Question

The Walton Toy Company manufactures a line of dolls and a doll dress sewing kit. Demand for the dolls 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	$13.50	$4.30	$3.20
Trish	42,000	$ 5.50	$1.10	$2.00
Sarah	35,000	$21.00	$6.44	$5.60
Mike	40,000	$10.00	$2.00	$4.00
Sewing kit	325,000	$ 8.00	$3.20	$1.60

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 $8 per hour is expected to remain unchanged during the coming year.

Fixed 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. Determine the contribution margin per direct labor-hour expended on each product. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Product Contribution Margin per DLH Debbie Trish Sarah Mike Sewing kit

2. Calculate the the total direct labor-hours that will be required to produce the units estimated to be sold during the coming year. (Do not round intermediate calculations.

	Product Total Hours Debbie Trish Sarah Mike Sewing Kit Total hours required 0

3. Based on response to Requirement 1 & 2, how much of 130,000 direct labor hours of capacity will be allocated to Walton Toy Company’s various products?

	Product Hours Debbie Trish Sarah Mike Sewing kit

4. What is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?

	Total contribution margin

5. What is the highest price, in terms of a rate per hour, that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?

	Highest price per hour

Answer 1

1. Determination of contribution margin per direct labor hour expended on each product:

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 = $7.56; direct labor hours per unit = 0.70 hours

Contribution per direct labor hour = $7.56/0.70 hours =$10.80

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

Product	Contribution per direct labor hour	Ranking
Debbie	$13.00	II
Trish	$7.60	IV
Sarah	$10.80	III
Mike	$6.00	V
Sewing Kit	$14.00	I

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	$13.50	$4.30	$3.20	$0.80	$8.30	$5.20	0.40 hours	$13.00
Trish	$5.50	$1.10	$2	$0.50	$3.60	$1.90	0.25 hours	$7.60
Sarah	$21	$6.44	$5.60	$1.40	$13.44	$7.56	0.70 hours	$10.80
Mike	$10	$2	$4	$1.00	$7.00	$3.00	0.50 hours	$6.00
Sewing Kit	$8	$3.20	$1.60	$0.40	$5.20	$2.80	0.20 hours	$14.00

1. Calculation of the total direct labor hours that will be required to produce the units estimated to be sold during the current year:

Product	Direct labor hours	estimated production	Total direct labor hours
Debbie	$0.40	50,000	20,000
Trish	$0.25	42,000	10,500
Sarah	0.7	35,000	24,500
Mike	0.5	40,000	20,000
Sewing Kit	0.2	325,000	65,000
Total direct labor hours			140,000

1. Determination of optimal product mix with direct labor hours as constraint:

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 = $7.56; direct labor hours per unit = 0.70 hours

Contribution per direct labor hour = $7.56/0.70 hours =$10.80

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

Product	Contribution per direct labor hour	Ranking
Debbie	$13.00	II
Trish	$7.60	IV
Sarah	$10.80	III
Mike	$6.00	V
Sewing Kit	$14.00	I

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 0.2 hours = 65,000 hours

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

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

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 = 20,500 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 = 20,500 – 10,500 = 10,000 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 0.50 = 20,000 hours

However, the available direct labor hours are 10,000

Hence, the number of units of Mike that can be produced with the available direct labor hours = 10,000 hrs/0.50 hrs

= 20,000 units

1. Determination of highest total contribution margin for the optimal mix:

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	20,000	$3.00	$60,000
Sewing Kit	325,000	$2.80	$910,000

Total contribution margin $1,574,400

Less: Fixed costs$520,000

Net operating income$1,054,400

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 $8
• Contribution margin per direct labor hour of Mike          $6

Total price for additional direct labor hour capacity$8 + $6 = $14 per hour