Chapter 11, Problem 25P

Requirement - 1:

To determine

Direct labor hour: Direct labor hour refers to the labor hour incurred by an employee to manufacture a unit of product. It refers to the direct labor cost because this cost can be easily assigned to a unit of production.

To identify: How many direct labor hours are used to manufacture one unit of the each of the company’s five products?

Answer to Problem 25P

Solution:

For Debbie;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$6}\text{.40}}{\text{\$16}}\\ =0.40\text{ per unit }\end{array}$

For Trish;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$4}}{\text{\$16}}\\ =0.25\text{ per unit }\end{array}$

For Sarah;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$11}\text{.20}}{\text{\$16}}\\ =0.70\text{ per unit }\end{array}$

For Mike;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$8}}{\text{\$16}}\\ =0.50\text{ per unit }\end{array}$

For Sewing kit;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$3}\text{.20}}{\text{\$16}}\\ =0.20\text{ per unit }\end{array}$

Thus total direct labor hours used to manufacture one unit of each of the company’s five products will be;

(0.40 + 0.25 + 0.70 + 0.50 + 0.20) = 2.05 hours

Explanation of Solution

Given:

Following information are given in the question:

Direct labor rate = $16 per hour

Debbie direct labor cost per unit = $6.40

Trish direct labor cost per unit = $4

Sarah direct labor cost per unit = $11.20

Mike direct labor cost per unit = $8

Sewing kit direct labor cost per unit = $3.20

Formula used:

Following formula will be used;

  $\text{Direct labor hour per unit = }\frac{\text{Direct labor cost per unit}}{\text{Direct labor rate per hour}}$

Calculation:

For Debbie;

Direct labor rate = $16 per hour

Direct labor cost per unit = $6.40

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$6}\text{.40}}{\text{\$16}}\\ =0.40\text{ per unit }\end{array}$

For Trish;

Direct labor rate = $16 per hour

Direct labor cost per unit = $4

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$4}}{\text{\$16}}\\ =0.25\text{ per unit }\end{array}$

For Sarah;

Direct labor rate = $16 per hour

Direct labor cost per unit = $11.20

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$11}\text{.20}}{\text{\$16}}\\ =0.70\text{ per unit }\end{array}$

For Mike;

Direct labor rate = $16 per hour

Direct labor cost per unit = $8

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$8}}{\text{\$16}}\\ =0.50\text{ per unit }\end{array}$

For Sewing kit;

Direct labor rate = $16 per hour

Direct labor cost per unit = $3.20

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Direct labor hour per unit = }\frac{\text{\$3}\text{.20}}{\text{\$16}}\\ =0.20\text{ per unit }\end{array}$

Thus total direct labor hours used to manufacture one unit of each of the company’s five products will be;

(0.40 + 0.25 + 0.70 + 0.50 + 0.20) = 2.05 hours

Conclusion

Thus above calculated direct labor hours used to manufacture one unit of each product.

Requirement - 2:

To determine

Variable overhead cost: Variable overhead cost refers to that portion of overhead cost which change as per the level of production. In other words we can say that when production increases then variable overhead cost will increase or vice versa.

To identify: How muchvariable overhead cost is incurred to manufacture one unit of the each of the company’s five products?

Answer to Problem 25P

Solution:

For Debbie;

Variable cost incurred (0.40 * $2) = $0.80

For Trish;

Variable cost incurred (0.25 * $2) = $0.50

For Sarah;

Variable cost incurred (0.70 * $2) = $1.40

For Mike;

Variable cost incurred (0.50 * $2) = $1

For Sewing kit;

Variable cost incurred (0.20 * $2) = $0.40

Thus total variable cost incurred to manufacture one unit of each of the company’s five products will be;

($0.80 + $0.50 + $1.40 + $1 + $0.40) = $4.10

Explanation of Solution

Given:

Following information are given in the question:

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Debbie = 0.40

Direct labor hour used for one unit of Trish = 0.25

Direct labor hour used for one unit of Sarah = 0.70

Direct labor hour used for one unit of Mike = 0.50

Direct labor hour used for one unit of Sewing kit = 0.20

Formula used:

Following formula will be used;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Calculation:

For Debbie;

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Debbie = 0.40

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Variable cost incurred (0.40 * $2) = $0.80

