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Hi Everyone,
I have come across a question to which i can’t wrap my head around, any help would be really great.
Q: A company has fixed costs of £1.3Mil. Variable costs are 55% of sales up to a sales level of £1.5Mil, but at higher volumes of production and sales, variable costs for incremental production unit falls to 52% of sales.
A: When sales revenue is 1.5 mil, total contribution is 45% x 1.5mil = 675,000.
This leaves a further 625,000 of fixed costs to cover. To achieve breakeven, sales in excess of 1.5mil need to be 625,000/0.48 = 1.302mil
Total sales revenue to breakeven = 1.5 mil + 1.302 mil = 2.802 milSo i get that 45% is the contribution as 55% are variable costs. It is the rest that is a bit of a blur.
Upto the sales of 1.5mil, the contribution is 45%. But, for the incremental sales above 1.5mil, the variable costs fall to 52%, hence the contribution would be 48% of incremental sales.
Now, breakeven is achieved when Contribution = Fixed Costs
From 1.5mil sales, the contribution is $675,000. So, another $625,000 ($1,300,000-$675,000) will be needed from the incremental sales to cover fixed costs and achieve breakeven.This extra contribution of $625,000 will be 48% of incremental sales i.e C/S ratio is 48%. Hence we can divide $675,000 by 48% to find out the sales revenue, which is $1,302,083 or $1.302mil.
We can verify this:
At Breakeven point,
Contribution = Fixed Costs
($1,500,000*45%) + ($1,302,083*48%) = $1,300,000
$675,000+$625,000 = $1,300,000
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