Question

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	63,000	$	21.00	$	5.60	$	4.20
Trish	55,000	$	7.50	$	2.40	$	1.44
Sarah	48,000	$	36.50	$	8.39	$	7.80
Mike	48,000	$	16.00	$	3.30	$	5.40
Sewing kit	338,000	$	9.30	$	4.50	$	0.84

The following additional information is available:  

1. The company’s plant has a capacity of 94,310 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.

2. The direct labor rate of $12 per hour is expected to remain unchanged during the coming year.

3. Fixed manufacturing costs total $650,000 per year. Variable overhead costs are $4 per direct labor-hour.

4. All of the company’s nonmanufacturing costs are fixed.

5. 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 94,310 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

Walton Toy Company

1. determination of the number of direct labor hours needed to manufacture one unit of each of the five products:

Product	Direct labor	Direct labor cost per hour	direct labor hours per unit
Debbie	$4.20	$12	0.35
Trish	$1.44	$12	0.12
Sarah	$7.80	$12	0.65
Mike	$5.40	$12	0.45
Sewing Kit	$0.84	$12	0.07

Note:

Direct labor hour per unit is calculated as follows,

Total direct labor hour per unit/direct labor hour

Direct labor hour rate = $12 per hour

For instance, direct labor hour for the product Debbie = $4.20/$12 =0.35 hours

2   determination of variable overhead cost for one unit of each of the five products:

Product	direct labor hours per unit	Variable overhead per hour	Variable overhead per unit
Debbie	0.35	$4	$1.40
Trish	0.12	$4	$0.48
Sarah	0.65	$4	$2.60
Mike	0.45	$4	$1.80
Sewing Kit	0.07	$4	$0.28

Computation of variable overhead per unit –

Variable overhead per unit for each product = variable overhead rate per hour x direct labor hours per unit

For Debbie, variable overhead per unit = $4 x 0.35 hours = $1.40

1. Contribution margin per hour for each of the company’s five products:

1. Determination of contribution margin per unit and per direct labor hour for all the products:

Product	selling price per unit	Direct material cost per unit	Direct labor cost per unit	Variable overhead per unit	Total variable cost per unit	Contribution margin per unit	direct labor hours per unit	contribution per direct labor hour
Debbie	$21.00	$5.60	$4.20	$1.40	$11.20	$9.80	0.35 hours	$28
Trish	$7.50	$2.40	$1.44	$0.48	$4.32	$3.18	0.12 hours	$26.50
Sarah	$36.50	$8.39	$7.80	$2.60	$18.79	$17.71	0.65 hours	$27.25
Mike	$16.00	$3.30	$5.40	$1.80	$10.50	$5.50	0.45 hours	$12.22
Sewing Kit	$9.30	$4.50	$0.84	$0.28	$5.62	$3.68	0.07 hours	$52.57

2. Optimal mix and contribution margin assuming direct labor hours as constrained resource:

Step 1: ranking based on contribution margin per direct labor hour –

Product	Contribution per direct labor hour	Ranking
Debbie	$28	II
Trish	$26.50	IV
Sarah	$27.25	III
Mike	$12.22	V
Sewing Kit	$52.57	I

2. Step 2: Determination of the total direct labor hours needed to produce units estimated to be sold:

Product	Units	Hours per Unit	Total Hours
Debbie	63,000	0.35	22,050
Trisha	55,000	0.12	6,600
Sarah	48,000	0.65	31,200
Mike	48,000	0.45	21,600
Sewing Kit	338,000	0.07	23,660
Total			105,110

Step 3: determining the highest total contribution margin if the company makes the optimal use of its constrained (direct labor hours) resource:

Since the product Sewing Kit earns highest contribution per direct labor hour, available direct labor hours are to allotted first for the production of the expected units of Sewing Kit.

Total available direct labor hours at the plant = 94,310 hours

Sewing Kit –

Demand in units for next year      338,000

Direct labor hour per unit             0.07 hours

Direct labor hours needed to produce 338,000 units = 338,000 x 0.07 hours = 23,660 hours

Remaining direct labor hours at plant = 94,310 – 23,660 = 70,650 hours

The next product with highest ranking is Debbie.

Debbie –

Demand in units for next year      63,000

Direct labor hours per unit           0.35

Direct labor hours needed to produce 63,000 units = 63,000 x 0.35 = 22,050 hours

Remaining direct labor hours at plant = 70,650 – 22,050 = 48,600 hours

The next product in terms of highest ranking is Sarah.

Sarah –

Demand in units for next year      48,000

Direct labor hours per unit           0.65 hours

Direct labor hours needed to produce 48,000 units = 48,000 x 0.65 =31,200 hours

Remaining direct labor hours at plant = 48,600 – 31,200 = 17,400 hours

The next product in terms of highest ranking is Trish.

Trish –

Demand in units for next year      55,000

Direct labor hours per unit           0.12 hours

Direct labor hours needed to produce 55,000 units = 55,000 x 0.12 = 6,600 hours

Remaining direct labor hours at plant = 17,400 – 6,600 = 10,800 hours

The product with the least ranking is Mike.

Mike –

Demand in units for next year      48,000

Direct labor hours per unit           0.45

Direct labor hours needed to produce 48,000 units = 48,000 x 0.45 = 21,600 hours

However, the available direct labor hours are 10,800

Hence, the number of units of Mike that can be produced with the available direct labor hours = 10,800 hrs/0.45 hrs

= 24,000 units

Step 4:

Computation of the highest total contribution margin that the company can earn by making the optimal use of constrained resource:

Product	Units	Contribution margin per unit	Contribution margin
Debbie	63,000	$9.80	$617,400
Trish	55,000	$3.18	$174,900
Sarah	48,000	$17.71	$850,080
Mike	24,000	$5.50	$132,000
Sewing Kit	338,000	$3.68	$1,243,840

Total contribution margin $3,018,220

3. Determination of the highest direct labor rate per hour that the company would be willing to pay for additional capacity:

Since the additional capacity would be used to produce the product Mike, the highest price the company would be willing to pay is as arrived at as follows,

• Direct labor rate per hour $12
• Contribution margin per direct labor hour of Mike         $12.22

Total price for additional direct labor hour capacity        $12 + $12.22 = $24.22 per hour