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 50,000 $ 16.70 $ 4.30 $ 6.40 Trish 42,000 $ 7.50 $ 1.10 $ 4.00 Sarah 35,000 $ 26.60 $ 6.44 $ 11.20 Mike 40,000 $ 14.00 $ 2.00 $ 8.00 Sewing kit 325,000 $ 9.60 $ 3.20 $ 3.20 The following additional information is available: The company’s plant has a capacity of 130,000 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 $16 per hour is expected to remain unchanged during the coming year. Fixed manufacturing costs total $520,000 per year. Variable overhead costs are $2 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 130,000 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

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	$6.40	$16	0.40
Trish	$4.00	$16	0.25
Sarah	$11.20	$16	0.70
Mike	$8.00	$16	0.50
Sewing Kit	$3.20	$16	0.20

Direct labor hour per unit is calculated as follows,

Total direct labor hour per unit/direct labor hour

Direct labor hour rate = $16 per hour

For instance, direct labor hour for the product Debbie = $6.40/$16 =0.40 hours

Product	direct labor hours per unit	Variable overhead per hour	Variable overhead per unit
Debbie	0.4	$2	$0.80
Trish	0.25	$2	$0.50
Sarah	0.7	$2	$1.40
Mike	0.5	$2	$1.00
Sewing Kit	0.2	$2	$0.40

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	$16.70	$4.30	$6.40	$0.80	$11.50	$5.20	0.40 hours	$13
Trish	$7.50	$1.10	$4.00	$0.50	$5.60	$1.90	0.25 hours	$7.60
Sarah	$26.60	$6.44	$11.20	$1.40	$19.04	$7.56	0.70 hours	$10.80
Mike	$14.00	$2.00	$8.00	$1.00	$11.00	$3.00	0.50 hours	$6.00
Sewing Kit	$9.60	$3.20	$3.20	$0.40	$6.80	$2.80	0.20 hours	$14.00

1. 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	$13	II
Trish	$7.60	IV
Sarah	$10.80	III
Mike	$6.00	V
Sewing Kit	$14.00	I

1. 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	50,000	0.40	20,000
Trisha	42,000	0.25	10,500
Sarah	35,000	0.70	24,500
Mike	40,000	0.50	20,000
Sewing Kit	325,000	0.20	65,000
Total			140,000

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 = 130,000 hours

Sewing Kit –

Demand in units for next year325,000

Direct labor hour per unit0.20 hours

Direct labor hours needed to produce 325,000 units = 325,000 x 0.20 hours = 65,000 hours

Remaining direct labor hours at plant = 130,000 – 65,000 = 65,000 hours

The next product with highest ranking is Debbie.

Debbie –

Demand in units for next year 50,000

Direct labor hours per unit0.40

Direct labor hours needed to produce 50,000 units = 50,000 x 0.40 = 20,000 hours

Remaining direct labor hours at plant = 65,000 – 20,000 = 45,000 hours

The next product in terms of highest ranking is Sarah.

Sarah –

Demand in units for next year 35,000

Direct labor hours per unit0.70 hours

Direct labor hours needed to produce 35,000 units = 35,000 x 0.70 = 24,500 hours

Remaining direct labor hours at plant = 45,000 – 24,500 = 15,500 hours

The next product in terms of highest ranking is Trish.

Trish –

Demand in units for next year42,000

Direct labor hours per unit0.25 hours

Direct labor hours needed to produce 42,000 units = 42,000 x 0.25 = 10,500 hours

Remaining direct labor hours at plant = 15,500 – 10,500 = 5,000 hours

The product with the least ranking is Mike.

Mike –

Demand in units for next year 40,000

Direct labor hours per unit0.50

Direct labor hours needed to produce 40,000 units = 40,000 x 0.5 = 20,000 hours

However, the available direct labor hours are 5,000

Hence, the number of units of Mike that can be produced with the available direct labor hours = 5,000 hrs/0.5 hrs

= 10,000 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	50,000	$5.20	$260,000
Trish	42,000	$1.90	$79,800
Sarah	35,000	$7.56	$264,600
Mike	10,000	$3.00	$30,000
Sewing Kit	325,000	$2.80	$910,000

Total contribution margin$1,544,400

1. 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 $16
• Contribution margin per direct labor hour of Mike          $6.00

Total price for additional direct labor hour capacity$16 + $6 = $22 per hour