Barlow Company manufactures three products—A, B, and C. The selling price, variable costs, and contribution margin for one unit of each product follow:
Product
| |||||||||||
| A | B | C | |||||||||
| Selling price | $ | 180 | $ | 300 | $ | 240 | |||||
| Variable expenses: | |||||||||||
| Direct materials | 18 | 90 | 27 | ||||||||
| Other variable expenses | 126 | 120 | 177 | ||||||||
| Total variable expenses | 144 | 210 | 204 | ||||||||
| Contribution margin | $ | 36 | $ | 90 | $ | 36 | |||||
| Contribution margin ratio | 20 | % | 30 | % | 15 | % | |||||
The same raw material is used in all three products. Barlow Company has only 6,300 pounds of raw material on hand and will not be able to obtain any more of it for several weeks due to a strike in its supplier’s plant. Management is trying to decide which product(s) to concentrate on next week in filling its backlog of orders. The material costs $9 per pound.
Required:
1. Calculate the contribution margin per pound of the constraining resource for each product.
2. Assuming that Barlow has unlimited demand for each of its three products, what is the maximum contribution margin the company can earn when using the 6,300 pounds of raw material on hand?
3. Assuming that Barlow’s estimated customer demand is 600 units per product line, what is the maximum contribution margin the company can earn when using the 6,300 pounds of raw material on hand?
4. A foreign supplier could furnish Barlow with additional stocks of the raw material at a substantial premium over the usual price. Assuming Barlow’s estimated customer demand is 600 units per product line and that the company has used its 6,300 pounds of raw material in an optimal fashion, what is the highest price Barlow Company should be willing to pay for an additional pound of materials?
Explanation
1.
| A | B | C | ||||||||||
| (1) | Contribution margin per unit | $ | 36 | $ | 90 | $ | 36 | |||||
| (2) | Direct material cost per unit | $ | 18 | $ | 90 | $ | 27 | |||||
| (3) | Direct material cost per pound | $ | 9 | $ | 9 | $ | 9 | |||||
| (4) | Pounds of material required per unit (2) ÷ (3) | 2 | 10 | 3 | ||||||||
| (5) | Contribution margin per pound (1) ÷ (4) | $ | 18 | $ | 9 | $ | 12 | |||||
2.
If the company has unlimited demand for all three products, it should concentrate all of its available material on product A, which would yield the highest total contribution margin of $113,400 computed as follows:
| A | B | C | |||||||||
| Contribution margin per pound (above) | $ | 18 | $ | 9 | $ | 12 | |||||
| Pounds of material available | × | 6,300 | × | 6,300 | × | 6,300 | |||||
| Total contribution margin | $ | 113,400 | $ | 56,700 | $ | 75,600 | |||||
Although product A has the lowest contribution margin per unit and the second lowest contribution margin ratio, it is preferred over the other two products because it has the highest contribution margin per pound of material, and material is the company’s constrained resource.
3.
If customer demand is limited to 600 units per product the maximum contribution margin of $72,900 is computed as follows:
| A | B | C | |||||||||||||
| Contribution margin per pound (above) | $ | 18 | $ | 9 | $ | 12 | |||||||||
| Pounds of material used | × | 1,200 | × | 3,300 | × | 1,800 | |||||||||
| Total contribution margin | $ | 21,600 | $ | 29,700 | $ | 21,600 | $ | 72,900 | |||||||
Product A would be produced first because it earns the highest contribution margin per pound. Since Product A has customer demand of 600 units, it would consume 1,200 pounds of material (= 600 units × 2 pounds per unit). Product C, which also has customer demand of 600 units, would be produced next because it has the second highest contribution margin per pound. It would consume 1,800 pounds of material (= 600 units × 3 pounds per unit). Since Products A and C consume a total of 3,000 pounds of material (= 1,200 pounds + 1,800 pounds = 3,000 pounds), it leaves 3,300 pounds available (= 6,300 pounds – 3,000 pounds) for making the least profitable product, which is Product B.
4.
Assuming Barlow has customer demand of 600 units per product line and that it has already used its 6,300 pounds in an optimal fashion, any additional raw materials would have to be used to make more of Product B. Thus, the company should be willing to pay up to $18 per pound ($9 usual price plus $9 contribution margin per pound) to manufacture more product B.
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