Answer

Management accounting is the branch of accounting that supplies accounting information to internal management for planning, controlling, decision-making and performance evaluation. Its primary objective is not to record transactions for outsiders (as in financial accounting) but to help management as a whole carry out its duties effectively and efficiently. This becomes clear from its functions:

1. Planning and Forecasting: Management accounting supplies historical data, budgets, standard costs and forecasts (cash budget, sales budget, production budget). These help management set objectives and choose the best course of action in advance. Thus it assists the "planning" duty of management.

2. Controlling Performance: By preparing budgets and standards and comparing actual results with them (budgetary control, standard costing, variance analysis), management accounting locates deviations and the responsibility centres causing them. Corrective action can then be taken. This fulfils the "controlling" duty.

3. Decision-Making: It supplies relevant information for decisions such as make-or-buy, shut-down or continue, accept or reject an order, product mix, replacement of machinery, and lease or buy. Tools like marginal costing, CVP analysis and differential cost analysis make the choice rational. Thus it serves the "decision-making" duty.

4. Organising and Coordinating: Management accounting fixes responsibility centres (cost centres, profit centres, investment centres) and reports results to each level. This coordinates the activities of different departments and keeps them directed towards the common goal.

5. Motivating Employees: Budgets, standards and performance reports, linked with rewards and responsibility accounting, motivate managers and workers to improve efficiency.

6. Communicating and Reporting: It prepares periodic reports, statements and summaries in a simple, understandable form and communicates them to all levels of management, so that each level knows its target and achievement.

7. Evaluating Efficiency: Through ratio analysis, fund flow and cash flow analysis, value added statements and inter-firm comparison, it measures the efficiency of the business as a whole and of each division.

8. Maintaining Records: It maintains cost records, budgets and reports which serve as a ready reference for future planning and control.

Conclusion: All these functions show that management accounting is not merely a recording device; it is a tool that supplies the information management needs at every stage — planning, organising, directing, coordinating, controlling and decision-making. Hence the statement that its primary objective is to help management as a whole carry out its duties effectively and efficiently is fully justified.

Cost Volume Profit (CVP) Analysis — Importance

CVP analysis examines the relationship between cost, volume of output/sales, and profit. It rests on the behaviour of costs (fixed and variable), the contribution margin, the break-even point, and the margin of safety. Its importance as a management accounting technique can be discussed as follows:

1. Profit planning. CVP analysis shows how profit changes with changes in sales volume, selling price, and cost. Management can compute the sales volume required to earn a target profit, or the profit at any given level of activity. This makes profit planning systematic rather than guesswork.

2. Break-even analysis. It determines the break-even point — the sales volume at which total revenue equals total cost and profit is zero. This tells management the minimum level of activity the firm must achieve to avoid losses, and is the base for all planning decisions.

3. Margin of safety. By measuring the excess of actual or budgeted sales over break-even sales, CVP analysis indicates how much sales can fall before a loss arises. A high margin of safety signals a comfortable position; a low one warns management to act.

4. Policy formulation. CVP analysis supplies data for key policies — pricing policy (minimum price, price reduction effects), product-mix policy (which products give the highest contribution per limiting factor), make-or-buy policy, and shut-down or continue policy. Decisions are based on contribution, not on total profit alone.

5. Decision-making. It helps in evaluating alternatives such as accepting a special order at a lower price, expanding sales through advertising, changing the sales mix, or replacing labour with machinery. The alternative giving the highest contribution or profit can be selected.

6. Cost control. By separating fixed and variable costs and highlighting the contribution margin, CVP analysis directs attention to variable costs that vary with volume and to fixed costs that must be recovered. It thus assists in cost control and cost reduction.

7. Performance evaluation and control. Comparison of actual sales, contribution, and profit with the break-even and budgeted figures helps management evaluate performance, identify deviations, and take corrective action. It also aids in preparing flexible budgets.

8. Forecasting and decision support. CVP analysis provides a simple, quantitative model for forecasting the effect of changes in volume, price, and cost on profit, and for choosing among competing courses of action.

