Financial Accounting Fundamentals

Contribution Margin Ratio and BEP in Rupees

Contribution Margin Ratio (C/M Ratio or P/V Ratio)

The contribution margin ratio expresses contribution margin as a percentage of sales revenue. It shows how much of each rupee of sales is available to cover fixed costs and then contribute to profit.

$\text{C/M Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}} \times 100$

where:

$\text{Contribution Margin (CM)} = \text{Sales} - \text{Variable Costs}$

Alternative formulas:

$\text{C/M Ratio} = \frac{\text{Change in Profit}}{\text{Change in Sales}} \times 100$

$\text{C/M Ratio} = 1 - \frac{\text{Variable Cost}}{\text{Sales}} = 1 - \text{Variable Cost Ratio}$

Break-Even Point (BEP) in Rupees

The BEP in rupees is the sales revenue at which total contribution equals total fixed cost, so profit is zero.

$\text{BEP (in Rs)} = \frac{\text{Fixed Cost}}{\text{C/M Ratio}}$

Equivalently:

$\text{BEP (in Rs)} = \frac{\text{Fixed Cost}}{1 - \dfrac{\text{Variable Cost}}{\text{Sales}}}$

Illustration

Fixed cost = Rs 40,000; Selling price per unit = Rs 20; Variable cost per unit = Rs 12.

Contribution margin per unit = Rs 20 − Rs 12 = Rs 8

$\text{C/M Ratio} = \frac{8}{20} \times 100 = 40\%$

$\text{BEP (in Rs)} = \frac{40{,}000}{0.40} = \text{Rs } 1{,}00{,}000$

Interpretation

• A C/M ratio of 40% means 40 paisa of every sales rupee covers fixed cost and profit.
• At Rs 1,00,000 sales, total contribution = Rs 40,000, which exactly equals fixed cost, so profit is nil.
• Sales above Rs 1,00,000 yield profit; sales below it yield loss.

The question as printed does not give the cost structure, so before-tax profit cannot be found from sales alone. We need the variable cost ratio (or variable cost) and the fixed cost.

$\text{Before-tax profit} = \text{Sales} - \text{Variable cost} - \text{Fixed cost} = S(1 - V) - F$

where $S$ = sales, $V$ = variable cost ratio and $F$ = fixed cost.

Illustration (assumed data: variable cost 60% of sales, fixed cost Rs 300,000):

$\text{Contribution} = 2{,}500{,}000 \times 0.40 = \text{Rs } 1{,}000{,}000$

$\text{Before-tax profit} = 1{,}000{,}000 - 300{,}000 = \text{Rs } 700{,}000$

If the original paper gives a different variable cost ratio or fixed cost, substitute those values into the same formula.

The question does not state the selling price, variable cost or fixed cost, so the method is given first and then applied to assumed data.

Method

$\text{Pre-tax profit required} = \frac{\text{After-tax profit}}{1 - \text{tax rate}} = \frac{210{,}000}{1 - 0.30} = \frac{210{,}000}{0.70} = \text{Rs } 300{,}000$

$\text{Required units} = \frac{\text{Fixed cost} + \text{Pre-tax profit required}}{\text{Contribution per unit}}$

Illustration (assumed: selling price Rs 100, variable cost Rs 60 per unit, fixed cost Rs 200,000)

$\text{Contribution per unit} = 100 - 60 = \text{Rs } 40$

$\text{Required units} = \frac{200{,}000 + 300{,}000}{40} = 12{,}500 \text{ units}$

Therefore 12,500 units must be sold to earn an after-tax profit of Rs 210,000. With the actual figures of the original paper, use the same steps. Sales value needed is units $\times$ selling price (here Rs 1,250,000).

Working notes

Total overhead $= 288{,}000 + 200{,}000 + 170{,}000 + 125{,}000 =$ Rs 783,000.

