Chapter 2, Problem 2TIF

(1)

To determine

Ascertain the predetermined factory overhead rate for each alternative base for F Industries.

Explanation of Solution

Predetermined factory overhead rate

Normally, factory overhead costs are applied or allocated to cost of job based on predetermined factory overhead rate. The formula to calculate the predetermined factory overhead rate is as follows:

$\text{Predetermined factory overhead rate = }\frac{\text{Estimated total factory overhead costs}}{\text{Estimated activity rate}}$

The predetermined overhead rate for alternative activity base is prepared as follows:

Direct labor cost:

$\begin{array}{c}\text{Predetermined overhead rate = }\frac{\text{Total overhead cost }Table\left(1\right)}{\text{Total direct labor cost }Table\left(2\right)}\\ =\frac{\$4,200,000}{\$21,000,000}\\ =20\%\text{ of direct labor cost}\end{array}$

Machine hours:

$\begin{array}{c}\text{Predetermined overhead rate = }\frac{\text{Total overhead cost }Table\left(1\right)}{\text{Total machine hours }Table\left(3\right)}\\ =\frac{\$4,200,000}{500,000}\\ =\$8.40\text{ per machine hour}\end{array}$

The total factory overhead is calculated by totaling all year’s actual overhead incurred in production. There are two activity bases. One is direct labor cost and another is machine hours. The total direct labor cost is determined by adding all year’s direct labor cost incurred. The total machine hours spent is determined by adding all year’s machine hours.

Working notes:

Total overhead for (Year 1 – Year 5) is calculated as follows:

Factory Overhead (Actual)	Amount($)
Year 1	790,000
Year 2	870,000
Year 3	935,000
Year 4	845,000
Year 5	760,000
	4,200,000

Table (1)

Total direct labor cost, (Year 1 – Year 5) is computed as below:

Direct labor cost	Amount($)
Year 1	3,885,000
Year 2	4,410,000
Year 3	4,620,000
Year 4	4,200,000
Year 5	3,885,000
	21,000,000

Table (2)

Total machine hours, (Year 1 – Year 5) is computed as follows:

Machine hours	Hours
Year 1	93,000
Year 2	104,000
Year 3	111,000
Year 4	100,400
Year 5	91,600
	500,000

Table (3)

Conclusion

The predetermined overhead rate for direct labor cost is 20% of direct labor cost and predetermined overhead rate for machine hours is $8.40 per machine hour.

(2)

To determine

Ascertain the over- or under applied overhead based on two predetermined overhead rates.

Explanation of Solution

		Actual Overhead ($)	Applied Overhead($)	(Over-) underapplied ($)
		(a)	(b)	(c) = (a) – (b)
Year 5	Direct Labor cost	790,000	777,000(1)	13,000
	Machine Hours	790,000	781,200 (6)	8,800
Year 4	Direct Labor cost	870,000	882,000(2)	(12,000)
	Machine Hours	870,000	873,600 (7)	(3,600)
Year 3	Direct Labor cost	935,000	924,000(3)	11,000
	Machine Hours	935,000	932,400 (8)	2,600
Year 2	Direct Labor cost	845,000	840,000(4)	5,000
	Machine Hours	845,000	843,360 (9)	1,640
Year 1	Direct Labor cost	760,000	777,000(5)	(17,000)
	Machine Hours	760,000	769,440 (10)	(9,440)

Table (4)

When actual overhead incurred is less than applied overhead, the overhead is said to be overapplied. Alternatively, when actual overhead incurred is greater than applied overhead, the overhead is said to be under applied.

Working note (1):

The applied overhead for direct labor activity base is calculated as follows:

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 5}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$3,885,000\times 20\%\\ =\$777,000\end{array}$

Working note (2):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 4}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$4,410,000\times 20\%\\ =\$882,000\end{array}$

Working note (3):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 3}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$4,620,000\times 20\%\\ =\$924,000\end{array}$

Working note (4):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 2}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$4,200,000\times 20\%\\ =\$840,000\end{array}$

Working note (5):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 1}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$3,885,000\times 20\%\\ =\$777,000\end{array}$

Working note (6):

The applied overhead for machine hour’s activity base is calculated as follows:

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 5}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{93,000}\times \$8.40\\ =\$781,200\end{array}$

Working note (7):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 4}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{104,000}\times \$8.40\\ =\$873,600\end{array}$

Working note (8):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 3}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =111\text{,000}\times \$8.40\\ =\$932,400\end{array}$

Working note (9):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 2}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =1\text{00,400}\times \$8.40\\ =\$843,360\end{array}$

Working note (10):

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 1}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{91,600}\times \$8.40\\ =\$769,440\end{array}$

(3)

To determine

Suggest in applying the best predetermined overhead rate as computed.

Explanation of Solution

The best predetermined overhead rate is machine hours. The total overhead applied is based on both machine hours and direct labor cost. The over- or underapplied overhead ranges from $9,440 (Overapplied) to $8,800 (Underapplied) when the rates are based on machine hours. The over- or underapplied overhead ranges from $17,000 (Overapplied) to $13,000 (Underapplied) when the rates are based on machine hours.

When comparing both, we could see less fluctuation in under or over applied overhead based on predetermined overhead rate based on machine hours in the year by year basis.