(a) Usually, „break-even analysis‟ is presented graphically as this method of visual presentation is particularly well-suited to the needs of business owing to the manager being able to appraise the situation at a glance. Thus, it removes the danger accompanying many accounting reports, a danger that the reader would get bogged down with unnecessary details in such a way that he may never come to grip with the heart of the matter. The graphical break-even analysis eliminate the details and presents the information in a simplified way. To that extent, it is especially attractive for a person of non-accounting background. When presented graphically the break-even analysis takes the shape of „break-even‟ chart or charts.
A break-even chart shows the profitability (or otherwise) of an undertaking at various levels of activity and, as a result, indicates the point at which neither profit is made nor loss is incurred. Break-even charts are frequently used and needed where a business is new or where it is experiencing trade
difficulties. In these cases, the chart assists management in considering the advantages and disadvantages of marginal sales. However, in a highly profitable enterprise, there is little need of break-even charts except when studying the implications of a major expansion scheme involving a heavy increase in fixed charges.
ILLUSTRATION 10-8
A company makes and sells a single product. The variable cost of production is N3 per unit, and the variable cost of selling is N1 per unit. Fixed costs totaled N6,000 and the unit sales price is N6. The company budgets to make and sell 3,600 units in the next year.
Required:
A break-even chart and a Profit-Volume graph, each showing the expected amount of output and sales required to break-even, and the safety margin in the budget.
SUGGESTED SOLUTION 10-8
A break-even chart records the amount of fixed costs, variable costs, total costs and total revenue at all volumes of sales and at a given sales price as follows:
Figure 10.1 Break-even Chart
Break-even point
6,000 18,000 21,600 Cost
N
Fixed costs
0 1000 2,000 3,000 3,600 4,000 Output/sales TR
TC
265
The break-even point is where revenues and total costs are exactly the same, so that there is neither profit nor loss. It may be expressed either in terms of units of sales or in terms of sales revenue. Reading from the graph (above), the break-even point would be determined as 3,000 units of sale and N18,000 in sales revenue.
The Profit-Volume graph is shown in figure 10-2 Margin of Safety (MOS)
The margin of safety is the amount by which actual output/sales may fall short of the budget without incurring a loss, usually expressed as percentage of the budgeted sales volume. It is, therefore, a crude measure of the risk that the company might make a loss if it fails to achieve budget. In this illustration, the margin of safety is:
Units
Budgeted sales 3,600
Break-even point 3,000
Margin of safety (MOS) 600
As a percentage of budgeted sales:
the MOS = (600/3,600 x 100%) = 16.7%
A high margin of safety indicates a good expectation of profit, even if budget is not achieved. In our illustration, it would not be clear without further investigation whether the safety margin in the budget is sufficient to indicate a good prospect of making profits. In other words, it would not be clear whether the forecast of 3,600 units of sale might be over optimistic by more than 16.67%.
Profit Volume Chart (P/V)
The profit/volume (P/V) chart, is similar to the break-even chart, and records the profit or loss at each level of sales at a given sale price. It is a straight line graph, drawn most simply by recording:
(a) The loss at zero sales, which is the full amount of fixed costs; and (b) The profit (or loss) at the budgeted level of sales; and joining up
the two points.
In our illustration, the profit volume graph would be:
Figure 10.2 P/V Chart
(a) The break-even point may be read from the graph as N18,000 in sales revenue, and the margin of safety is N3,600 in sales volume of 16.67% budgeted sales revenue
(b) Another way of presenting information pertaining to cost volume profit relationship is by using simple formulae. This could take two forms:
(i) Equation technique, or
(ii) Contribution margin technique.
The equation technique
This technique uses the formulae which also expresses the relationship of the items of income statement.
Sales = Variable Expenses + Fixed Expenses + Profit This simple equation may be adapted to any break-even or profit estimate situation.
Contribution Margin or Marginal Income Technique
This is obviously based on the concept of marginal costing.
Contribution margin is the difference between sales and variable Margin
safety of
Sales revenue Budget (N)
(N21,600) Break-even point
N18,000
6,000 Loss Profit N
267
expenses. Where break-even point is desired, sales and expenses are analysed thus:
Unit selling price – Unit variable expenses = Unit contribution to cover fixed expenses.
