Relevant Costing

A company needs 400kg of material Z to fulfil a customer order in one month’s time.

It currently has no material Z in inventory. The current purchase price of material Z is $20 per kg and this is expected to rise to $24 per kg in one month’s time. Material Z is perishable and normally 20% of stored material is lost per month.

Material Y is able to be converted to material Z at a cost of $4 per kg. The company expects to have 200kg of material Y in inventory in one month’s time. Material Y could be sold as is for $18 per kg or could be converted into 200kg of material Z. Material Y is not perishable.

What is the total relevant cost of material Z to fulfil the customer order?

Solution:
Tutorial note: The total relevant cost is the lowest cost of the three options: (1) buy now and store for a month, (2) buy in one month’s time or (3) convert material Y.

WORKING

Cost per kg:

1) Buy Z now and store, allowing for loss ($20/(1 – 20%)) $25
2) Buy Z in one month’s time $24
3) Convert material Y
($18 proceeds foregone + $4 conversion cost) $22

Therefore, convert 200kg material Y and buy 200kg Z in one month’s time. The relevant cost is (200kg × $22) + (200kg × $24) = $9200

I do not understand as to why we divide $20 by 0.8?? Should we not multiply 0.8 kgs with $20 to calculate the cost of amount that is not lost?
For the third option, do we not choose the higher of alternate use and loss of scrap value? I.e $18?

Kindly let me know as I think I’m mixing different concepts together? Thanks in advance!