Marginal Costing and Decision Making — Practice

Question 1

A company sells 10,000 units at Rs.80 per unit. Variable cost per unit is Rs.50. Fixed cost for the period is Rs.2,10,000. Prepare a marginal cost statement, compute P/V ratio, and state the profit.

Accepted Answer

Sales are 10,000 units at 80 per unit, giving 8,00,000. Variable cost is 10,000 units at 50 per unit, giving 5,00,000. Contribution is Sales less Variable Cost: 8,00,000 less 5,00,000, giving 3,00,000. Fixed cost for the period is 2,10,000, charged in full as a period cost under marginal costing regardless of the level of production or sales. Profit is Contribution less Fixed Cost: 3,00,000 less 2,10,000, giving 90,000. P/V Ratio is Contribution divided by Sales: 3,00,000 divided by 8,00,000, giving 0.375, that is 37.5%, meaning every rupee of sales generates 37.5 paise of contribution towards covering fixed cost and then profit. The marginal cost statement is deliberately structured in this two-stage way, first arriving at Contribution and only then deducting the whole of the period's fixed cost, rather than building unit cost up to include a share of fixed overhead the way an absorption costing statement would; this structure is what makes contribution, and the P/V ratio derived from it, directly usable in the break-even and decision-making formulas that follow throughout this chapter.

Question 2

A company produces 12,000 units and sells 10,000 units in a period. Fixed overhead for the period is Rs.3,60,000, and normal/budgeted production is 12,000 units, giving a fixed overhead absorption rate of Rs.30 per unit. Compute the difference between profit reported under absorption costing and profit reported under marginal costing, and explain the direction of the difference.

Accepted Answer

Production of 12,000 units exceeds sales of 10,000 units, so closing stock builds up by 2,000 units during the period (assuming no opening stock for simplicity). The difference between profit under absorption costing and profit under marginal costing is computed as the change in stock, closing less opening, multiplied by the fixed overhead rate per unit: (2,000 less 0) times 30, giving 60,000. Since production exceeds sales, absorption costing reports profit higher than marginal costing by this 60,000. The reasoning is that under absorption costing, each of the 2,000 units added to closing stock carries 30 of fixed overhead absorbed into its cost, and that 30 per unit, 60,000 in total, is carried forward in the closing stock valuation on the balance sheet rather than being charged against the current period's profit and loss account; under marginal costing, by contrast, the full 3,60,000 of fixed overhead for the period is charged in full against the period's revenue regardless of how many units were actually sold, so none of it is deferred into closing stock. The general direction to remember is that when production exceeds sales, inventory is building up, and absorption costing reports the higher profit because it defers part of the period's fixed cost into that growing inventory; when sales exceed production, inventory is running down, and marginal costing reports the higher profit instead, because absorption costing in that case releases fixed cost that had been carried forward in opening stock from an earlier period, inflating that period's absorption-costing cost of goods sold and correspondingly lowering absorption profit relative to marginal profit.

Question 3

A company has fixed costs of Rs.4,50,000 and a P/V ratio of 30%. Current sales are Rs.20,00,000. Compute the break-even point in sales value, the margin of safety, and the sales required to achieve a target profit of Rs.3,00,000.

Accepted Answer

Break-even point in sales value is Fixed Cost divided by P/V Ratio: 4,50,000 divided by 0.30, giving 15,00,000. Current sales of 20,00,000 exceed this break-even point, so the company is currently operating profitably; the margin of safety, being actual sales less break-even sales, is 20,00,000 less 15,00,000, giving 5,00,000, meaning sales could fall by 5,00,000 before the company reaches the break-even point and starts making a loss. As a cross-check, margin of safety can also be computed as Profit divided by P/V Ratio: current profit is contribution less fixed cost, where contribution is 30% of 20,00,000, that is 6,00,000, less fixed cost of 4,50,000, giving profit of 1,50,000; margin of safety by this route is 1,50,000 divided by 0.30, giving 5,00,000, matching the first computation exactly and confirming the figures are internally consistent. Sales required for a target profit of 3,00,000 is (Fixed Cost plus Target Profit) divided by P/V Ratio: (4,50,000 plus 3,00,000) divided by 0.30, that is 7,50,000 divided by 0.30, giving 25,00,000, meaning the company would need to increase sales from its current 20,00,000 to 25,00,000, a further 5,00,000, in order to achieve the higher target profit of 3,00,000 rather than its current profit of 1,50,000.

