase by 15%.
Solution to Example 10
10.1
Operating leverage factor = Contribution ÷ Net profit
= N$80 000 ÷ N$40 000
=2
10.2
% increase in net income = % increase in sales x operating leverage factor
= 15% x 2
= 30%
Activity 11
The following income statement has been supplied to you:
Sales revenue
Less: Variable costs
= Contribution
Less: Fixed costs
= Net income
N$500 000
300 000
200 000
150 000
50 000
Required:
11.1
Show the firm’s cost structure by indicating the percentage of the firm’s revenue represented by each
item on the income statement.
11.2
Suppose the firm’s revenue declines by 15%. Use the contribution % to calculate the resulting
decrease in net income.
11.3
Compute the firm’s operating leverage factor when sales revenue is N$500 000.
11.4
Use the operating leverage factor to calculate the increase in net income resulting from a 20%
increase in sales revenue.
19
Activity 12
George Awarab recently opened a shop that specialises in car polish, a product that he has developed
himself. He has just received a diploma in accounting and is anxious to apply the principles he has learned at
the Polytechnic. As a first step, he has prepared the following analysis for his new store:
Sales price per tin
Variable costs per tin
Marginal income per tin
N$40
16
N$24
Fixed costs per year:
Rent on building
Depreciation on equipment
Selling expenses
Administrative expenses
Total fixed costs
N$15 000
7 000
20 000
18 000
N$60 000
Required:
12.1
12.2
12.3
12.4
Determine how many tins of polish must be sold each year in order to break even. What does this
represent in total N$ sales?
George has decided that he must earn at least N$18 000 during the first year to justify his time and
effort. Determine how many tins of polish he must sell to reach this target profit.
George now has a part-time sales person working in the store. It will cost him an additional N$8 000
per year to convert the part-time position to a full-time post. George believes that the change would
bring in an additional N$25 000 in sales each year. Determine whether he should convert the
position. Use the incremental approach (do not prepare an income statement).
Refer to the original data. During the first year, the store sold only 3 000 tins of polish and reported
the following operating results:
Sales (3 000 tins)
Less variable costs
Marginal income
Less fixed costs
Net income
N$120 000
48 000
72 000
60 000
N$ 12 000
12.4.1 Determine the store’s degree of operating leverage.
12.4.2 George is confident that with a more intense sales effort and with a more creative advertising
program he can increase sales by 50% next year. Determine what the expected percentage increase in
net income would be (use the degree of operating leverage to compute your answer).
Cost-volume-profit analysis assumptions
It is highly unlikely that selling price and variable costs per unit as well as fixed costs in total will remain
constant for a given period. Therefore, certain assumptions are part of break-even analysis. These
assumptions have given rise to criticism against CVP analysis. However, despite this criticism it remains a
useful management tool for short-term decision-making and profit planning.
Summary
CVP analysis is a useful tool with which to do certain short-term investigations and make decisions. It puts
an enterprise in a position to calculate its sales in order to make an expected profit level. It is therefore also
useful in evaluating the effect of operating changes on profit. These changes include changes in the selling
price and fixed costs. CVP analysis is liable to contain certain simplified assumptions that are necessary to
make the analysis clear and understandable.
20
Solution to Activity 2
2.1 Product
Contribution x Sales mix
Solvex
N$3
0,6
Dysolve
N$8
0,4
Weighted average contribution per unit
Weighted contribution
N$1,80
N$3,20
N$5,00
Break-even point = Fixed costs ÷ Average marginal income per unit
= N$29 700 ÷ N$5
= 5 940 units
2.2 Product
Contribution x Sales mix
Solvex
N$3
0,5
Dysolve
N$8
0,5
Weighted average contribution per unit
Weighted contribution
N$1,50
N$4,00
N$5,50
Break-even point = Fixed costs ÷ Average marginal income per unit
= N$29 700 ÷ N$5,50
= 5 400 units
Solution to Activity 3
Product
Selling price Variable cost
Cassette
N$2
N$0,60
Cartridge
N$3
N$1,10
Weighted average contribution per unit
Contribution
N$1,40
N$1,90
Sales mix
0,6
0,4
Weighted contribution per unit
N$0,84
N$0,76
N$1,60
Break-even point (in units) = Fixed cost ÷ Average contribution per unit
