Accounting for Managers: Interpreting accounting information for decision-making

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

=

£200, 000 +£150, 000

0. 5

=£700, 000