(a) Traditional costing (overhead on DLH)

$\text{Overhead rate} = \frac{783{,}000}{57{,}000} = \text{Rs } 13.7368 \text{ per DLH}$

(b) Activity-based costing

(c) Why ABC is more appropriate

1. Multiple cost drivers: traditional costing spreads all overhead on one volume base (DLH), while ABC uses a driver for each activity (machine hours, runs, orders).
2. More accurate product cost: here the total is the same (Rs 4,613,000) but the split differs. Product C is charged Rs 324.95 per unit traditionally and Rs 322.24 under ABC, while A rises from Rs 189.34 to Rs 190.10 and B from Rs 251.21 to Rs 254.93. Traditional costing over-costs products with high DLH and under-costs those that use many runs and orders.
3. Cause-and-effect link: overhead follows the activities that actually consume resources.
4. Better decisions: reliable costs support pricing, product mix and make-or-buy decisions.
5. Better cost control: ABC shows which activities (scheduling, procurement) are costly and can be reduced.
6. Fits modern production: where overhead is large relative to labour, DLH is a poor base.

Hence ABC gives more accurate and decision-useful product costs than the traditional approach.

Management accounting is the branch of accounting that collects, analyses, interprets and communicates economic information to internal management so that the managerial functions of planning, decision making and control can be performed efficiently. Unlike financial accounting, which reports to outsiders, management accounting serves managers inside the organisation. The statement can be explained by taking each of the three management processes in turn.

1. Planning. Planning means setting objectives and deciding in advance how to achieve them. Management accounting supplies the economic information needed to prepare budgets, forecasts and standards. For example, a company planning next year's production prepares a sales budget from past sales data, market trends and cost estimates. The budget quantifies the plan in rupees and units, and also provides the yardstick against which actual performance will later be compared.

2. Decision making. Managers must choose among alternatives — make or buy, accept or reject a special order, continue or discontinue a product, replace or retain a machine. Management accounting provides relevant cost and revenue data for such choices. For example, if a firm can buy a component for Rs 80 per unit while its own variable cost of manufacture is Rs 95 (fixed costs being unavoidable), the relevant cost analysis shows that buying saves Rs 15 per unit, so the decision is to buy. Techniques such as marginal costing, CVP analysis and differential costing are used here.

3. Control. Control means comparing actual performance with the planned standards and taking corrective action. Management accounting supplies performance reports, variance analysis and responsibility accounting information. For example, if the standard material cost of producing 1,000 units is Rs 50,000 but the actual cost is Rs 56,000, the material cost variance of Rs 6,000 (adverse) is reported to the production manager, who investigates the causes — price rise or wastage — and takes corrective steps. Budgetary control and standard costing are the main tools.

Illustration (combined example): A company budgets sales of 10,000 units at Rs 100 each with a variable cost of Rs 60 per unit and fixed cost of Rs 2,00,000, giving a planned profit of Rs 2,00,000. During the year actual sales are only 9,000 units. The management accounting report shows a sales volume variance of Rs 40,000 adverse (1,000 units × Rs 40 contribution). On the basis of this information management (a) plans a revised sales target, (b) decides to increase advertising by Rs 30,000 to push sales, and (c) controls operations by fixing responsibility on the sales manager for the shortfall. Thus the same economic information serves planning, decision making and control.

Conclusion. Management accounting is not an end in itself but a means of supplying economic information — costs, revenues, budgets, variances and forecasts — that makes planning realistic, decision making rational and control effective. Hence the statement is fully justified.