Question 4

A company currently makes a component in-house at a variable cost of Rs.45 per unit, using machine capacity that could otherwise be used to make Product Z, which earns a contribution of Rs.12 per unit using the same machine time. A supplier offers to supply the component at Rs.52 per unit. Fixed costs of the department making the component, Rs.1,80,000 per year, will continue regardless of the decision. Should the company make or buy the component, and what role does the opportunity cost play?

Accepted Answer

The fixed costs of 1,80,000 per year are irrelevant to this decision, since they continue regardless of whether the component is made in-house or bought in, and including them in the comparison would be exactly the classic error the relevant costing principle warns against; only costs and revenues that actually change with the decision belong in the analysis. Comparing the variable cost of making, 45 per unit, against the purchase price of 52 per unit, making in-house looks 7 per unit cheaper on this comparison alone, which might suggest continuing to make it. But making the component in-house uses machine capacity, and that capacity has an alternative use: producing Product Z, which earns a contribution of 12 per unit using the same machine time that making the component would otherwise occupy. If the company buys the component instead of making it, the machine capacity is freed up, and that freed capacity can be used to produce Product Z, earning the 12 per unit contribution that would otherwise be forgone. This opportunity cost must be brought into the comparison: the effective cost of making the component in-house is not simply its variable cost of 45, but 45 plus the 12 per unit contribution forgone by not using that capacity for Product Z instead, giving an effective cost of making of 57 per unit. Comparing this effective cost of making, 57, against the purchase price of 52, buying is now the better decision by 5 per unit, the opposite conclusion from the naive variable-cost-only comparison. This illustrates precisely why opportunity cost is the twist that turns a simple price comparison into a genuinely relevant-costing decision: ignoring the alternative use of freed capacity would have led the company to continue making the component in-house at a real net cost to the business of 5 per unit relative to the better available alternative.

Question 5

A company's normal selling price is Rs.100 per unit, with variable cost of Rs.60 and fixed cost absorbed of Rs.25 per unit at normal volume, giving a full cost of Rs.85. A new customer offers to buy 2,000 units at Rs.70 per unit, a price below the normal Rs.100 but above the Rs.60 variable cost. The company has spare capacity sufficient for this order without affecting existing sales. Should the order be accepted, and on what basis?

Accepted Answer

The order should be accepted, and the basis for the decision is a comparison of incremental revenue against incremental (variable) cost, not against the full absorbed cost of 85 per unit that would make the offer of 70 look unprofitable at first glance. Because the company has spare capacity sufficient for this order without affecting existing sales at the normal price, none of the existing 100-per-unit business is displaced, and the fixed costs of 25 per unit absorbed at normal volume will be incurred in full regardless of whether this special order is accepted, since they do not change with the decision and are therefore not relevant to it; comparing the offer against the full cost of 85 would incorrectly treat those unavoidable fixed costs as though they were caused by, and avoidable through rejecting, this specific order. The relevant comparison is incremental revenue of 70 per unit against incremental variable cost of 60 per unit, giving an incremental contribution of 10 per unit, positive and therefore beneficial to accept; across 2,000 units this adds 20,000 of contribution, and since none of it needs to cover any additional fixed cost that would not otherwise be incurred, the entire 20,000 flows through to additional profit. Two qualifications are worth noting in a full answer even though the arithmetic favours acceptance: the order must not undermine the normal pricing structure in the regular market, for instance by leaking into that market or setting an expectation of lower prices from existing customers, and the spare capacity condition must genuinely hold, since accepting the order would be a poor decision if it turned out to displace higher-margin existing sales rather than filling genuinely idle capacity.

