Problem 1:
Budgeted BES to earn the target profit:
A company which has started developing the annual profit plan has just reviewed the draft annual income statement & is concerned with the $ 220000 indicating profit on a sales volume of 40000 units. The fixed cost structure of $ 1980000 appears to be high and regarding departing from the annual sales price of $ 200, they have some doubts. Profit target of $ 440000 is a general agreement. Several tentative alternative plans have been suggested during the meeting of the executive’s committee which has just reviewed the tentative profit plan.
Compute:
(a) The budgeted breakeven point in $ & in units & the number of units that needed to be sold for earning the target profit.
(b) You are required to directly respond to each of the following two alternatives which are being considered by the management. (Consider each independent of other & state any assumption that needed to be made)
Alternative1: A sales price increase of 20% is contemplated; it has been estimated by the sales executives that drop in units will be resulted from this that can be sold by 15%. What would be the new breakeven point in $ & in units? What would be the new profit figures? For earning the target profit, how many units would have to be sold?
Alternative 2: A decrease
in variable cost of 6% & a decrease in fixed cost of $ 110000 are contemplated.
What would be the new breakeven point in $? For earning the target profit, how many
units would have to be sold?
Solution: We know that Sales – Variable cost = Fixed cost +
Profit
Sales Volume (units) 20000
units
Total
($) Per
unit ($)
Sales (a) 4000000 200.00
Fixed cost 1980000 99.00
Profit 220000 11.00
Contribution (b) 2200000 110.00
Variable cost 1800000 90.00
P/V ratio = (Contribution / Sales) * 100 = 2200000/4000000 = 55%
B.E. in sales in units = Fixed cost / Contribution per unit = $ 1980000/110 = 18000 units
B.E. in sales in $ = 18000 units * $ 200 = $ 3600000
Target Profit $ 440000
Fixed cost 1980000
Target Contribution 2420000 …… (i)
Number of units to be sold = Target contribution / Contribution per unit
= $2420000/ $110 = 22000 units
(a) Alternative 1
20% increase in price = $ 200 *120% = $ 240
Less: Variable cost per unit 90
Contribution 150
B.E. point = $ 1980000 / $ 150 = 13200 units
B.E. Sales = 13200 * $ 240 = $ 3168000
Net profit figure with 15% reduction in sales (17000 units) is:
Contribution (17000 units * $ 150) $
2550000
Less: Fixed cost 1980000
Net Profit 570000
No of units to be sold to earn target contribution of $ 2420000 as per (i) above
= Target contribution / Contribution per unit
= $ 2420000 / 150 = 16133 units
(b) Alternative 2
Revised fixed cost $
1870000
Revised Variable cost per unit $ 90 less 6% $
84.60
Revised contribution per unit = $200 - $84.60 $
115.40
P/V ratio = 115.40/200 57.7%
B.E. Sales = Revised Fixed cost / Revised P/V ratio = $ 1870000/57.7% = $ 3240901
Target Profit $
440000
Revised fixed cost $ 1870000
Revised Contribution $ 2310000
No of units to be sold = $ 2310000/ $ 115.40 = 20117 units
Problem 2:
Break-even analysis before/after allocated H.O. expenses- Evaluation of Profit
Plans:
Cost-volume-profit analysis has been
prepared by a company named X for each plant as per details below:
(a)Annual budgeted fixed costs of $ 360000, variable cost $ 2520000 & sales value of production of $ 6600000 has been shown by the profit plan for Plant A. Allocated head office budgeted fixed costs are $ 960000. Prepare an analysis which indicates the breakeven point before & after the cost allocation. Also, explain why the breakeven points change (in $) is greater than the allocated amount.
(b) A product which sells at $ 120 is produced by Plant B. When 15000 units are produced, it costs $ 127.50, whereas cost per unit is $ 114.375 when 20000 units are produced. What is the break-even point in $ & in units.
(c) Budgeted income & cost estimates of Plant C are as follows: $
Sales (annual) $ 3000000
Costs: Fixed 1200000
Variable 900000
Head office expenses
allocated 1050000 3150000
Loss 50000
Sale of Plant Z is under consideration. On the basis of the data given, what will be your recommendation? Also justify your recommendation.
(d) Plant D produces 1 product: the budgeted income & cost estimates are as follows:
Sales (annual) @ $ 600 per unit 6000000
Costs: Fixed 2242500
Variable 4050000
Head office expenses 1507500 7800000
Loss 1800000
In order to break-even, how many additional
units need to be manufactured in the plant?
Above the breakeven, what would be the profit pick-up per unit?
Solution: (a) Sales
Value 6600000
Variable
cost 2520000
Contribution 4080000
P/V ratio = (4080000/6600000) = 61.82%
Breakeven point before allocation: BES * P/V ratio = Fixed cost
BES * 61.82% = 3600000
BES
= $ 5823358
Breakeven point after allocation: BES * P/V ratio =
Fixed cost including allocated expenses
Or, BES * 61.82% = $ 3600000+ $ 960000
Or, BES = $ 7376253
(b) Cost for 20000 units = 20000*114.375 = $2287500
Less: Cost for 15000 units = 15000*127.50 = 1912500
5000
units 375000
Variable cost per unit = change in cost / change in quantities
= $ 375000 / 5000 units = $ 75
Thereby, Variable cost for 15000 units = 15000 units * $75 = $ 1125000
Fixed cost = Total cost at level of 15000 units – Variable cost at level of 15000
units
= $ 1912500 - $ 1125000 = $ 787500
P/V ratio = (120-75) / 120 = 37.5%
BEP * P/V ratio = Fixed cost
BEP = $ 787500 / 37.5% = $ 2100000
BEP in units = $ 2100000 / $ 120 = 17500 units
(c) P/V ratio of Plant C = (3000000 – 900000) / 3000000 = 70%
Fixed cost of Plant C = $ 1200000
BES of Plant C = $ 1200000/70% = $ 1714285
The Plant is operating above the break-even the point & it is yielding contribution for absorbing head office expenses. As head office expenses will be there in any case, the plant should not be closed down. Decision to close Plant 1 will lead to a loss of contribution of $ 2100000.
