Question

Contact WheelsLtd manufactures and sells car tyres. It has developed two new models, ‘Z-Grip’ and ‘Y-Slip’, for use in long distance driving which will be launched in January 2021.These will be sold exclusively in the company’s new car-mart. The annual fixed cost is $180,000. From a pre-launch market survey, it expects that sixty percent of the potential customers prefer ‘Z-Grip’ while forty percent prefer ‘’Y-Slip’. The following information has been extracted to facilitate a Cost-Volume-Profit analysis:

	Z-Grip	Y-Slip
Selling Price per tyre	$300	$400
Variable Cost per tyre	$80	$120
Sales commission per unit	$20	$30

Required:

1. Calculate the Unit contribution margin for each model of the tyres.   
2. Calculate the weighted average contribution margin, assuming the sales mix as determined from the survey is expected to remain constant
3. Calculate the break-even point in units and in sales dollars (in total and per product) for Contact Wheels Ltd’s new car-mart. Assume a constant sales mix.
4. How many tyres of each modelneedto be sold to earn a target net profit of $66,000? Assume a constant sales mix.
5. Identify any two factors that may affect a cost-volume-profit analysis  

Answer 1

a. Calculation of Unit contribution margin for each model of the tyres:

Item	Z-Grip	Y-Slip
Selling price per tyre	$300	$400
Less: Variable Costs per tyre	$80	$120
Less: Sales commission per unit	$20	$30
Contribution margin per unit	$200	$250

b. Calculation of weighted average contribution margin, assuming the sales mix as determined from the survey is expected to remain constant:

Given sales mix is 60% Z-Grip and 40% Y-Slip i.e. 3:2 ratio of sales mix

Item	Z-Grip	Y-Slip	Total
Selling price per tyre	$300	$400
Less: Variable Costs per tyre	$80	$120
Less: Sales commission per unit	$20	$30
Contribution margin per unit	$200	$250
Sales Mix	3	2	5
Contribution margin (Contribution margin per unit x Sales mix)	$600	$500	$1,100

Weighted Average Contribution Margin = Total Contribution Margin / Total Sales mix

= $1,100 / 5 = $220

c. Calculation of break-even point in units and in sales dollars (in total and per product) for Contact Wheels Ltd’s new car-mart. Assume a constant sales mix.

Given, Fixed cost = $180,000

Break-even point in unit sales = Fixed Cost / Weighted Average Contribution margin per unit

Z-Grip = $180,000 / $600 = 300 units

Y-Slip = $180,000 / $500 = 360 units

Total Break-even point in unit sales = $180,000 / $220 = 819 units

Calculation of Weighted Average Contribution margin Ratio:

	Z-Grip	Y-Slip	Total
Selling price per tyre	$300	$400
Less: Variable Costs per tyre	$80	$120
Less: Sales commission per unit	$20	$30
Contribution margin per unit	$200	$250
Contribution margin Ratio (%) (Contribution margin/Sales)	66.67%	62.50%
Sales Mix (%)	60%	40%
Weighted average contribtution margin (Contribution margin Ratio x Sales Mix)	40%	25%	65%

Break-even point in dollar sales = Fixed Cost / Weighted Average Contribution margin Ratio

Z-Grip = $180,000 / 40% = $450,000

Y-Slip = $180,000 / 25% = $720,000

Total Break-even point in dollar sales = $180,000 / 65% = 276,924 (approx.)

d. Calculation of unts to be sold to earn a profit of $66,000, assuming the constant sales mix:

Required sales units = (Fixed cost + Target Profit) / Weighted Average Contribution margin per unit

= ($180,000 + $66,000) / $220 = 1,119 units (approx.)

e. Identification of any two factors that may affect a cost-volume-profit analysis:

The two factors that might affect the cost-volume-profit will be:

1. Sales mix ratio and

2. Contribution margin per unit.

Explanation: If any change has been made in the above, it results in differece of cost-volume and profit of the firm.