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	65,000	$	28.00	$	4.20	$	4.05
Trish	57,000	$	6.00	$	1.10	$	1.26
Sarah	50,000	$	35.00	$	8.69	$	6.75
Mike	40,000	$	14.00	$	3.50	$	4.95
Sewing kit	340,000	$	9.50	$	4.70	$	0.81

The following additional information is available:  

The company’s plant has a capacity of 116,330 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 $9 per hour is expected to remain unchanged during the coming year.

Fixed manufacturing costs total $535,000 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:

1A) How many direct labor hours are used to manufacture one unit of each of the company’s five products?

1B) How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?

1C) What is the contribution margin per direct labor-hour for each of the company’s five products?

1D) 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?

1E) Assuming that the company has made optimal use of its 116,330 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)?

Thank you, please show work so I can learn.

Answer 1

Solution

Walton Toy Company

1a. 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	Variable overhead per unit at $2 per DLH
Debbie	$4.05	$9	0.45	$0.90
Trish	$1.26	$9	0.14	$0.28
Sarah	$6.75	$9	0.75	$1.50
Mike	$4.95	$9	$0.55	$1.10
Sewing Kit	$0.81	$9	0.09	$0.18

Direct labor hour per unit is calculated as follows,

Total direct labor hour per unit/direct labor hour

Direct labor hour rate = $9 per hour

For instance, direct labor hour for the product Debbie = $6.40/$16 =0.4 hours

1B. determination of the amount of variable overhead cost incurred to manufacture one unit of each of the five products:

Product	direct labor hours per unit	Variable overhead per unit at $2 per DLH
Debbie	0.45	$0.90
Trish	0.14	$0.28
Sarah	0.75	$1.50
Mike	0.55	$1.10
Sewing Kit	0.09	$0.18

1. 1C. 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	$28.00	$4.20	$4.05	$0.90	$9.15	$18.85	0.45 hours	$41.88
Trish	$6.00	$1.10	$1.26	$0.28	$2.64	$3.36	0.14 hours	$24.00
Sarah	$35.00	$8.69	$6.75	$1.50	$16.94	$18.06	0.75 hours	$24.08
Mike	$14.00	$3.50	$4.95	$1.10	$9.55	$4.45	0.55 hours	$8.09
Sewing Kit	$9.50	$4.70	$0.81	$0.18	$5.69	$3.81	0.09 hours	$42.33

1. Determination of contribution per direct labor hour is as follows,

Contribution per direct labor hour = contribution per unit/direct labor hours per unit

For instance, contribution per direct labor hour for the product Sarah is arrived at as follows,

Contribution per unit = $18.06; direct labor hours per unit = 0.75 hours

Contribution per direct labor hour = $18.06/0.75 hours =$24.08

Accordingly, the contribution per direct labor hour for each product and respective ranking is as follows,

Product	Contribution per direct labor hour	Ranking
Debbie	$41.88	II
Trish	$24.00	IV
Sarah	$24.08	III
Mike	$8.09	V
Sewing Kit	$42.33	I

1D. 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 = 116,330 hours

Sewing Kit –

Demand in units for next year340,000

Direct labor hour per unit0.09 hours

Direct labor hours needed to produce 340,000 units = 340,000 x 0.09 hours = 30,600 hours

Remaining direct labor hours at plant = 116,330 – 30,600 = 85,730

The next product with highest ranking is Debbie.

Debbie –

Demand in units for next year 65,000

Direct labor hours per unit0.45

Direct labor hours needed to produce 65,000 units = 65,000 x 0.45 = 29,250 hours

Remaining direct labor hours at plant = 85,730 -29,250 =56,480 hours

The next product in terms of highest ranking is Sarah.

Sarah –

Demand in units for next year 50,000

Direct labor hours per unit0.75 hours

Direct labor hours needed to produce 50,000 units = 50,000 x 0.75 = 37,500 hours

Remaining direct labor hours at plant = 56,480 - 37,500= 18,980 hours

The next product in terms of highest ranking is Trish.

Trish –

Demand in units for next year57,000

Direct labor hours per unit0.14 hours

Direct labor hours needed to produce 57,000 units = 57,000 x 0.14 = 7,980 hours

Remaining direct labor hours at plant = 18,980 – 7,980 =11,000 hours

The product with the least ranking is Mike.

Mike –

Demand in units for next year 40,000

Direct labor hours per unit0.55

Direct labor hours needed to produce 40,000 units = 40,000 x 0.55 = 22,000 hours

However, the available direct labor hours are 11,000

Hence, the number of units of Mike that can be produced with the available direct labor hours = 11,000 hrs/0.55 hrs

= 20,000 units

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	65,000	$18.85	$1,225,250
Trish	57,000	$3.36	$191,520
Sarah	50,000	$18.06	$903,000
Mike	20,000	$4.45	$89,000
Sewing Kit	340,000	$3.81	$1,295,400

Total contribution $3,704,170

1E. 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 $9
• Contribution margin per direct labor hour of Mike          $8.09

Total price for additional direct labor hour capacity$9 + $8.09 = $17.09