Working data

• Actual material: Rs 150,000 $\div$ Rs 50 = 3,000 kg (AQ, AR = Rs 50)
• Actual labour: Rs 49,500 $\div$ Rs 55 = 900 hours (AH, AR = Rs 55)
• Standard for 1,000 units: materials SQ $= 1{,}000 \times 5 = 5{,}000$ kg at Rs 60; labour SH $= 1{,}000 \times 2 = 2{,}000$ hours at Rs 50

i. Material variances

$\text{MPV} = AQ \times (SR - AR) = 3{,}000 \times (60 - 50) = \text{Rs } 30{,}000 \text{ (F)}$

$\text{MUV} = SR \times (SQ - AQ) = 60 \times (5{,}000 - 3{,}000) = \text{Rs } 120{,}000 \text{ (F)}$

$\text{MCV} = SQ \times SR - AQ \times AR = 300{,}000 - 150{,}000 = \text{Rs } 150{,}000 \text{ (F)}$

Check: 30,000 + 120,000 = 150,000.

ii. Labour variances

$\text{LRV} = AH \times (SR - AR) = 900 \times (50 - 55) = \text{Rs } 4{,}500 \text{ (A)}$

$\text{LEV} = SR \times (SH - AH) = 50 \times (2{,}000 - 900) = \text{Rs } 55{,}000 \text{ (F)}$

$\text{LCV} = 100{,}000 - 49{,}500 = \text{Rs } 50{,}500 \text{ (F)}$

Check: $-4{,}500 + 55{,}000 = 50{,}500$.

Materials were bought cheaper and used far less than standard, and labour was efficient, though paid a higher rate than standard.

Let $X$ = units (in thousands) and $Y$ = manufacturing cost of goods sold (Rs in thousands). Here $n = 5$.

i. Least square method ($Y = a + bX$)

$b = \frac{n\sum XY - \sum X \sum Y}{n\sum X^2 - (\sum X)^2} = \frac{5(1{,}300) - 20(250)}{5(110) - 400} = \frac{1{,}500}{150} = 10$

$a = \bar{Y} - b\bar{X} = 50 - 10(4) = 10$

So $Y = 10 + 10X$: fixed cost = Rs 10,000 and variable cost = Rs 10 per unit.

ii. Coefficient of determination

$r = \frac{n\sum XY - \sum X\sum Y}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]}} = \frac{1{,}500}{\sqrt{150 \times (77{,}500 - 62{,}500)}} = \frac{1{,}500}{\sqrt{150 \times 15{,}000}} = \frac{1{,}500}{1{,}500} = 1$

$r^2 = 1 \text{ (100\%)}$

All the variation in cost is explained by the number of units; the points lie exactly on the line.

iii. Standard error of regression

$S_e = \sqrt{\frac{\sum Y^2 - a\sum Y - b\sum XY}{n - 2}} = \sqrt{\frac{15{,}500 - 10(250) - 10(1{,}300)}{3}} = \sqrt{\frac{0}{3}} = 0$

The standard error is zero, so the fitted line predicts cost without error. The estimated cost at any activity level is Rs 10,000 + Rs 10 $\times$ units.

Opening stock $=$ Sales $+$ Closing stock $-$ Production $= 42{,}000 + 2{,}000 - 38{,}000 =$ 6,000 units

Working notes

$\text{Fixed overhead absorption rate} = \frac{120{,}000}{40{,}000} = \text{Rs } 3 \text{ per unit}$

Fixed overhead absorbed $= 38{,}000 \times 3 =$ Rs 114,000, so under-absorbed overhead $= 120{,}000 - 114{,}000 =$ Rs 6,000.

i. Income statement under absorption costing

ii. Profit under variable costing (with reconciliation)

Reconciliation

Since sales exceed production, stock falls, and absorption costing shows Rs 12,000 less profit than variable costing.

Step 1: Separate the mixed costs

Repair and maintenance (high-low method):

$\text{Variable cost per unit} = \frac{60{,}000 - 40{,}000}{10{,}000 - 5{,}000} = \text{Rs } 4$

$\text{Fixed cost} = 40{,}000 - 4 \times 5{,}000 = \text{Rs } 20{,}000$

Step 2: Total cost

Total cost $= 30{,}000 + 42 \times \text{units}$

Cost per unit falls from Rs 48 to Rs 45 because the fixed cost of Rs 30,000 is spread over more units.