Advanced Cost and Management Accounting

a. Weighted average contribution margin per unit.

Calculation:

1. Total Sales Units: $10,000 \text{ (Product X)} + 10,000 \text{ (Product Y)} = 20,000 \text{ units}$
2. Total Contribution Margin: Rs. $70,000$
3. Weighted Average Contribution Margin per Unit: $\text{Weighted Average CM per Unit} = \frac{\text{Total Contribution Margin}}{\text{Total Sales Units}}$ $\text{Weighted Average CM per Unit} = \frac{\text{Rs. } 70,000}{20,000 \text{ units}} = \text{Rs. } 3.5 \text{ per unit}$

Answer: The weighted average contribution margin per unit is Rs. $3.5$.

b. Overall BEP in units and amount.

Calculation:

1. Total Fixed Costs (TFC): $\text{TFC} = \text{Product wise fixed cost} + \text{Joint fixed cost}$ $\text{TFC} = \text{Rs. } 30,000 + \text{Rs. } 22,000 = \text{Rs. } 52,000$
2. Overall BEP in Units: $\text{BEP (Units)} = \frac{\text{Total Fixed Costs}}{\text{Weighted Average Contribution Margin per Unit}}$ $\text{BEP (Units)} = \frac{\text{Rs. } 52,000}{\text{Rs. } 3.5/\text{unit}} \approx 14,857.14 \text{ units}$ Since units must be whole numbers, we round up to ensure fixed costs are covered. $\text{BEP (Units)} = 14,858 \text{ units}$
3. Overall BEP in Amount (Sales Revenue): $\text{BEP (Amount)} = \text{BEP (Units)} \times \text{Weighted Average Selling Price per Unit}$ First, calculate the weighted average selling price per unit: $\text{Weighted Average SP per Unit} = \frac{\text{Total Sales Revenue}}{\text{Total Sales Units}} = \frac{\text{Rs. } 400,000}{20,000 \text{ units}} = \text{Rs. } 20 \text{ per unit}$ $\text{BEP (Amount)} = 14,858 \text{ units} \times \text{Rs. } 20/\text{unit} = \text{Rs. } 297,160$

Answer:

• Overall BEP in Units: $14,858 \text{ units}$
• Overall BEP in Amount: Rs. $297,160$

c. Linear programming model for profit maximization, under both raw materials and labours are in short supply and for the next year direct material will be available 5,000 kgs and labour hours of 4,000 hours only.

Model Formulation:

1. Decision Variables: Let $X_1$ be the number of units of Product X to produce. Let $X_2$ be the number of units of Product Y to produce.

2. Objective Function (Maximize Profit): First, calculate the contribution margin per unit for each product:

• Product X CM per unit: $\frac{\text{Rs. } 40,000 \text{ (CM for X)}}{\text{10,000 units}} = \text{Rs. } 4 \text{ per unit}$
• Product Y CM per unit: $\frac{\text{Rs. } 30,000 \text{ (CM for Y)}}{\text{10,000 units}} = \text{Rs. } 3 \text{ per unit}$

Note: The fixed costs (Rs. 52,000) are sunk costs for the decision of production mix and are ignored in the marginal profit maximization model.

$\text{Maximize } Z = 4X_1 + 3X_2$

3. Constraints:

a) Raw Material Constraint (Direct Material):

• Material required for X: $\frac{\text{Rs. } 100,000 \text{ (DM for X)}}{\text{10,000 units}} = 10 \text{ Rs./unit}$. Since DM is Rs. 5/kg, the material required per unit of X is $\frac{100,000}{10,000 \times 5} = 2 \text{ kg/unit}$.
• Material required for Y: $\frac{\text{Rs. } 50,000 \text{ (DM for Y)}}{\text{10,000 units} \times \text{Rs. } 5/\text{kg}} = 1 \text{ kg/unit}$.
• Available Material: $5,000 \text{ kgs}$.

