[mzchoclit1]

Sale price per unit $40
Variable expense per unit $25
CM per unit $15

Fixed cost = $832,500

If fixed expenses increase by 10%, to maintain the original break-even sales in units, the sale price per unit would have to be increased by? Or decreased by?

Could someone explain to me the logical method for analyzing this problem? I did get the new fixed cost, which is $915,750. Where do I go from here. Thank you for any assistance you provide.

[CaptainForest]

The first question is what is the CURRENT break-even point.

Sale price per unit $40
Variable expense per unit $25
CM per unit $15
Fixed cost = $832,500

$CM x break even units – Fixed Costs = Net Income
15x – 832,500 = 0
15x = 832,500
x = 55,500

Therefore, the current break-even point is 55,500 units.


The second question is what is the break-even point if fixed costs increase by 10%. Also, we are told we want to keep the break-even units at 55,500

Therefore, Fixed Costs would be 832,500 x 1.10 = 915,750

$CM x break even units – Fixed Costs = Net Income
$CM x 55,500 – 915,750 = 0
$CM x 55,500 = 915,750
$CM = 915,750 / 55,500
$CM = 16.50

Therefore, the new break-even point for the CM per unit is $16.50

How much of an increase is that?
CM 15 to CM 16.50?

15x = 16.50
x = 1.1 or 10%

Therefore, there must be a 10% increase in the sales price to keep the same break even units.

Let's make sure…
Sales = 40x x 1.10 = 44x
VC = 25x x 1.10 = 27.5x
CM = 16.5x

And we already know that the CM should be 16.5

But let's keep going…
CM = 16.5 x 55,500 = 915,750
Less Fixed Costs 915,750
Net Income = 0

Therefore, the new Sales Price is $44