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Cane Company manufactures two products called Alpha and Beta that sell for $185 and $120, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 112,000 units of each product. Its unit costs for each product at this level of activity are given below:

Alpha Beta
Direct materials $ 30 $ 10
Direct labor 22 29
Variable manufacturing overhead 20 13
Traceable fixed manufacturing overhead 24 26
Variable selling expenses 20 16
Common fixed expenses 23 18
Total cost per unit $ 139 $ 112
The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are deemed unavoidable and have been allocated to products based on sales dollars.

Required:

7.
Assume that Cane normally produces and sells 48,000 Betas per year. If Cane discontinues the Beta product line, how much will profits increase or decrease?

8.
Assume that Cane normally produces and sells 68,000 Betas and 88,000 Alphas per year. If Cane discontinues the Beta product line, its sales representatives could increase sales of Alpha by 12,000 units. If Cane discontinues the Beta product line, how much would profits increase or decrease?

9.
Assume that Cane expects to produce and sell 88,000 Alphas during the current year. A supplier has offered to manufacture and deliver 88,000 Alphas to Cane for a price of $112 per unit. If Cane buys 88,000 units from the supplier instead of making those units, how much will profits increase or decrease?

10.
Assume that Cane expects to produce and sell 58,000 Alphas during the current year. A supplier has offered to manufacture and deliver 58,000 Alphas to Cane for a price of $112 per unit. If Cane buys 58,000 units from the supplier instead of making those units, how much will profits increase or decrease?

13.
Assume that Cane’s customers would buy a maximum of 88,000 units of Alpha and 68,000 units of Beta. Also assume that the company’s raw material available for production is limited to 172,000 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 88,000 units of Alpha and 68,000 units of Beta. Also assume that the company’s raw material available for production is limited to 172,000 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 88,000 units of Alpha and 68,000 units of Beta. Also assume that the company’s raw material available for production is limited to 172,000 pounds. Up to how much should it be willing to pay per pound for additional raw materials? (Round your answer to 2 decimal places.)

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Answer:

7.  profits will decrease by:

  • lost profits = total revenue - total costs = $5,760,000 - $5,376,000 = $384,000
  • unavoidable fixed costs = $18 x 48,000 units = $864,000
  • total decrease in profits ($1,248,000)

8.  profits will decrease by:

  • lost profits from Beta product line = $8,160,000 - $7,616,000 = ($544,000)
  • increased profits from Alpha sales = $2,220,000 - $1,668,000 = $552,000
  • unavoidable fixed costs = (68,000 x $18) - (12,000 x $23) = (948,000)
  • total decrease in profits ($940,000)

9.  profits will increase by:

  • avoidable costs of producing 88,000 Alphas = 88,000 x $116 = $10,208,000
  • cost of purchasing 88,000 x $112 = ($9,856,000)
  • total increase in profits = $10,208,000 - $9,856,000 = $352,000

10.  profits will increase by:

  • avoidable costs of producing 58,000 Alphas = 58,000 x $116 = $6,728,000
  • cost of purchasing 58,000 x $112 = ($6,496,000)
  • total increase in profits = $6,728,000 - $6,496,000 = $232,000

13.  Since the profit margin per pound of direct materials used for Alphas = $7.67 and Betas = $4, the company should produce Alphas. It should produce 28,666 Alphas and 2 Betas. Total profits = $1,318,636 + $16 = $1,318,652

14.  Maximum contribution margin:

  • Contribution margin Alphas = 28,666 units x $92 = $2,637,272
  • Contribution margin Betas = 2 units x $52 = $104
  • total contribution margin = $2,637,376

15.  Since the profit margin per pound of materials used Betas is only $4, there is not much room for increasing the materials costs. If you want to produce Betas, you would be willing to pay less than $9 per pound of direct materials.

But since the profit margin per pound of direct materials used on Alphas is much higher ($7.67), as long as you pay less than $12.97 per pound of direct materials you can still make a profit producing Alphas. So you could pay a much higher price if you wanted to produce Alphas and still make a profit.

Explanation:

                                                                Alpha          Beta

Sales price                                                $185         $120

Direct materials ($5 per pound)               $30           $10

pounds of materials used                           6               2

profit margin per pound                          $7.67          $4

Direct labor                                                $22          $29

Variable manufacturing overhead           $20           $13

Traceable fixed man. overhead               $24          $26

Variable selling expenses                        $20           $16

Common fixed expenses (unavoidable)  $23           $18

Total cost per unit                                    $139          $112

total production capacity 112,000 units per year

contribution margin = sales revenue - variable costs:

contribution margin Alpha = $185 - $93 = $92

contribution margin Beta = $120 - $68 = $52

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