Dean's Office Official Model Question Paper

Answer:

Answer:

Sunk Cost: A historical expenditure that has already been incurred in the past and cannot be altered, recovered, or avoided by any present or future management decision (e.g., historical R&D costs, past machinery depreciation).

Why Irrelevant: Because sunk costs remain completely identical across all future alternatives under evaluation, they generate zero incremental impact and must be disregarded in forward-looking capital budgeting decisions.

Solution:

Given:

• Annual Requirement ($A$) = 12,000 units
• Ordering Cost ($O$) = Rs. 150
• Carrying Cost ($C$) = Rs. 4 per unit/year

$$\text{EOQ} = \sqrt{\frac{2AO}{C}} = \sqrt{\frac{2 \times 12{,}000 \times 150}{4}} = \sqrt{\frac{3{,}600{,}000}{4}} = \sqrt{900{,}000} = \mathbf{948.68 \approx 949 \text{ units}}$$

(Or exactly $\sqrt{900{,}000} = \mathbf{300 \text{ if } 2 \times 12{,}000 \times 150 = 3{,}600{,}000 / 40}$, here $\sqrt{900{,}000} = \mathbf{948.68}$ units; exactly $949$ units).

Answer:

1. Reorder Level ($ROL$):

   $$ROL = \text{Maximum Consumption} \times \text{Maximum Reorder Period}$$
   (Or: $ROL = \text{Safety Stock} + (\text{Normal Consumption} \times \text{Normal Lead Time})$)

2. Maximum Stock Level:

   $$\text{Maximum Level} = ROL + EOQ - (\text{Minimum Consumption} \times \text{Minimum Reorder Period})$$

Answer:

• Prime Cost: The aggregate of all direct production costs directly traceable to the manufactured unit:
  $$\text{Prime Cost} = \text{Direct Materials} + \text{Direct Labor} + \text{Direct Expenses}$$
• Conversion Cost: The cost required to convert raw materials into finished commercial goods:
  $$\text{Conversion Cost} = \text{Direct Labor} + \text{Factory (Manufacturing) Overheads}$$

Answer:

Under-Absorption of Overheads: Occurs when the actual factory overhead expenses incurred exceed the overheads absorbed into production based on the predetermined absorption rate:

$$\text{Under-Absorption} = \text{Actual Overheads Incurred} - \text{Absorbed Overheads} > 0$$

It represents an unrecovered production cost resulting from lower-than-anticipated production volume or unexpected cost inflation, and is debited to the Costing Profit and Loss Account at period-end.

Solution:

Given:

• Selling Price ($P$) = Rs. 100
• Variable Cost ($V$) = Rs. 60
• Contribution Margin per unit ($CM$) = $100 - 60 = \text{Rs. } 40$
• Fixed Costs ($FC$) = Rs. 200,000

1. BEP (in units):

   $$\text{BEP}_{\text{units}} = \frac{FC}{P - V} = \frac{200{,}000}{40} = \mathbf{5{,}000 \text{ units}}$$

2. BEP (in sales revenue):

   $$\text{BEP}_{\text{sales}} = \text{BEP}_{\text{units}} \times P = 5{,}000 \times 100 = \mathbf{500{,}000 \text{ Rs.}}$$

Answer:

Margin of Safety (MOS): The excess of actual or budgeted sales over the break-even sales volume. It measures the buffer by which sales can decline before the enterprise incurs an operating loss.

Formulas:

$$\text{MOS (in Rs.)} = \text{Actual Sales} - \text{Break-Even Sales} = \frac{\text{Net Profit}}{P/V \text{ Ratio}}$$

$$\text{MOS Ratio} = \frac{\text{Actual Sales} - \text{Break-Even Sales}}{\text{Actual Sales}} \times 100\%$$

Answer:

Answer:

Let $S$ = Standard time allowed, $T$ = Time taken, $R$ = Wage rate per hour, and $(S - T)$ = Time saved.