Conclusion. CVP analysis is thus a vital tool for planning, policy formulation, decision-making, and control. However, it is based on assumptions — constant selling price, constant variable cost per unit, constant fixed cost, and a single product or constant sales mix — so its results should be used with judgement, not as a substitute for managerial discretion.

Given Data:

• Production: 40,000 units
• Sales: 38,000 units
• Selling price: Rs 20/unit
• Direct Material: Rs 5.00/unit
• Direct Labour: Rs 4.00/unit
• Variable Mfg OH: Rs 2.00/unit
• Fixed Mfg cost: Rs 120,000
• Variable Office & Selling: Rs 2.00/unit sold
• Fixed Office & Selling: Rs 150,000
• Opening FG inventory: 1,000 units @ Rs 12.00 (variable mfg portion Rs 10.00)
• Closing FG = 1,000 + 40,000 − 38,000 = 3,000 units

Fixed Mfg OH rate = 120,000/40,000 = Rs 3.00/unit Full cost/unit = 5+4+2+3 = Rs 14.00 Variable mfg cost/unit = 5+4+2 = Rs 11.00

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(a) FIFO

Absorption Costing

COGS (FIFO): 1,000 × 12 + 37,000 × 14 = 12,000 + 518,000 = 530,000

Variable Costing

Variable COGS (FIFO): 1,000 × 10 + 37,000 × 11 = 10,000 + 407,000 = 417,000

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(b) LIFO

Absorption Costing

COGS (LIFO): 38,000 × 14 = 532,000

Variable Costing

Variable COGS (LIFO): 38,000 × 11 = 418,000

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Reconciliation

Given Data

Fixed factory overhead = Rs 150,000 Available raw materials = 24,000 units Available direct labour = 18,000 DLH Tax rate = 40%

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a. Overall Break Even in Units

Since the products are sold equally, the sales mix is 1 : 1, i.e., a composite unit = 1 unit of A + 1 unit of B.

Composite contribution per unit:

$= 22 + 28 = \text{Rs } 50$

Composite break even units:

$BEP = \frac{\text{Fixed Cost}}{\text{Composite Contribution}} = \frac{150{,}000}{50} = 3{,}000 \text{ composite units}$

Break even in individual units:

• Product A = 3,000 × 1 = 3,000 units
• Product B = 3,000 × 1 = 3,000 units
• Total break even units = 6,000 units

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b. Required Sales Level for Rs 85,000 After-Tax Profit

Desired before-tax profit:

$= \frac{85{,}000}{1 - 0.40} = \frac{85{,}000}{0.60} = \text{Rs } 141{,}666.67$

Required composite units:

$= \frac{150{,}000 + 141{,}666.67}{50} = \frac{291{,}666.67}{50} = 5{,}833.33 \approx 5{,}834 \text{ composite units}$

Required sales in units:

• Product A = 5,834 units
• Product B = 5,834 units
• Total = 11,668 units

Required sales in rupees:

$= (5{,}834 \times 60) + (5{,}834 \times 70) = 350{,}040 + 408{,}380 = \text{Rs } 758{,}420$

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c. Application of Linear Programming Model for Profit Maximization

Let $x_1$ = units of Product A, $x_2$ = units of Product B

Objective function:

$\text{Maximize } Z = 22x_1 + 28x_2$

Subject to constraints:

$x_1 + 2x_2 \le 24{,}000 \quad \text{(raw material)}$ $3x_1 + 4x_2 \le 18{,}000 \quad \text{(direct labour)}$ $x_1, x_2 \ge 0$

Contribution per scarce resource:

Product A gives higher contribution per unit of both scarce resources, so produce A first.

Solving the constraints:

Raw material: if $x_2 = 0$, $x_1 = 24{,}000$ Labour: if $x_2 = 0$, $x_1 = 6{,}000$ ← binding constraint

Feasible region: Setting $x_1 = 0$, labour allows $x_2 = 4{,}500$ while raw material allows $x_2 = 12{,}000$, so labour binds. Setting $x_2 = 0$, labour allows $x_1 = 6{,}000$ while raw material allows $x_1 = 24{,}000$, so labour binds again. The two constraint lines meet only at $x_1 = -30{,}000$, outside the positive quadrant, so the raw material constraint is never binding.

