Budgeting

Dear Mr Moffat

I need your help to understand one step of below question, I would really appreciate if you could explain to me where I made the mistake, When I did it ‘s sound easy enough to me, but unfortunately I have missed two correct answers.

J Co makes a component M which uses 3 kg of raw material X. The opening inventory at the start of next year is expected to be as follow

Opening inventory of raw material x 5000kg @ 4
Opening inventory of component M 3000 units

Budgeted sales of component M are expected to be 48,000 units (occurring evenly throughout the year)

Closing inventory at the end of the year is as follow:

Closing inventory of raw material X One month’s worth of production
Closing inventory of component M Two month’s worth of sales

a) How many units of component M are to be produced in the year?

My answer. 53,000 (no problem with this)

48000/12*2 = 8,000 closing inventory

Then: 48,000-3000+8000 = 53,000

b) How many kg of material X are required for production in the year?

My answer 159,000 (no problem with it)

Working 53,000 unit *3Kg

c) What is the material X purchases budget for the year?

My answer 167,250 (based on the book my answer is wrong, Closing inventory is the wrong number)

My working

Opening inventory (5000)
Production 159000

Closing inventory 13250

As closing inventory is worth one month of production for raw material to me is

total production 159000/12 = 13250

The answer provided in the book is

96000/12 +159000-5000

I cannot understand where does 96000 come from

Could you kindly help me?

Thanks again for your help

Gabbi