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A company makes two products with the following characteristics:
Product X Product Y
Contribution to sales ratio 0.3 0.5
Selling price per unit $3.00 $4.80
Maximum demand 8,000 units 3,000 unitsFixed costs are $9,000.
A $20,400
B $25,800
C $29,400
D $24,000In the examiners report the correct answer is A by seeing which one gives the highest contribution per unit.
———————————————-Question:
I calculated it using a mix and found the answer to be D- 5000 units of X and 1875 units of Y. Both below the maximum demand and breaking even.The question does not state anything about trying to maximize contribution nor have any of the practice questions, how are we supposed to assume that is what they are asking?
The question was: What is the minimum revenue required for production to break even?
To determine the minimum revenue required to break even i.e. the break-even revenue, the
break-even point for each product needs to be calculated.To do that the contribution per unit for each product needs to be established.
Contribution per unit (C/S ratio x selling price)
Product X 0.3 x $3.00 = $0.90
Product Y 0.5 x $4.80 = $2.40Break-even point (Fixed costs/contribution per unit)
$9,000/$0.90 = 10,000 units
$9,000/$2.40 = 3,750 units
Maximum demand
8,000 units and 3,000 unitsFrom the table above, either 10,000 units of product X or 3,750 units of product Y need to be
produced to break-even.But maximum demand for both products, the break-even sales units cannot be achieved on either product. If the break-even point cannot be achieved with only one of the products, then the combination of units of products X and Y to be sold in order to break even needs to be determined.
To do this, the product with the highest contribution per unit would be produced first, up to its
maximum demand, to cover the fixed costs as quickly as possible.Product Y contributes $2.40 per unit, so it will be produced first, up to its maximum demand of 3,000 units, giving a total contribution of (3,000 units x $2.40) $7,200.
Therefore sales of product Y would cover $7,200 of the fixed costs but there will be $1,800 of
fixed costs remaining, which need to be covered by sales of product X.Production of product X will therefore be (remaining fixed costs/contribution per unit of product
X – $1,800/$0.90) = 2,000 units.As the question asks for the minimum revenue (break-even revenue), the last step would be to calculate the sales revenue from the production plan calculated above.
Product X sales revenue = 2,000 units x $3.00 = $6,000
Product Y sales revenue = 3,000 units x $ 4.80 = $14,400
The minimum sales revenue required to break even would therefore be $ 20,400.But this method is specifically for maximizing contribution, the question only asks to breakeven. How would we know which method to choose.
I have explained above:
Read it again………….To determine the minimum revenue required to break even i.e. the break-even revenue, the
break-even point for each product needs to be calculated.Then the contribution per unit for each product needs to be established
Then work out the Break-even point (Fixed costs/contribution per unit)
But its either 10,000 units of product X or 3,750 units of product Y need to be
produced to break even.But there is a maximum demand for both products, the break-even sales units cannot be achieved on either product.
If the break-even point cannot be achieved with only one of the products, then the “combination of units of products X and Y to be sold in order to break even needs to be determined.”As the question asks for the minimum revenue (break-even revenue), the last step would be to calculate the sales revenue from the production plan that you have just decided.
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