Worked Solution
✓ VerifiedSub-part (a): Degree of Operating Leverage
Given: Break-even point = 20,000 units; Selling price = ₹14; Variable cost = ₹9 per unit.
Contribution per unit = ₹14 − ₹9 = ₹5
Fixed Cost = BEP × Contribution per unit = 20,000 × ₹5 = ₹1,00,000
Degree of Operating Leverage (DOL) = Total Contribution / EBIT (Profit before interest and tax)
At 25,000 units: Total Contribution = 25,000 × ₹5 = ₹1,25,000; EBIT = ₹1,25,000 − ₹1,00,000 = ₹25,000. DOL = 1,25,000 / 25,000 = 5
At 30,000 units: Total Contribution = 30,000 × ₹5 = ₹1,50,000; EBIT = ₹1,50,000 − ₹1,00,000 = ₹50,000. DOL = 1,50,000 / 50,000 = 3
A DOL of 5 at 25,000 units means a 1% change in sales will cause a 5% change in operating profit. Higher sales volume reduces operating risk, as evidenced by DOL falling from 5 to 3.
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Sub-part (b): Labour Turnover
Given: Replacement method rate = 8%; Number replaced = 36; Flux method rate = 14%; Separation method rate = 6%.
Step 1 – Average number of workers (using Replacement method):
Replacement Rate = (Workers Replaced / Average Workers) × 100
8 = (36 / Average Workers) × 100 → Average Workers = 450
Step 2 – Workers left and discharged (using Separation method):
Separation Rate = (Separations / Average Workers) × 100
6 = (Separations / 450) × 100 → (ii) Workers left and discharged = 27
Step 3 – Workers recruited and joined (using Flux method):
Flux Rate = (Separations + New Accessions) / Average Workers × 100
14 = (27 + New Joinings) / 450 × 100
27 + New Joinings = 63 → (i) Workers recruited and joined = 36
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Sub-part (c): Compound Interest
Principal (P) = ₹2,40,000; Rate = 10% p.a.; Time = 3 years. Formula: A = P(1 + r/n)^(nt)
(i) Annual compounding: A = 2,40,000 × (1.10)³ = 2,40,000 × 1.331 = ₹3,19,440
(ii) Semi-annual compounding: Rate per period = 5%; Periods = 6. A = 2,40,000 × (1.05)⁶ = 2,40,000 × 1.340096 = ₹3,21,623 (approx.)
Semi-annual compounding yields ₹2,183 more than annual compounding due to more frequent interest application.
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Sub-part (d): Economic Order Quantity for Material 'X'
Annual demand of material X = 8,000 units/quarter × 4 × 3 kg = 96,000 kgs; Ordering cost (Co) = ₹1,000; Carrying cost (Cc) = 15% × ₹20 = ₹3 per kg per annum.
(i) EOQ = √(2 × 96,000 × 1,000 / 3) = √(6,40,00,000) = 8,000 kgs
(ii) Evaluation of 2% discount with 4 quarterly instalments:
Current Total Cost (at EOQ): Purchase cost = 96,000 × ₹20 = ₹19,20,000; Orders = 96,000/8,000 = 12; Ordering cost = 12 × ₹1,000 = ₹12,000; Carrying cost = (8,000/2) × ₹3 = ₹12,000. Total = ₹19,44,000
With Discount (order qty = 24,000 kgs, 4 orders): New price = ₹20 × 0.98 = ₹19.60; Carrying cost/kg = 15% × ₹19.60 = ₹2.94; Purchase cost = 96,000 × ₹19.60 = ₹18,81,600; Ordering cost = 4 × ₹1,000 = ₹4,000; Carrying cost = (24,000/2) × ₹2.94 = ₹35,280. Total = ₹19,20,880
Saving = ₹19,44,000 − ₹19,20,880 = ₹23,120
Conclusion: The company should accept the supplier's offer as it results in a net saving of ₹23,120 per annum.
Write it like this
1The skeleton
- Label each sub-part clearly (a), (b), (c), (d) with a one-line 'Given' block — examiners allocate marks sub-part-wise and skip unlabelled workings entirely.
- In DOL, derive Fixed Cost from BEP first, then show DOL formula before plugging numbers — if you jump straight to the ratio without writing DOL = Contribution/EBIT, you lose the formula mark even if the answer is right.
- In Labour Turnover, solve in the exact order: Replacement → Separation → Flux — each method feeds the next; reversing the order breaks your working chain and you get zero carry-forward marks.
- In EOQ, show the annual demand derivation line-by-line (quarterly units × 4 quarters × kg per unit) — this single line is worth a mark and students treat it as 'obvious', skipping it and losing easy marks.
- In the discount evaluation, build a comparison table with three rows: Purchase Cost, Ordering Cost, Carrying Cost, Total — examiners are trained to tick each row; a paragraph narrative gets maybe half the marks a clean table gets.
- End every sub-part with a one-sentence conclusion in bold — 'The company should accept the offer…' or 'DOL falls from 5 to 3 indicating reduced operating risk' — this is the inference mark and it's almost always the last tick on the examiner's checklist.
2Examiner-rewarded phrases
3Common trap
Heads up — in the EOQ discount part, most students calculate carrying cost on the original price ₹20 instead of the discounted price ₹19.60. That one slip cascades into a wrong total and you drop 3-4 marks even though your EOQ formula is textbook perfect.