a.
Calculate the operating profit in case of satisfying all the annual demands.
a.
Answer to Problem 71P
The operating profit is $672,000 in case of satisfying all the annual demands.
Explanation of Solution
Operating profit:
The operating profit is the excess of total revenues over total expenses after adjusting for
Calculate the operating profit:
| Particulars |
Basic (a) |
Classic (a) |
Formal (a) |
Total |
| Total revenue (2) | $600,000 | $640,000 | $5,700,000 | $6,940,000 |
| Less: variable costs | ||||
| Direct material (2) | $200,000 | $60,000 | $360,000 | $620,000 |
| Direct labor (2) | $224,000 | $320,000 | $3,360,000 | $3,904,000 |
| Variable | $56,000 | $80,000 | $840,000 | $976,000 |
| Variable marketing (3) | $60,000 | $64,000 | $570,000 | $694,000 |
| Total variable costs | $540,000 | $524,000 | $5,130,000 | $6,194,000 |
| Contribution margin | $60,000 | $116,000 | $570,000 | $746,000 |
| Fixed cost | $74,000 | |||
| Operating profit | $672,000 |
Table: (1)
Thus, the operating profit is $672,000 in case of satisfying all the annual demands.
Working note 1:
Calculate the revenue and costs:
| Particulars |
Units (a) |
Rate (b) |
Amount |
| Revenue: | |||
| Basic | 20,000 | $30 | $600,000 |
| Classic | 10,000 | $64 | $640,000 |
| Formal | 30,000 | $190 | $5,700,000 |
| Direct material: | |||
| Basic | 20,000 | $10 | $200,000 |
| Classic | 10,000 | $6 | $60,000 |
| Formal | 30,000 | $12 | $360,000 |
| Direct labor: | |||
| Basic | 20,000 | $11 | $224,000 |
| Classic | 10,000 | $32 | $320,000 |
| Formal | 30,000 | $112 | $3,360,000 |
| Variable overhead: | |||
| Basic | 20,000 | $3 | $56,000 |
| Classic | 10,000 | $8 | $80,000 |
| Formal | 30,000 | $28 | $840,000 |
Table: (2)
Working note 3:
Calculate the variable marketing costs:
| Particulars |
Revenue (a) |
Rate (b) | Amount |
| Basic | $600,000 | 10% | $60,000 |
| Classic | $640,000 | 10% | $64,000 |
| Formal | $5,700,000 | 10% | $570,000 |
Table: (3)
b.
Calculate the most profitable product.
b.
Answer to Problem 71P
The most profitable product line is classic.
Explanation of Solution
Contribution margin:
The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.
Calculate the contribution margin per constrain:
| Particulars | Basic | Classic | Formal |
| Contribution margin | $60,000 | $116,000 | $570,000 |
| Units | 20000 | 10000 | 30000 |
| Contribution margin per unit | $3 | $11.9 | $19 |
| Hours per unit | 0.7 | 2 | 7 |
| Contribution margin per constrained | $4.29 | $5.80 | $2.71 |
Table: (4)
The product line with the highest contribution margin per constrained resource will be most profitable. The classic product line is the most profitable as the profit is $5.8.
Thus, the most profitable product line is classic.
c.
Recommend the product mix as per the given information.
c.
Answer to Problem 71P
The ideal product mix should be 10,000 units of Classic and 14,285 units of Basic.
Explanation of Solution
Product mix:
When a company deals in more than one product, then it has to establish a product mix for its products. The company has limited resources, so it can only produce a limited number of products. It has to consider all the factors and recognize which product mix is most profitable for the company.
Calculate the ideal product mix:
The classic product line is the most profitable product line. It has the highest contribution margin of $5.8, so the management if the company should produce the product of classic line to its highest demand which is 10,000 units.
Company total has 30,000 hours. 10,000 units of Classic product will require 20,000
Thus, the ideal product mix should be 10,000 units of Classic and 14,285 units of Basic.
d.
Calculate the operating profit in case of ideal product mix.
d.
Answer to Problem 71P
The operating profit is $84,855 in case of ideal product mix.
Explanation of Solution
Operating profit:
The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.
Calculate the operating profit in case of ideal product mix:
| Particulars | Basic | Classic | Total |
| Total revenue | $428,550 | $640,000 | $1,068,550 |
| Less: variable costs | |||
| Direct material | $142,850 | $60,000 | $202,850 |
| Direct labor | $159,992 | $320,000 | $479,992 |
| Variable overhead | $39,998 | $80,000 | $119,998 |
| Variable marketing | $42,855 | $64,000 | $106,855 |
| Total variable costs | $385,695 | $524,000 | $909,695 |
| Contribution margin | $42,855 | $116,000 | $158,855 |
| Fixed cost | $74,000 | ||
| Operating profit | $84,855 |
Table: (5)
Thus, the operating profit is $84,855 in case of ideal product mix.
Working note 4:
Calculate the revenue and costs:
| Particulars | Units | Rate | Amount |
| Revenue: | |||
| Basic | 14,285 | $30 | $428,550 |
| Classic | 10,000 | $64 | $640,000 |
| Direct material: | |||
| Basic | 14,285 | $10 | $142,850 |
| Classic | 10,000 | $6 | $60,000 |
| Direct labor: | |||
| Basic | 14,285 | $11 | $159,992 |
| Classic | 10,000 | $32 | $320,000 |
| Variable overhead: | |||
| Basic | 14,285 | $3 | $39,998 |
| Classic | 10,000 | $8 | $80,000 |
Table: (6)
Working note 5:
Calculate the variable marketing costs:
| Particulars | Revenue | Rate | Amount |
| Basic | $428,550 | 10% | $42,855 |
| Classic | $640,000 | 10% | $64,000 |
Table: (7)
e.
Calculate the additional company should produce as per the conditions.
e.
Answer to Problem 71P
The operating profit is $5,143 in case of ideal product mix.
Explanation of Solution
Contribution margin:
Contribution margin is the amount left for the profit and fixed cost of the business. It is calculated by subtracting the variable cost from the revenue of the business.
Calculate the change in contribution margin:
Contribution margin before the increase in the labor costs is $3, $11.6 and $19 for Basic, Classic, and Formal.
| Particulars | Contribution margin | Labor hours | Hour cost | Labor costs | Adjusted contribution margin |
| Basic | $3 | 0.7 | $3 | $2.10 | $0.90 |
| Classic | $11.6 | 2.0 | $3 | $6.00 | $5.60 |
| Formal | $19 | 7.0 | $3 | $21.00 | -$2.00 |
Table: (8)
The contribution margin is highest in case of Classic, but it cannot produce any more units because it has already produced till the highest potential. So it has to produce the product with the second highest contribution margin which is Basic.
It is already producing 14,285 units of Basic so it can produce 5,715
The profit on one unit of Basic is $0.9, so the Company can earn $5,143
Thus, the operating profit is $5,143 in case of ideal product mix.
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