Question 6

A company has three product lines. Product C shows an absorption-costing loss of Rs.40,000, computed after charging it Rs.1,50,000 of allocated common factory overhead that would continue regardless of whether Product C is discontinued, plus Rs.30,000 of overhead specific to Product C's own production line that would be saved if discontinued. Product C's contribution is Rs.1,40,000. Advise on whether Product C should be discontinued, showing the relevant comparison.

Accepted Answer

Product C should not be discontinued, despite showing an absorption-costing loss, because the correct comparison is its contribution against only the fixed costs genuinely avoidable by discontinuing it, and on that comparison Product C is worth keeping. The reported loss of 40,000 has been arrived at by charging Product C with 1,50,000 of allocated common factory overhead, which is stated to continue regardless of whether Product C is discontinued or not; this is an unavoidable fixed cost from the perspective of the shutdown decision, exactly the kind of cost the relevant costing principle requires to be excluded from the analysis, since it does not actually change whatever is decided about Product C. The only fixed cost genuinely avoidable by discontinuing Product C is the 30,000 specific to its own production line. The correct shutdown test is whether Product C's contribution exceeds its avoidable fixed cost: contribution of 1,40,000 against avoidable fixed cost of only 30,000, leaving Product C generating a net relevant benefit of 1,10,000 towards covering the company's unavoidable common costs and overall profit. Discontinuing Product C would not save the 1,50,000 of common overhead at all, since it continues regardless; it would only save the 30,000 avoidable cost, while losing the entire 1,40,000 of contribution Product C currently generates, making the company worse off by 1,10,000 if the decision were made on the basis of the misleading absorption-costing loss alone. This is the single most consequential insight in this sub-chapter: an absorption-costing loss, driven by an allocation of costs that will not actually disappear, routinely misleads managers into shutting down a segment that is, in relevant-cost terms, still contributing genuine value to the business.

Question 7

A company makes three products using a single scarce machine hour resource, of which only 12,000 hours are available. Product P earns contribution of Rs.60 per unit and requires 3 machine hours per unit. Product Q earns contribution of Rs.90 per unit and requires 6 machine hours per unit. Product R earns contribution of Rs.40 per unit and requires 1 machine hour per unit. Demand for each is 2,000 units. Rank the products correctly and determine the optimal production plan to maximise total contribution.

Accepted Answer

Ranking products by contribution per unit alone, without reference to the scarce resource each consumes, would rank Q highest at 90 per unit, then P at 60, then R at 40, and would be a fundamental error given machine hours are the binding constraint here. The correct ranking criterion is contribution per unit of the scarce resource, that is contribution per unit divided by machine hours required per unit. For Product P: 60 divided by 3, giving 20 per machine hour. For Product Q: 90 divided by 6, giving 15 per machine hour. For Product R: 40 divided by 1, giving 40 per machine hour. Ranked by this correct criterion, the order is R first at 40 per hour, then P at 20 per hour, then Q last at 15 per hour, a ranking that inverts the naive per-unit ranking almost completely: Q, which looked most profitable on a simple per-unit basis, ranks last once the scarce resource is properly accounted for, precisely illustrating why this ranking rule rather than raw contribution per unit is what must be applied. Allocating the 12,000 available machine hours in this order: Product R first, demand of 2,000 units at 1 hour each requires 2,000 hours, fully satisfying its demand, leaving 10,000 hours; Product P next, demand of 2,000 units at 3 hours each requires 6,000 hours, fully satisfying its demand, leaving 4,000 hours; Product Q last, with only 4,000 hours remaining and each unit requiring 6 hours, only 4,000 divided by 6, that is 666 units approximately, can be produced, well short of its 2,000 unit demand. Total contribution under this optimal plan is (2,000 times 40) plus (2,000 times 60) plus (666 times 90), that is 80,000 plus 1,20,000 plus 59,940, giving approximately 2,59,940, the maximum achievable total contribution given the binding 12,000 hour constraint and the demand limits on each product.

Question 8

State the key assumptions underlying marginal costing and CVP analysis, and explain why a manager should be cautious about applying break-even results well beyond the range of activity on which the underlying cost data was based.

