Absorption Costing – OAR- Departmental Rates

Morning John Moffat,

I’m stuck on the following question and need your help please.

The following information is available regarding fixed overhead costs and output of 2 production Depts (S&T) of a firm.

Dept S
Allocated / Apportioned Fixed Overhead $60,000
Total Cost of direct materials used $120,000 (I think its Dept Mat Cost)
Total productive labour hours 5,000 hrs

Dept T
Allocated / Apportioned Fixed Overhead $100,000
Total Cost of direct materials used $100,000 (I think its Dept Mat Cost)
Total productive labour hours 10,000 hrs

A product has the following variable cost
Materials
Dept S 3kg @ $4 per kg $12
Dept T 2kg @ $4 per kg $ 8

Labour
Dept S 0.5hrs @ $10 per hr $5
Dept T 1.5hrs @ $10 per hr $15

Variable overheads
1hr @ $5 per hr $5
_________
Total: $45

What is the fixed overhead cost per unit if fixed overheads are absorbed on the basis of departmental material cost ?

My answer:

OAR = Budgeted Overhead / Budgeted Activity
OAR here = Fixed Overheads / basis of departmental material cost

Departmental OAR – Dept S
$60,000 / $120,000 = $0.5

Departmental OAR – Dept T
$100,000 / $100,000 = $1

Dept S
$12 * $0.5 = $6

Dept T
$8 * $1 = $8

Total = ($6+$8) = $14

Could you please tell me whether I am correct in my approach to answering this question.
Every question I have previously encountered has fixed overheads absorbed by reference to labour hours, not dept material cost.
Thanks.