For Trish;

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Trish = 0.25

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Variable cost incurred (0.25 * $2) = $0.50

For Sarah;

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Sarah = 0.70

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Variable cost incurred (0.70 * $2) = $1.40

For Mike;

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Mike = 0.50

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Variable cost incurred (0.50 * $2) = $1

For Sewing kit;

Variable overhead rate per direct labor hour = $2

Direct labor hour used for one unit of Sewing kit = 0.20

Now let’s put the values in given formula;

  $\begin{array}{l}\text{Variable cost incurred to manufacture one unit = }\\ \text{Direct labor hour used for one unit \&*\#x00A0;Rate of variable overhead per hour}\end{array}$

Variable cost incurred (0.20 * $2) = $0.40

Thus total variable cost incurred to manufacture one unit of each of the company’s five products will be;

($0.80 + $0.50 + $1.40 + $1 + $0.40) = $4.10

Conclusion

Thus above calculated is the variable cost incurred to manufacture one unit of each of the company’s five products.

Requirement - 3:

To determine

Contribution margin: Contribution margin is the difference between selling price and variable cost. In other words we can say that excess of selling price over variable cost is known as contribution margin.

To identify: Contribution margin per direct labor for each of the company’s five products.

Answer to Problem 25P

Solution:

Contribution margin per direct labor for each of the company’s five products will be calculated with the help of following table;

	Debbie	Trish	Sarah	Mike	Sewing Kit
Selling price	$16.70	$7.50	$26.60	$14.00	$9.60
Less: Variable costs;
Direct material	$4.30	$1.10	$6.44	$2.00	$3.20
Direct labor	$6.40	$4.00	$11.20	$8.00	$3.20
Total variable costs	($10.70)	($5.10)	($17.64)	($10.00)	($6.40)
Contribution margin per unit	$6.00	$2.40	$8.96	$4.00	$3.20
Direct labor hours used per unit	0.40	0.25	0.70	0.50	0.20
Contribution margin per direct labor hour	$15	$9.60	$12.80	$8	$16

Explanation of Solution

Given:

Following information are given in the question:

Selling price for one unit of Debbie = $16.70

Selling price for one unit of Trish = $7.50

Selling price for one unit of Sarah = $26.60

Selling price for one unit of Mike = $14.00

Selling price for one unit of Sewing kit = $9.60

Total variable costs for one unit of Debbie = $10.70

Total variable costs for one unit of Trish = $5.10

Total variable costs for one unit of Sarah = $17.64

Total variable costs for one unit of Mike = $10.00

Total variable costs for one unit of Sewing kit = $6.40

Direct labor hour used for one unit of Debbie = 0.40

Direct labor hour used for one unit of Trish = 0.25

Direct labor hour used for one unit of Sarah = 0.70

Direct labor hour used for one unit of Mike = 0.50

Direct labor hour used for one unit of Sewing kit = 0.20

Formula used:

Following formula will be used;

  $\text{Contribution margin per unit = Selling price per unit - Variable cost per unit }$

  $\text{Contribution margin per direct labor hour = }\frac{\text{Contribution margin per unit }}{\text{Direct labor hour used in one unit}}$

Calculation:

Contribution margin per direct labor for each of the company’s five products will be calculated with the help of following table;

	Debbie	Trish	Sarah	Mike	Sewing Kit
Selling price	$16.70	$7.50	$26.60	$14.00	$9.60
Less: Variable costs;
Direct material	$4.30	$1.10	$6.44	$2.00	$3.20
Direct labor	$6.40	$4.00	$11.20	$8.00	$3.20
Total variable costs	($10.70)	($5.10)	($17.64)	($10.00)	($6.40)
Contribution margin per unit	$6.00	$2.40	$8.96	$4.00	$3.20
Direct labor hours used per unit	0.40	0.25	0.70	0.50	0.20
Contribution margin per direct labor hour	$15	$9.60	$12.80	$8	$16

Contribution margin per unit is calculated as follow;

For Debbie;

($16.70 − $10.70) = $6.00

For Trish;

($7.50 − $5.10) = $2.40

For Sarah;

($26.60 − $17.64) = $8.96

For Mike;

($14.00 − $10.00) = $4.00

For Sewing Kit;

