CHAPTER 16: VOLUME-COST-PROFIT ANALYSIS
Solution RQ.16.11
(a) Selling price of motor
Less variable costs
Material
Rs 50
Labour
80
Variable overheads (0.75 ¥ Rs 80)
60
Contribution margin per motor
BEP (motors) = Rs 2,40,000 ∏ Rs 40
(b) Desired sales volume (units) to have a profit of Rs 1,00,000 = (Rs 2,40,000
+ Rs 1,00,000) ∏ Rs 40 = 8,500 motors
(c) Revised selling price (Rs 230 – Rs 15)
Less total variable costs
Contribution margin per motor
BEP (motors) = Rs 2,40,000 ∏ Rs 25
Rs 230
190
40
6,000
Rs 215
190
25
9,600
Solution RQ.16.12
(i) Statement Showing P/V Ratio, BEP, BESR, and Present Level of Profit
Particulars
Selling price per unit (Rs 2,00,000/10,000 units sold)
Less variable cost per unit
Contribution per unit
Profit-volume ratio (Rs 8/Rs 20) (%)
Total fixed cost
BEP (units) (Rs 40,000/Rs 8)
BESR (Rs 40,000/0.4)
Profit [(Rs 2,00,000 – Rs 1,00,000 BESR) ¥ 0.4 P/V ratio]
Amount
Rs 20
12
8
40
Rs 40,000
5,000
Rs 1,00,000
40,000
(ii) Statement Showing P/V Ratio, BEP, BESR, and Desired Sales Revenue (In Future)
Particulars
Revised selling price (Rs 20 – 10% or Rs 2)
Less variable cost per unit
Contribution per unit
P/V ratio (Rs 6/Rs 18) (%)
BEP (units) (Rs 40,000/Rs 6)
BESR (Rs 40,000/33-1/3%)
Desired sales revenue to earn Rs 40,000 (FC + Rs 40,000)/33-1/3%
[(Rs 40,000 + Rs 40,000) ∏ 33-1/3%]
Amount
Rs 18
12
6
33 1/3
6,667
Rs 1,20,000
2,40,000
Solution RQ.16.13
(a) Determination of Break-even Sales Revenue, BESR
Particulars
Selling price per unit
Less variable cost per unit
Contribution per unit
P/V ratio (Rs 8/Rs 20) (%)
BESR (Rs 2,40,000 Fixed costs/0.4)
Amount
Rs 20
12
8
40
Rs 6,00,000
16.2 Management Accounting—OLC
(b) Determination of Number of Units to Earn 10% of Sales
Let the number of units to be sold be
Sales revenue of X units @ Rs 20 per unit
Profit 10% (i.e. 10% (¥) 20X)
Total costs (20X – 2X)
Total variable costs @ Rs 12 per unit
Contribution per unit
X = (Rs 2,40,000 + 2X)/Rs 8
6X = Rs 2,40,000 or X = 40,000 units
X
20X
2X
18X
12X
Rs 8
Solution RQ.16.14
(a) Determination of BESR
P/V ratio = (Increase in profits ∏ Increase in sales) = (Rs 40,000 ∏ Rs 1,00,000) = 40%
V/V ratio = 100% – P/V ratio 40% = 60%
BESR = TFC/PV ratio = Rs 60,0001/0.40 = Rs 1,50,000
(b) Desired Sales Revenue to Earn Rs 2,00,000
= (FC + Desired profit)/0.4 = (Rs 60,000 + Rs 2,00,000)/0.4 = Rs 6,50,000
(c) Profit at Sales revenue of Rs 6,00,000
Particulars
Amount
Sales revenue
Less variable costs (Rs 6,00,000 ¥ 0.60)
Contribution
Less fixed cost
Profit
Rs 6,00,000
3,60,000
2,40,000
60,000
1,80,000
(d) Margin of Safety (MS) at Profit Level of Rs 50,000
= (Total sales revenue – BESR) ¥ C/V ratio = Rs 50,000
= (Total sales revenue – Rs 1,50,000) ¥ 0.4 = Rs 50,000
= Total sales revenue – Rs 1,50,000 = Rs 50,000/0.4 i.e., Rs 1,25,000
= Total sales revenue = Rs 2,75,000
MS = Rs 2,75,000 – Rs 1,50,000 = Rs 1,25,000
Working Notes:
(1) Sales revenue = Fixed cost + Variable cost + Total profit
Rs 4,00,000 = FC + 0.6 (Rs 4,00,000) + Rs 1,00,000
FC = Rs 60,000 i.e. (Rs 4,00,000 – Rs 1,00,000 – Rs 2,40,000)
Solution RQ.16.15
(a and b) Statement Showing P/V Ratio, BEP, Margin of Safety and Desired Sales Revenue
Particulars
Sales revenue
Less variable cost
Total contribution
Fixed expenses
P/V ratio (%) (Total contribution/Sales revenue)
BEP (Amount) (Fixed expenses/P/V ratio)
Margin of safety (sales revenue – BESR)
Desired sales revenue to earn profits of Rs 30,000
(TFC + Rs 30,000)/PV ratio
P Ltd.
