Problem 12-25 Volume Trade-Off Decisions [LO12-5, LO12-6] The Walton Toy Company
ID: 2530013 • Letter: P
Question
Problem 12-25 Volume Trade-Off Decisions [LO12-5, LO12-6]
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:
The following additional information is available:
The company’s plant has a capacity of 152,800 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 $625,000 per year. Variable overhead costs are $3 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 152,800 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)?
Product DemandNext year
(units) Selling
Price
per Unit Direct
Materials Direct
Labor Debbie 74,000 $ 25.50 $ 5.10 $ 3.85 Trish 66,000 $ 5.20 $ 2.00 $ 1.12 Sarah 59,000 $ 33.00 $ 10.04 $ 5.95 Mike 40,000 $ 17.00 $ 4.40 $ 4.55 Sewing kit 349,000 $ 10.40 $ 5.60 $ 0.77
Explanation / Answer
Solution 1:
No. of hours required per unit can be computed by dividing the direct labor cost with Labor rate per hour. A table for all the products will look like below:
Item
Direct Labor per unit (1)
Labor rate per hour (2)
No. of hours per unit (1) / (2)
Debbie
3.85
7
0.55
Trish
1.12
7
0.16
Sarah
5.95
7
0.85
Mike
4.55
7
0.65
Sewing Kit
0.77
7
0.11
Direct Labor rate of $7 is unchanged throughout the year
Solution 2:
It should be noted that question states variable overhead costs are $3 per direct labor-hour. For a unit, since we know the labor hours required, we can multiply the number of hours with 3 and can get to know the variable overhead costs per product.
Item
No. of hours per unit
Variable Overhead per labor hour
Variable Overhead
Debbie
0.55
3
1.65
Trish
0.16
3
0.48
Sarah
0.85
3
2.55
Mike
0.65
3
1.95
Sewing Kit
0.11
3
0.33
Solution 3:
Now we have all the information. To compute Contribution, we need to apply the Formulae as
Selling Price- Direct Material- Direct Labor- Variable Overhead
Since we have already computed Direct Labor hour, we can divide the contribution by labor hour to reach at the required numbers:
Item
Selling Price
(1)
Direct Material
(2)
Direct Labor
(3)
Variable Overhead
(4)
Contribution
(1-2-3-4)
No. of
Direct Labor Hour
Contribution
per labor hour
Debbie
25.5
5.1
3.85
1.65
14.9
0.55
27.09
Trish
5.2
2
1.12
0.48
1.6
0.16
10.00
Sarah
33
10.04
5.95
2.55
14.46
0.85
17.01
Mike
17
4.4
4.55
1.95
6.1
0.65
9.38
Sewing Kit
10.4
5.6
0.77
0.33
3.7
0.11
33.64
Solution 4:
Since the company has limited number of labor hours, to reach at the best contribution margin, it will have to prioritize the product having best contribution per labor hours. We can see Sewing Kit is having the best contribution per labor hour for instance.
Let’s make a table to show the number of possible units.
Item
Units In demand
Ranking as per contribution per hour
No. of
Direct Labor Hour per unit
Hours required for maximum demand
Debbie
74000
2
0.55
40700
Trish
66000
4
0.16
10560
Sarah
59000
3
0.85
50150
Mike
40000
5
0.65
Sewing Kit
349000
1
0.11
38390
Total
139800
No. of hours available
152800
No. of excess hours
13000
No .of hours required for one unit of Mike
0.65
No .of possible unit of Mike
20000
Let’s compute the contribution for the above units:
Item
Units to be produced
Contribution per unit
Contribution
Debbie
74000
14.9
1,102,600
Trish
66000
1.6
105,600
Sarah
59000
14.46
853,140
Mike
20000
6.1
122,000
Sewing Kit
349000
3.7
1,291,300
Total
3,474,640
Solution 5:
Since the company will be fulfilling the demands in full for all the products except Mike. As per the market demand, company can make extra 20,000 quantity of Mike. Since Mike gives an additional contribution of $6.1, company may pay an extra of $6.1 in addition to the current labor rate of 4.55 per unit. In total, if Company pay $10.65 ($6.1 + $4.55) for a unit of Mike, it will not make any profit but this is the highest rate. Since Mike takes 0.65 hours for one unit production, Company may pay $16.38 per hour ($10.65/ 0.65)
Item
Direct Labor per unit (1)
Labor rate per hour (2)
No. of hours per unit (1) / (2)
Debbie
3.85
7
0.55
Trish
1.12
7
0.16
Sarah
5.95
7
0.85
Mike
4.55
7
0.65
Sewing Kit
0.77
7
0.11