= N$3 000 ÷ N$1,60
= 1 875 units
Individual break-even sales in units:
Cassettes: 1 875 x 0,6 = 1 125 units
Cartridges: 1 875 x 0,4 = 750 units
1 875 units
Break-even point (in sales value):
Cassettes: 1 125 units x N$2 = N$2 250
Cartridges: 750 units x N$3 = N$2 250
Total sales to break even
= N$4 500
3.2
Required sales = (Fixed cost + Expected profit) ÷ Average contribution per unit
= (N$3 000 + 600) ÷ N$1,60
= 2 250 units
Individual break-even sales in units:
Cassettes: 2 250 x 0,6 = 1 350 units
Cartridges: 2 250 x 0,4 = 900 units
2 250 units
21
Break-even point (in sales value):
Cassettes: 1 350 units x N$2 = N$2 700
Cartridges: 900 units x N$3 = N$2 700
Total sales to break even
= N$5 400
Solution to Activity 4
Product Contribution per unit x Sales mix
X
N$4
0,80 (80 000 ÷ 100 000)
Y
N$5
0,20 (20 000 ÷ 100 000)
Weighted average contribution per unit
= Weighted contribution
N$3,20
N$1,00
N$4,20
Fixed costs
Break-even point in units = Average contribution per unit
N$273 000
= N$4,20
= 65 000 units
Solution to Activity 5
Product Selling price Variable cost
Cassette
N$2
N$0,60
Cartridge
N$3
N$1,10
Average
Contribution
N$1,40
N$1,90
Sales mix
0,6
0,4
Weighted contribution
N$0,84
N$0,76
N$1,60
Break-even point (in units) = Fixed cost ÷ Average marginal income
= N$3 000 ÷ N$1,60
= 1 875 units
Individual break-even sales in units:
Cassettes: 1 875 x 0,6 = 1 125 units
Cartridges: 1 875 x 0,4 = 750 units
Break-even point (in sales value):
Cassettes: 1 125 units x N$2 = N$2 250
Cartridges: 750 units x N$3 = N$2 250
Total sales to break even
= N$4 500
5.2
Required sales = (Fixed cost + Expected profit) ÷ Average marginal income
= (N$3 000 + 600) ÷ N$1,60
= 2 250 units
Individual break-even sales in units:
Cassettes: 2 250 x 0,6 = 1 350 units
Cartridges: 2 250 x 0,4 = 900 units
Break-even point (in sales value):
Cassettes: 1 350 units x N$2 = N$2 700
Cartridges: 900 units x N$3 = N$2 700
Total sales to break even
= N$5 400
22
Solution to Activity 6
Product
J
K
Totals
Sales revenue
N$105 000¹
N$315 000²
N$420 000
¹
1 N$420 000
4X
1
²
3 N$420 000
4X
1
x P/V ratio
0,4
0,5
= Contribution
N$ 42 000
N$157 500
N$199 500
Total contribution
Average contribution ratio = Total sales
N$199 500
= N$420 000
= 0,475
Fixed costs
Break-even point in sales value = Average contribution ratio
=
N$120 000
0,475
= N$252 631,57
Therefore, answer = C
Solution to Activity 7
The average contribution to sales ratio is 48% (given in question)
48% x 3 = 144%
Therefore, Product Cee = 144% – (40% + 50%)
= 54%
Product Contribution x Sales mix
Aye
0,40 (40%)
0,40
Bee
0,50 (50%)
0,25
Cee
0,54 (54%)
0,35
Weighted average contribution
= Weighted contribution
0,16
0,125
0,189
0,474 (47,4%)
Answer = C
Solution to Activity 8
8.1 Product
Contribution x Sales mix
P
N$5
4/7
E
N$2
3/7
Weighted average contribution per unit
= Weighted contribution
2,857
0,857
3,714
Break-even point (in units) = Fixed cost ÷ Average contribution per unit
= N$561 600 ÷ 0,3714
23
= 151 212 units
Individual break-even sales in units:
Product P = 151 212 x 4/7 = 86 407 units
Product E = 151 212 x 3/7 = 64 805 units
151 212 units
Break-even point in sales value:
Product P = 86 407 units x N$10 selling price = N$ 864 070
Product E = 64 805 units x N$12 selling price = N$ 777 660
N$ 1 641 730
8.2
When the products are sold in equal proportions the average contribution is calculated by simply
dividing the total contribution by two. Thus:
Average contribution per unit = (N$5 + N$2) ÷ 2 = N$3,50
Break-even point (in units) = Fixed cost ÷ Average contribution per unit
= N$561 600 ÷ N$3,50
= 160 457 units (consisting of 80 228 units of each product).
Break-even point in sales value:
Product P = 80 228 units x N$10 selling price = N$ 802 280
Product E = 80 228 units x N$12 selling price = N$ 962 736
N$ 1 765 016
8.3
Advice to management:
The product mix in 9.1 above is preferable because it yields the higher average contribution per unit
and consequently the break-even point is reached sooner.
Solution to Activity 9
9.1 Calculations
Sales
Less Variable costs
= Contribution
Less Fixed costs
= Net income
Contribution ratio
Product A
N$
600 000
590 000
10 000
Product B
N$
500 000
160 000
40 000
Product C
N$
200 000
150 000
50 000
0,02
0,08
0,25
Total
N$
1 300 000
1 200 000
100 000
40 000
60 000
0,08
C+B
N$
700 000
50 000
C+B+A
N$
1 300 000
60 000
Ranking = C, B, A.
Cumulative figures
Sales (X-axis)
Net income (Y-axis)
N$
0
(40 000)
C
N$
200 000
10 000
24
Profit-volume graph (P/V chart)
Net income N$’000
70
Profit area
60