Accepted Answer

CVP analysis rests on several simplifying assumptions that should be stated explicitly whenever the limitations of a conclusion are relevant. Costs can be reliably split into fixed and variable components, an assumption that in practice requires techniques such as the high-low method to actually achieve, and which is itself an approximation for genuinely semi-variable costs. Selling price per unit and variable cost per unit remain constant across the relevant range of activity being analysed, ignoring, for instance, bulk purchase discounts on materials at higher volumes or the need to cut price to sell additional units in a more competitive segment of the market. Fixed cost remains constant in total across the relevant range, ignoring step-fixed costs that might jump upward if activity grows enough to require, say, an additional supervisor or an additional piece of equipment. In a multi-product setting, the sales mix is assumed to remain constant, since a change in the proportion of higher-margin and lower-margin products sold changes the blended P/V ratio the whole analysis depends on, unless a question specifically asks for analysis of a changed mix. The caution about extrapolating well beyond the range of activity the cost data was based on follows directly from the relevant range assumption embedded in several of these points: cost behaviour that appears linear and stable within an observed range of output, say between 60% and 90% of capacity, cannot be safely assumed to hold at, say, 20% or 150% of that same capacity, since fixed costs may need to step up at very high volumes, and per-unit variable costs may behave quite differently at very low volumes where fixed overheads per unit dominate differently or where discounts and efficiencies available at higher volumes disappear entirely; break-even and CVP conclusions are reliable predictions only within the range of activity the underlying data genuinely reflects.

Question 9

In one period, sales were Rs.12,00,000 and profit was Rs.1,80,000. In the next period, sales rose to Rs.15,00,000 and profit rose to Rs.2,70,000. Compute the P/V ratio using the change method, and then compute fixed cost.

Accepted Answer

Where two periods' sales and profit figures are given and fixed cost is assumed constant across both, P/V ratio can be computed from the change in profit relative to the change in sales, without needing variable cost or contribution figures directly: P/V Ratio equals change in profit divided by change in sales, that is (2,70,000 less 1,80,000) divided by (15,00,000 less 12,00,000), that is 90,000 divided by 3,00,000, giving 0.30, that is 30%. This works because, with fixed cost constant across the two periods, any change in profit between them must come entirely from the change in contribution, and the change in contribution relative to the change in sales is exactly what the P/V ratio measures. Fixed cost can then be derived using either period's data: contribution in the first period is P/V ratio times sales, that is 30% of 12,00,000, giving 3,60,000; fixed cost is contribution less profit, that is 3,60,000 less 1,80,000, giving 1,80,000. Checking against the second period: contribution is 30% of 15,00,000, giving 4,50,000; fixed cost is 4,50,000 less 2,70,000, giving 1,80,000, matching exactly, confirming the assumption of constant fixed cost across the two periods and the correctness of the derived figures.

Question 10

A company sells two products in a constant mix: Product X, 60% of sales value with a 40% P/V ratio, and Product Y, 40% of sales value with a 25% P/V ratio. Fixed cost is Rs.3,08,000. Compute the composite (weighted average) P/V ratio and the break-even sales value.

Accepted Answer

In a multi-product setting with a constant sales mix, a single composite P/V ratio can be computed by weighting each product's own P/V ratio by its share of total sales value: Product X contributes 60% of sales at a 40% P/V ratio, giving a weighted contribution of 60% times 40%, that is 24%; Product Y contributes 40% of sales at a 25% P/V ratio, giving a weighted contribution of 40% times 25%, that is 10%. Composite P/V ratio is the sum of these weighted contributions: 24% plus 10%, giving 34%. Break-even sales value, using this composite ratio exactly as the single-product formula uses an ordinary P/V ratio, is Fixed Cost divided by Composite P/V Ratio: 3,08,000 divided by 0.34, giving approximately 9,05,882. This composite break-even figure is valid only so long as the assumed sales mix, 60% Product X and 40% Product Y by value, actually holds; if the mix shifts, for instance towards a higher proportion of the lower-margin Product Y, the composite P/V ratio itself would fall, and the break-even sales value required would correspondingly rise, since a lower blended margin requires more total sales to generate the same fixed cost coverage, which is exactly why the constant-sales-mix assumption is one of the standard CVP assumptions explicitly flagged as needing to hold for a multi-product break-even computation to remain valid over time.

