SOLUTIONS TO QUESTIONS 415

8.6
Variable costs are £750,000/300,000 batons=£2.50/baton. As the selling price is £5/baton,
the normal contribution/baton=£2.50 (£5−£2.50).
If 240,000 batons are sold at the normal price:
Contribution= 240 ,000 @ £2. 50 £600,000
−Fixed costs 450,000

Operating profit £150, 000

If 60,000 batons are sold at a 40% discount:

Sales=60% of £5=£3/baton, and contribution is 50p (£3 – variable

costs £2.50)

Contribution= 60 ,000 @ 50p/baton £30, 000

Total operating profit £180, 000

8.7
Profit=selling price per unit×number of units−(VC/unit×no. units+fixed costs)
therefore, £40, 000 =SP× 20 , 000 −((£8× 20 , 000 )+£100k)

Selling price=

£40, 000 +£160, 000 +£100, 000

20 ,000 units

=£300, 000 / 20 ,000 units=£15

8.8
Breakeven is:
( 10 , 000 × 35 )+ 450 , 000 + 0
10 , 000

800 , 000
10 , 000
=£80

Or:

Profit=price×no. of units−(fixed costs+variable costs×no. of units)
0 = 10 ,000P−( 450 , 000 + 35 × 10 , 000 )
0 = 10 ,000P−( 450 , 000 + 350 , 000 )
0 = 10 ,000P− 800 , 000
800 , 000 = 10 ,000P
P= 800 , 000 / 10 , 000 = 80

Proof
10 , 000 ×( 80 − 35 )= 10 , 000 × 45 = 450 , 000 − 450 , 000 = 0

8.9
Contribution per unit is 75− 30 = 45
Fixed costs are 1, 000 × 12 = 12 , 000

Breakeven=

12 , 000 + 10 , 000

45

=489 p.a.

8.10
200 , 000 ×12%
18 ,000 units

=

£24, 000

18 , 000

=£1.33 per unit