Cost and Management Accounting 2nd edition
Solutions (Additional questions)
CHAPTER 3
SOLUTIONS (ADDITIONAL QUESTIONS)
3.1
D
3.2
B
3.3
D
3.4
B
3.5
A
397 500 / 750 000 x 100
= 53%
3.6
D
=225 000 / 53%
= R424 528.30
3.7
B
= [(750 000 – 424 528.30) / 750 000] x 100
= 43%
3.8
C
= (225 000 + 0.10 / 0.53
3.9
0.53
=
(225 000 + 0.10)
0.43x
=
225 000
x
=
225 000 / 0.43
x
=
R523 255.81
C
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
3.10
A
53%
CM ratio
-2%
commission
49%
new CM ratio
= 225 000 / 0.49
= R 459 183.67 new BEP
= R 459 183.67 – R 424 528.30
= R 34 655.37 difference
3.11
3.12
B
New contribution (750 000 + 72 500) x 53%
R435 925
Current contribution
R397 500
Net profit
R 38 425
A
Total sales R630 000
Contribution S1
= R100 800
[(R630 000 x 2/5) x 0.40]
Contribution S2
= R189 000
[(R630 000 x 3/5) x 0.50]
Total contribution
= R289 800
WA contribution ratio = R289 800 / R 630 000 x 100
= 46%
BEP Rands
= R180 000 / 0.46
= R450 000
3.13
3.14
3.15
D
=
[R450 000 + (R800 x 90) + (R65 x 500)] / (R90 – R30)
=
[450 000 + 72 000 + 32 500] / R60
=
9 242 units
D
=
[R450 000 + (R700 x 90) + (R65 x 400)] / (R90 – R30)
=
[450 000 + 63 000 + 26 000] / R60
=
8 983 units
A
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
3.16
(a)
Managers can use CVP analysis to conduct a ‘what if’ analysis. This permits
managers to estimate the effects of the various changes on the profitability of the
business. For example, by manipulating the CVP model the impact of changes in the
sales volume, selling price, variable costs or fixed costs on the contribution and net
profit can be easily determined.
(b)
The absorption costing/traditional income statement groups costs according to
function, i.e. manufacturing (product) and non-manufacturing (period). On the other
hand, the Marginal costing income statement which is used for CVP analysis groups
costs according to their behaviour, i.e. variable and fixed costs.
(c)
There are various assumptions associated with the CVP context and these need to be
taken into account since they affect their reliability for planning and decision
making;

As the activity level changes, the price of a product or service will remain the
same, within the relevant range.

Within the relevant range costs are linear and can all be accurately divided into
their fixed or variable elements. The variable costs are constant per unit and the
fixed cost remains fixed within the relevant range.

All variable cost will vary or change with only either production level or sales
level.

The cost structure of an organisation is constant within the relevant range.

In manufacturing organisations there is no stock, the number of units produced
equals the number of units sold.
With taking cognisance of the above assumptions the risk or danger lies when a
manager is considering a change in activity level outside of the relevant range.
3.17
(a)
The degree of operating leverage can be used to forecast changes in net income. It
measures how the net income is affected by percentage changes in sales. A company
with a higher proportion of fixed costs in their cost structure will have a higher
operating leverage. It is calculated as: Contribution / Net income.
(b)
An increase in the selling price with the volume sold remaining unchanged, will
result in an increase in the contribution as well as the net profit. The operating
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
leverage factor would decrease, since the percentage change in the contribution
would be lower than the percentage change in the net profit.
(c)
The contribution margin would increase due to the decrease in the variable costs.
However, the net profit would remain unchanged as a result of the increase in the
fixed costs. Consequently, the operating leverage factor would increase.
3.18
(a)
Contribution per unit:
R24.00 – R8.60 – R1.20 = 14.20
Break even point = R880 400 / R14.20 = 62 000 units
(b)
Margin of safety:
(90 000 – 62 000) / 90 000 = 31.1%
(c)
Revised contribution per unit:
= R25.00 – R8.60 – R2.00 = R14.40
Breakeven point = R890 400 / R14.40 = 61.833 units
3.19
(a)
BEP in jumps
= Fixed costs / Contribution per jump
Model A
= 389 325 / (100 – 13)
= 4 475 jumps
Model B
= 423 950/ (135 – 13)
= 3 475 jumps
(b)
Target profit in jumps:
= (Fixed costs + Target profit) / Contribution per jump
Model A
= (389 325 + 302 325) / (100 – 13)
= 691 650 / 87
= 7 960 jumps
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
Model B
= (423 950 + 302 325) / (136 – 13)
= 726 275 / 122
= 5 953 jumps
(c)
Based on the calculations in (a) and (b) above, Model B would be more profitable as
it has a lower BEP than Model A.
Factors to be considered before a decision is taken on the model to be acquired are as
follows:

Ease of operations, transportability and accessibility of the respective models;

Confirmation of customer attitudes, affordability and anxiety towards jumps of
45 metres and 60 metres respectively in terms of both models; and

3.20
(a)
Risk linked to the respective models, based on the expected margin of safety.
Income statement:
Sales (12 000 000 x 0.95 x 1.20)
13 680 000
Less: Direct materials (3600 000 x 1.05 x 1.20)
4 536 000
Direct labour (3 000 000 x 1.03 x 1.20)
3 708 000
Variable overheads (1 200 000 x 1.20)
1 440 000
Fixed overheads (2 700 000 + 300 000)
3 000 000
Net profit
(b)
996 000
It is difficult to determine whether the proposal to reduce the selling price in order to
increase sales volume is justified because the answer in (a) above includes the cost
increases which are independent of the selling price reduction. If the selling price is
not reduced, the budgeted profit will be as follows:
Income statement:
Sales
12 000 000
Less: Direct materials (3600 000 x 1.05)
3 780 000
Direct labour (3000 000 x 1.03)
3 090 000
Variable overheads
1 200 000
Fixed overheads (2700 000 + 300 000)
3 000 000
Net profit
930 000
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
From the above, it appears that the proposal to reduce the selling price is not
justified. When a business considers reducing the selling price of its product or
products, the following factors should be considered:

How confident is the company that sales will increase by the predicted volume?

Could the reduction in the selling price cause a price war resulting in competitors
matching the price reduction? The effect of this is that sales volume will remain
unchanged.

Does the company have sufficient productive resources to meet the proposed
expansion in demand?
(c)
Original budget
Revised budget
12 000 000
13 680 000
4 200 000
3 996 000
35%
29.2%
Sales
Contribution
Contribution / Sales x 100
3.21
Workings:
Fixed costs
Rental
6000
Labour (250 x 36)
9000
Service
1200
Electricity (45 x 36) 1620
17820
(a)
Breakeven point in units:
= Fixed costs / Contribution per unit
= 17 820 / 2(10 – 8)
= 8 910 units per year OR 248 units per week (8 910 / 36)
Margin of safety:
= (Budgeted sales units – Breakeven sales units) / Budgeted sales units x 100
= (99 000 / 10) – 8910 / 9 900) x 100
= 990 / 9 900 x 100
= 10%
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
Profit on budgeted sales is all the contribution beyond the breakeven point
= 990 x 2
= R1 980
(b)
Target profit in units
= (Fixed costs + Target profit) / Contribution per unit
= (17 820 + 5 000) / 2
= 22 850 / 2
= 11 410 units per year OR 317 units per week (11 410 / 36)
(c)
Increase in rent 6 000 x 3% = 180
Therefore fixed costs increase to R18 000 (17 820 + 180)
Breakeven point in units:
= Fixed costs / Contribution per unit
=18 000 / 2
= 9 000 units per year OR 250 units per week (9 000 / 36)
Margin of safety:
= (Budgeted sales units – Breakeven sales units) / Budgeted sales units x 100
= (9 900 – 9 000 / 9 900) x 100
= 900 / 9900 x 100
= 9%
Profit on budgeted sales is all the contribution beyond the breakeven point.
= 900 x 2
= R1 800
If the rental for the vending machines is increased, then the number of units sold in
order to break even would increase as well. The budgeted net profit would decrease
by R180.
The margin of safety % is lower which means that DUT would be operating closer to
its breakeven point.
(d)
R15 000 / 12 vending machines
= R1 250 advertising per vending machine
= Fixed costs / Contribution per unit
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
= 1250 / 2
= 625 extra units must be sold per vending machine in order to pay for the
advertising campaign.
This is equivalent to an extra 6% in sales (625 / 9 900 x 100)
3.22
(a)
Expected profit
325 000
+ Fixed costs
87 500
Contribution
412 500
Contribution per unit R12.50 – 5 = R 7.50
Number of units (loaves) sold in order to earn a net profit of R325 000.
Current sales volume:
= 412 500 / 7.50 = 55 000 loaves
Alternative strategies:
Strategy
Selling price
Contribution per
per loaf
loaf
Sales volume
Total
contribution
1
12.13
7.13 (12.13 – 5.00)
58 300
415 679
2
11.75
6.75
60 500
408 375
3
11.38
6.38
63 250
403 535
Considering the fixed costs of 87 500, strategy 1 is the most profitable.
415 679 – 87 500 = 328 179 net profit
(b)
3.23
(a)
Other factors to consider:

Will the estimated fixed costs remain the same?