This unit contribution is divided into total fixed expenses to secure the number of units which have to be sold to break-even.
That is, Fixed expenses Contribution per unit
These two techniques can be illustrated by:
ILLUSTRATION 10-9
Alhaji Gazali plans to sell a toy rocket at Kano International Trade Fair.
He may purchase these rockets at N5 each, with the privilege of returning all unsold rockets. The booth rent at the fair is N2,000 payable in advance. The rockets will be sold at N9 each.
Determine the number of rockets, which must be sold, to break-even as well as the number of rockets to be sold to yield a 20 percent operating margin on sales.
SUGGESTED SOLUTION 10-9
ALHAJI GAZALI
(a) DETERMINATION OF ROCKETS TO BREAKEVEN Equation Technique
Sales = Variable costs + Fixed Costs + Profit.
Assuming that A is the number of units to be sold to break-even.
The values in the above formula can be substituted as follows:
9A = 5A + N2,000 + 0
9A – 5A = N2,000
Therefore 4A = N2,000 Therefore A = N2,000/4 Therefore A = 500 units.
DETERMINATION OF ROCKETS (b) TO YIELD 20% OF MARGIN OF SALES
Contribution Margin Technique
Unit selling price – Unit variable cost = Unit contribution to cover the fixed charges.
Substituting the values, we have:
N9 – N5 = N4 Then:
Fixed cost = No of units to be sold to break-even Contribution per unit
= N 2,000 = 500 units.
N4
Determination of volume at 20% profit on sales.
Sales = Variable costs + Fixed costs + Profit
Assuming that X is the number of units to be sold to yield desired profit, the values in the above formula can be substituted as:
9X = 5X + N2,000 + 0.2(9X) 9X = 5X + N2,000 + 1.8X 9X – 1.8X – 5X = N2,000
2.2X = N2,000
X = 909.09 units approximately.
or X = 910 units.
OTHER FORMULA TO DETERMINE COST VOLUME PROFIT
Other simple formula that can be used to determine cost-volume-profit relationship are as follow:
(a) Break-even point (in N)
= Fixed cost x Sales price/unit Contribution per unit
or Fixed cost x 1___
C/S ratio
269
(b) C/S ratio =Contribution per unit x 100 Sales price per unit
(c) Level of sales to result in target profit (in units)
= Fixed cost + Target profit Contribution per unit
(d) Level of sales to result in target profit (in N)
= Fixed cost + Target profit x Sales price/unit Contribution per unit
(e) Level of sales to result in target profit after tax (in units) Target profit = Fixed cost + (1 - tax rate)
Contribution per unit Note
The above formula are applicable only to single product firms or one with constant mix of sales. In case of a multi-product firms, the break- even point is calculated as follows:
Break-even point = Fixed cost x Sales value Contribution
ILLUSTRATION 10-10
Umar Ibrahim Nigeria Limited manufactures and sells a unique product. The selling price of which is N20.00.
The summarized profit and loss statement for last year is as follows:
N N
Sales 800,000
Direct materials 120,000
Direct wages 160,000
Variable production overhead 80,000
Fixed production overhead 100,000
Administration overhead 75,000
Selling and Distribution Overhead 60,000 595,000
Net Profit before tax 205,000
Less: provision for taxation (40%) 82,000
Net Profit after tax 123,000
Required
(a) Calculate the break-even point in naira and in units for last year.
(b) What do you understand by the terms profit volume ratio and margin
of safety. Illustrate using last year‟s result.
(c) Determine the number of units to sell in the current year to achieve an after-tax profit of N150,000.
(d) Calculate the sales value required to achieve a net profit before tax of 15% of total revenue.
(e) Assuming no change in unit selling price and cost structure, calculate the percentage increase in sales volume required in the current year to produce a profit before tax of 20% higher than last year‟s results.
(f) Calculate the selling price per unit that the company must charge in the current year to cover a potential increase of 12% in variable production costs this current year and still maintain last year‟s contribution margin ratio.
(g) Determine the volume of sales (in N) that the company must achieve in the current year to maintain the same net profit of last year, if the selling price remains at N20 and variable cost per unit increases by 12%.
