The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 68,000 | $ | 31.00 | $ | 4.50 | $ | 4.20 |
| Trish | 60,000 | $ | 5.00 | $ | 1.40 | $ | 0.77 |
| Sarah | 53,000 | $ | 44.50 | $ | 9.14 | $ | 6.30 |
| Mike | 34,000 | $ | 17.00 | $ | 3.80 | $ | 4.90 |
| Sewing kit | 343,000 | $ | 9.80 | $ | 5.00 | $ | 0.42 |
The following additional information is available:
The company’s plant has a capacity of 127,580 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $7 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $565,000 per year. Variable overhead costs are $5 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 127,580 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
1) Calculation of direct labor hours per unit for each product
| Particulars | Debbie | Trish | Sarah | Mike | Sewing Kit |
| Direct Labor per unit (A) | $4.20 | $0.77 | $6.30 | $4.90 | $0.42 |
| Direct Labor Rate per hour (B) | $7.00 | $7.00 | $7.00 | $7.00 | $7.00 |
| Direct Labor hours per unit (A/B) | 0.60 | 0.11 | 0.90 | 0.70 | 0.06 |
2) Calculation of Variable Overhead Cost
| Particulars | Debbie | Trish | Sarah | Mike | Sewing Kit |
| Direct Labor hours per unit (A) | 0.60 | 0.11 | 0.90 | 0.70 | 0.06 |
| Variable Overhead Cost per hour (B) | $5.00 | $5.00 | $5.00 | $5.00 | $5.00 |
| Total Variable Overhead Cost (A*B) | $3.00 | $0.55 | $4.50 | $3.50 | $0.30 |
3) Calculation of contribution margin per labor hour (Amounts in $)
| Particulars | Debbie | Trish | Sarah | Mike | Sewing Kit |
| a) Selling Price per unit | 31.00 | 5.00 | 44.50 | 17.00 | 9.80 |
| b) Direct Materials per unit | 4.50 | 1.40 | 9.14 | 3.80 | 5.00 |
| c) Direct Labor per unit | 4.20 | 0.77 | 6.30 | 4.90 | 0.42 |
| d) Variable Overhead cost per unit | 3.00 | 0.55 | 4.50 | 3.50 | 0.30 |
| e) Contribution Margin per unit (a-b-c-d) | 19.30 | 2.28 | 24.56 | 4.80 | 4.08 |
| f) Direct Labor hours per unit | 0.60 | 0.11 | 0.90 | 0.70 | 0.06 |
| g) Contribution Margin per hour (e/f) | 32.17 | 20.73 | 27.29 | 6.86 | 68.00 |
| h) Ranking on the basis of contribution margin per hour | 2 | 4 | 3 | 5 | 1 |
4) Based on the ranking given in requirement 3, the product with highest contribution margin per hour (i.e. with ranking 1) should be produced first and so on.
Available Direct Labor Hours = 127,580 labor hrs
Calculation of Maximum Contribution Margin (Amounts in $)
| Particulars | Debbie | Trish | Sarah | Mike | Sewing Kit | Total |
| a) Direct Labor hours per unit | 0.60 | 0.11 | 0.90 | 0.70 | 0.06 | |
| b) Demand Next year (units) | 68,000 | 60,000 | 53,000 | 34,000 | 343,000 | |
| c) Total Required Labor Hours (a*b) | 40,800 | 6,600 | 47,700 | 23,800 | 20,580 | 139,480 |
Shortage of Labor Hours = Total Required Labor Hours - Total Available Labor Hours
= 139,480 - 127,580 = 11,900 hours
As the last ranking (i.e. ranking 5) is given to the product Mike, this shortage of labor hours of 11,900 will be set off from the total hours required for Mike.
Hence the labor hours available to Mike = 23,800 - 11,900 = 11,900 hrs.
The possible units of Product Mike = 11,900 hrs/0.70 hr per unit = 17,000 units
Therefore, the demand for all other products will be fulfilled completely but the production of product Mike will be only 17,000 units. The contribution margin from the optimal use of labor hours is shown as follows:-
| Particulars | Debbie | Trish | Sarah | Mike | Sewing Kit | Total |
| a) Units to be sold | 68,000 | 60,000 | 53,000 | 17,000 | 343,000 | |
| b) Contribution Margin per unit | 19.30 | 2.28 | 24.56 | 4.80 | 4.08 | |
| c) Total Contribution Margin (a*b) | 1,132,400 | 136,800 | 1,301,680 | 81,600 | 1,399,400 | 4,051,920 |
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