1. Halsey Premium Plan (50% Sharing):

   $$\text{Total Earnings} = (T \times R) + 50\%(S - T) \times R$$

2. Rowan Incentive Plan:

   $$\text{Total Earnings} = (T \times R) + \left(\frac{S - T}{S}\right) \times (T \times R)$$

Solution:

Given:

• Annual Demand ($A$) = 20,000 units
• Ordering Cost ($O$) = Rs. 500 per order
• Unit Price ($P$) = Rs. 100
• Carrying Cost ($C$) = $10\% \times 100 = \text{Rs. } 10$ per unit/year

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Part (a): EOQ and Number of Orders

$$\text{EOQ} = \sqrt{\frac{2AO}{C}} = \sqrt{\frac{2 \times 20{,}000 \times 500}{10}} = \sqrt{\frac{20{,}000{,}000}{10}} = \sqrt{2{,}000{,}000} \approx \mathbf{1{,}414 \text{ units}}$$

$$\text{Number of Orders} = \frac{A}{\text{EOQ}} = \frac{20{,}000}{1{,}414.21} \approx \mathbf{14.14 \text{ orders/year}}$$

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Part (b): Total Annual Cost at EOQ (Without Discount)

1. Purchase Cost = $20{,}000 \times 100 = \text{Rs. } 2{,}000{,}000$
2. Total Ordering Cost = $\left(\frac{20{,}000}{1{,}414.21}\right) \times 500 = \text{Rs. } 7{,}071.07$
3. Total Carrying Cost = $\left(\frac{1{,}414.21}{2}\right) \times 10 = \text{Rs. } 7{,}071.05$$\text{Total Cost at EOQ} = 2{,}000{,}000 + 7{,}071.07 + 7{,}071.05 = \mathbf{2{,}014{,}142.12 \text{ Rs.}}$$

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Part (c): Evaluation of 3% Quantity Discount Offer (Order Size = 5,000 units)

• Discounted Purchase Price: $P' = 100 - (3\% \times 100) = \text{Rs. } 97$
• New Carrying Cost per unit: $C' = 10\% \times 97 = \text{Rs. } 9.70$
• Order Size ($Q'$) = 5,000 units

Cost Calculations under Discount Offer:

1. Purchase Cost = $20{,}000 \times 97 = \text{Rs. } 1{,}940{,}000$
2. Total Ordering Cost = $\left(\frac{20{,}000}{5{,}000}\right) \times 500 = 4 \times 500 = \text{Rs. } 2{,}000$
3. Total Carrying Cost = $\left(\frac{5{,}000}{2}\right) \times 9.70 = 2{,}500 \times 9.70 = \text{Rs. } 24{,}250$$\text{Total Cost under Offer} = 1{,}940{,}000 + 2{,}000 + 24{,}250 = \mathbf{1{,}966{,}250 \text{ Rs.}}$$

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Comparison and Decision:

$$\text{Net Annual Savings} = 2{,}014{,}142.12 - 1{,}966{,}250.00 = \mathbf{47{,}892.12 \text{ Rs.}}$$

Recommendation: The company should accept the 3% discount offer because it results in a net annual financial saving of Rs. 47,892.12.

Solution:

Given:

• Standard Time ($S$) = 50 hours
• Hourly Wage Rate ($R$) = Rs. 80
• Worker A: Time Taken ($T_A$) = 40 hours $\implies$ Time Saved ($S - T_A$) = 10 hours
• Worker B: Time Taken ($T_B$) = 30 hours $\implies$ Time Saved ($S - T_B$) = 20 hours

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1. Halsey Premium Plan (50% Bonus)

$$\text{Total Earnings} = (T \times R) + 50\%(S - T) \times R$$

• For Worker A:

  $$\text{Basic Wage} = 40 \times 80 = \text{Rs. } 3{,}200$$
  $$\text{Bonus} = 0.5 \times (10 \times 80) = \text{Rs. } 400$$
  $$\text{Total Earnings}_A = 3{,}200 + 400 = \mathbf{3{,}600 \text{ Rs.}}$$
  $$\text{Effective Hourly Rate}_A = \frac{3{,}600}{40} = \mathbf{90.00 \text{ Rs./hour}}$$

• For Worker B:

  $$\text{Basic Wage} = 30 \times 80 = \text{Rs. } 2{,}400$$
  $$\text{Bonus} = 0.5 \times (20 \times 80) = \text{Rs. } 800$$
  $$\text{Total Earnings}_B = 2{,}400 + 800 = \mathbf{3{,}200 \text{ Rs.}}$$
  $$\text{Effective Hourly Rate}_B = \frac{3{,}200}{30} = \mathbf{106.67 \text{ Rs./hour}}$$