(h) Recalculate last year‟s result if salesmen commission of 10% is introduced, selling price is reduced by 13% and volume increases by 30%.
SUGGESTED SOLUTION 10-10
(a) UMAR IBRAHIM NIGERIA LIMITED
(i) Break-even point (in N)
B/E point = Fixed Costs x selling price/unit Contribution/unit
= N235,000 x N20
11
= N427,273 (ii) Break-even point (in units) = Fixed costs Contribution/unit
= N235,000 11
= 21,364 units
271 Workings
1. Calculation of fixed costs:
N
Production overhead 100,000
Administration overhead 75,000 Selling & Distribution overhead 60,000 235,000 2. Contribution per unit:
Selling price per unit - Variable cost per unit N20 - N9 = N11
(b)(i) A profit volume (P/V) ratio indicates the relationship between contribution and revenue. It is otherwise referred to as contribution margin ratio (CMR) or contribution sales ratio (CSR).
It is calculated in the following ways:
P/V ratio = SP - VC SP
P/V ratio = CM SP
P/V ratio = TS - TVC TS
P/V ratio = Total contribution Total sales
P/V ratio = FC + Profit Total Sales
Calculation of P/V ratio:
P/V ratio = CM = N11 = 0.55 SP N20
Interpretation
The P/V ratio of 0.55 means that for every one N sale generated 55 kobo would accrue as contribution margin.
(ii) Margin of safety: It shows the difference between the sales level and the break-even point. It could be expressed either in units or in monetary terms. It could also be expressed in relation to sales (in percentage term).
Calculation of Margin of Safety
N units
Sales (B) 800,000 40,000
Break-even point 427,273 21,364 Margin of safety (A) 372,727 18,636 in percentage term:
(A/B x 100%) 47% 47%
The margin of safety of 47% means that sales must fall by more than 47% before a loss is sustained.
(c) Level of sales required to achieve a target profit (after tax) of N150,000 (in units).
The answer is given by:
Target profit
FC + Target Profit (1 - tax rate)
Contribution per unit
= N235,000 + (150,000 /(1 - 0.4)) 11
= 235,000 + 250,000 11
= 44,091 units
(d) Level of sales to result in net profit before tax of 15% of total revenue.
Y = Fixed Cost + Target profit Contribution margin ratio Y = 235,000 + 0.15Y
0.55 0.55Y = N235,000 + 0.15Y 0.55Y – 0.15Y = N235,000 0.40Y = N235,000 Y = N235,000
0.4
= N587,500
273 Workings
Contribution margin ratio is determined as follows:
= Selling price - Variable cost Selling price
= 20 - 9
20
= 11 20
= 0.55
(e) Level of sales to result in target profit.
= Fixed costs + Target profit Contribution per unit
= N235,000 + (120% of 205,000) 11
= N235,000 + N246,000 11
= 43,727 units Percentage increase:
= 43,727 units - 40,000 units x 100%
40,000 units
= 9.32%
(f) Contribution margin ratio of last year = contribution margin ratio of this year 0.55 = Revised SP - Revised VC per unit (RSP - RVC/U) Revised SP. (RSP)
0.55 RSP = RSP - RVC/U
0.55 RSP = RSP - (3 + 4 + (2 x 1.12)) 0.55 RSP = RSP - 9.24
0.55 RSP - RSP = -9.24 -0.45 RSP = -9.24
RSP = -9.24 -0.45
= N20.53
(g) Sales value required to achieve a target profit of N205,000
= FC + TP x Unit selling price Contribution/unit
= N235,000 + 205,000 x N20 9.92
= N887,097 Workings
Contribution per unit is determined as follows:
= SP - RVC/U
= N20 - (N9 x 1.12)
= N20 - N10.08 = N 9.92 (h) Revised Income Statement
N N Sales ((N20 x 0.87) x (40,000 x1.30)) 904,800 Less: Variable production 468,000
overhead (52,000 x 9)
Salesmen Comm. (10% of 904,800) 90,480 558,480
Total Contribution 346,320
Less: Fixed Costs 235,000
Net Profit before tax 111,320
Less: 30% tax 33,396
Net Profit after tax 77,924