Worked Solution
✓ VerifiedPreliminary Calculations:
Since procurement time is given in days and consumption in weeks, convert to a common base (days), using 365 days per year.
- Minimum daily consumption = 210 ÷ 7 = 30 kgs/day
- Maximum daily consumption = 350 ÷ 7 = 50 kgs/day
- Average daily consumption = (30 + 50) ÷ 2 = 40 kgs/day
- Average lead time = (5 + 9) ÷ 2 = 7 days
- Annual Demand (D) = 40 × 365 = 14,600 kgs
- Carrying Cost (Cc) = (1% per month × ₹100) × 12 months + ₹2 = ₹12 + ₹2 = ₹14 per kg per annum
- Ordering Cost (Co) = ₹200 per order
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(a) Economic Order Quantity (EOQ):
EOQ = √(2 × D × Co ÷ Cc) = √(2 × 14,600 × 200 ÷ 14) = √4,17,142.86 = 646 kgs (approx.)
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(b) Re-Order Level (ROL):
ROL = Maximum daily consumption × Maximum lead time = 50 × 9 = 450 kgs
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(c) Maximum Stock Level:
Maximum Stock Level = ROL + EOQ − (Minimum daily consumption × Minimum lead time)
= 450 + 646 − (30 × 5) = 450 + 646 − 150 = 946 kgs
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(d) Minimum Stock Level:
Minimum Stock Level = ROL − (Average daily consumption × Average lead time)
= 450 − (40 × 7) = 450 − 280 = 170 kgs
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(e) Average Stock Level:
Average Stock Level = Minimum Stock Level + ½ × EOQ
= 170 + (646 ÷ 2) = 170 + 323 = 493 kgs
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(f) Number of Orders per Year:
Number of Orders = Annual Demand ÷ EOQ = 14,600 ÷ 646 = 22.60 ≈ 23 orders
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(g) Total Inventory Cost (at EOQ):
| Component | Calculation | Amount (₹) |
|---|---|---|
| Purchase Cost | 14,600 × ₹100 | 14,60,000 |
| Ordering Cost | (14,600 ÷ 646) × ₹200 | 4,520 |
| Carrying Cost | (646 ÷ 2) × ₹14 | 4,522 |
| Total | ₹14,69,042 |
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(h) Evaluation of 1% Discount Offer (2 orders per year):
Order quantity = 14,600 ÷ 2 = 7,300 kgs; Discounted price = ₹99/kg; Revised Cc = (12% × ₹99) + ₹2 = ₹13.88/kg
| Component | Calculation | Amount (₹) |
|---|---|---|
| Purchase Cost | 14,600 × ₹99 | 14,45,400 |
| Ordering Cost | 2 × ₹200 | 400 |
| Carrying Cost | (7,300 ÷ 2) × ₹13.88 | 50,662 |
| Total | ₹14,96,462 |
Since ₹14,96,462 > ₹14,69,042 (EOQ total cost), the offer is NOT acceptable — it increases total cost by ₹27,420.
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(i) Counter-Offer — Minimum Discount Percentage:
Let the minimum required discount = d%
For the offer to be acceptable: Total cost at 2 orders with d% discount ≤ ₹14,69,042
Setting total cost equal to EOQ cost and solving:
[14,60,000 − 14,600d] + 400 + 3,650 × [14 − 0.12d] = 14,69,042
15,11,500 − 15,038d = 14,69,042
15,038d = 42,458
d = 42,458 ÷ 15,038 = 2.82%
Counter-offer: M/s Tanishka should negotiate a minimum discount of 2.83% (rounding up) on the total annual purchase quantity for the offer to be financially beneficial.
Write it like this
1The skeleton
- Open with a 'Preliminary Calculations' block — convert weekly consumption to daily AND compute average figures before touching any formula; examiners award step marks here even if your EOQ is wrong later.
- Write the formula first, then substitute — for every stock level (ROL, Max, Min, Average) write the textbook formula line, THEN plug in numbers; a bare answer with no formula gets zero even if it's correct.
- Sequence your stock levels as ROL → Max → Min → Average — this is the ICAI model answer order; deviating forces the examiner to hunt for answers and they stop awarding part marks.
- For the carrying cost build-up, show the split — break it as '1% × ₹100 × 12 = ₹12' and '+ ₹2 fixed = ₹14 total' on separate lines; examiners are trained to check this component specifically because students collapse it into one wrong number.
- For the discount evaluation, use a three-row table (Purchase + Ordering + Carrying) for BOTH scenarios side by side — then write one conclusion sentence comparing totals; the table earns format marks and the sentence earns the decision mark.
- For the counter-offer, write the inequality first ('For offer to be acceptable, Total Cost ≤ ₹14,69,042'), then set up the equation — showing the direction of logic earns the setup mark before you even solve for d.
2Examiner-rewarded phrases
3Common trap
The single biggest mark-killer here is using average consumption for ROL — most students instinctively write 'average × average' because it 'feels safer', but ROL always uses MAXIMUM consumption × MAXIMUM lead time. If you do that, your Max Stock Level cascades wrong too and you bleed marks across three sub-parts from one line.