Question

'Happy Hands Ltd. manufactures liquid hand wash for children with minimal chemicals. They have three varieties of liquid soap. The fixed cost for the production process is 2,49,000.

Variety	Scrub Hand Wash	Gel Hand Wash	Foam Hand Wash
Selling Price per 100 ml in (₹)	155	175	195
Variable Cost per 10 ml in (₹)	75	95	105
Sales Mix	40%	30%	30%

Form the above data, calculate the following:

1. Total weighted average contribution margin.
2. Break-even-quantity for each variety of liquid hand wash.
3. Break-even-point in rupees for Scrub Hand Wash.

Answer 1

(a) First, we need to calculate the contribution margin per 100 ml for each variety:

Scrub Hand Wash:

• Selling Price per 100 ml: ₹155
• Variable Cost per 100 ml (since 10 ml costs ₹75, 100 ml costs ₹75 × 10): ₹750
• Contribution Margin per 100 ml: ₹155 − ₹75 = ₹80

Gel Hand Wash:

• Selling Price per 100 ml: ₹175
• Variable Cost per 100 ml (since 10 ml costs ₹95, 100 ml costs ₹95 × 10): ₹950
• Contribution Margin per 100 ml: ₹175 − ₹95 = ₹80

Foam Hand Wash:

• Selling Price per 100 ml: ₹195
• Variable Cost per 100 ml (since 10 ml costs ₹105, 100 ml costs ₹105 × 10): ₹1050
• Contribution Margin per 100 ml: ₹195 − ₹105 = ₹90

Now, let's calculate the weighted average contribution margin using the sales mix:

Weighted Average Contribution Margin:

= (0.40 × ₹80) + (0.30 × ₹80) + (0.30 × ₹90)

= ₹32 + ₹24 + ₹27

= ₹83

(b) To find the break-even quantity, we need the total fixed costs and the weighted average contribution margin:

Fixed Cost: ₹2,49,000

Weighted Average Contribution Margin: ₹83

Break-Even Point (in units):

`= ("Fixed Cost")/("Weighted Average Contribution Margin")`

`=  (₹2,49,000)/(₹83)`

= 3,000 units

Now, we'll distribute this break-even quantity according to the sales mix for each variety:

Scrub Hand Wash:

• Sales Mix: 40%
• Break-Even Quantity: 3,000 units × 40% = 1,200 units

Gel Hand Wash:

• Sales Mix: 30%
• Break-Even Quantity: 3,000 units × 30% = 900 units

Foam Hand Wash:

• Sales Mix: 30%
• Break-Even Quantity: 3,000 units × 30% = 900 units

(c) To calculate the break-even point in rupees for Scrub Hand Wash, we use the break-even quantity and the selling price:

Break-Even Quantity for Scrub Hand Wash: 1,200 units

Selling Price per 100 ml: ₹155

Break-even Point in Rupees:

= Break-Even Quantity × Selling Price per 100 ml

= 1,200 units × ₹155

= ₹1,86,000