Question 11

A company is deciding whether to discontinue Product D, which shows a loss. A director argues the company has invested Rs.20,00,000 in specialised equipment for Product D over the years and should not discontinue it now, having come this far. Explain why this argument is a sunk cost fallacy, and state what the director should instead be asked to establish before the decision is made.

Accepted Answer

The director's argument is a sunk cost fallacy because the 20,00,000 already invested in specialised equipment for Product D has already been spent, is unrecoverable regardless of what is now decided about the product's future, and will not change whether the company continues or discontinues Product D going forward; the argument treats past investment as though it creates an ongoing obligation to continue, or as though continuing would somehow recover that past spending, when in fact the only way the 20,00,000 relates to a decision made today is if the equipment itself has some genuine alternative value, such as resale value or an alternative use elsewhere in the business, that would be forgone by continuing to use it for Product D, and that alternative value, not the original historical cost, is what would actually be relevant. Rather than being swayed by how much has already been spent, the director should instead be asked to establish, using the shutdown decision framework developed in this chapter, whether Product D's current contribution exceeds the fixed costs that would genuinely be avoided by discontinuing it; if contribution exceeds avoidable fixed cost, the product is worth continuing regardless of how much or how little was historically invested in it, and if contribution falls short of avoidable fixed cost, the product is worth discontinuing regardless of how much was historically invested, since in neither case does the sunk historical investment change the correct forward-looking answer. The size of the past investment is emotionally salient, which is exactly why the sunk cost fallacy is so common in real business decisions, but it carries no genuine analytical weight in a decision about what to do now.

Question 12

A company finds that both machine hours and a specific raw material are simultaneously in short supply, each constraining different products to different degrees. Explain, without full computation, why the simple contribution-per-unit-of-scarce-resource ranking method developed for a single limiting factor is inadequate here, and what kind of technique would be needed instead.

Accepted Answer

The simple ranking method developed for a single limiting factor works because, with only one binding constraint, maximising contribution per unit of that one scarce resource and then allocating the resource strictly in that ranked order genuinely does maximise total contribution, since there is only one constraint to satisfy and the ranking correctly identifies which products deliver the most contribution per unit of the one thing genuinely holding output back. Where two resources are simultaneously scarce, and different products consume the two resources in different proportions to each other, a single ranking by contribution per unit of either resource alone is inadequate, because a product ranking highly on contribution per machine hour might rank poorly on contribution per unit of the scarce material, and vice versa, so there is no single ranking that correctly reflects the product mix that satisfies both constraints simultaneously while maximising contribution; a product mix optimal against one constraint considered alone may not even be feasible once the second constraint is also respected, since it might require more of the second scarce resource than is actually available. The technique needed instead is linear programming, which can handle multiple simultaneous constraints together, typically solved either graphically for a two-product, two-constraint problem, plotting the feasible region bounded by both constraints and identifying the corner point that maximises the contribution objective function, or through the simplex method for problems involving more products or more constraints than a graphical approach can practically handle; this more advanced technique, briefly introduced in outline at Intermediate level and developed further at Final level, is what genuinely multiple-constraint decision problems require, going beyond the single-constraint ranking rule that suffices when only one resource is actually binding.

Question 13

Two companies, X and Y, both report a current profit of Rs.2,00,000. Company X has a margin of safety of Rs.1,00,000 and Company Y has a margin of safety of Rs.8,00,000. Explain what this difference reveals about the relative fragility of the two companies' current profit positions, despite identical current profit.

