Chapter 15, Problem 44P

a.

To determine

Find the contribution margin according to the information given in the question.

Answer to Problem 44P

The total contribution margin of home when selling 87,500 units is $2,345,625.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.

Compute the contribution margin of the home if it sells 87,500 units outside:

Particulars	Details	Amount
Outside sales revenue $\left(87,500\times \text{\$}72.00\right)$	$6,300,000
Less: material and out-of-pocket cost for outside sales $\left(87,500\times \text{\$}7.20\right)$	$630,000	$5,670,000
Leftover DLH	$2,278,125(1)
Less: material and out-of-pocket cost for units transferred $\left(28,125\times \$7.20\right)$	$202,500	$2,075,625
		$7,745,625
Labor costs $\left(375,000\times \$14.40\right)$		$5,400,000
Total contribution margin $\left(\text{Total revenue}-\text{Total cost}\right)$		$2,345,625

Table: (1)

Thus, the total contribution margin of home when selling 87,500 units is $2,345,625.

Working note 1:

Compute the leftover DLH:

$\begin{array}{c}\text{Leftover DLH =}\frac{\left(\text{Direct labor hours}-\left(\begin{array}{l}\text{Number of units absorbed}\\ \times \text{Requirment of labor hours to produce}\end{array}\right)\right)}{\text{Total labor hours required to produce}}\\ \text{= }\frac{\left(375,000-\left(87,500\times 3\right)\right)}{4}\\ =\frac{\left(375,000-262,500\right)}{4}\\ =28,125\end{array}$

b.

To determine

Find the contribution margin according to the information given in the question.

Answer to Problem 44P

The contribution margin of home at transferring 75,000 units to mobile is $1,755,000.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.

Compute the contribution margin to home if it sells 75,000 units to mobile:

Particulars	Details	Amount
Units transferred $\left(75,000\times \text{\$}81\right)$	$6,075,000
Less: material and out-of-pocket costs for units transferred $\left(75,000\times \$7.20\right)$	$540,000	$5,535,000
Leftover DLH	$1,800,000(2)
Less: material and out-of-pocket costs for outside sales $\left(25,000\times \text{\$}7.20\right)$	$180,000	$1,620,000
		$7,155,000
Labor costs $\left(375,000\times \text{\$}14.40\right)$		$5,400,000
Contribution margin $\left(\text{Total revenue}-\text{Total cost}\right)$		$1,755,000

Table: (2)

Thus, the contribution margin of home at transferring 87,500 units to mobile is $1,755,000.

Working note 1:

Compute the leftover DLH:

$\begin{array}{c}\text{Leftover DLH =}\frac{\left(\text{Direct labor hours}-\left(\begin{array}{l}\text{Number of units absorbed}\\ \times \text{ Total labor hours to produce}\end{array}\right)\right)}{\text{Required labor hours required to produce}}\\ \text{= }\frac{\left(375,000-\left(75,000\times 4\right)\right)}{3}\\ =\frac{\left(375,000-300,000\right)}{3}\\ =25,000\end{array}$

c.

To determine

Compute the costs to be considered according to the information given in the question.

Answer to Problem 44P

The contribution margin of the company at the capacity of producing 87,500 units is $8,730,000.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.

Compute the costs to be considered in determining the optimal company policy:

Particulars	Home	Mobile	Company
Sales by the home to outside $\left(87,500\times \$72\right)$	$6,300,000		$6,300,000
Sales by the home to mobile $\left(28,125\times \$81\right)$	$2,278,125		$2,278,125
Sales by mobile to outside $\left(75,000\times \$204\right)$		$15,300,000	$15,300,000
Total sales	$8,578,125	$15,300,000	$23,878,125
Cost of materials, etc. at home $\left(115,625\times \$7.20\right)$	$832,500		$832,500
Cost of labor in the home	$5,400,000		$5,400,000
Cost of units transferred to mobile		$2,278,125	$2,278,125
Cost of units purchased from outside by mobile $\left(\left(\text{75,500-28,125}\right)\text{×\$84}\right)$		$3,937,500	$3,937,500
Conversion cost in mobile $\left(\$36\times 75,000\right)$		$2,700,000	$2,700,000
Contribution	$2,345,625	$9,084,375	$8,730,000

Table: (3)

Thus, the contribution margin of the company at the capacity of producing 87,500 units is $8,730,000.

d.

To determine

Compute the annual contributions and cost according to the information given in the question.

Answer to Problem 44P

The difference in company contribution margin is $450,000.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin

As computed in the previous part the contribution margin for the situation if the home sold 75,000 units to mobile is $1,755,000

Compute the mobile contribution if 75,000 units were transferred to mobile:

$\begin{array}{c}\text{Contribution margin = }\left(\text{Total sales}-\left(\begin{array}{l}\text{Cost of units transferred to mobile }\\ \text{+ Conversion cost}\end{array}\right)\right)\\ \text{=\$15,300,000}-\left(\$6,075,000+\$2,700,000\right)\\ =\$15,300,000-\$8,775,000\\ =\$6,525,000\end{array}$

Thus, the company contribution at selling 75,000 would be:

$\begin{array}{c}\text{Company contribution=Contribution margin of home and mobile}\\ \text{= \$1,755,000 +\$6,525,000}\\ \text{=\$8,280,000}\end{array}$

The contribution margin compute at 87,500 units is $8,730,000

Thus,

Compute the difference in company contribution margin:

$\begin{array}{c}\text{Difference in contribution margin=}\left(\begin{array}{l}\text{Contribution margin of company at 87,500 units}\\ -\text{Contribution margin of company at 75,000 units}\end{array}\right)\\ \text{=\$8,730,000}-\$8,280,000\\ =\$450,000\end{array}$

Thus, the difference in company contribution margin is $450,000.