Lace Ltd –Corporation tax payable for the nine-month period ended 31 Dec

For capital allowances purposes Lace Ltd brought forward the following tax written down values as at 1 April 2018:

Main pool

£210,000

Special rate pool

£30,000

Lace Ltd purchased a new machine for £240,000 on 14 June 2018 and sold an old machine, which had cost £24,000, for £28,800 on 4 December 2018. All figures relating to machinery additions and disposals are inclusive of VAT.

so here’s where I’m stuck:

Additions qualifying for AIA
14 June 2018 -£240,000 x 5/6 = 200,000 (why do we multiply the purchase by 5/6 if we are time apportioned to 9 months??
AIA -£200,000 x 9/12= 150,000 (this I understand)
Disposal:
4 December 2018 -£24,000 * 5/6 = 20,000 (same here we multiply the original costs by 5/6 ??