Question

GT has three products that it sells: Copper, Bauxite, and Gravel. Results of the fourth quarter are presented below:

	copper	bauxite	Gravel	total
Tonnage sold	10,000	20,000	20,000
revenue	22,000,000	40,000,000	23,000,000	85,000,000
Variable cost	17,000,000	22,000,000	12,000,000	51,000,000
Direct fixed costs	1,000,000	3,000,000	2,000,000	6,000,000
Allocated fixed costs	8,000,000	8,000,000	8,000,000	24,000,000
Net income	4,000,000	7,000,000	1,000,000	4,000,000

The allocated fixed costs are unavoidable. Demand of individual products is not affected by changes in other product lines.

Q. do a break-even analysis on each product to confirm the level of production needed for each product line.

Answer 1

Calculation of contribution margin per unit

	Copper	Bauxite	Gravel
Sales	22000000	40000000	23000000
less:variable cost	17000000	22000000	12000000
contribution margin [a]	5000000	18000000	11000000
Number of units [b]	10000	20000	20000
contribution per unit [a/b]	500	900	550

Calculation of weights :

	Copper	Bauxite	Gravel	Total
Number of units [b]	10000	20000	20000	50000
weights	10000/50000=.20	20000/50000=.4	.40

weighed average contribution per unit = [500 *.20 ]+[900 *.40 ]+ [550*.40 ] = 100+360+ 220= 680

Total fixed cost =6000000+24000000=30,000,000

Calculation of breakeven point

Breakeven point in totality /overall for company =Fixed cost /weighted average contribution per unit

                       = 30000000/680

                      = 44118 units rounded

Product	Breakeven point for individual product line (Total breakeven point * weights)
cooper	44118*.20 = 8824
Bauxite	44118*.4= 17647
Gravel	17647
Total	44118