Question

A company's prime costs total $5,100,000 and its conversion costs total $9,100,000. If direct materials are $2,050,000 and factory overhead is $6,050,000, then direct labor is:

Answer 1

Direct Labor = $3,050,000

Step-by-step explanation:

Definitions:

Prime costs:

• Prime costs: These are expenditures that are directly related to the production of finished goods. The following types of costs are considered as prime costs:

`\displaystyle\mathsf{Prime\:costs:\: \left \{ {{\:\:\:Direct\:materials} \atop {Direct\:Labor}} \right. }`

• Prime Cost Formula:

⇒
`\displaystyle\mathsf{Prime\:costs\:=\:Direct\:Materials\:+\:Direct\:Labor}`

Conversion Costs:

• Conversion Costs: These are costs incurred during the conversion of raw materials into finished goods. The following types of expenditures are considered as conversion costs:

`\displaystyle\mathsf{Conversion\:costs:\: \left \{ {{\:Factory\:overhead\:costs} \atop {Direct\:Labor}} \right. }`

• Conversion Costs Formula:

⇒
`\displaystyle\mathsf{Conversion\:costs\:=\:Direct\:Labor\:+\:Factory\:Overhead}`

Solution:

We are given the following values for the firm's expenditures:

• Prime costs: $5,100,000
• Conversion costs: $9,100,000
• Direct materials: $2,050,000
• Factory overhead: $6,050,000

Since we are provided the values for the company's prime costs and direct materials, we can use the following formula to determine the firm's prime costs:

⇒ Prime costs = Direct Materials + Direct Labor

Step 1: Algebraically isolate "Direct Labor" from the prime cost formula by subtracting "Direct Materials" from both sides:

Prime costs - Direct Materials = Direct Materials - Direct Materials + Direct Labor

⇒ Prime costs - Direct Materials = Direct Labor

Step 2: Switch sides:

Direct Labor = Prime costs - Direct Materials

Step 3: Substitute the given values into the Direct Labor formula:

Direct Labor = Prime costs - Direct Materials

Direct Labor = $5,100,000 - $2,050,000

Direct Labor = $3,050,000

Double-check:

As defined in the previous section of this post, direct labor costs are also considered as conversion costs. We can substitute our derived value for the direct labor into the conversion costs formula:

Conversion costs = Direct Labor + Factory Overhead

$9,100,000 = $3,050,000 + $6,050,000

$9,100,000 = $9,100,000 (True statement).

Final Answer:

Therefore, the company's direct labor cost is: $3,050,000