A manufacturing Company produces 2 products – A and B.
The following information is presented for both products:
A
B
Selling Price per unit
$18
$12
Variable Cost per unit
$14
$6
Total Fixed Costs are $468,000.
Compute:
The contribution margin for each product.
Break-even point in units of both A and B if the sales mix is 3 units of A for every unit of B.
Break-even volume in total dollars if the sales mix is 2 units of A for every 3 units of B.
Question 2
Davis Manufacturing gathered the following information:
Variable Costs $630,000
Income Tax Rate 40%
Contribution Margin Ratio 30%
Required:
Compute total fixed costs assuming a break-even volume in dollars of $900,000.
Compute sales volume in dollars to produce an after-tax net income of $72,000.
To compute the contribution margin for each product, you subtract the variable cost per unit from the selling price per unit.
For Product A:
Contribution margin = Selling price per unit - Variable cost per unit
= $18 - $14
= $4
For Product B:
Contribution margin = Selling price per unit - Variable cost per unit
= $12 - $6
= $6
To calculate the break-even point in units of both A and B, we need to consider the sales mix. The sales mix here is given as 3 units of A for every unit of B.
Let's assume the number of units sold for both A and B as 'x' and 'y' respectively.
Total contribution margin = (Contribution margin for A * x) + (Contribution margin for B * y)
= ($4x) + ($6y)
Total fixed costs = $468,000
To calculate the break-even point, total contribution margin should cover total fixed costs. So, we can set up the equation as follows:
Total contribution margin = Total fixed costs
($4x) + ($6y) = $468,000
Now, since the sales mix is given as 3 units of A for every unit of B, we can also set up the equation as:
x/y = 3/1 => x = 3y
Substituting this value into the previous equation:
($4(3y)) + ($6y) = $468,000
Solving this equation will give us the break-even point in units of both A and B.
To calculate the break-even volume in total dollars, we need to consider the sales mix ratio. Here it is given as 2 units of A for every 3 units of B.
Let's assume the number of units sold for A and B as 'x' and 'y' respectively.
Total sales volume = (Selling price per unit of A * x) + (Selling price per unit of B * y)
= ($18x) + ($12y)
To calculate the break-even volume in total dollars, the total sales volume should cover the break-even point in units in both A and B. We can set up the equation as follows:
Total sales volume = (Break-even point in units of A * Selling price per unit of A) + (Break-even point in units of B * Selling price per unit of B)
Total sales volume = ($18 * break-even point in units of A) + ($12 * break-even point in units of B)
Given the sales mix as 2 units of A for every 3 units of B, we can convert the break-even point in units of A and B accordingly. Solving this equation will give us the break-even volume in total dollars.
For Question 2:
To compute total fixed costs, we use the break-even volume in dollars and the contribution margin ratio.
Total fixed costs = (Break-even volume in dollars * Contribution margin ratio) / (1 - Contribution margin ratio)
Here, the break-even volume in dollars is given as $900,000, and the contribution margin ratio is given as 30%. Plugging in these values will give us the total fixed costs.
To compute the sales volume in dollars to produce an after-tax net income of $72,000, we can use the following equation:
Sales volume in dollars = (After-tax net income + Total fixed costs) / (1 - Tax rate)
Here, the after-tax net income is given as $72,000, and the tax rate is given as 40%. Using these values, we can calculate the sales volume in dollars.