Rs 3,00,000
2,00,000
1,00,000
50,000
33.33
1,50,000
1,50,000
2,40,000
Q Ltd.
Rs 3,00,000
2,25,000
75,000
25,000
25
1,00,000
2,00,000
2,20,000
Volume-Cost-Profit Analysis 16.3
(c) Since P/V ratio is higher in the case of P Ltd., it will show better result (compared to Q Ltd.) when
sales increase; in the event of decrease in sales, company Q will show better results as its fixed costs as
well as BESR is lower.
Solution RQ.16.16
Statement Showing BESR and Budget Profit
Particulars
Fixed costs:
Factory overheads
Rs 1,89,900
Distribution overheads
58,400
Administrative overheads
66,700
Variable costs (as percentage of sales):
Direct materials
32.8
Direct labour
28.4
Factory overheads
12.6
Distribution overheads
4.1
Administrative overheads
1.1
P/V ratio (100% – 79.0%) (%)
(a) BESR (Rs 3,15,000/0.21)
(b) Profit at budget sales of Rs 18,50,000
(Budgeted sales – BESR) ¥ P/V ratio; (Rs 18,50,000 – Rs 15,00,000) ¥ 0.21
Amount
Rs 3,15,000
79.0
21.0
Rs 15,00,000
73,500
Solution RQ.16.17
(i) Determination of Sales for Year 2
Let us assume sales revenue of year 2 as S
Sales revenue (S) – Variable costs = Contribution
S – Rs 4,00,0001 = 0.375 (¥) S
or 0.625 S Rs 4,00,000, or S = Rs 4,00,000/0.625 = Rs 6,40,000
(ii and iii) Fixed Cost and BESR for Year 2
(a) Margin of Safety ratio = (Sales revenue – BESR)/Sales revenue
21.875% = (Rs 6,40,000 – BESR) ∏ Rs 6,40,000
Rs 1,40,000 = Rs 6,40,000 – BESR
or BESR = Rs 5,00,000
(b) BESR = Fixed cost/PV ratio or (37.5%)
Fixed cost = Rs 5,00,000 ¥ 0.375 = Rs 1,87,500
Working Notes:
(1) Determination of variable costs
Sales revenue
Less variable costs (Rs 8,00,000 ¥ 0.50* V/V ratio)
Variable costs in year 1
Rs 8,00,000
4,00,000
4,00,000**
*1-P/V ratio = V/V ratio; 1 – 0.5 = 0.5 V/V ratio
**Since sales quantity in year 2 remains unchanged, variable cost in year 2 will be equal to year 1.
Solution RQ.16.18
P/V ratio = (Decrease in loss ∏ Increase in sales)
= Rs 1,50,000/Rs 5,00,000 = 30%
V/V ratio = 100% – 30% P/V ratio = 70%
BESR = TFC/P/V ratio = Rs 5,00,0001/0.30 = Rs 16,66,667
16.4 Management Accounting—OLC
Working Notes:
1. Determination of fixed cost
SR = TFC + TVC – Losses
Rs 10,00,000 = TFC + 0.7 (Rs 10,000,000) – Rs 2,00,000
TFC = Rs 5,00,000
Solution RQ.16.19
(i) Determination of Break-even Point
Product
A
B
Total
Expected sales revenue
(units ¥ selling price
per unit)
Variable costs
(units ¥ variable cost
per unit)
Rs 3,60,000
6,60,000
10,20,000
Rs 2,40,000
4,20,000
6,60,000
Contribution
Rs 1,20,000
2,40,000
3,60,000
Weighted P/V ratio = (Rs 3,60,000 ∏ Rs 10,20,000) ¥ 100 = 35.3 per cent
BEP (amount) = Rs 3,60,000, FC ∏ (36/102) = Rs 10,20,000.