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2. Rowan Incentive Plan

$$\text{Total Earnings} = (T \times R) + \left(\frac{S - T}{S}\right) \times (T \times R)$$

• For Worker A:

  $$\text{Basic Wage} = 40 \times 80 = \text{Rs. } 3{,}200$$
  $$\text{Bonus} = \left(\frac{10}{50}\right) \times 3{,}200 = 0.2 \times 3{,}200 = \text{Rs. } 640$$
  $$\text{Total Earnings}_A = 3{,}200 + 640 = \mathbf{3{,}840 \text{ Rs.}}$$
  $$\text{Effective Hourly Rate}_A = \frac{3{,}840}{40} = \mathbf{96.00 \text{ Rs./hour}}$$

• For Worker B:

  $$\text{Basic Wage} = 30 \times 80 = \text{Rs. } 2{,}400$$
  $$\text{Bonus} = \left(\frac{20}{50}\right) \times 2{,}400 = 0.4 \times 2{,}400 = \text{Rs. } 960$$
  $$\text{Total Earnings}_B = 2{,}400 + 960 = \mathbf{3{,}360 \text{ Rs.}}$$
  $$\text{Effective Hourly Rate}_B = \frac{3{,}360}{30} = \mathbf{112.00 \text{ Rs./hour}}$$

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Summary Table:

Solution:

Comprehensive Cost Sheet for Chaitra 2080

(Output: 10,000 units produced; 9,500 units sold)

Solution:

Reconciliation Statement of Cost and Financial Accounts

For the Year Ended Ashad 31, 2080

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Verification:

Starting from Cost Profit:

$$185{,}500 + 12{,}000 + 6{,}000 + 15{,}000 + 3{,}000 - 8{,}000 - 40{,}000 - 2{,}500 - 6{,}000 = \mathbf{165{,}000 \text{ Rs. (Financial Profit)}}$$

The accounts reconcile completely.

Solution:

Segregation of Costs per unit (at 60% capacity = 6,000 units):

1. Direct Materials: $240{,}000 / 6{,}000 = \mathbf{40 \text{ Rs./unit}}$ (100% variable)
2. Direct Labor: $180{,}000 / 6{,}000 = \mathbf{30 \text{ Rs./unit}}$ (100% variable)
3. Production Overheads (Total Rs. 120,000):
   • Fixed (40%): $120{,}000 \times 40\% = \mathbf{48{,}000 \text{ Rs. (constant)}}$
   • Variable (60%): $120{,}000 \times 60\% = \text{Rs. } 72{,}000 \implies \mathbf{12 \text{ Rs./unit}}$
4. Administrative Overheads (Total Rs. 80,000):
   • Fixed (60%): $80{,}000 \times 60\% = \mathbf{48{,}000 \text{ Rs. (constant)}}$
   • Variable (40%): $80{,}000 \times 40\% = \text{Rs. } 32{,}000 \implies \mathbf{5.333 \text{ Rs./unit}}$
5. Selling Overheads (Total Rs. 60,000):
   • Fixed (50%): $60{,}000 \times 50\% = \mathbf{30{,}000 \text{ Rs. (constant)}}$
   • Variable (50%): $60{,}000 \times 50\% = \text{Rs. } 30{,}000 \implies \mathbf{5 \text{ Rs./unit}}$

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Flexible Budget

Solution:

Secondary Overhead Apportionment (Repeated Distribution Method)

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Verification:

$$\text{Total Original Overheads} = 120{,}000 + 80{,}000 + 40{,}000 + 30{,}000 = \mathbf{270{,}000 \text{ Rs.}}$$

$$\text{Total Production Dept Overheads} = 158{,}960 + 111{,}040 = \mathbf{270{,}000 \text{ Rs.}}$$

The reapportionment reconciles to the rupee.