Product A

50
40
Product B
30
20

10
Product C
0
100
200
300
400
500
600
700
800
-10
900
1 000
1 100 1 200 1 300
Volume (sales) units ‘000
-20
Break-even point (N$500 000)
-30
Loss area
-40
9.2
Fixed costs
Break-even sales = Fixed costs ÷ Contribution ratio
= N$40 000 ÷ 0,08
= N$500 000
Solution to Activity 10
10.1
Calculations:
Sales
Variable costs
Contribution
Fixed costs
Net income
Product A
N$
100 000
70 000
30 000
Product B
N$
100 000
90 000
10 000
25
Product C
N$
600 000
560 000
40 000
Total
N$
800 000
720 000
80 000
50 000
30 000
Contribution ratio
Sales
Net income
0,30
0,10
0,067
0,10
N$
0
(50 000)
A
N$
100 000
(20 000)
A+B
N$
200 000
10 000
A+B+C
N$
800 000
30 000
Contribution graph (Profit-volume chart):
Profit-volume graph (P/V chart):
Net income N$’000
Profit area

30
Product C
20

10
0
100
-10
-20
200
300
400
500
Product B
600
700

Break-even point (N$500 000)
-30
Product A
Loss area
-40
-50
10.2
800
Volume (sales) units ‘000
Fixed costs
Break-even sales = Fixed costs ÷ Marginal income ratio
= N$50 000 ÷ 0,10
= N$500 000
26
Solution to Activity 11
11.1
Income Statement
Sales revenue
Less: Variable costs
= Contribution
Less: Fixed costs
= Net income
Amount
N$500 000
300 000
200 000
150 000
50 000
11.2
Contribution = 40% of sales revenue
= 40% of N$425 000 (N$500 000 less 15%)
= N$170 000
Percentage
100%
60%
40%
30%
10%
Net income = Contribution – Fixed costs
= N$170 000 – N%150 000
= N$20 000
Therefore, net income has decreased by 60% (from N$50 000 to N$20 000)
11.3
Operating leverage factor = Contribution ÷ Net profit
= N$200 000 ÷ N$50 000
=4
11.4
% increase in net income = % increase in sales x operating leverage factor
= 20% x 4
= 80%
Solution to Activity 12
12.1
Break-even point (in units) = Fixed costs ÷ Marginal income per unit
= N$60 000 ÷ N$24
= 2 500 tins
Break-even point (in N$)
= 2 500 x N$40
= N$100 000
12.2
Required sales = (Fixed costs + Target profit) ÷ Marginal income per unit
= (N$60 000 + N$18 000) ÷ N$24
= N$78 000 ÷ N$24
= 3 250 tins
12.3
Incremental sales N$25 000. Incremental marginal income = N$15 000
Incremental fixed costs
=
8 000
Incremental net income
= N$ 7 000
Yes, he should convert this position because he will earn an extra N$7 000.
12.4.1 Operating leverage = Marginal income ÷ Net income
= N$72 000 ÷ N$12 000
=6
12.4.2 Percentage increase in net income
= Percentage increase in sales x operating leverage
= 50% x 6
= 300%
27