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	51,000	$	15.50	$	4.40	$	2.70
Trish	43,000	$	6.00	$	1.20	$	1.20
Sarah	36,000	$	25.00	$	6.59	$	4.50
Mike	40,000	$	11.00	$	2.10	$	3.30
Sewing kit	326,000	$	8.10	$	3.30	$	0.90

The following additional information is available:  

a.The company’s plant has a capacity of 118,450 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.

b.The direct labor rate of $6 per hour is expected to remain unchanged during the coming year.

c.Fixed manufacturing costs total $530,000 per year. Variable overhead costs are $3 per direct labor-hour.

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

e.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 118,450 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

1) Calculation of direct labor hours per unit for each product

Particulars	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct Labor per unit (A)	$2.70	$1.20	$4.50	$3.30	$0.90
Direct Labor Rate per hour (B)	$6.00	$6.00	$6.00	$6.00	$6.00
Direct Labor hours per unit (A/B)	0.45	0.20	0.75	0.55	0.15

2) Calculation of Variable Overhead Cost

Particulars	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct Labor hours per unit (A)	0.45	0.20	0.75	0.55	0.15
Variable Overhead Cost per hour (B)	$3.00	$3.00	$3.00	$3.00	$3.00
Total Variable Overhead Cost (A*B)	$1.35	$0.60	$2.25	$1.65	$0.45

3) Calculation of contribution margin per labor hour (Amounts in $)

Particulars	Debbie	Trish	Sarah	Mike	Sewing Kit
a) Selling Price per unit	15.50	6.00	25.00	11.00	8.10
b) Direct Materials per unit	4.40	1.20	6.59	2.10	3.30
c) Direct Labor per unit	2.70	1.20	4.50	3.30	0.90
d) Variable Overhead cost per unit	1.35	0.60	2.25	1.65	0.45
e) Contribution Margin per unit (a-b-c-d)	7.05	3.00	11.66	3.95	3.45
f) Direct Labor hours per unit	0.45	0.20	0.75	0.55	0.15
g) Contribution Margin per hour (e/f)	15.67	15.00	15.55	7.18	23.00
h) Ranking on the basis of contribution margin per hour	2	4	3	5	1

4) Based on the ranking given in requirement 3, the product with highest contribution margin per hour (i.e. with ranking 1) should be produced first and so on.

Available Direct Labor Hours = 118,450 labor hrs

Calculation of Maximum Contribution Margin (Amounts in $)

Particulars	Debbie	Trish	Sarah	Mike	Sewing Kit	Total
a) Direct Labor hours per unit	0.45	0.20	0.75	0.55	0.15
b) Demand Next year (units)	51,000	43,000	36,000	40,000	326,000
c) Total Required Labor Hours (a*b)	22,950	8,600	27,000	22,000	48,900	129,450

Shortage of Labor Hours = Total Required Labor Hours - Total Available Labor Hours

= 129,450 - 118,450 = 11,000 hours

As the last ranking (i.e. ranking 5) is given to the product Mike, this shortage of labor hours of 11,000 will be set off from the total hours required for Mike.

Hence the labor hours available to Mike = 22,000 - 11,000 = 11,000 hrs.

The possible units of Product Mike = 11,000 hrs/0.55 hr per unit = 20,000 units

Therefore, the demand for all other products will be fulfilled completely but the production of product Mike will be only 20,000 units. The contribution margin from the optimal use of labor hours is shown as follows:-

Particulars	Debbie	Trish	Sarah	Mike	Sewing Kit	Total
a) Units to be sold	51,000	43,000	36,000	20,000	326,000
b) Contribution Margin per unit	7.05	3.00	11.66	3.95	3.45
c) Total Contribution Margin (a*b)	359,550	129,000	419,760	79,000	1,124,700	2,112,010