Statement Showing the Operating Income (Loss)
Particulars
Sales revenue
Less variable costs
Contribution
Less fixed costs
Operation income
Product A
Product B
Combined
Rs 3,60,000
2,40,000
1,20,000
Rs 6,60,000
4,20,000
2,40,000
Rs 10,20,000
6,60,000
3,60,000
3,60,000
Nil
(ii) Statement Showing Operating Income at Different Sales-mixes
Particulars
Sales revenue
Less variable costs
Contribution
Less fixed costs
Income (loss)
Product A
Product B
Rs 5,40,000
3,60,000
1,80,000
Rs 4,40,000
2,80,000
1,60,000
Combined
Rs 9,80,000
6,40,000
3,40,000
3,60,000
(20,000)
Break-even point = FC ∏ P/V ratio = Rs 3,60,000 ∏ (34/98) = Rs 10,37,647
Solution RQ.16.20
Present level of profit: Rs 50 per cycle ¥ 1,00,000 = Rs 50,00,000.
Fixed overheads = Rs 50 ¥ 1,00,000 = Rs 50,00,000.
It is assumed that the Cycle Company Ltd. was absorbing the entire fixed overheads from 1 lakh
cycles only.
Revised Contribution Margin When Sales Price is Reduced
Sales price
Less variable costs per cycle
Contribution margin
Situation (a)
Rs 180
100
80
Desired sales volume = (FC + Desired profit) ∏ Revised MC per unit
Situation (b)
Rs 160
100
60
Volume-Cost-Profit Analysis 16.5
(a) Rs 1,00,00,000 ∏ Rs 80 = 1,25,000 cycles
(b) Rs 1,00,00,000 ∏ Rs 60 = 1,66,667 cycles
Solution RQ.16.21
(a) (i) BEP = FC ∏ P/V ratio = Rs 24,000 ∏ 0.20 [(Rs 1,60,000 ¥ 100) ∏ Rs 80,000] = Rs 1,20,000.
(ii) Desired sales volume to earn profit of Rs 8,000 = (Rs 24,000 + Rs 8,000) ∏ 0.20 = Rs 1,60,000.
(b) (i) BEP = [Rs 50,000 ∏ 0.75 (Rs 60,000 ¥ Rs 100) ∏ Rs 80,000] = Rs 66,667 (company A)
= [Rs 10,000 ∏ 0.25 (Rs 20,000 ¥ 100) ∏ Rs 80,000] = Rs 40,000 (company B)
(ii) Since fixed costs of company A are higher than those of company B, its break-even point is
higher.
Solution RQ.16.22
BEP = Total fixed costs ∏ Contribution margin per unit.
As the contribution margin per unit (CMPU) is not uniform for all units to be sold during the current
year, the BEP would be: (6,000 units from previous year + Total fixed costs – Contribution of 6,000 units
from previous year) ∏ CMPU of the current year = 6,000 + [Rs 86,000 – Rs 30,000 (i.e. 6,000 ¥ Rs 5)] ∏
Rs 4 = 20,000 units.
Solution RQ.16.23
(i) Determination of BEP of the Merged Plant (100% Capacity) (Rs lakh)
Particulars
Company 1
Sales revenue
Less variable costs
Total contribution
C/V ratio (Rs 285 ¥ 100) ∏ 1,100(%)
Company 2
600
440
160
500
375
125
Merged company
1,100
815
285
25.9
Break-even sales revenue of merged plant = Rs 130 lakh ∏ 0.259 = Rs 501.75 lakh.
Break-even capacity of merged plant = (Rs 501.75 lakh ∏ Rs 1,100 lakh) ¥ 100 = 45.6 per cent.
(ii) Profitability of Merged Plant (80 per cent capacity)
Sales revenue (Rs 1,100 lakh ¥ 0.80)
Less variable costs (Rs 880 lakh ¥ 0.741, variable cost ratio)
Total contribution
Less fixed costs
Profit
(iii) Desired sales revenue to earn Rs 75 lakh profit =
Rs 880
652
228
130
93
Rs 130 lakh + Rs 75 lakh
= Rs 791.23 lakh.
0.259
(iv) Increase in fixed overheads, 5% = Rs 6.5 lakh
Desired increase in selling price to sustain 5% increase in fixed overheads = (Rs 6.5 lakh ∏
Rs 791.23) lakh ¥ 100 = 0.82 per cent.
