CM Per Constraint Unit - Cost Accounting

1. If the company buys the component, the freed-up machine time can be used to produce other products that generate, on average, $70 of contribution margin per machine hour. What is the financial advantage or disadvantage per unit of buying the component externally?
   Answer: $2 advantage per unit This is a make-or-buy decision involving a constrained resource. First, calculate the net cost of purchasing externally per unit, ignoring the opportunity cost. Purchase cost ($62) - Internal variable cost ($50) = $12 extra cost to buy. Next, calculate the opportunity benefit of freeing up the machine time. The time freed up is 0.2 hours per component. The benefit generated by this time is 0.2 hours * $70/hour = $14. The net financial impact is the opportunity benefit minus the extra cost of buying: $14 - $12 = $2 advantage per unit. Therefore, it is financially advantageous to buy the component.
2. The company has committed to a contract to supply 200 bags of Lush-Lawn each month. After fulfilling this contract, how should the remaining nitrogen concentrate be allocated to maximize profit?
   Answer: Allocate all remaining concentrate to producing Grow-Fast because it is more profitable per kilogram of concentrate. First, determine the contribution margin per unit of the constrained resource (kg of concentrate). Grow-Fast: $24 / 4 kg = $6/kg. Lush-Lawn: $25 / 5 kg = $5/kg. Grow-Fast is more profitable in terms of the constraint. The company must first fulfill its contract for 200 bags of Lush-Lawn, which uses 200 bags * 5 kg/bag = 1,000 kg of concentrate. This leaves 4,000 kg - 1,000 kg = 3,000 kg of concentrate. To maximize profit, this remaining resource should be allocated to the most profitable product per unit of constraint, which is Grow-Fast.
3. Product Alpha has a selling price of $100 and variable costs of $60 per unit, and it requires 1.0 machine hour per unit. Product Beta has a selling price of $150 and variable costs of $90 per unit, and it requires 2.0 machine hours per unit. Maximum market demand is 3,000 units for Alpha and 2,000 units for Beta. What is the maximum total contribution margin the company can generate in the period?
   Answer: $225,000 First, calculate the contribution margin (CM) per unit and per machine hour for each product. Alpha: CM/unit = $100 - $60 = $40; CM/hour = $40 / 1.0 hr = $40/hr. Beta: CM/unit = $150 - $90 = $60; CM/hour = $60 / 2.0 hrs = $30/hr. Since Alpha has a higher CM per machine hour, it should be prioritized. The company should produce Alpha up to its market demand of 3,000 units, which uses 3,000 hours. The remaining 3,500 hours (6,500 - 3,000) are used for Beta, producing 1,750 units (3,500 hrs / 2.0 hrs/unit). The total contribution margin is (3,000 Alpha units × $40/unit) + (1,750 Beta units × $60/unit) = $120,000 + $105,000 = $225,000.
4. The company is considering outsourcing the production of Gamma to a reliable supplier for a price of $200 per unit. The variable cost to produce Gamma internally is $80 per unit. If outsourced, the resources would be used to produce Delta. What is the net financial impact per unit of outsourcing Gamma?
   Answer: A benefit of $80 per unit. This is a make-or-buy decision involving an opportunity cost. First, calculate the direct financial impact of buying Gamma. Cost to buy is $200. Cost to make (variable cost) is $80. The extra direct cost of buying is $200 - $80 = $120. Second, calculate the opportunity benefit. Outsourcing Gamma frees up 5 hours of the resource. This resource can be used to make Delta. The profitability of Delta per resource hour is $120 CM / 3 hours = $40/hour. The opportunity benefit from the 5 freed-up hours is 5 hours * $40/hour = $200. Finally, calculate the net impact: Opportunity Benefit - Extra Direct Cost = $200 - $120 = $80. There is an $80 benefit per unit from outsourcing Gamma and using the freed resources to make Delta.
5. If the company mistakenly prioritizes production based on the highest contribution margin per unit instead of contribution margin per labor hour, what is the opportunity cost for every labor hour that is misallocated?
