Chapter 2, Problem 31E

a.

To determine

Identify variable cost per unit.

Answer to Problem 31E

4. $18

Explanation of Solution

Variable cost per unit: The variable cost per unit refers to the unit variable cost of product including the variable manufacturing costs.

Calculate variable cost per unit.

$\begin{array}{c}\text{Variable cost per unit}\text{=}\left(\begin{array}{l}\text{Materials per unit + labor per unit}\\ \text{ + plant supervision}\text{per unit+ selling}\\ \text{ and administrative}\text{per unit}\end{array}\right)\\ \text{=}\text{\$8}\text{+\$4+}\text{\$1+\$5}\\ \text{=}\text{\$18}\text{per unit}\end{array}$

Therefore, variable cost per unit amount is $18. The other options like 1, 2, and 3 are incorrect answers.

b.

To determine

Identify variable production cost per unit.

Answer to Problem 31E

2. $13

Explanation of Solution

Production cost per unit: The production cost per unit refers to the unit cost of production including direct materials, direct labor and manufacturing overheads.

Calculate variable production cost per unit.

$\begin{array}{c}\text{Variable production cost per unit =}\left(\begin{array}{l}\text{Materials per unit + labor per }\\ \text{unit+ plant supervision}\text{per unit}\end{array}\right)\\ =\$8+\$4+\$1\\ =\$13\text{per unit}\end{array}$

Therefore, variable production cost per unit amount is $13. The other options like 1, 3 and 4 are incorrect answers.

c.

To determine

Identify full cost per unit.

Answer to Problem 31E

4. $23

Explanation of Solution

Calculate full cost per unit.

$\begin{array}{c}\text{Full cost per}\text{unit}\text{=}\left(\begin{array}{l}\text{Materials per unit + labor per unit+ plant supervision}\\ \text{per unit+ variable sellingand administrative}\text{per unit}\\ \text{+}\text{Fixed selling andadministrative per unit + Fixed }\\ \text{production cost per unit }\end{array}\right)\\ =\$8+\$4+\$1+\$5+\left(\frac{\$675,000}{225,000\text{units}}\right)+\left(\frac{\$450,000}{225,000\text{units}}\right)\\ =\$8+\$4+\$1+\$5+\$3+\$2\\ =\$23\text{per unit}\end{array}$

Therefore, full cost per unit amount is $23. The other options like 1, 2 and 3 are incorrect answers.

d.

To determine

Identity full absorption cost per unit.

Answer to Problem 31E

3. $16

Explanation of Solution

Full cost per unit: The full cost per unit refers to the total cost of the product including the fixed and variable cost per unit.

Calculate full absorption cost per unit.

$\begin{array}{c}\text{Absorption cost per}\text{unit}\text{=}\left(\begin{array}{l}\text{Materials per unit + labor per unit+ }\\ \text{plant supervision}\text{per unit}+\\ \text{Fixed production cost per unit }\end{array}\right)\\ =\$8+\$4+\$1+\left(\frac{\$675,000}{225,000\text{units}}\right)\\ =\$8+\$4+\$1+\$3\\ =\$16\text{per unit}\end{array}$

Therefore, full absorption cost per unit amount is $16. The other options like 1, 2 and 4 are incorrect answers.

e.

To determine

Identify prime cost per unit.

Answer to Problem 31E

2. $12

Explanation of Solution

Prime cost per unit: The cost including materials cost per unit, labor cost per unit and outsource cost per unit refers to the prime cost per unit.

Calculate prime cost per unit.

$\begin{array}{c}\text{Prime cost per unit}\text{=}\text{Material per unit + labor per unit}\\ \text{=}\text{\$8}\text{per unit +}\text{\$4 per unit}\\ \text{=}\$12\text{per unit}\end{array}$

Therefore, prime cost per unit amount is $12. The other options like 1. 3 and 4 are incorrect answers.

f.

To determine

Identify conversion cost per unit.

Answer to Problem 31E

1.  $8

Explanation of Solution

Conversion cost per unit: The conversion cost per unit refers to the total unit cost of labor, outsourcing and production overhead.

Calculate conversion cost per unit.

$\begin{array}{c}\text{Conversion cost per unit = }\left(\begin{array}{l}\text{Labor per unit + Plant supervision per unit }\\ \text{+ Fixed production cost per unit }\end{array}\right)\\ \text{= \$4 per unit + \$1}\text{per unit +}\left(\frac{\$675,000}{225,000\text{units}}\right)\\ =\text{\$4 per unit + \$1}\text{per unit +}\$3\text{per unit}\\ =\$8\text{per unit}\end{array}$

Therefore, conversion cost per unit amount is $8. The other options like 2, 3 and 4 are incorrect answers.

g.

To determine

Identify contribution margin per unit.

Answer to Problem 31E

1. $9

Explanation of Solution

Contribution margin per unit:

The contribution margin per unit refers to the difference between sales price per unit and the variable cost per unit. The contribution margin as a percentage of sales is referred to as the contribution margin ratio (CM ratio).

Calculate contribution margin per unit.

$\begin{array}{c}\text{Contribution margin per unit = Sales per unit }-\text{Variable expense per unit}\\ \text{= \$27}\text{per unit }-\$18\text{per unit}\\ \text{= \$9}\text{per unit}\end{array}$

Therefore, contribution margin per unit amount is $9. The other options like 2, 3 and 4 are incorrect answers.

h.

To determine

Identify gross margin per unit.

Answer to Problem 31E

2. $11

Explanation of Solution

Gross margin per unit:

The gross margin per unit is the difference of selling price per unit and the absorption cost per unit.

Calculate gross margin per unit.

$\begin{array}{c}\text{Gross margin per unit = Sales per unit }-\text{Cost of goods sold per unit}\\ \text{= \$27}\text{per unit }-\$16\text{per unit}\\ \text{= \$11}\text{per unit}\end{array}$

Therefore, gross margin per unit amount is $11. The other options like 1, 3 and 4 options are incorrect answers.