Solution RQ.16.24
(i) Determination of Break-even Capacity of Merged Plant: 100 Per cent Capacity
Particulars
A
B
C
Merged plant
Turnover (Rs lakh)
Less variable costs
Total contribution
300
200
100
400
300
100
300
150
150
1,000
650
350
16.6 Management Accounting—OLC
Weighted C/V ratio = (Rs 350 lakh ∏ Rs 1,000 lakh) ¥ 100 = 35 per cent
BEP = [Rs 182 (Rs 70 + Rs 50 + Rs 62)] ∏ 0.35 = Rs 520 lakh.
BEP (% capacity) = (Rs 520 lakh ∏ Rs 1,000 lakh) ¥ 100 = 52 per cent.
(ii) Profit at 75 per cent capacity of merged plant: (Budgeted sales at 75 % capacity – Break-even sales
revenue) ¥ C/V ratio = Rs 80.5 lakh (Rs 750 lakh – Rs 520 lakh) ¥ 0.35
(iii) Desired sales turnover to give profit of Rs 28 lakh = (Rs 182 lakh + Rs 28 lakh) ∏ 0.35 = Rs 600 lakh
Solution RQ.16.25
Determination of Income at 60 per cent Level of Capacity
Particulars
Total amount
Sales revenue (6,000 units1 ¥ Rs 300)
Less variable costs
Variable costs (6,000 units ¥ Rs 60)
Variable component in semi-variable costs (6,000 units ¥ Rs 10)
Total variable costs (6,000 units ¥ Rs 70)
Total contribution (6,000 units ¥ Rs 230)
Less fixed costs
Less fixed component in semi-variable costs
Profit
Rs 18,00,000
3,60,000
60,000
4,20,000
13,80,000
3,00,000
1,20,000
9,60,000
(Rs 18,00,000 ∏ Rs 300) = 6,000 units at 60 per cent or 10,000 units at 100 per cent capacity.
1
Statement Showing Determination of Desired Sales Volume to Maintain Profit of Rs 9,60,000 When Sales
Price is Reduced by 20 Per cent
Revised selling price [Rs 300 – (20%)] per unit
Rs 240
Less variable costs
70
Revised contribution per unit
170
Desired sales volume to maintain profit = (Rs 4,20,000 + Rs 9,60,000) ∏ Rs 170 = 8,118 units or 81.2 per cent.
Capacity expansion beyond 80 per cent will require additional fixed costs of Rs 60,000. Therefore, the desired sales
volume to maintain profit = (Rs 4,80,000 + Rs 9,60,000) ∏ Rs 170 = 8,471 units 84.7 per cent
The company should operate at 84.7 per cent level of capacity to maintain the existing profit of Rs 9,60,000.
Solution RQ.16.26
(a) Determination of Break-even Point of Machines A and B
Particulars
Sales revenue (10,000 ¥ Rs 10)
Less fixed costs
Less profit
Variable costs (balancing figure)
Contribution (sales revenue – VC)
C/V ratio (%)
Contribution per unit
Variable cost per unit
BEP (in units)
BEP (amount)
Machine A
Machine B
Rs 1,00,000
30,000
30,000
40,000
60,000
60
6
4
5,000
50,000
Rs 1,00,000
16,000
24,000
60,000
40,000
40
4
6
4,000
40,000
(b) The level of sales at which both machines would earn equal profit:
Since the selling price per unit of output of machines A and B is the same, the two machines will
have equal profit at the sales level at which their costs of operations (variable + fixed) are equal.
Volume-Cost-Profit Analysis 16.7
Let us assume the sales level is ‘X’ units. Total costs at this level of sales for machines A and B would
be 4X + 30,000 and 6X + 16,000 respectively. Solving for X, we have 4X + 30,000 = 6X + 16,000 = 30,000
– 16,000 = 6X – 4X = 14,000 = 2X = 7,000 = X (level of sales).
At the level of 7,000 units of sales, both machines will yield equal profit (Rs 12,000).
(c) Since the BEP is lower in machine B, it will be more profitable than A for unit sales range of
4,000 – 6,999. For sales ranges beyond 7,000, machine A will be more profitable due to higher C/V ratio.