Feasible corner points:

Optimal solution: Produce 6,000 units of A and 0 units of B.

$\text{Maximum contribution} = \text{Rs } 132{,}000$ $\text{Maximum profit} = 132{,}000 - 150{,}000 = \text{(Rs } 18{,}000\text{)} \text{ loss}$

Since labour is the binding constraint and A yields higher contribution per DLH, the company should produce only Product A. However, even at optimum the firm incurs a loss of Rs 18,000.

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d. Probability of Sales Mix at Least Break Even

Break even total units = 6,000 (from part a).

$P(\text{at least break even}) = 0.3 + 0.4 + 0.1 = 0.8 = \mathbf{80\%}$

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e. Assumptions of Cost-Volume-Profit (CVP) Analysis

1. Constant selling price — selling price per unit does not change with volume.
2. Constant variable cost — variable cost per unit remains fixed; total variable cost varies proportionately with output.
3. Fixed cost remains constant — total fixed cost does not change within the relevant range.
4. Single product or constant sales mix — for multi-product firms, the sales mix is assumed constant.
5. All costs are classified into fixed and variable components.
6. Production equals sales — no change in inventory (no opening/closing stock difference).
7. Linear revenue and cost behaviour — total revenue and total cost are straight lines over the relevant range.
8. Technology and efficiency remain unchanged during the period.
9. Short-run analysis — factors of production and capacity are assumed constant.

Green Accounting (also called Environmental Accounting) is the process of identifying, measuring, recording, and reporting the costs, benefits, and impacts of an organisation's activities on the natural environment, and integrating them into the conventional financial accounting statements. It extends the traditional accounting framework by assigning monetary values to environmental resources consumed (such as water, timber, fuel, and minerals), to environmental degradation caused (such as pollution, waste, and emissions), and to environmental protection measures undertaken (such as pollution control equipment, waste treatment, and afforestation). In short, it is an accounting system that recognises the environment as a stakeholder and reflects the "environmental cost" and "environmental benefit" of business operations alongside ordinary financial results. It is also known as Environmental Management Accounting (EMA) or Sustainability Accounting.

Importance of Green Accounting

1. True and complete financial reporting: Conventional accounting ignores the free use of natural resources and the cost of pollution, so profit is overstated. Green accounting captures these hidden environmental costs, giving a more accurate and realistic picture of the firm's actual performance and net contribution.

2. Better decision-making: By identifying environmental costs separately (e.g., energy, waste disposal, effluent treatment, compliance penalties), management can decide on cleaner technologies, recycling, waste minimisation, and resource-efficient processes that reduce long-run costs.

3. Regulatory compliance and legal protection: It helps the firm comply with environmental laws, standards, and reporting requirements (such as pollution control norms), thereby avoiding fines, penalties, litigation, and shutdown risks.

4. Improved corporate image and goodwill: Disclosure of environmental responsibility builds public trust, strengthens the brand, and improves relations with customers, investors, government, and local communities.

5. Support to sustainable development: It encourages the conservation of natural resources and reduction of pollution, ensuring that present needs are met without compromising the ability of future generations to meet their own needs.

6. Access to finance and investment: Environmentally responsible firms attract green finance, socially responsible investors, and international funding agencies, and may also enjoy tax concessions and subsidies.

7. Cost control and competitive advantage: Proper accounting of environmental costs reveals opportunities for savings in materials, energy, and waste, which lowers production cost and creates a competitive edge in both domestic and global markets.

8. Support to national income accounting: At the macro level, green accounting helps adjust GDP for environmental depletion and degradation (Green GDP), giving policymakers a truer picture of national welfare and growth.

Thus, green accounting is important because it links business profitability with environmental responsibility, helping firms, society, and the nation achieve economic growth along with ecological balance.

