Chapter 17, Problem 17.5CP

(1)

To determine

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:

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

To Calculate: The predetermined factory overhead rate for each alternative base for M Industries.

Explanation of Solution

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:

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

Working notes:

Total overhead for (2012 – 2016) is calculated as follows:

Factory Overhead (Actual)	Amount ($)
2012	790,000
2013	870,000
2014	935,000
2015	845,000
2016	760,000
	4,200,000

Table (1)

Total direct labor cost, (2012 – 2016) is computed as below:

Direct labor cost	Amount ($)
2012	3,885,000
2013	4,410,000
2014	4,620,000
2015	4,200,000
2016	3,885,000
	21,000,000

Table (2)

Total machine hours, (2012 – 2016) is computed as follows:

Machine hours	Hours
2012	93,000
2013	104,000
2014	111,000
2015	100,400
2016	91,600
	500,000

Table (3)

Explanation:

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.

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

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)
2016	Direct Labor cost	790,000	777,000 (1)	13,000
	Machine Hours	790,000	781,200 (6)	8,800
2015	Direct Labor cost	870,000	882,000 (2)	(12,000)
	Machine Hours	870,000	873,600 (7)	(3,600)
2014	Direct Labor cost	935,000	924,000 (3)	11,000
	Machine Hours	935,000	932,400 (8)	2,600
2013	Direct Labor cost	845,000	840,000 (4)	5,000
	Machine Hours	845,000	843,360 (9)	1,640
2012	Direct Labor cost	760,000	777,000 (5)	(17,000)
	Machine Hours	760,000	769,440 (10)	(9,440)

Table (4)

Working note:

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

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 5}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$3,885,000\times 20\%\\ =\$777,000\end{array}$ (1)

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 4}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$4,410,000\times 20\%\\ =\$882,000\end{array}$ (2)

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

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

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 1}\right)=\left[\begin{array}{l}\text{Direct labor cost }\times \text{ Predetermined overhead }\\ \text{rate based on Direct labor cost}\end{array}\right]\\ =\$3,885,000\times 20\%\\ =\$777,000\end{array}$ (5)

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

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 5}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{93,000}\times \$8.40\\ =\$781,200\end{array}$ (6)

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 4}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{104,000}\times \$8.40\\ =\$873,600\end{array}$ (7)

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 3}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =111\text{,000}\times \$8.40\\ =\$932,400\end{array}$ (8)

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 2}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =1\text{00,400}\times \$8.40\\ =\$843,360\end{array}$ (9)

$\begin{array}{c}\text{Applied overhead }\left(\text{Year 1}\right)=\left[\begin{array}{l}\text{Machine hours }\times \text{ Predetermined overhead }\\ \text{rate based on machine hours}\end{array}\right]\\ =\text{91,600}\times \$8.40\\ =\$769,440\end{array}$ (10)

Explanation:

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 underapplied.

(3)

To determine

To Discuss: 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