relevant cost

[Question]
A company needs 400kg of material Z to fulfill 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.

The company expects to have 200kg of material Y in inventory in one month’s time with no alternative use other than to sell it for scrap for $18 per kg. The 200kg of material Y could be converted into 200kg of material Z in one month’s time at a cost of $4 per kg. Material Y is not perishable.

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

[My Answer]
We need 400 kg of material Z in one month’s time for the contract so the current purchase cost of $20 is irrelevant because we have been given material cost of $24 in one month’s time which is relevant because we need to material in one month not today. [so it is not relevant]

We are not concerned about whether the material is perishable or not and whether how much % of stores material is lost every month. [so it is not relevant]

We are told that 200 kg of material Y is expected to be in the inventory in one month’s time:

Now we have two scenerios either we can sell the material Y in scrap for $18 or we can modify the material Y at the cost of $4 and use it for material Z.

[The cheaper scenerio would be preferred which is to modify at cost of $4]

Since it would be silly not to modify and simply purchase it from market at cost of $18 which would be costly but rather we should modify it at cost of $4 and use it for material Z because it is cheaper but we should include the scrap value as lost contribution (ie. opportunity cost) which we could have earned otherwise.

Relevant costs are therefore as follows:
New material = (200kg x $24) = 4800

Opportunity cost :
Scrap value = (200kg x $18) = 3600
Modify cost = (200kg x $4) = 800

Total relevant cost would be = $9200

Is it all correct? Thanks in advancee