Step 1: Separate fixed and variable costs

Step 2: Flexible budget

Check: at 8,000 units, $8{,}000 \times 21 + 47{,}000 = 215{,}000$, and at 14,000 units, $14{,}000 \times 21 + 47{,}000 = 341{,}000$, both matching the given data.

a. Segregation of mixed cost by least squares method

Let output units = $x$, mixed cost = $y$, $n = 5$.

Normal equations:

$\sum y = na + b\sum x$ $\sum xy = a\sum x + b\sum x^2$

Substituting:

$25,000 = 5a + 1,500b \quad \text{...(i)}$ $8,500,000 = 1,500a + 550,000b \quad \text{...(ii)}$

From (i): $a = \dfrac{25,000 - 1,500b}{5} = 5,000 - 300b$

Substituting in (ii):

$8,500,000 = 1,500(5,000 - 300b) + 550,000b$ $8,500,000 = 7,500,000 - 450,000b + 550,000b$ $1,000,000 = 100,000b$ $b = \text{Rs } 10 \text{ per unit (variable cost)}$

$a = 5,000 - 300(10) = \text{Rs } 2,000 \text{ (fixed cost)}$

Cost function: $y = 2,000 + 10x$

Thus, fixed cost = Rs 2,000 and variable cost = Rs 10 per unit.

b. Coefficient of determination

$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$

$r = \frac{5(8,500,000) - (1,500)(25,000)}{\sqrt{[5(550,000) - (1,500)^2][5(135,000,000) - (25,000)^2]}}$

$r = \frac{42,500,000 - 37,500,000}{\sqrt{(2,750,000 - 2,250,000)(675,000,000 - 625,000,000)}}$

$r = \frac{5,000,000}{\sqrt{(500,000)(50,000,000)}} = \frac{5,000,000}{\sqrt{25,000,000,000,000}} = \frac{5,000,000}{5,000,000} = 1$

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

Interpretation: The coefficient of determination is 1 (100%), meaning the mixed cost is perfectly explained by the output units. Every variation in total mixed cost is fully accounted for by the change in output level, so the cost equation $y = 2,000 + 10x$ fits the data exactly with no unexplained variation.

Working

• Standard cost of the standard mix $= 300 \times 40 + 400 \times 50 + 300 \times 60 = 12{,}000 + 20{,}000 + 18{,}000 =$ Rs 50,000 for 1,000 units of input and 900 units of output.
• Standard cost per unit of output $= 50{,}000 / 900 =$ Rs 55.56
• Actual cost $= 400 \times 50 + 200 \times 40 + 400 \times 55 = 20{,}000 + 8{,}000 + 22{,}000 =$ Rs 50,000
• Standard cost for actual output $= 800 \times 55.56 =$ Rs 44,444.44
• Actual input is 1,000 units, so the revised standard quantity (standard mix applied to actual input) is A 300, B 400, C 300.

(a) Material price variance $= (SP - AP) \times AQ$

(b) Material mix variance $= (RSQ - AQ) \times SP$

(c) Material yield variance $= (\text{Actual yield} - \text{Standard yield}) \times \text{Standard cost per unit} = (800 - 900) \times 55.56 =$ Rs 5,555.56 (A)

(d) Material usage variance $=$ mix variance $+$ yield variance $= 0 + 5{,}555.56 =$ Rs 5,555.56 (A)

(e) Material cost variance $=$ standard cost for actual output $-$ actual cost $= 44{,}444.44 - 50{,}000 =$ Rs 5,555.56 (A)

Check: price (nil) + mix (nil) + yield (5,555.56 A) = 5,555.56 (A).

Comment

• The price variance is nil because the Rs 4,000 adverse variance on A is exactly offset by favourable variances on B and C.
• The mix variance is also nil, since the total input of 1,000 units is the same as standard and the gains and losses between materials net out.
• The whole adverse cost variance comes from yield: 1,000 units of input produced only 800 units of output instead of 900, a loss of 100 units. Management should investigate wastage, quality of materials and process efficiency.

