108 ACCOUNTING FOR MANAGERS
to solve the above equation for u (the number of units) where N (net profit) is 0,
as follows:
0 =Pu−(F+Bu)
0 =20u−( 200 , 000 +10u)
u=
200 , 000
10
u= 20 , 000
However, a simpler formula for breakeven is:
breakeven sales (in units)=
fixed costs
selling price per unit−variable cost per unit
=
£200, 000
20 − 10
= 20 ,000 units
Note that £10 is theunit contribution, i.e. the difference between the selling price
and the variable cost per unit. The unit contribution can also be expressed as a
percentage of sales of 0.5 or 50% (£10/£20), which applies to any level of sales as
the ratio of contribution (£10) to selling price (£20) remains constant within the
relevant range.
breakeven sales (in £s)=
fixed costs
unit contribution as a % of sales
=
£200, 000
0. 5
=£400, 000
This is equivalent to the breakeven units of 20,000 at £20 selling price per unit.
Businesses establish profit targets, and a variation on the above calculations is
to calculate the number of units that need to be sold to generate a target net profit.
sales (in units) for profit of £150,000=
fixed costs+target profit
selling price per unit−
variable cost per unit
=
£200, 000 +£150, 000
20 − 10
= 35 ,000 units
sales (in £s) for profit of £150,000=
fixed costs+target profit
unit contribution as a % of sales
=