($9.60 − $6.40) = $3.20

Contribution per direct labor hour is calculated as follow;

For Debbie;

  $\begin{array}{l}\text{Contribution margin per direct labor hour = }\frac{\text{\$6}\text{.00 }}{\text{0}\text{.40}}\\ =\$15\end{array}$

For Trish;

  $\begin{array}{l}\text{Contribution margin per direct labor hour = }\frac{\text{\$2}\text{.40 }}{\text{0}\text{.25}}\\ =\$9.60\end{array}$

For Sarah;

  $\begin{array}{l}\text{Contribution margin per direct labor hour = }\frac{\text{\$8}\text{.96 }}{\text{0}\text{.70}}\\ =\$12.80\end{array}$

For Mike;

  $\begin{array}{l}\text{Contribution margin per direct labor hour = }\frac{\text{\$4}\text{.00}}{\text{0}\text{.50}}\\ =\$8.00\end{array}$

For Sewing Kit;

  $\begin{array}{l}\text{Contribution margin per direct labor hour = }\frac{\text{\$3}\text{.20}}{\text{0}\text{.20}}\\ =\$16.00\end{array}$

Conclusion

Thus above calculated is the contribution margin per direct labor hour of each of the company’s five products.

Requirement - 4:

To determine

Contribution margin: Contribution margin is the difference between selling price and variable cost. In other words we can say that excess of selling price over variable cost is known as contribution margin.

To identify: Highestcontribution margin that the company can earn if it makes optimal use of its’ constrained resources.

Answer to Problem 25P

Solution:

For getting maximum contribution margin company will use direct labor hours to the products those have higher contribution margin. So let’s calculate highest contribution margin;

	Debbie	Trish	Sarah	Mike	Sewing Kit
Total direct labor hours used	20000	10500	24500	20000	65000
Contribution margin per direct labor hour	$15	$9.60	$12.80	$8	$16
Total contribution margin	$300000	$100800	$313600	$80000	$1040000

Thus total highest contrubution margin will be;

($300000 + $100800 + $313600 + $80000 + $1040000) = $1834400

Explanation of Solution

Given:

Following information are given in the question:

Total direct labor hours available = 130000

Contribution margin per direct labor hour of Debbie = $15

Contribution margin per direct labor hour of Trish = $9.60

Contribution margin per direct labor hour of Sarah = $12.80

Contribution margin per direct labor hour of Mike = $8.00

Contribution margin per direct labor hour of Sewing kit = $16.00

Total unitsof Debbie = 50000

Totalunits of Trish = 42000

Total units of Sarah = 35000

Total units of Mike = 40000

Total units of Sewing kit = 325000

Direct labor hour used for one unit of Debbie = 0.40

Direct labor hour used for one unit of Trish = 0.25

Direct labor hour used for one unit of Sarah = 0.70

Direct labor hour used for one unit of Mike = 0.50

Direct labor hour used for one unit of Sewing kit = 0.20

Formula used:

Following formula will be used;

  $\text{Total direct labor hours used = Direct labor hour used for one unit \&*\#x00A0;Number of units}$

Calculation:

First of all let’s calculate total direct labor hours used for each product

	Debbie	Trish	Sarah	Mike	Sewing Kit
Direct labor hour used for one unit	0.40	0.25	0.70	0.50	0.20
Number of units	50000	42000	35000	40000	325000
Total direct labor hours	20000	10500	24500	20000	65000

As per above table total direct labor hours are (20000 + 10500 + 24500 + 20000 + 65000) = 140000

But total direct labor hours that can be used are 130000, so company will use direct labor hours to the products those have higher contribution margin.

For getting maximum contribution margin company will use direct labor hours to the products those have higher contribution margin. So let’s calculate highest contribution margin;

	Debbie	Trish	Sarah	Mike	Sewing Kit
Total direct labor hours used	20000	10500	24500	20000	65000
Contribution margin per direct labor hour	$15	$9.60	$12.80	$8	$16
Total contribution margin	$300000	$100800	$313600	$80000	$1040000

Thus total highest contrubution margin will be;

($300000 + $100800 + $313600 + $80000 + $1040000) = $1834400

Conclusion

Thus above calculated is the Highest contribution margin that the company can earn if it makes optimal use of its’ constrained resources.