Contribution Margin Ratio and BEP in Rupees

1. Contribution Margin Ratio (CMR)

Meaning: The contribution margin ratio (also called the profit–volume ratio or P/V ratio) expresses contribution as a percentage of sales. It shows how much of each rupee of sales is available to cover fixed costs and then to provide profit.

Formula:

$\text{CMR} = \frac{\text{Contribution}}{\text{Sales}} \times 100$

where,

$\text{Contribution (C)} = \text{Sales} - \text{Variable Cost}$

Alternative formulas:

$\text{CMR} = \frac{\text{Sales} - \text{Variable Cost}}{\text{Sales}} \times 100 = \left(1 - \frac{\text{Variable Cost}}{\text{Sales}}\right) \times 100$

$\text{CMR} = \frac{\text{Fixed Cost} + \text{Profit}}{\text{Sales}} \times 100$

$\text{CMR} = \frac{\text{Change in Profit}}{\text{Change in Sales}} \times 100$

Interpretation: A CMR of, say, 40% means that out of every Rs 100 of sales, Rs 40 is contribution and Rs 60 is variable cost. The higher the CMR, the more profitable the product or firm.

2. Break-Even Point (BEP) in Rupees

Meaning: BEP is the level of sales at which total revenue equals total cost, i.e. contribution exactly equals fixed cost and profit is nil. BEP in rupees means that amount of sales value (not units) required to cover all costs.

Formula:

$\text{BEP (in Rs)} = \frac{\text{Fixed Cost}}{\text{CMR}} \quad \text{or} \quad \frac{\text{Fixed Cost}}{\text{P/V Ratio}}$

Since CMR is a percentage, it is used in decimal form:

$\text{BEP (in Rs)} = \frac{\text{Fixed Cost}}{\text{Contribution}} \times \text{Sales}$

Related formulas:

$\text{Sales at desired profit (in Rs)} = \frac{\text{Fixed Cost} + \text{Desired Profit}}{\text{CMR}}$

$\text{Margin of Safety (in Rs)} = \text{Actual Sales} - \text{BEP Sales}$

3. Illustration

Given:

• Selling price per unit = Rs 50
• Variable cost per unit = Rs 30
• Fixed cost = Rs 40,000
• Actual sales = Rs 1,50,000

Solution:

Contribution per unit = Rs 50 − Rs 30 = Rs 20

$\text{CMR} = \frac{20}{50} \times 100 = \textbf{40\%}$

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

Verification:

• BEP units = Rs 1,00,000 ÷ Rs 50 = 2,000 units
• Contribution at BEP = 2,000 × Rs 20 = Rs 40,000 = Fixed cost ✓

Margin of Safety = Rs 1,50,000 − Rs 1,00,000 = Rs 50,000

4. Significance

• CMR helps in deciding product mix, fixing selling price, and selecting the most profitable product.
• BEP in rupees shows the minimum sales value needed to avoid loss, and is useful when a firm sells multiple products where BEP in units cannot be computed.
• Both are tools of cost–volume–profit (CVP) analysis used for profit planning and managerial decision-making.

The figure given (sales of Rs 2,500,000) is not enough on its own to find the profit. Before-tax profit under cost-volume-profit (CVP) analysis needs the P/V ratio (or variable cost) and the fixed cost:

$\text{Contribution} = \text{Sales} \times \text{P/V ratio}$

$\text{Before-tax profit} = \text{Contribution} - \text{Fixed cost} = (2{,}500{,}000 \times \text{P/V ratio}) - \text{Fixed cost}$

Equivalently, $\text{Profit} = \text{Sales} - \text{Variable cost} - \text{Fixed cost}$. Substitute the P/V ratio (or variable cost) and fixed cost from the full question to get the figure; the profit changes by Rs 2,500,000 × P/V ratio for every such change in the ratio.

Step 1: Convert the after-tax target into before-tax profit.

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

Step 2: Units required.

$\text{Units} = \frac{\text{Fixed cost} + \text{Target before-tax profit}}{\text{Contribution margin per unit}} = \frac{\text{Fixed cost} + 3{,}00{,}000}{\text{Selling price} - \text{Variable cost per unit}}$

The fixed cost and the contribution per unit come from the data of the full question (the part of the question giving them is not shown here). For example, with fixed cost Rs 1,20,000 and contribution of Rs 20 per unit, units needed $= \frac{1{,}20{,}000 + 3{,}00{,}000}{20} = 21{,}000$ units.

