Question on ABC, F5

Hello John,

I have a doubt regarding an MCQ exercise n.8 from Kaplan Exam Kit, regarding Activity Based Costing. It states:

A company is changing its costing system from traditional absorption costing based on labour hours to ABC. It has overheads of $ 156,000 which are related to taking material deliveries:

Product X Y Z
Units required 1,000 2,000 3,000
Delivery size 200 400 1,000
Total Labour costs are $ 360,000 for 45,000 hours. Each unit of each product takes the same number of direct hours.
Assuming that the company uses the number of deliveries as its cost driver, what is the increase/decrease in unit costs fir Z arising from the change from Absorption costing to ABC?

Now, I have done the following:

# of deliveries (units/delivery size) for Z = 3,000 / 1,000 = 3, for X,Y=5.
OH cost per unit using absorption costing=$ 156,000 / (1,000 + 2,000 +3,000) = $ 26 per unit of each X,Y,Z since they all require equal amount of hours.
OH cost per delivery using ABC = OH / total # of deliveries = $ 156,000 / (5+5+3) = $ 12,000.
In order to assign the correct portion of the OH cost using ABC to product Z, we need to multiply the OH cost per delivery with number of deliveries for Z = $ 12,000 * 3 = $ 36,000 and then divide this amount by number of units of Z = 36,000 / 3,000 = $ 12 which is the OH cost per unit of Z, using ABC method.
Nevertheless, the solutions to this question are stating that the OH cost per unit of Z is simply = $ 12,000 / 3,000 = $ 4 ? Aren’t we suppose to allocate the cost per delivery according to the number of deliveries needed for product Z and then divide this amount by number of units? I am a bit confused with the offered solution from Kaplan…
Please advise what am I getting wrong here 🙂

Thanks for your immense support!
Rgs

Marko