Solution RQ.16.27
(a) Budgeted Income Statement When 4,000 Students Take up the Entrance Test
Particulars
Gross revenue/fees (Rs 50 ¥ 4,000)
Less variable costs
Valuation (Rs 20 ¥ 4,000)
Question booklets (Rs 10 ¥ 4,000)
Supervision charges (40 supervisors ¥ Rs 50 per day ¥ 4 days)
Contribution
Less fixed costs
Hall rent
Honorarium to chief administrator
General administration expenses
Net revenue
Amount
Rs 2,00,000
Rs 80,000
40,000
8,000
Rs 8,000
6,000
6,000
1,28,000
72,000
20,000
52,000
Working Notes:
Number of students in year 2 (Rs 1,50,000 ∏ Rs 50) = 3,000
Valuation charges per student (Rs 60,000 ∏ 3,000) = Rs 20
Question booklets (Rs 30,000 ∏ 3,000)
= Rs 10
(b) Since the supervision charges are on the basis of 100 students, the BEP has been determined with
reference to 100 students:
Gross revenue (Rs 50 ¥ 100)
Less variable costs
Valuation (Rs 20 ¥ 100)
Question booklets (Rs 10 ¥ 100)
Supervision charges (Rs 50 ¥ 4)
Contribution per 100 students
Contribution margin per student (Rs 1,800 ∏ 100)
BEP (students) (Rs 20,000 ∏ Rs 18)
Rs 5,000
Rs 2,000
1,000
200
3,200
1,800
18
1,111
Since one supervisor is needed for every 100 students, variable supervision charges included above is
Rs 2 per student. Therefore, unrecovered expenses will be Rs 178 (Rs 200 – Rs 22). Additional candidates
required would be Rs 178 ∏ Rs 20 and contribution per student (excluding supervision charges) would
be 9. Therefore, BEP is 1,120 candidates (1,111 + 9).
(c) The desired number of candidates to have income of Rs 20,000 = (Rs 20,000 + Rs 20,000) ∏ Rs 18
= 2,222.
As stated in part (b), 22 candidates will need one supervisor. Therefore, under-recovery of supervision cost = Rs 200 – Rs 44 = Rs 156.
Number of students required to recover Rs 156 = Rs 156 ∏ Rs 20 = 8.
Therefore, the desired number of candidates = 2,230 = (2,222 + 8).
16.8 Management Accounting—OLC
Solution RQ.16.28
(i) Comparative Income Statements Under Alternative Profit-volume Relationships
Particulars
Existing
Price per unit
Rs 9
Sales (in units)
Sales volume
Less variable costs:
Direct materials @ Rs 1.50 per unit
Direct labour @ Rs 3 per unit
Variable overheads @ Re 0.75 per unit
Contribution (manufacturing)
Less variable selling expenses
@ Re 0.30 per unit
Contribution (final)
Less fixed costs
Manufacturing overheads
Selling expenses
Administration expenses
Net income (loss)
P/V ratio (per rupee)
BESR
Proposed changes
Reduction in
price by 20%
to Rs 7.20 per unit
Reduction in
price by 331/3%
to Rs 6 per unit
1,20,000
Rs 10,80,000
1,80,000
Rs 12,96,000
2,00,000
Rs 12,00,000
1,80,000
3,60,000
90,000
4,50,000
2,70,000
5,40,000
1,35,000
3,51,000
3,00,000
6,00,000
1,50,000
1,50,000
36,000
4,14,000
54,000
2,97,000
60,000
90,000
1,35,000
50,000
22,000
2,07,000
1,44,000
50,000
22,000
81,000
1,46,000
52,000
28,000
(1,36,000)
414./1,080
5,40,000
297./1,296
9,42,546
9. /120
30,13,333
Solution RQ.16.29
(i) Determination of Break-even Point
Sales revenue
Less variable costs
Direct materials
Rs 1,75,000
Direct labour
50,000
Variable overheads
65,000
Semi-variable overheads (50% variable)
35,000
Contribution
P/V ratio (%)
BEP (amount) = Fixed costs ∏ P/V ratio = (Rs 55,000 + Rs 35,000) ∏ 0.1875 = Rs 4,80,000.
BEP (in units) = Rs 4,80,000 ∏ Rs 800 (selling price per unit) = 600.
