Cane Company manufactures two products called Alpha and Beta

Cane Company manufactures two products called Alpha and Beta that sell for $130 and $90, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 102,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are unavoidable and have been allocated to products based on sales dollars.

11. How many pounds of raw material are needed to make one unit of each of the two products?

12. What contribution margin per pound of raw material is earned by each of the two products? (Round your answers to 2 decimal places.)

13. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. How many units of each product should Cane produce to maximize its profits?

14. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?

15. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. If Cane uses its 162,000 pounds of raw materials, up to how much should it be willing to pay per pound for additional raw materials? (Round your answer to 2 decimal places.)

Solution

11. There is only one raw material (say X) used in both products which costs $5 per pound. Hence, the entire direct material cost as shown is of X. Hence both use different weights of these raw material.

Alpha : 25/5 = 5 pounds

Beta : 10/5 = 2 pounds

12. Contribution margin calculation :

Contribution margin per pound of raw materials :

Alpha : 52/5 = 10.4

Beta : 42/2 = 21

13. Fixed cost is generally not relevant for decision making as it will not change with change in units sold. As Beta gives us higher contribution margin per pound of raw material, we should first produce and sell Beta, then Alpha.

Raw material for Beta : 62000*2 = 134000

Residual Raw material : 162000-134000 = 28000

Question arises should we manufacture Alpha at all ? Alpha that can be produced = 28000/5 = 5600

Break-even for Alpha : Total fixed cost (traceable) for Alpha = 102000*18 = 1836000

Breakeven point in units = Fixed cost/contribution per unit = 1836000/52 = 35,307.69

Hence we should not manufacture Alpha. We should just manufacture and sell 62000 units of Beta.

14. As we are selling only Beta as explained above, maximum contribution margin is 62000*42 = 2604000

15. If we go ahead with the fact that Cane company fulfills its customer demand to full, it will have to sell 82000 units of Alpha. Raw material required = 82000*5 = 410000 pounds. Out of this we already have 28000 pounds. Hence additional raw material required = 410000-28000 = 382000 pounds. Now lets calculate total contribution margin for Alpha = 82000*52=4264000. To find out profits, let us deduct the fixed cost = 4264000-1836000=$2428000. This amount can be spent additionally to acquire raw material. Hence additional amount that can be spent per pound of raw material = 2428000/382000 = $6.36. Note that we have not considered the common fixed expenses as that is irrelevant for decision making. It cannot be avoided whether or not Alpha is produced.