Accepted Answer

Margin of safety measures how far current sales can fall before the business reaches its break-even point and starts making a loss, so a smaller margin of safety indicates a more fragile position, closer to the point at which continued profitability tips into loss, while a larger margin of safety indicates a more robust position with a greater cushion against a sales downturn before losses would begin. Company X, with a margin of safety of only 1,00,000, would move from its current 2,00,000 profit into loss territory after a comparatively modest 1,00,000 fall in sales, meaning even a relatively small downturn, a lost customer, a competitive pricing pressure, a modest market contraction, could tip it into an unprofitable position. Company Y, with a margin of safety of 8,00,000, could absorb a substantially larger sales decline, eight times the size of Company X's cushion, before reaching the same break-even risk. Despite reporting identical current profit of 2,00,000, the two companies are in materially different underlying positions: Company X's profit is being generated relatively close to its break-even point, likely reflecting either a high fixed cost base relative to its contribution, or a lower P/V ratio, or both, while Company Y's identical profit is generated with much greater headroom above break-even, likely reflecting a more favourable cost structure relative to its sales volume. A lender, investor, or manager comparing the two companies purely on reported profit alone, without also examining margin of safety, would miss this significant difference in underlying financial resilience.

Question 14

State the single defining difference between marginal costing and absorption costing as techniques, and explain why this single difference is enough to explain every other consequence that follows from choosing one over the other.

Accepted Answer

The single defining difference is the treatment of fixed overhead: under absorption costing, fixed overhead is absorbed into the cost of each unit produced and therefore enters closing stock valuation, while under marginal costing, fixed overhead is charged in full against the period's revenue as a period cost, regardless of how many units were produced or sold, and closing stock is valued at variable cost only. Every other consequence of choosing one technique over the other follows directly from this one design choice. Because absorption costing lets fixed overhead ride into closing stock, while marginal costing charges it all to the period incurred, the two techniques necessarily report different profit whenever production and sales volumes diverge within a period, with the direction and magnitude of the difference computable directly from the change in stock multiplied by the fixed overhead rate per unit. Because marginal costing keeps fixed cost separate from unit cost entirely, it naturally supports the contribution-based reasoning that underlies break-even analysis and all the relevant-costing decision techniques in this chapter, since contribution, sales less variable cost only, is exactly the figure marginal costing's own statement format produces directly, whereas absorption costing's unit cost figure, blending fixed and variable cost together, obscures the distinction relevant costing depends on. Understanding this one root difference, rather than memorising a list of separate consequences, is what lets a candidate correctly predict how the two techniques will differ in any new situation a problem presents, rather than needing to have seen that specific situation before.

Question 15

A company currently uses all its available machine hours making Product E, contribution Rs.18 per unit, 2 machine hours per unit. A special order for a new Product F is offered, contribution Rs.30 per unit, 4 machine hours per unit, using machine hours that would otherwise make Product E. Should the company accept the special order, and on what basis?

Accepted Answer

Because the company's machine hours are already fully utilised making Product E, this is not a straightforward special order question of the kind where spare capacity exists; accepting Product F's order would necessarily displace some Product E production, since there is no idle capacity to absorb the new order without taking machine hours away from existing use. The correct comparison is therefore not simply Product F's own contribution in isolation, but Product F's contribution per unit of the scarce machine hour resource against Product E's contribution per unit of that same scarce resource, exactly the limiting factor ranking principle developed elsewhere in this chapter, since machine hours are the binding constraint being fought over between the existing product and the new order. Product E's contribution per machine hour is 18 divided by 2, giving 9 per hour. Product F's contribution per machine hour is 30 divided by 4, giving 7.50 per hour. Since Product E generates more contribution per unit of the scarce machine hour resource than Product F would, accepting the special order for Product F and displacing Product E production to make room for it would reduce the company's total contribution, because each machine hour redirected from Product E to Product F would sacrifice 9 of contribution to gain only 7.50. The special order should therefore be declined, not because Product F's absolute contribution per unit of 30 looks unattractive on its own, which it does not compared to Product E's 18, but because Product F uses the genuinely scarce resource, machine hours, less efficiently than the production it would displace, which is precisely why the naive incremental-revenue-versus-incremental-cost test for an ordinary special order is insufficient here and the limiting factor comparison must be applied instead.

Practice — Marginal Costing and Decision Making

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