(d) Sales of Plant D $
6000000
Variable cost 4050000
Contribution 1950000
BEP * P/V ratio = $ 2242500
BEP * (1950000/6000000) = 2242500
BEP * 32.5% = 2242500
BEP = 2242500/32.5% = $ 6900000 or 11500 units
Additional units required to break even = 11500 – 10000 = 1500 units.
Profit pickup will be equal to contribution per unit = 1950000 / 10000 = $ 195 per unit.
Problem 3: Break-even analysis of candidates – semi-variable cost
For the post of junior officers, competitive examinations are conducted by a bank every year for the selection of candidates. For admission to the examination, each candidate is charged an entrance fee of $ 300. From the last 2 years the data gathered are as under:
2009
($) 2010 ($)
Fees collected 1200000 1500000
Costs:
Valuation of answer books 480000 600000
Question papers 320000 400000
Hire of Hall 48000 48000
Honorarium to Examination Superintendent 40000 40000
Invigilators at the rate of one invigilator for every
50 students at $ 400 per day for 2 days 64000 80000
General expenses 48000 48000
Total 1000000 1216000
Net Income 200000 284000
In 2011, it is expected that for the entrance examination, 6000 candidates will appear. The hall rent & general expenses are expected to increase by $ 12000 & $ 32000 respectively. For the year 2011, calculate the following:
(a) Budgeted income;
(b) Break-even number of candidates;
(c) For the purpose of earning net revenue of $ 400000, number of candidates required
to sit for the examination.
Solution: Statement showing the nature of cost & variable cost per unit
2009 2010 Nature Variable
cost
Per
candidate
Fees ($) 1200000 1500000
Fees collected per candidate ($) 300 300
Number of candidates 4000 5000
$ $ $
Valuation of answer papers 480000 600000 Variable 120
Question papers 320000 400000 Variable 80
Hire of Hall 48000 48000 Fixed
Honorarium to Examination Suptd. 40000 40000 Fixed
Invigilators
($400 / 50) * 4000 * 2 64000
($400 / 50) * 5000 * 2 80000 Step
cost
General expenses 48000 48000 Fixed
(a) Budget
for 2011
Number of candidates 6000
Fees @ $ 300 $
1800000
Less: Variable costs/ Semi-variable cost
Valuation of answer
papers 720000
Question papers 480000
Step cost
Invigilators ($400 / 50) * 6000 * 2 96000 1296000
Contribution 504000
Less: Fixed cost
Hire of Hall 60000
Honorarium to Examination
Suptd 40000
General
expenses 80000 180000
Profit 324000
Consideration per candidate after considering Invigilators cost = 504000 / 6000 = $ 84
Consideration per candidate without considering Invigilators cost = 600000 / 6000 =
$100
(b) Breakeven point is that
point of sales where contribution is just sufficient to meet fixed cost. At this point,
there is no profit no loss, because all costs (variable, step & fixed) are recovered.
In the given situation, in 2011, the position will be as follows:
Variable cost $
1200000
Step cost 96000
1296000
Therefore, contribution available to recover the fixed cost was $ 504000
Thus, P/V ratio at the level 2011 was = (Contribution / Sales) * 100
= ($ 504000 / 1800000) * 100 = 28%
We know that Break-even point: Break-even Sales * P/V ratio = Fixed cost
Or, Break-even sales (in $) = 180000/28% = $ 642857.14
Or, Break-even sales (in units) = $ 642857.14/300 = 2142.86 candidates.
Here consideration has to be given to 2 points:
(i) For each 50 candidate, step cost increases @ $ 800.
(ii) Thereby, at the level of 2142.86 candidates, all costs have not been recovered.
Now, Break-even sales (in units) = 2142.86 candidates
Candidates in multiple of 50 = 2100.00 candidates
Balance 142.86 candidates
But invigilator’s cost (step cost) increase for 50 candidates = $ 800
Invigilator’s cost (step cost) recovered for 42.86 candidates =
(800 /50) * 42.86 $ 685.76
Balance $
114.24
Thus, for breaking even additional candidates required = $ 114.24 / $ 100 = 1.14
Break-even points (in candidates) = 2142.86 + 1.14 = 2144
(c) Net income required = $
400000
Fixed cost required = 180000
Contribution required 580000
No of candidates required = $ 580000 / 84 = 6904.76 candidates
In multiples of 50 6900.00
Balance 4.76
Minimum invigilation cost = $
800.00
Invigilation cost recovered from 4.76
Candidates = ($ 800/50) * 4.76 76.16
Balance invigilation cost 723.84
Additional candidate required = $ 723.84/ 100 = 7.24 candidates
Thus total candidates required = 6904.76 + 7.24=6912 candidates
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