Rs 4,00,000
3,25,000
75,000
18.75
(ii) Comparative Cost Statement Per Unit to Determine Tender Price Per Unit
Particulars
Variable costs
Direct material
Direct labour
Overheads (including 50% of semi-variable)
Fixed costs
Overheads (including 50% fixed part of semi-variable overheads)
Total costs
+ 12% profit margin on total cost in year 3
Tender price per unit
Cost per unit
Year 2
Year 3
Rs 350
100
200
180
830
Rs 420
120
240
198
978
117.36
1,095.36
[It is assumed that total fixed costs are absorbed by 500 units produced (Rs 4,00,000 ∏ Rs 800)].
Volume-Cost-Profit Analysis 16.9
Solution RQ.16.30
Pre-expansion BEP (amount) = [Rs 4,20,000 ∏ 0.575 (Rs 9.20 ∏ Rs 16) ¥ 100]
BEP (in units) = (Rs 7,30,434.78 ∏ Rs 16)
Post-expansion BEP (amount) = [Rs 5,45,000 ∏ 0.60 (Rs 9.6 ∏ Rs 16) ¥ 100]
BEP (in units) = (Rs 9,08,333 ∏ Rs 16)
Rs 7,30,435
45,653
9,08,333
56,771
Comparative Income Statement (Pre-expansion and Post-expansion Progamme) Assuming Sales Equal to
Plant Capacity
Particulars
Pre-expansion
Production/sales (units)
Selling price
Sales revenue
Less variable costs
Contribution
Less fixed costs
Net income
80,000
Rs 16
Rs 12,80,000
5,44,000
7,36,000
4,20,000
3,16,000
Post-expansion
1,20,000
Rs 16
Rs 19,20,000
7,68,000
11,52,000
5,45,000
6,07,000
As to which alternative is better, the answer hinges upon the sales volume. Simply on the basis of
BEP, one may be tempted to conclude that since BEP is higher with expansion, the alternative of the
status-quo is better. But this decision, in fact, may not be an optimal decision if the firm is able to
increase its sales. The very fact that the firm is contemplating an increase in its plant capacity is a
pointer to the inadequacy of the existing plant capacity to cater to the customers’ demand. The
alternative of expansion of plant capacity appears to be a better one.
Solution RQ.16.31
Sales
1st half
2nd half
Rs 2,70,000
3,42,000
Profit
Rs 7,200
20,700
Cost
Rs 2,62,800
3,21,300
(i) P/V ratio = (D Profit ∏ DSales) ¥ 100 = (Rs 13,500 ∏ Rs 72,000) ¥ 100 = 18.75 per cent.
(ii) Profit When Sales are Rs 2,16,000
6 months
Sales revenue
Less variable cost [81.25% (100% – 18.75%)]
Contribution
Less fixed cost
Net profit (loss)
Rs 2,16,000
1,75,500
40,500
43,425@
(2,925)
12 months
Rs 2,16,000
1,75,500
40,500
86,850
(46,350)
(iii) Desired sales volume to earn a profit of Rs 36,000 = (Rs 86,850 + Rs 36,000) ∏ 0.1875 = Rs 6,55,200.
Working Notes:
@Determination of FC
Rs 2,70,000 = FC + 81.25% ¥ (Rs 2,70,000) + Rs 7,200
Rs 2,70,000 = FC + Rs 2,19,375 + Rs 7,200
Rs 2,70,000 – Rs 2,26,575 = FC
Rs 43,425 = FC (for 6 months)
Rs 86,850 = FC (for 12 months).
16.10 Management Accounting—OLC
Solution RQ.16.32
Statement Showing the Impact of Changes in Sales Price on Income
Particulars
Present sales price
(Rs 1,000)
Sales price
Sales volume (units)
Sales revenue (gross)
Less variable costs @ Rs 500 per unit
Profit contribution
Less fixed costs
Net profit
1,000
6,600
Rs 66,00,000
33,00,000
33,00,000
30,00,000
3,00,000
Proposed selling price
Decrease 10%
Increase 10%
900
7,900
Rs 71,10,000
39,50,000
31,60,000
30,00,000
1,60,000
1,100
5,700
Rs 62,70,000
28,50,000
34,20,000
30,00,000
4,20,000
The suggestion of an increase in sales price is recommended as it would augment profits from
Rs 3,00,000 to Rs 4,20,000.