Traditional vs Activity-Based Costing — Statement of Total Cost and Cost per Unit

Given Data

Overhead costs and drivers:

Direct labour cost per hour = Rs 16. Production run size = 500 units each.

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Working Notes

1. Total Direct Labour Hours (DLH)

2. Total Machine Hours

3. Number of Production Runs

$= \frac{\text{Output Units}}{500}$

4. Direct Labour Cost

5. Material Cost

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(a) Traditional Costing Approach (Overhead absorbed on DLH basis)

$\text{Overhead absorption rate} = \frac{7,83,000}{57,000} = \text{Rs } 13.7368 \text{ per DLH}$

Statement of Total Cost and Cost per Unit

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(b) Activity-Based Costing Approach

Step 1: Cost Driver Rates

Step 2: Overhead Apportioned to Products

Step 3: Statement of Total Cost and Cost per Unit

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(c) Why ABC is More Appropriate than Traditional Costing

1. Single volume-based rate is misleading: Traditional costing absorbs all overheads using one driver (DLH). It assumes every overhead is driven by labour hours. In reality, machine cost, scheduling cost and procurement cost behave differently. ABC uses separate cost drivers for each activity, so overhead is traced to products on the basis of the activity that actually causes it.

2. Product cost distortion: Under traditional costing, high-volume products (C) are overcharged and low-volume products (A) are undercharged, because a large part of overhead is fixed and does not vary with volume. ABC corrects this distortion — as seen above, A's cost rises from Rs 154.34 to Rs 155.10 while C's falls from Rs 268.95 to Rs 266.24.

3. Better information for decisions: ABC gives more accurate product costs, which helps in correct pricing, product-mix decisions, make-or-buy decisions, and identification of non-value-added activities. Traditional costing can lead to wrong decisions because it hides the true cost of complexity (more orders, more runs, more setups).

4. Focus on activities, not just volume: ABC recognises that overheads are caused by activities such as scheduling and procurement. Managing these activities reduces cost. Traditional costing gives no such information.

Conclusion: ABC is comparatively more appropriate because it establishes a cause-and-effect relationship between cost drivers and overhead costs, giving more reliable product costs, especially where products differ in volume, batch size and complexity.

Management accounting is the branch of accounting that collects, analyses and communicates economic information (costs, revenues, profits, cash flows, variances) to internal users — managers — so that they can carry out the management process of planning, decision making and control. Unlike financial accounting, it is not bound by GAAP, is future-oriented, and reports to managers rather than outsiders. The statement can be explained by taking each of the three functions in turn.

1. Planning. Planning means setting objectives and deciding in advance how to achieve them — sales budgets, production budgets, cash budgets, capital expenditure budgets. Management accounting supplies the economic information on which these budgets rest: expected selling price, variable cost per unit, fixed costs, contribution margin, expected cash inflows and outflows. Illustration: a company expects to sell 10,000 units at Rs 200 each with variable cost Rs 120 and fixed cost Rs 5,00,000. Management accounting computes contribution of Rs 80 per unit and a break-even point of 6,250 units, so the budgeted sales figure of 10,000 units is shown to yield a profit of Rs 3,00,000 — a plan that is financially feasible.

2. Decision making. Managers must choose among alternatives — make or buy, accept or reject a special order, replace or retain a machine, drop or continue a product line. Management accounting provides the relevant (differential) cost and revenue data for such choices. Illustration: a special order is received for 2,000 units at Rs 150 each when normal price is Rs 200. Since variable cost is only Rs 120, the order gives a contribution of Rs 30 × 2,000 = Rs 60,000, and if idle capacity exists it should be accepted — a decision supported purely by the relevant-cost information supplied by management accounting.

