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:

Product	Demand Next 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

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)?

Answer 1

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)