$2X_1 + 1X_2 \le 5,000 \quad \text{(Raw Material Constraint)}$

b) Labour Constraint (Direct Labour):

• Labour hours for X: $\frac{\text{Rs. } 60,000 \text{ (DL for X)}}{\text{10,000 units} \times \text{Rs. } 6/\text{DLH}} = 1 \text{ hour/unit}$.
• Labour hours for Y: $\frac{\text{Rs. } 120,000 \text{ (DL for Y)}}{\text{10,000 units} \times \text{Rs. } 6/\text{DLH}} = 2 \text{ hours/unit}$.
• Available Labour Hours: $4,000 \text{ hours}$.

$1X_1 + 2X_2 \le 4,000 \quad \text{(Labour Constraint)}$

c) Non-negativity Constraints: $X_1 \ge 0, X_2 \ge 0$

Summary of the Linear Programming Model:

$\text{Maximize } Z = 4X_1 + 3X_2$ $\text{Subject to:}$ $2X_1 + X_2 \le 5,000 \quad \text{(Raw Material)}$ $X_1 + 2X_2 \le 4,000 \quad \text{(Labour)}$ $X_1, X_2 \ge 0$

Working notes

Closing inventory = 6,000 + 25,000 − 27,000 = 4,000 units

Variable production cost per unit = 4 + 3 + 2 = Rs 9

Fixed factory overhead absorption rate (normal capacity 20,000 units):

$\frac{80{,}000}{20{,}000} = \text{Rs } 4 \text{ per unit}$

Full production cost per unit = 9 + 4 = Rs 13. Opening and closing inventory are valued at this cost.

Fixed factory overhead absorbed = 25,000 × 4 = Rs 1,00,000 against actual Rs 80,000, so it is over-absorbed by Rs 20,000. This is added back to profit.

Selling and distribution overheads are period costs: variable = 27,000 × 2 = Rs 54,000 and fixed = Rs 70,000. Office overhead (Rs 50,000) is also a period cost.

Budgeted Absorption Costing Income Statement

The net profit is Rs 3,05,000 after correcting for the over-absorbed overhead (Rs 2,85,000 before that adjustment).

Given: new machine cost = 3,00,000 + 20,000 installation = Rs 3,20,000; salvage Rs 20,000 after 3 years; annual cash saving Rs 80,000; extra working capital Rs 20,000; old machine market value Rs 1,50,000 and salvage Rs 10,000; straight-line depreciation; tax 25%; cost of capital 10%.

(a) Net cash outflow

$NCO = 3{,}20{,}000 + 20{,}000 - 1{,}50{,}000 = \text{Rs } 1{,}90{,}000$

(b) Differential annual CFAT

• Depreciation on new machine = (3,20,000 − 20,000)/3 = Rs 1,00,000
• Depreciation on old machine = (1,50,000 − 10,000)/3 = Rs 46,667
• Differential depreciation = Rs 53,333

$CFAT = (80{,}000 - 53{,}333)(1-0.25) + 53{,}333 = 20{,}000 + 53{,}333 = \text{Rs } 73{,}333$

(c) Final year CFAT

$73{,}333 + 20{,}000 \text{ (salvage)} + 20{,}000 \text{ (working capital released)} = \text{Rs } 1{,}13{,}333$

(d) Replacement decision

IRR: at 16%, NPV = about +Rs 324; at 17%, NPV = −Rs 2,990.

$IRR \approx 16\% + \frac{324}{324+2{,}990}\times 1\% \approx 16.1\%$

Decision: NPV is positive (Rs 22,419) and IRR (about 16.1%) exceeds the 10% cost of capital, so the existing machine should be replaced by the automatic high-tech machine.

Master budget of Kiran Trading House Ltd. (January to March 2025)

The monthly sales figures are not reproduced in the question, so the following assumptions are used: sales Jan Rs 4,00,000, Feb Rs 5,00,000, Mar Rs 4,50,000, Apr Rs 5,00,000 (January sales fit the opening stock of Rs 2,40,000 = 60% of Rs 4,00,000); 40% of sales in cash and 60% on credit collected the next month; administration and selling expenses 10% of sales, paid the next month; debenture interest of 12% on Rs 1,00,000 paid at the end of March. The same method applies to any other sales figures.

1. Sales budget

2. Purchase budget (closing stock = next month's cost of sales; April cost of sales = Rs 3,00,000)

3. Cash budget

4. Budgeted income statement (Jan to Mar)

5. Budgeted balance sheet as on 31 March 2025