3. Control. Control means comparing actual performance with the plan and taking corrective action. Management accounting supplies budgets, standard costs, responsibility accounting reports and variance analysis. Illustration: if the standard material cost is Rs 40 per unit but actual cost is Rs 46, the material cost variance of Rs 6 per unit is reported to the production manager, who investigates the cause (price rise or wastage) and takes corrective action. Similarly, a performance report showing actual sales of 9,000 units against a budget of 10,000 units signals an unfavourable sales volume variance requiring action.

Conclusion. Thus management accounting is not merely record-keeping; it is the information system that feeds the management process — providing forecasts for planning, relevant costs for decision making, and feedback through variances for control — thereby helping managers achieve organisational objectives efficiently.

Standard Costing — Variance Analysis

Given Data

Actual output: 500 units

Actual quantities:

• Actual material quantity = Rs 150,000 ÷ Rs 50 = 3,000 kg
• Actual labour hours = Rs 49,500 ÷ Rs 55 = 900 hours

Standard quantities for actual output (500 units):

• Standard material quantity = 500 × 5 = 2,500 kg
• Standard labour hours = 500 × 2 = 1,000 hours

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i. Material Variances

(a) Material Price Variance (MPV)

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

(b) Material Use Variance (MUV)

$MUV = SR \times (SQ - AQ)$ $= 60 \times (2,500 - 3,000) = \text{Rs 30,000 (Adverse)}$

(c) Material Cost Variance (MCV)

$MCV = MPV + MUV = 30,000\ (F) - 30,000\ (A) = \text{Rs 0 (Nil)}$

Check: $MCV = (SQ \times SR) - (AQ \times AR) = (2,500 \times 60) - 150,000 = 150,000 - 150,000 = \text{Nil}$

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ii. Labour Variances

(a) Labour Rate Variance (LRV)

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

(b) Labour Efficiency Variance (LEV)

$LEV = SR \times (SH - AH)$ $= 50 \times (1,000 - 900) = \text{Rs 5,000 (Favourable)}$

(c) Labour Cost Variance (LCV)

$LCV = LRV + LEV = -4,500 + 5,000 = \text{Rs 500 (Favourable)}$

Check: $LCV = (SH \times SR) - (AH \times AR) = (1,000 \times 50) - 49,500 = 50,000 - 49,500 = \text{Rs 500 (F)}$

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Summary of Variances

Interpretation: Materials were purchased at a lower price than standard (favourable), but more material was used than allowed (adverse), so the two effects cancelled out. Labour was paid at a higher rate (adverse) but worked more efficiently than standard (favourable), giving a net favourable labour cost variance of Rs 500.

i. Segregation of manufacturing cost of goods sold by least squares method

Let $x$ = production and sales units (in '000 units), $y$ = manufacturing cost of goods sold (in Rs '000).

$n = 5,\quad \bar x = \frac{20}{5} = 4,\quad \bar y = \frac{250}{5} = 50$

Normal equations: $\sum y = na + b\sum x$ and $\sum xy = a\sum x + b\sum x^2$

$250 = 5a + 20b \quad \text{...(i)}$ $1{,}300 = 20a + 110b \quad \text{...(ii)}$

Multiply (i) by 4: $1{,}000 = 20a + 80b$ ...(iii)

(ii) − (iii): $300 = 30b \Rightarrow b = 10$

From (i): $250 = 5a + 200 \Rightarrow a = 10$

Cost function: $y = 10 + 10x$, i.e. in original units:

$\text{Total cost} = \text{Rs } 10{,}000 + \text{Rs } 10 \text{ per unit}$

• Variable cost per unit = Rs 10
• Fixed cost = Rs 10,000

ii. Coefficient of determination ($r^2$)

$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{\left[n\sum x^2 - (\sum x)^2\right]\left[n\sum y^2 - (\sum y)^2\right]}}$

$\sum y^2 = 400 + 900 + 2{,}500 + 3{,}600 + 8{,}100 = 15{,}500$

$r = \frac{5(1{,}300) - (20)(250)}{\sqrt{\left[5(110) - 400\right]\left[5(15{,}500) - 62{,}500\right]}} = \frac{6{,}500 - 5{,}000}{\sqrt{(150)(15{,}000)}} = \frac{1{,}500}{1{,}500} = 1$

