How do i calculate this break even question?

Question

Online CD’s PLC produced and sold 20,000 copies of a CD last month. The variable costs per CD are £1.15 and the selling price is £6.35. Last month the company made a loss of £5,000. The company charges its fixed costs monthly. It has no opening or closing stock. To make a profit of £10,000 next month how many CD's does the company need to produce?

Answer 1

This is relatively an easy question.  Start with contribution per item  This is £5.20 because SP = 6.35 and variable cost = £1.15.

Now, 20,000 items will produce a gross contribution of :£104,000

because (20, 000 x £5.20 = £104,000)

The company made a loss of £5,000, therefore its fixed costs must be £109.000.

Now to produce a profit of £10,000, the company needs to cover not only its fixed costs of £109,000 but also to make a profit of £10,000.  So it must produce a contribution of  Ã‚£119,000.  This requires the company to sell (119,000 / 5.20) 22,885 units.

hope this helps.

Answer 2

Okay, I'll do your homework for you.  :o)

20,000 copies at £6.35 each makes the company £127,000

These 20,000 cost £1.15 each or £23,000

The profit per piece is £5.20 and the company needs to make an extra £15,000 (£5000 loss + £10,000 profit).

£15,000 divided by £5.20 is an extra 2885 units or 22,885 total units needing to be sold.