   Answer: $5.00 First, calculate the contribution margin (CM) per labor hour for each product. CM per hour for X = $50 / 2 hours = $25/hour. CM per hour for Y = $60 / 3 hours = $20/hour. The correct strategy is to prioritize Product X. The incorrect strategy, based on CM per unit, would prioritize Product Y ($60 > $50). The opportunity cost of this error is the difference in profitability per constrained resource unit. For every hour misallocated to producing Y instead of X, the company earns $20 instead of the $25 it could have earned. Therefore, the opportunity cost is $25 - $20 = $5.00 per labor hour.
6. Assuming the company's objective is to maximize profit, what is the opportunity cost of producing one Widget?
   Answer: $48 The opportunity cost of producing one product is the contribution margin of the alternative product that is forgone. First, determine which product is more profitable per machine hour. Gizmo: $20 / 0.5 hr = $40/hr. Widget: $36 / 1.2 hrs = $30/hr. Gizmo is the more profitable product. Therefore, producing a Widget means forgoing the production of Gizmos. To produce one Widget requires 1.2 hours of machine time. In those 1.2 hours, the company could have generated a contribution margin of 1.2 hours * $40/hour (from Gizmos) = $48. Thus, the opportunity cost of producing one Widget is $48.
7. Titan Manufacturing uses specialized molding equipment operating 2,800 hours monthly. The equipment produces two products: Deluxe (4 hours per unit, $180 CM) and Premium (6 hours per unit, $240 CM). Monthly demand is 400 units for Deluxe and 250 units for Premium. A customer offers to purchase an additional 100 Premium units at a reduced price that would generate only $200 contribution margin per unit. Should Titan accept this special order?
   Answer: Reject the order; the $33.33 CM per hour for special order is less than $45 CM per hour for displaced Deluxe production First, check capacity usage: Regular production needs (400 × 4) + (250 × 6) = 1,600 + 1,500 = 3,100 hours. This exceeds 2,800 available hours, so capacity is constrained. Calculate CM per hour: Deluxe = $\$180 ÷ 4 = \$45$; Premium = $\$240 ÷ 6 = \$40$; Special order = $\$200 ÷ 6 = \$33.33$. Since Deluxe has higher CM per constraint hour ($45), it should receive priority. The special order CM per hour ($33.33) is less than Deluxe CM per hour ($45), so accepting would displace higher-value production. Reject the order.
8. Product A has a contribution margin ratio of 40% and sells for $200 per unit. It requires 10 machine minutes per unit. Product B has variable costs of $150 per unit and requires 12 machine minutes per unit. To be prioritized over Product A, the selling price of Product B must be at least:
   Answer: $246 First, calculate the contribution margin (CM) per machine minute for Product A to establish the profitability benchmark. CM for A = $200 40% = $80/unit. CM per minute for A = $80 / 10 min = $8/min. For Product B to be prioritized, its CM per minute must be greater than or equal to $8/min. The required CM per unit for B is $8/min 12 min/unit = $96. The selling price is the sum of the required contribution margin and the variable costs. Minimum Selling Price for B = Variable Costs + Required CM = $150 + $96 = $246.
9. Product R generates a contribution margin of $12 per unit and requires 0.5 hours of machine time. Product S has a selling price of $50, variable costs of $20, and requires 1.25 hours of machine time. Product T generates a contribution margin of $32 per unit. To be the least profitable option in terms of resource utilization, Product T must require more than how many hours of machine time?
   Answer: 1.33 hours First, calculate the contribution margin (CM) per machine hour for products R and S. R: $12 / 0.5 hr = $24/hr. S: CM = $50 - $20 = $30. CM per hour = $30 / 1.25 hr = $24/hr. Both R and S have the same profitability per hour. For Product T to be the least profitable option, its CM per hour must be less than $24/hr. We can set up an inequality: CM_T / Hours_T < $24/hr. Substituting the known CM for T: $32 / Hours_T < $24. Solving for Hours_T: Hours_T > $32 / $24. Hours_T > 1.333... hours. Therefore, Product T must require more than 1.33 hours to be the least profitable choice.
