To determine whether Randall Company has underapplied or overapplied overhead, and by how much, we need to go through several calculations step-by-step:
### Step 1: Calculate the Direct Materials Used
Direct materials used are calculated by:
[tex]\[ \text{Direct Materials Used} = \text{Direct Materials (Jan 1)} + \text{Direct Materials Purchases} - \text{Direct Materials (Dec 31)} \][/tex]
Plugging in the values:
[tex]\[ \text{Direct Materials Used} = \$77,000 + \$324,000 - \$40,000 = \$361,000 \][/tex]
### Step 2: Calculate the Cost of Goods Manufactured
The cost of goods manufactured (COGM) is calculated by:
[tex]\[ \text{COGM} = \text{Work in Process (Jan 1)} + \text{Direct Materials Used} + \text{Other Production Costs} - \text{Work in Process (Dec 31)} \][/tex]
To find Other Production Costs, we use the given value for the cost of goods available for sale and the finished goods.
[tex]\[ \text{Other Production Costs} = \text{Cost of Goods Available for Sale} - \text{Finished Goods (Jan 1)} \][/tex]
[tex]\[ \text{Other Production Costs} = \$950,000 - \$115,000 = \$835,000 \][/tex]
Hence,
[tex]\[ \text{COGM} = \$66,000 + \$361,000 + \$835,000 - \$42,000 = \$1,220,000 \][/tex]
### Step 3: Calculate the Applied Overhead
Applied overhead is determined based on the factory overhead rate and the actual overhead costs. The factory overhead rate is [tex]\(125\%\)[/tex] of the direct labor cost. We use the cost of goods manufactured to find the applied overhead.
[tex]\[ \text{Applied Overhead} = \text{Factory Overhead Rate} \times (\text{COGM} - \text{Actual Factory Overhead Costs}) \][/tex]
[tex]\[ \text{Applied Overhead} = 1.25 \times (\$1,220,000 - \$260,000) \][/tex]
[tex]\[ \text{Applied Overhead} = 1.25 \times \$960,000 = \$1,200,000 \][/tex]
### Step 4: Calculate Underapplied or Overapplied Overhead
The amount of underapplied or overapplied overhead is the difference between actual factory overhead costs and applied overhead.
[tex]\[ \text{Overapplied or Underapplied Overhead} = \text{Actual Factory Overhead Costs} - \text{Applied Overhead} \][/tex]
[tex]\[ \text{Overapplied or Underapplied Overhead} = \$260,000 - \$1,200,000 = -\$940,000 \][/tex]
A negative value indicates that the overhead was overapplied. Therefore, the company has overapplied overhead.
The result is:
[tex]\[ \boxed{940,000 \text{ overapplied}} \][/tex]
