Worked Solution
✓ VerifiedStep 1 – Segregate Fixed and Variable Overheads for FY 2024-25
Let Fixed Overhead = F and Variable Overhead (for 40,000 units) = V.
Given: F + V = ₹25,000 crores.
For FY 2025-26, the fixed component decreases by ₹500 crores and total overhead (fixed + variable for 50,000 units) = ₹28,500 crores. Since variable overhead is assumed to vary proportionately with units:
New Fixed OH = (F − 500)
New Variable OH = V × (50,000 ÷ 40,000) = 1.25V
So: (F − 500) + 1.25V = 28,500 → F + 1.25V = 29,000
Subtracting F + V = 25,000: 0.25V = 4,000 → V = ₹16,000 crores; F = ₹9,000 crores
Step 2 – Per Unit Cost Structure for FY 2024-25
All figures in ₹ crores per unit (dividing by 40,000 units):
- Selling Price per unit = ₹2.50
- Raw Material per unit = ₹1.25
- Direct Wages per unit = ₹0.375
- Variable Overhead per unit = 16,000 ÷ 40,000 = ₹0.40
- Fixed Overhead (total) = ₹9,000 crores
- Profit per unit = 10,000 ÷ 40,000 = ₹0.25 crores ← target to sustain
Step 3 – Revised Cost Structure for FY 2025-26
- Selling Price per unit = ₹2.50 (no change stated)
- Raw Material per unit = ₹1.25 (no change stated)
- Direct Wages per unit = ₹0.375 × 1.20 = ₹0.45 (20% increase)
- Variable Overhead per unit = ₹0.40 (unchanged per unit)
- Fixed Overhead = 9,000 − 500 = ₹8,500 crores
Step 4 – Contribution per Unit (FY 2025-26)
Contribution = SP − Variable Cost per unit
= 2.50 − (1.25 + 0.45 + 0.40)
= 2.50 − 2.10 = ₹0.40 crores per unit
Step 5 – Minimum Units for Same Per Unit Profit
Let N = minimum units to be sold.
Required: Profit ÷ N = ₹0.25 crores → Total Profit = 0.25N
Using P/V relationship:
Total Contribution − Fixed Costs = Total Profit
0.40N − 8,500 = 0.25N
0.15N = 8,500
N = 8,500 ÷ 0.15 = 56,667 units (rounded up)
The minimum number of units Axion Industries must sell in FY 2025-26 to sustain a per unit profit of ₹0.25 crores is 56,667 units.
Write it like this
1The skeleton
- Start with two simultaneous equations to crack the overhead split — write 'Let Fixed OH = F, Variable OH = V' and set up both equations immediately; examiners award a carry-forward mark here even if your final number slips.
- Derive all per-unit figures in one clean table for FY 2024-25 — SP, RM, wages, variable OH, then profit per unit (₹0.25 crores); locking this target profit per unit visually signals to the examiner you understand what 'sustain' means.
- Show the revised cost line for each element separately in FY 2025-26 — don't club wages and variable OH in one line; examiners check each adjustment (wages ×1.20, fixed OH −500) individually and award a mark per correct change.
- Write the contribution formula explicitly — 'Contribution = SP − Variable Cost per unit = 2.50 − 2.10 = ₹0.40' on its own line; skipping this step loses the formula mark even if your final answer is right.
- Frame the final equation as 'Total Contribution − Fixed Cost = Total Profit' with profit expressed as 0.25N — this is the non-obvious pivot of the question; write it out in one line so the examiner sees you've correctly treated per-unit profit as a variable, not a constant.
2Examiner-rewarded phrases
3Common trap
The single biggest killer here: students treat this like a normal BEP question and set Total Contribution − Fixed Cost = 10,000 (the old total profit) instead of 0.25N — that's wrong because you need the *same profit per unit*, not the same total profit. The moment you fix total profit at 10,000, your N comes out at 46,250 and you've answered a different question entirely.