10. The company currently prioritizes the Standard chair. Management is considering a price increase for the Deluxe chair. Assuming variable costs and labor time per unit remain unchanged, what is the minimum price increase per Deluxe chair needed to make it equally preferable to the Standard chair from a resource allocation perspective?
    Answer: $10 First, determine the benchmark contribution margin per constrained resource unit (labor hour) from the prioritized product, Standard. CM per hour for Standard = $120 / 1.5 hours = $80/hour. For the Deluxe chair to be equally preferable, it must also generate $80/hour. Currently, Deluxe generates $150 / 2.0 hours = $75/hour. To reach the $80/hour target, the total CM for Deluxe must be $80/hour * 2.0 hours = $160. The required increase in contribution margin per unit is $160 - $150 = $10. Since variable costs are unchanged, a $10 increase in contribution margin requires a $10 price increase.
11. Given the constraint and the contractual obligation, which statement best describes the company's optimal production strategy?
    Answer: Produce the required 100 units of A, then allocate remaining capacity to B. First, determine the profitability per unit of the constrained resource (Machine Z hours). Product A: $40 / 2 hours = $20/hour. Product B: $30 / 1 hour = $30/hour. Product B is more profitable per machine hour. A rational company would want to produce as much of B as possible. However, the contractual obligation for 100 units of A must be met. This is a fixed requirement that must be satisfied before any discretionary optimization can occur. The company should first allocate resources to produce the 100 units of A. After that obligation is met, any remaining machine capacity should be dedicated to the most profitable product per hour, which is Product B.
12. By how much would the firm's total contribution margin decrease if management incorrectly prioritized production based on contribution margin per unit instead of contribution margin per finishing hour?
    Answer: $6,000 First, determine the correct priority. Lux: CM/hour = $200 / 4 hrs = $50/hr. Basic: CM/hour = $80 / 1 hr = $80/hr. Correct priority is Basic. Correct Plan: Produce 1,000 units of Basic, using 1,000 hours. Remaining hours = 2,000 - 1,000 = 1,000 hours. Use these to produce 1,000 / 4 = 250 units of Lux. Total CM = (1,000 × $80) + (250 × $200) = $80,000 + $50,000 = $130,000. Incorrect Plan (prioritize Lux based on CM/unit): Produce 300 units of Lux, using 300 × 4 = 1,200 hours. Remaining hours = 2,000 - 1,200 = 800 hours. Use these to produce 800 units of Basic. Total CM = (300 × $200) + (800 × $80) = $60,000 + $64,000 = $124,000. Difference = $130,000 - $124,000 = $6,000.
13. Zenith Manufacturing produces three products using a shared machine that operates 2,400 hours monthly. Product A requires 0.5 hours per unit with a contribution margin of $12 per unit. Product B requires 1.2 hours per unit with a contribution margin of $18 per unit. Product C requires 0.8 hours per unit with a contribution margin of $16 per unit. Market demand exceeds capacity for all products. If the company currently produces equal quantities of each product but wants to maximize profit, which product should receive the highest production priority and what is the monthly profit increase from optimal reallocation?
    Answer: Product A should receive highest priority; monthly profit increase is $9,600 from reallocating all capacity to Product A only First, calculate contribution margin per constraint hour: Product A = $\$12 ÷ 0.5 = \$24$ per hour; Product B = $\$18 ÷ 1.2 = \$15$ per hour; Product C = $\$16 ÷ 0.8 = \$20$ per hour. Product A has the highest CM per constraint hour. Current production with equal quantities: each product gets 800 hours (2,400 ÷ 3), generating total CM of (800 × $24) + (800 × $15) + (800 × $20) = $47,200. Optimal allocation to Product A only: 2,400 hours × $24 = $57,600. Profit increase = $\$57,600 - \$47,200 = \$9,600$.
14. The company receives a special order to produce a new, customized product for a client. This new product would require 0.5 machine hours per unit and has direct variable costs of $120 per unit. To accept this order, the company would have to reduce production of its regular product. What is the minimum selling price per unit the company should charge for the special order?