How accurate are the demand estimates?

How would competitors react to the proposed price reduction?
Expected net profit for next year:
Sales (5 250 000 x 0.95 x 1.2)
5 985 000.00
Less: Direct materials (1 680 000 x 1.07 x 1.2)
2 157 120.00
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
Direct Labour (1 102 500 x 1.07 x 1.2)
1 415 610.00
Total overheads *Workings 1
1 243 238.14
Net profit/loss
1 169 031.86
Workings 1:
Overheads
R1 627 500 – R1 578 675
= R48 825 (difference in overhead cost which represents the variable portion)
R 48 825 / R 1 578 675 x 100
= 3%
The activity level increased by 10% last year
Variable overheads portion of the total overhead cost = 30% last year [3 / 10 x 100]
&
Fixed overheads portion of the total overheads cost = 70%
Estimated overheads:
Last year
Variable
Current year
(1 578 675 x 0.30 x 0.10)
47 360.25
(47 360.25 x 1.07 x 1.2)
(1 578 675 x 0.7)
1 105 072.50
60 810.56
overheads
Fixed overheads
(1 105 075.50 x 1.07)
1 182 427.58
Total overheads
1 152 432.75
1 243 238.14
(b)
Last year
Sales
Current year
5 250 000
5 985 000.00
2 829 860.25
3 633 540.56
Direct materials
1 680 000
2 157 120.00
Direct labour
1 102 500
1 415 610.00
Variable overheads
47 360.25
60 810.56
2 420 139.25
2 351 459.44
Less: Variable costs
Contribution
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
CM ratio
46%
39%
1 105 072.50 / 0.46
1 182 427.58 / 0.39
= R2 402 331.52
= R3 031 865.59
BEP rand
Fixed costs / CM ratio
(c)
No, management should not implement the new strategy. The breakeven point has
increased by 26% as a result of the decrease in the selling price and the inflation
linked cost increases. [(3 301 865.59 – 2 401 331.52) / 2 404 331, 52 x 100]= 26%
more units would have to be sold in order to break even; this has put a strain on
profits and profits have decreased as a result.
3.24
(a)
Y
Z
120 000
195 000
90 000
405 000
Less: Variable costs
54 000
132 600
51 300
237 900
Contribution
66 000
62 400
38 700
167 100
CM ratio
55%
32%
43%
Sales mix
(2 / 5 x 100)
(2 / 5 x 100)
(2 / 5 x 100)
= 40%
= 40%
= 20%
Sales
Weighted average contribution margin ratio:
= (0.55 x 0.40) + (0.32 x 0.40) + (0.43 x 0.20)
= 0.434 OR 43%
(b)
Total
X
BEP in Rand
Fixed costs / WA contribution ratio
= 90 000 / 0.43
= R209 302.33
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
(c)
X
Sales
Y
Total
Z
800 000*
1000 000**
300 000***
2 100 000
Less: Variable costs
360 000
680 000
171 000
1 211 000
Contribution
440 000
320 000
129 000
889 000
Less: Fixed costs
90 000
Net profit
799 000
*10 000 units x 2 x R40; **10 000 units x 2 x R50; ***10 000 units x 1 x R30
Variable costs are calculated in line with the present cost structure.
(d)
Contribution per unit:
X
22 (40 x 0.55)
Y
16 (50 x 0.32)
Z
12.90 (30 x 0.43)
WA contribution per unit:
(22 x 0.40) + (16 x 0.40) + (12.90 x 0.20)
= R17.78
(Fixed costs + Target profit) / WA contribution per unit
= (90 000 + 120 000) / 17.78
= 11 811 units
Of 11 811 units , 40% would be for X, 40% for Y and 20% for Z.
3.25
A
Sales
B
C
Total
100 000
162 500
75 000
337 500
Less: Variable costs
50 000
113 750
45 000
208 750
Contribution
50 000
48 750
30 000
128 750
Less: Fixed costs
37 500
Net profit
91 250
Cost and Management Accounting 2nd edition
Solutions (Additional questions)
Product
Sales mix
CM ratio
A
50% (50 000 / 100 000 x 100)
30% (100 000 / 337 500 x 100)
B
30% (48 750 / 162 500 x 100)
48% (162 500 / 337 500 x 100)
C
40% (30 000 / 75 000 x 100)
22% (75 000 / 337 500 x 100)
Weighted average contribution margin ratio:
= ( 0.50 x 0.30 ) + (0.30 x 0.48) + (0.40 x 0.22)
= 0.382 or 38%
BE Sales:
= Fixed costs / WA contribution margin ratio
= 37 500 / 0.38
= R 98 684.21
Cost and Management Accounting 2nd edition
Solutions (Additional questions)