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(a) AK Limited — Production Budget and Break-Even
(i) Quarterly Production Budget:
Total annual sales = 18,000 + 22,000 + 35,000 + 27,000 = 1,02,000 units
Total production required = 1,02,000 + 8,000 (closing) − 6,000 (opening) = 1,04,000 units
Production formula: 70% of current quarter sales + 30% of next quarter sales.
| Quarter | Current Qtr Sales | 70% | Next Qtr Sales | 30% | Production (units) |
|---------|-------------------|-----|----------------|-----|--------------------|
| I | 18,000 | 12,600 | 22,000 | 6,600 | 19,200 |
| II | 22,000 | 15,400 | 35,000 | 10,500 | 25,900 |
| III | 35,000 | 24,500 | 27,000 | 8,100 | 32,600 |
| IV | — | — | — | — | 26,300 (balancing) |
| Total | | | | | 1,04,000 |
*Closing inventory verification:* Q1: 6,000+19,200−18,000=7,200 → Q2: 11,100 → Q3: 8,700 → Q4: 8,000 ✓
(ii) Break-Even Point in Q1:
*Note: The question states raw material at 20 units @ ₹40 = ₹800, which exceeds the selling price of ₹40; this appears to be a data error. Assuming variable (raw material) cost = ₹20 per unit.*
Selling price = ₹40 | Variable cost = ₹20 | Contribution per unit = ₹20
P/V Ratio = ₹20/₹40 = 50%
Fixed overhead per quarter = (17,000 hours × ₹2) ÷ 4 = ₹8,500
BEP (units) = ₹8,500 ÷ ₹20 = 425 units
BEP (₹ sales) = 425 × ₹40 = ₹17,000
Since Q1 sales budget is 18,000 units (well above BEP of 425 units), the company is expected to comfortably achieve and surpass break-even in Q1.
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(b) Machine Hour Rate
*Note: Scrap value stated as ₹90 lacs for a machine costing ₹10 lacs is clearly a data error; assumed scrap value = ₹90,000.*
Annual Cost Statement for New Machine:
| Item | Calculation | Amount (₹) |
|------|------------|------------|
| Depreciation (SLM) | (10,00,000 − 90,000) ÷ 10 | 91,000 |
| Repairs & Maintenance | Given | 5,000 |
| Power | 4,200 hrs × 5 units × ₹3.25 | 68,250 |
| Rent | ₹2,400 × 12 × 1/10 | 2,880 |
| Total Annual Cost | | 1,67,130 |
Effective (productive) hours = 4,200 − 200 = 4,000 hours
Machine Hour Rate = ₹1,67,130 ÷ 4,000 = ₹41.78 per hour
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(c) RES Ltd. — M&M Model with Taxes
Given: V_U = ₹25,00,000; k_e(U) = 16%; Debt (D) = ₹25,00,000 at k_d = 15%; Tax rate (T) = 30%
Levered firm value (M&M with taxes):
V_L = V_U + T×D = 25,00,000 + (0.30 × 25,00,000) = ₹32,50,000
Equity value (S) = 32,50,000 − 25,00,000 = ₹7,50,000
EBIT = V_U × k_e(U) = 25,00,000 × 16% = ₹4,00,000
(i) EPS (Earnings available to equity shareholders):
EBIT: ₹4,00,000
Less: Interest (25,00,000 × 15%): ₹3,75,000
EBT: ₹25,000
Less: Tax @ 30%: ₹7,500
EAT (Earnings to equity) = ₹17,500
(ii) Cost of Equity (k_e_L) — M&M Proposition II with Taxes:
k_e_L = k_e_U + (k_e_U − k_d)(1−T)(D/S)
= 16% + (16%−15%)(1−0.30)(25,00,000/7,50,000)
= 16% + 1% × 0.70 × 3.333
= 16% + 2.33% = 18.33%
(iii) Weighted Average Cost of Capital:
WACC = k_d(1−T)(D/V_L) + k_e_L(S/V_L)
= 15%(0.70)(25,00,000/32,50,000) + 18.33%(7,50,000/32,50,000)
= 10.5% × 0.7692 + 18.33% × 0.2308
= 8.08% + 4.23% = 12.31%
Comment: WACC declines from 16% (unlevered) to 12.31% (levered). In the M&M framework with corporate taxes, the tax shield on debt (₹7,50,000) increases firm value. WACC continuously falls as debt increases, implying the optimal capital structure under M&M with taxes is maximum debt (100% debt financing).
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(d) Credit Terms Evaluation — RES Ltd.
Should the company liberalise credit terms from 1/10 n/45 to 2/10 n/45?
Incremental Analysis:
| Particulars | Existing | Proposed | Increment |
|-------------|----------|----------|-----------|
| Credit Sales (₹) | 12,00,000 | 36,00,000 | 24,00,000 |
| Contribution @50% (₹) | 6,00,000 | 18,00,000 | +12,00,000 |
| Bad Debts | 12L×1.5%=18,000 | 36L×2%=72,000 | (54,000) |
| Cash Discount | 12L×50%×1%=6,000 | 36L×40%×2%=28,800 | (22,800) |
Investment in Debtors:
Current = (12,00,000 × 50% ÷ 360) × 30 = ₹50,000
Proposed = (36,00,000 × 50% ÷ 360) × 20 = ₹1,00,000
Incremental investment = ₹50,000
Opportunity cost = ₹50,000 × 15% = (₹7,500)
Net Benefit Statement:
| Particulars | ₹ |
|------------|---|
| Incremental Contribution | 12,00,000 |
| Less: Incremental Bad Debts | (54,000) |
| Less: Incremental Cash Discount | (22,800) |
| Less: Opportunity Cost on incremental debtors | (7,500) |
| Net Benefit (Pre-Tax) | 11,15,700 |
| Less: Tax @ 30% | (3,34,710) |
| Net Benefit (After Tax) | ₹7,80,990 |
Decision: The company SHOULD change its credit terms. The liberalisation generates a positive net after-tax benefit of ₹7,80,990, primarily driven by a 3x increase in sales, despite higher bad debts and discount costs.