    Answer: $220 The minimum selling price for the special order must cover its own variable costs plus the opportunity cost of using the constrained resource. First, calculate the contribution margin per machine hour for the regular product, which represents the opportunity cost. Opportunity cost per hour = $80 CM / 0.4 hours = $200/hour. The special order requires 0.5 machine hours. Therefore, the opportunity cost for one unit of the special order is 0.5 hours * $200/hour = $100. The minimum price must cover the variable costs ($120) and this opportunity cost ($100). Minimum Price = $120 + $100 = $220.
15. C1 has a contribution margin of $45 per unit and uses 15 minutes of station time. C2 has a contribution margin of $90 per unit and uses 30 minutes of station time. A new process is discovered that can reduce the station time for C1 by 20% or the station time for C2 by 10%. Which process improvement should be implemented to maximize annual profit, and what is the incremental contribution margin from that choice?
    Answer: Improve C1; incremental CM of $90,000 First, calculate the baseline CM per hour. C1: 15 min = 0.25 hr. CM/hr = $45 / 0.25 = $180/hr. C2: 30 min = 0.50 hr. CM/hr = $90 / 0.50 = $180/hr. Both are equally profitable. Current total annual CM = 2,000 hrs * $180/hr = $360,000. Now evaluate the improvements. Option 1 (Improve C1): New time for C1 = 15 min (1 - 0.20) = 12 min (0.2 hr). New CM/hr for C1 = $45 / 0.2 hr = $225/hr. C2 remains at $180/hr. The company would switch to producing only C1. New total CM = 2,000 hrs $225/hr = $450,000. Incremental CM = $450,000 - $360,000 = $90,000. Option 2 (Improve C2): New time for C2 = 30 min (1 - 0.10) = 27 min (0.45 hr). New CM/hr for C2 = $90 / 0.45 hr = $200/hr. C1 remains at $180/hr. The company would switch to producing only C2. New total CM = 2,000 hrs $200/hr = $400,000. Incremental CM = $400,000 - $360,000 = $40,000. Comparing the incremental gains, improving C1 yields a higher profit increase ($90,000 > $40,000).
16. How should the company rank the products for production priority to maximize profit?
    Answer: Z, Y, X (based on contribution margin per labor hour) To maximize profit when a resource is constrained, products should be ranked based on their contribution margin per unit of the constrained resource. We must calculate the contribution margin per labor hour for each product. Product X: $100 / 4 hours = $25/hour. Product Y: $75 / 3 hours = $25/hour. Product Z: $60 / 2 hours = $30/hour. Based on these calculations, Product Z is the most profitable ($30/hr), while Products X and Y are equally profitable ($25/hr) and less profitable than Z. The correct ranking is Z first, followed by Y and X in any order. The choice Z, Y, X reflects this.
17. The company has the option to use a lower-grade material for Product K. Using it would decrease Product K's variable cost by $3 per unit but would increase its material requirement to 4 kg per unit. Should the company make this change?
    Answer: No, because the contribution margin per kg of material for Product K decreases. The decision should be based on the contribution margin per kg of the constrained material. Original situation: Product J: $30 / 2 kg = $15/kg. Product K: $42 / 3 kg = $14/kg. Product J is currently superior. Proposed change for Product K: New CM for K = $42 (original CM) + $3 (cost savings) = $45. New material requirement for K = 4 kg. New CM per kg for K = $45 / 4 kg = $11.25/kg. While the contribution margin per unit of K increases from $42 to $45, its contribution margin per unit of the constrained resource decreases from $14/kg to $11.25/kg, making it an even less effective use of the rare material. Therefore, the company should not make the change.
18. The contribution margin per testing hour is $120 for the Standard model and $100 for the Premium model. The company currently produces only the Standard model. If the company shifts 100 testing hours from producing Standard models to producing Premium models, what will be the change in total contribution margin?
    Answer: $2,000 decrease The decision is based on comparing the profitability per hour of the constrained resource. The Standard model is more profitable, generating $120 per testing hour compared to the Premium model's $100 per testing hour. Shifting production from a more profitable product to a less profitable one will result in a decrease in total contribution margin. The difference in profitability is $120/hour - $100/hour = $20/hour. Since 100 hours are being shifted, the total change in contribution margin will be 100 hours * ($20/hour decrease) = $2,000 decrease.

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