Solution:

Part (a): Contribution Margin and P/V Ratio per Model

1. Standard Model:

   • Selling Price ($P_S$) = Rs. 1,200
   • Total Variable Cost ($V_S$) = $400 + 200 + 120 = \text{Rs. } 720$
   • Contribution Margin ($CM_S$): $1{,}200 - 720 = \mathbf{480 \text{ Rs./unit}}$
   • P/V Ratio ($P/V_S$):
     $$P/V_S = \frac{480}{1{,}200} = \mathbf{0.40} \quad (\text{or } \mathbf{40\%})$$

2. Deluxe Model:

   • Selling Price ($P_D$) = Rs. 2,000
   • Total Variable Cost ($V_D$) = $650 + 350 + 200 = \text{Rs. } 1{,}200$
   • Contribution Margin ($CM_D$): $2{,}000 - 1{,}200 = \mathbf{800 \text{ Rs./unit}}$
   • P/V Ratio ($P/V_D$):
     $$P/V_D = \frac{800}{2{,}000} = \mathbf{0.40} \quad (\text{or } \mathbf{40\%})$$

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Part (b): Composite P/V Ratio

In an assumed batch of 10 units (6 Standard + 4 Deluxe):

• Total Batch Revenue = $(6 \times 1{,}200) + (4 \times 2{,}000) = 7{,}200 + 8{,}000 = \text{Rs. } 15{,}200$
• Total Batch Contribution = $(6 \times 480) + (4 \times 800) = 2{,}880 + 3{,}200 = \text{Rs. } 6{,}080$$\text{Composite P/V Ratio} = \frac{\text{Total Contribution}}{\text{Total Revenue}} = \frac{6{,}080}{15{,}200} = \mathbf{0.40} \quad (\text{or } \mathbf{40\%})$$

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Part (c): Overall Break-Even Point (BEP)

1. Total BEP in Sales Revenue:

   $$\text{BEP}_{\text{sales}} = \frac{\text{Fixed Costs}}{\text{Composite P/V Ratio}} = \frac{2{,}880{,}000}{0.40} = \mathbf{7{,}200{,}000 \text{ Rs.}}$$

2. BEP Allocation across Models (Sales Mix Value):

   • Standard Sales Revenue share = $\frac{7{,}200}{15{,}200} = \frac{72}{152} \times 7{,}200{,}000 = \text{Rs. } 3{,}410{,}526.32$$\text{BEP Units (Standard)} = \frac{3{,}410{,}526.32}{1{,}200} \approx \mathbf{2{,}842 \text{ units}}$$
   • Deluxe Sales Revenue share = $\frac{8{,}000}{15{,}200} = \frac{80}{152} \times 7{,}200{,}000 = \text{Rs. } 3{,}789{,}473.68$$\text{BEP Units (Deluxe)} = \frac{3{,}789{,}473.68}{2{,}000} \approx \mathbf{1{,}895 \text{ units}}$$

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Part (d): Sales Revenue for Target PAT of Rs. 900,000 (Tax 25%)

Target Profit Before Tax ($PBT$):

$$PBT = \frac{\text{PAT}}{1 - t} = \frac{900{,}000}{1 - 0.25} = \frac{900{,}000}{0.75} = \text{Rs. } 1{,}200{,}000$$

$$\text{Required Sales} = \frac{\text{Fixed Costs} + PBT}{\text{Composite P/V Ratio}} = \frac{2{,}880{,}000 + 1{,}200{,}000}{0.40} = \frac{4{,}080{,}000}{0.40} = \mathbf{10{,}200{,}000 \text{ Rs.}}$$

The required sales revenue is Rs. 10.20 Million.

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Part (e): Margin of Safety and Net Profit at Rs. 8,000,000 Sales

1. Margin of Safety ($MOS$):

   $$\text{MOS (in Rs.)} = \text{Actual Sales} - \text{BEP Sales} = 8{,}000{,}000 - 7{,}200{,}000 = \mathbf{800{,}000 \text{ Rs.}}$$
   $$\text{MOS Ratio} = \frac{800{,}000}{8{,}000{,}000} \times 100\% = \mathbf{10.00\%}$$

2. Net Profit Before Tax:

   $$\text{Net Profit} = \text{MOS} \times \text{P/V Ratio} = 800{,}000 \times 0.40 = \mathbf{320{,}000 \text{ Rs.}}$$

Solution:

Product Cost per Unit:

• Variable Costing Product Cost:
  $$\text{Unit Cost} = \text{DM } (40) + \text{DL } (30) + \text{V.OH } (10) = \mathbf{80 \text{ Rs./unit}}$$
• Absorption Costing Product Cost:
  $$\text{Unit Cost} = \text{Variable } (80) + \text{Fixed Overhead Rate } (20) = \mathbf{100 \text{ Rs./unit}}$$
  $$\text{Fixed OH Rate} = \frac{\text{Rs. } 200{,}000}{10{,}000 \text{ normal units}} = \mathbf{20 \text{ Rs./unit}}$$

Inventory Quantities:

• Year 1: Opening = 0, Production = 11,000, Sales = 9,000 $\implies$ Closing = 2,000 units
• Year 2: Opening = 2,000, Production = 8,000, Sales = 10,000 $\implies$ Closing = 0 units

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Part (a): Income Statement under Variable Costing

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Part (b): Income Statement under Absorption Costing

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Part (c): Reconciliation of Net Income

$$\text{Absorption Profit} - \text{Variable Profit} = (\text{Closing Inventory} - \text{Opening Inventory}) \times \text{Fixed Overhead Rate}$$

• For Year 1:

  • Difference: $325{,}000 - 285{,}000 = \mathbf{+40{,}000 \text{ Rs.}}$
  • Inventory Change: $(2{,}000 - 0) \times 20 = \mathbf{+40{,}000 \text{ Rs.}}$ (Absorption profit is higher by Rs. 40,000 because fixed overheads were capitalized into ending inventory).

• For Year 2:

  • Difference: $310{,}000 - 350{,}000 = \mathbf{-40{,}000 \text{ Rs.}}$
  • Inventory Change: $(0 - 2{,}000) \times 20 = \mathbf{-40{,}000 \text{ Rs.}}$ (Absorption profit is lower by Rs. 40,000 because deferred fixed overheads from Year 1 were released into Year 2 cost of goods sold).

Solution:

Working Notes:

1. Collections from Debtors (80% of Sales, 1 month lag):

   • Shrawan: 80% of Ashad Sales ($400{,}000 \times 80\%$) = Rs. 320,000
   • Bhadra: 80% of Shrawan Sales ($500{,}000 \times 80\%$) = Rs. 400,000
   • Ashwin: 80% of Bhadra Sales ($600{,}000 \times 80\%$) = Rs. 480,000
   • Kartik: 80% of Ashwin Sales ($700{,}000 \times 80\%$) = Rs. 560,000

2. Cash Sales (20% current month):

   • Shrawan: $500{,}000 \times 20\% = \text{Rs. } 100{,}000$
   • Bhadra: $600{,}000 \times 20\% = \text{Rs. } 120{,}000$
   • Ashwin: $700{,}000 \times 20\% = \text{Rs. } 140{,}000$
   • Kartik: $550{,}000 \times 20\% = \text{Rs. } 110{,}000$

3. Payments to Creditors (Purchases of previous month):

   • Shrawan: Ashad Purchases = Rs. 250,000
   • Bhadra: Shrawan Purchases = Rs. 300,000
   • Ashwin: Bhadra Purchases = Rs. 350,000
   • Kartik: Ashwin Purchases = Rs. 400,000

4. Wages (Lag 0.5 month: 50% current month + 50% previous month):

   • Shrawan: $0.5(40{,}000) + 0.5(45{,}000) = 20{,}000 + 22{,}500 = \text{Rs. } 42{,}500$
   • Bhadra: $0.5(45{,}000) + 0.5(50{,}000) = 22{,}500 + 25{,}000 = \text{Rs. } 47{,}500$
   • Ashwin: $0.5(50{,}000) + 0.5(60{,}000) = 25{,}000 + 30{,}000 = \text{Rs. } 55{,}000$
   • Kartik: $0.5(60{,}000) + 0.5(45{,}000) = 30{,}000 + 22{,}500 = \text{Rs. } 52{,}500$

5. Overheads (1 month lag):

   • Shrawan: Ashad Overheads = Rs. 30,000
   • Bhadra: Shrawan Overheads = Rs. 35,000
   • Ashwin: Bhadra Overheads = Rs. 40,000
   • Kartik: Ashwin Overheads = Rs. 45,000

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Cash Budget for Four Months (Shrawan to Kartik 2080)

The cash budget indicates robust positive liquidity across all four months, with the ending cash balance climbing to Rs. 322,500 by Kartik 2080.