'Star Bakery Pvt. Ltd.' produces two types of cakes- Chocolate Cake and Vanilla Cake. The company wants to know the break-even point of each type of cake. For the same, the following information is available:
Total fixed cost is Rs. 1,15,600.
On the basis of the given text, answer the following questions -
Calculate the break-even point in units of sales mix.
Show Hint
For multi-product break-even calculations, always compute the Weighted Average Contribution (WAC) first:
$$\text{WAC} = (\text{Contribution}_A \times \text{Mix}_A) + (\text{Contribution}_B \times \text{Mix}_B)$$
Then, divide the Total Fixed Cost by this WAC to find the composite break-even units.
Step 1: Formulating the Multi-Product Break-Even Equation:
For a multi-product enterprise, calculating the Break-Even Point (BEP) requires finding the Weighted Average Contribution (WAC) based on the sales mix percentage of each product.
WAC = \sum ( Contribution of Product_i \times Sales Mix Percentage_i )
Break-Even Point in Units of Sales Mix = \frac{Total Fixed Cost}{WAC}
Step 2: Calculating Individual Product Contributions:
Contribution is calculated as Selling Price (SP) minus Variable Cost (VC) per unit:
Contribution of Chocolate Cake (C_c) &= 200 - 120 = Rs. 80
Contribution of Vanilla Cake (C_v) &= 150 - 90 = Rs. 60
Step 3: Calculating the Weighted Average Contribution (WAC):
Substitute the contributions and sales mix percentages (Chocolate = 40% or 0.40, Vanilla = 60% or 0.60) into our formula:
WAC &= (C_c \times 0.40) + (C_v \times 0.60)
WAC &= (80 \times 0.40) + (60 \times 0.60)
WAC &= 32 + 36 = Rs. 68 per composite unit
Step 4: Calculating the Composite Break-Even Point:
Divide the Total Fixed Cost by the WAC:
Composite BEP in Units &= \frac{1,15,600}{68}
Composite BEP in Units &= 1,700 units
Therefore, Star Bakery Pvt. Ltd. must sell a total of 1,700 units across both products to break even.
