Question

Coastal Minerals (CM) owns the rights to extract minerals from beach sands on Fraser Island.

CM has costs in three areas:

a.

Payment to a mining subcontractor who charges $80 per tonne of beach sand mined and returned to the beach

(after being processed on the mainland to extract three minerals: ilmenite, rutile, and zircon).

b.

Payment of a government mining and environmental tax of $30 per tonne of beach sand mined.

c.

Payment to a barge operator. This operator charges $140,000 per month to transport each batch of beach sand

— up to 100 tonnes per batch per day — to the mainland and then return to Fraser Island (that is, 0 to 100 tonnes per day = $140,000 per month; 101 to 200 tonnes per day

= $280,000 per month, and so on).

Each barge operates 25 days per month. The $140,000 monthly charge must be paid even if fewer than 100 tonnes are transported on any day and even

if CM requires fewer than 25 days of barge transportation in that month. CM is currently mining 160 tonnes of beach sands per day for 25 days per month.

Requirements

1)

What is the variable cost per tonne of beach sand

mined? What is the fixed cost to CM per month?

2)

Is the concept of relevant range applicable to this question? Explain.

3)

What is the unit cost per tonne of beach sand mined

(a) if 160 tonnes are mined each day and

(b) if 230 tonnes are mined each day? Explain the difference in the unit - cost figures.

Answer 1

1) variable cost =

Payment to mining sub contractor = 320000

( 160 tonnes per day×$80/ tonne× 25 days)

Payment to governments mining and

Environmen tax = 120000

( 160 tonnes/ day × $30× 25 days)

Total variable cost = 440000 per month

Fixed cost. 160 tonnes per day

Hence it is between 101- 200 = 280000 per month

2) The relevant range is a range of activity where the assumption that cost behaviour is a staraight line is reasonably valid.

But in the given question cost is not staraight line with activity because fixed changes with level of activity beyond 100 upto 200 and thereafter. Hence it is changing with respect to certain limits of activity.

Hence concept of relevant range is not applicable.

3) total cost if

a) 160 units are mined each day

Total variable cost = 440000

Total fixed cost. = 280000

Total cost. = 720000

b) if 230 units are mined each day

Total variable cost. = 632500

( $80+$30)×230 units× 25 days

Total fixed cost. = 420000

(Given that Fixed cost for 101 - 200units = 280000 and thereon hence for next level 201 - 300 it is 420000)

Total cost. For 230 units per day =. 10,52,500