Solution RQ.16.33
(a) Determination of Current Profit-volume Ratio
Selling price per unit
Less variable costs per unit
Material
Labour
Overhead
Contribution per unit
P/V ratio or C/V ratio (Rs 36 ∏ Rs 90)(%)
Determination of new selling price to have 40 per cent P/V ratio:
Revised material cost (Rs 40 + 7 1/2%)
Revised labour cost (Rs 10 + 10%)
Revised variable overheads (Rs 4 + 5%)
Revised variable costs
(SP – VC) ∏ SP = 0.4
SP – Rs 58.20 = 0.4 SP
SP – 0.4 SP = Rs 58.20, or 0.6 SP = Rs 58.20, or SP =
Rs 90
Rs 40
10
4
54
36
40
43
11
4.20
58.20
Rs 58.20
= Rs 97
0.6
(b) Desired Sales Revenue to Maintain Current Profits at Sales Price of Rs 90 Per Unit
(i) Profits in the current year:
Contribution (Rs 13,50,000 ¥ 0.40)
Less fixed costs
Rs 5,40,000
1,40,000
4,00,000
(ii) (Fixed costs + Additional fixed costs + Rs 4,00,000) ∏ Contribution per unit (Rs 90 – Rs 58.20)
= (Rs 1,40,000 + Rs 4,200 + Rs 4,00,000) ∏ Rs 31.80 = 17,114 units.
Solution RQ.16.34
(a) 1. Let total costs be represented by x and total profits by y.
Therefore, x + y = Rs 45,000
2. Increase in:
Material costs from 50% to 57.5% (7.5%).
Direct labour costs from 20% to 25% (5%).
This increase of 12.5% in total costs reduces profits by 25%. From this it follows that:
(i)
(Contd.)
Volume-Cost-Profit Analysis 16.11
Revised costs are x + 12.5% = 1.125x
Revised profits are y – 0.25y = 0.75y
Therefore, 1.125x + 0.75y = Rs 45,000
3. Thus,
x + y = Rs 45,000
1.125x + 0.75y = Rs 45,000
Multiplying equation (i) by 1.125,
1.125x + 1.125y = Rs 50,625
1.125x + 0.75y = Rs 45,000
Subtracting equation (ii) from equation (i),
0.375y = Rs 5,625, or y = Rs 5,625 ∏ 0.375 = Rs 15,000
y (profits) = Rs 15,000
x (costs) = Rs 30,000 (Rs 45,000 – Rs 15,000).
(ii)
(i)
(ii)
(i)
(ii)
Statement of Profit
Selling price
Less costs
Direct material (Rs 30,000 ¥ 0.50)
Direct labour (Rs 30,000 ¥ 0.20)
Overheads (Rs 30,000 ¥ 0.30)
Profit
Profit as per cent of sales (Rs 15,000 ∏ Rs 45,000)
Profit as per cent of costs (Rs 15,000 ∏ Rs 30,000)
Rs 45,000
Rs 15,000
6,000
9,000
30,000
15,000
33.1/3
50
(b) Determination of Revised Selling Price
Direct material costs (Rs 15,000 + 15% per unit)
Direct labour costs (Rs 6,000 + 25% per unit)
Overheads (Rs 9,000 per unit)
Revised total cost
Add desired profit (331/3 per cent of sales price or 50 per cent of cost price)
Revised selling price
Rs 17,250
7,500
9,000
33,750
16,875
50,625
Solution RQ.16.35
(i) Income statement contains sales revenue, variable costs, fixed costs, and profit (loss). In the problem,
sales and income are known; we are required to determine variable costs and fixed costs. Given the P/
V ratio of 0.40, the expected contribution margin is Rs 1,60,000, (0.40 ¥ 8,000 ¥ Rs 50) and expected
profit is Rs 96,000. Hence, expected fixed costs would be Rs 64,000 (Rs 1,60,000 – Rs 96,000). The actual
fixed costs were higher by the amount of advertisement expenditure of Rs 4,000, that is actual fixed
costs would be Rs 68,000. Since actual income was Rs 1,26,400 and fixed costs were Rs 68,000, total
actual contribution must have been Rs 1,94,400 (Rs 1,26,400 + Rs 68,000). Variable costs, then, should be
Rs 2,59,200 (Rs 4,53,600 – Rs 1,94,400).
The income statement for the year would be as follows:
Sales
Less variable costs
Contribution
Less fixed costs
Net income
Rs 4,53,600
2,59,200
1,94,400
68,000
1,26,400
16.12 Management Accounting—OLC
(ii) (a) Since variable costs per unit were as expected, variable costs per unit = (0.60 ¥ Rs 50) = Rs 30.
Total actual variable costs were Rs 2,59,200. Units sold were (Rs 2,59,200 ∏ Rs 30) = 8,640
(b) Sales price per unit = Total sales revenue ∏ Number of units sold = Rs 4,53,600 ∏ 8,640 =
Rs 52.50
Mr. Mukesh’s answer to the chief executive should highlight change in the selling price and fixed
costs. In the cost-volume-profit-relationships, assumptions are critical. If they vary, the planned and
actual results are bound to differ. Here, selling price has gone up causing higher P/V ratio (variable cost
per unit remains constant) and, hence, more profit rate than Re 0.40 per rupee of additional sales.
Revised P/V ratio is 42.86 per cent (9/21 per rupee of sales). Furthermore, additional fixed costs have
been incurred. These two factors have distorted the cost-volume profit-relationship stipulated by Mr.
Mukesh.
ANSWERS
RQ.16.11
RQ.16.12
RQ.16.13
RQ.16.14
RQ.16.15
RQ.16.16
RQ.16.17
RQ.16.18
RQ.16.19
RQ.16.20
RQ.16.21
RQ.16.22
RQ.16.23
RQ.16.24
RQ.16.25
RQ.16.26
RQ.16.27
RQ.16.28
RQ.16.29
RQ.16.30
RQ.16.31
RQ.16.32
RQ.16.33
RQ.16.34
RQ.16.35
(a) BEP 6,000 motors, (b) 8,500 motors, (c) 9,600 motors
(a) P/V ratio 40% and 331/3 , (b) BEP 5,000 and 6,667 units, (c) Rs 2,40,000
(a) BESR Rs 6,00,000, (b) 40,000 units
(a) BESR Rs 1,50,000, (b) Rs 6,50,000, (c) Rs 1,80,000, (d) Rs 1,25,000
(a) P Ltd.: P/V ratio 331/3 %, BESR Rs 1,50,000, Margin of safety Rs 1,50,000; Q Ltd.: P/V ratio
25%, BESR Rs 1,00,000, Margin of safety Rs 2,00,000 (b) P (Rs 2,40,000), Q (Rs 2,20,000)
(c) (i) Company P (ii) Company Q
(a) BESR Rs 15,00,000 (b) Rs 73,500
(i) Rs 6,40,000 (ii) Rs 1,87,500 (iii) Rs 5,00,000
BESR Rs 16,66,667
(i) BESR Rs 10,20,000, operating income is zero (ii) BESR Rs 10,37,647, operating loss
Rs 20,000
(a) 1,25,000 cycles, (b) 1,66,667 cycles
(a) (i) BESR Rs 1,20,000 (ii) Rs 1,60,000
(b) (i) BSER Rs 66,667 (Company A), Rs 40,000 (Company B)
(ii) Fixed costs of Company A are higher than those of Company B
BEP = 20,000 units
(i) Rs 25.9 lakh, (ii) Rs 93 lakh, (iii) Rs 791.23 lakh, (iv) 0.82%
(i) 52%, (ii) Rs 80.5 lakh, (iii) Rs 600 lakh
84.7% level of capacity
(a) BEP 5,000 units (Machine A), 4000 units (Machine B) (b) 7,000 units (c) 4,000 – 6,999 (B
will be more profitable) for 7,000 units and above (A will be more profitable)
(a) Rs 52,000 (b) 1,111 (c) 2,230
(i) Net income Rs 2,07,000 (Existing), Rs 81,000 (Reduction in price by 20% loss Rs 1,36,000
(Reduction in price by 331/3% (ii) BESR Rs 5,40,000 (Existing), Rs 9,42,546 (Reduction in price
by 20%) Rs 30,13,333 (Reduction in price by 331/3 %).
(i) 600 units (ii) Rs 1,095.36
BEP 45,653 (Pre-expansion), BEP 56,771 (Post-expansion)
Net income Rs 3,16,000 (Pre-expansion), Rs 6,07,000 (Post-expansion)
(i) P/V ratio 18.75% (ii) Net loss Rs 2,925 (6 months), Rs 46,350 (12 months) (iii) Rs 6,55,200
Increase in selling price is recommended
(a) Rs 97 (b) 17,114 units
(a) Profit Rs 15,000 (b) Rs 50,625
(i) Net income Rs 1,26,400 (ii) (a) 8,640 units (b) Rs 52.50 (iii) Change in assumptions of VCP
relationships