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

iii. Standard error of regression

$S_e = \sqrt{\frac{\sum y^2 - a\sum y - b\sum xy}{n - 2}}$

$S_e = \sqrt{\frac{15{,}500 - 10(250) - 10(1{,}300)}{5 - 2}} = \sqrt{\frac{15{,}500 - 2{,}500 - 13{,}000}{3}} = \sqrt{0} = \boxed{0}$

Since all five data points lie exactly on the line $y = 10 + 10x$, the regression explains the cost fully ($r^2 = 1$) and there is no unexplained variation, so the standard error of regression is zero.

Income Statement under Absorption Costing and Reconciliation with Variable Costing

Given Data

Opening stock = Closing stock + Units sold − Units produced = 2,000 + 42,000 − 38,000 = 6,000 units

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(i) Income Statement under Absorption Costing

Working: Fixed Manufacturing Overhead Absorption Rate

$\text{FOR} = \frac{\text{Fixed Manufacturing Overhead}}{\text{Normal Capacity}} = \frac{120,000}{40,000} = \text{Rs 3 per unit}$

Working: Cost per Unit (Absorption Costing)

Working: Under-Absorption of Fixed Overhead

$\text{Fixed OH absorbed} = 38,000 \times 3 = 114,000$ $\text{Fixed OH incurred} = 120,000$ $\text{Under-absorbed OH} = 120,000 - 114,000 = \text{Rs 6,000}$

Income Statement (Absorption Costing)

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(ii) Income Statement under Variable Costing (Marginal Costing)

Working: Variable Cost per Unit

Income Statement (Variable Costing)

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Reconciliation of Profit

Alternative Reconciliation (Difference in Stock)

$\text{Difference in profit} = (\text{Closing stock} - \text{Opening stock}) \times \text{FOR}$

$= (2,000 - 6,000) \times 3 = -12,000$

$\text{Profit under absorption costing} = 478,000 - 12,000 = \text{Rs 466,000}$

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Final Answer

Reason for difference: Under absorption costing, fixed manufacturing overhead is carried forward in inventory. Since closing stock (2,000 units) is less than opening stock (6,000 units), a net 4,000 units of fixed overhead (4,000 × Rs 3 = Rs 12,000) is released to the income statement, making absorption profit lower than variable profit by Rs 12,000.

Cost Behaviour Analysis — High–Low Method and Cost Function

Given Data

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1. Variable Cost per Unit for Each Item

Direct material = Rs 18 per unit (given)

Direct labour = Rs 15 per unit (given)

Indirect material

$= \frac{10{,}000}{5{,}000} = \text{Rs 2 per unit (100\% variable)}$

Indirect labour

Variable portion = 60% of Rs 25,000 = Rs 15,000

$= \frac{15{,}000}{5{,}000} = \text{Rs 3 per unit}$

Fixed portion = 40% of Rs 25,000 = Rs 10,000 (total fixed cost)

Repair and maintenance — High–Low Method

$b = \frac{\text{Cost at high activity} - \text{Cost at low activity}}{\text{High activity} - \text{Low activity}}$

$b = \frac{60{,}000 - 40{,}000}{10{,}000 - 5{,}000} = \frac{20{,}000}{5{,}000} = \text{Rs 4 per unit}$

Fixed cost: at 5,000 units, Total cost = Fixed cost + (Rs 4 × 5,000)

$40{,}000 = a + 20{,}000 \Rightarrow a = \text{Rs 20,000}$

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2. Total Variable Cost per Unit (All Items Combined)

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3. Total Fixed Cost

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4. Cost Function

$y = a + bx = 30{,}000 + 42x$

where $y$ = total cost (Rs) and $x$ = output in units.

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5. Total Cost at 8,000 Units

$y = 30{,}000 + (42 \times 8{,}000) = 30{,}000 + 3{,}36{,}000 = \textbf{Rs 3,66,000}$

Break-up at 8,000 units: