Chapter 9, Problem 9P

To determine

Compare the cost allocations to M Products and R Markets under simplified costing and activity-based costing, and indicate the difference as undercosted or overcosted.

Explanation of Solution

Budgeted overhead allocation rate: The budgeted overhead allocation rate is the rate at which the overhead is allocated. This is calculated by dividing the total fixed and variable overheads cost by the base of the allocation.

Prepare job cost sheets for M Products and R Markets using simplified costing.

	M Products	R Markets
Professional labor cost:
50 hours×$60 (1)	$3,000
20 hours×$60 (1)		$1,200
Professional support:
50 hours×$40 (2)	2,000
20 hours×$40 (2)		800
Total	$5,000	$2,000

Working Note (1):

Compute the cost of professional labor per hour.

$\begin{array}{c}\text{Cost per hour=}\left[\frac{\left(\begin{array}{l}\text{Partner salary}\times \\ \text{Number of partners}\end{array}\right)+\left(\begin{array}{l}\text{Associate salary}\times \\ \text{Number of associates}\end{array}\right)}{\left(\begin{array}{l}\text{Number of hours}\times \\ \text{Number of partners and associates}\end{array}\right)}\right]\\ \text{=}\left[\frac{\left(\$150,000\times 2\right)\text{+}\left(\text{\$60,000}\times \text{4}\right)}{\left(1,500\text{hours}\times \text{6}\right)}\right]\\ \text{=\$60}\end{array}$

Working Note (2):

Computed the cost of professional support per hour.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of professional }\\ \text{support per hour}\end{array}\right)\text{=}\frac{\text{Cost of professional support}}{\text{Number of hours}}\\ \text{=}\frac{\$360,000}{\left\{\begin{array}{l}\left(50\text{ hours}\times \text{2}\text{partners}\right)+\\ \left(20\text{hours}\times \text{4 associates}\right)\end{array}\right\}}\\ \text{=}\frac{\$360,000}{9,000\text{hours}}\\ =\$40\end{array}$

Prepare job cost sheets for the two clients using activity-based costing.

	M Products	R Markets
Professional labor cost:
30 hours×$100 (3)	$3,000
5 hours×$100 (3)		$500
Associate labor cost:
20 hours×$40 (4)	800
15 hours×$40 (4)		600
Design support:
$3,800×.22 (5)	836
$1,100×.22 (5)		242
Staff support:
50 hours×$26.67 (6)	1,334
20 hours×$26.67 (6)		533
Total	$5,970	$1,875

Working Note (3):

Compute the cost of partner labor per hour.

$\begin{array}{c}\text{Cost per hour=}\left[\frac{\text{Partners salary}}{\text{Number of hours}}\right]\\ \text{=}\left[\frac{\$150,000}{1,500\text{hours}}\right]\\ \text{=\$100}\end{array}$

Working Note (4):

Computed the cost of associate labor per hour.

$\begin{array}{c}\text{Cost per hour=}\left[\frac{\text{Associates salary}}{\text{Number of hours}}\right]\\ \text{=}\left[\frac{\$60,000}{1,500\text{hours}}\right]\\ \text{=\$40}\end{array}$

Working Note (5):

Computed the cost of design support per partner and associate.

$\begin{array}{c}\text{Cost per partner associate=}\left[\frac{\text{Cost of design support}}{\left(\begin{array}{l}\text{Partner salary}\times \\ \text{Number of partners}\end{array}\right)+\left(\begin{array}{l}\text{Associate salary}\times \\ \text{Number of associates}\end{array}\right)}\right]\\ \text{=}\left[\frac{\$120,000}{\left(\$150,000\times 2\right)\text{+}\left(\text{\$60,000}\times \text{4}\right)}\right]\\ \text{=\$}\text{.22}\end{array}$

Working Note (6):

Computed the cost of staff support per partner and associate.

$\begin{array}{c}\text{Cost per partner associate=}\left[\frac{\text{Cost of staff support}}{\left(\begin{array}{l}\text{Number of partners and associates}\\ \times \text{Number of hours}\end{array}\right)}\right]\\ \text{=}\left[\frac{\$240,000}{\left(6\times 1,500\right)}\right]\\ \text{=\$26}\text{.67}\end{array}$

Calculate the difference between the total cost using simplified system and activity-based system:

	M Products	R Markets
Cost using simplified system	$5,000	$2,000
Cost using activity-based system	$5,970	$1,875
Difference	$(970)	$125

Using the simplified costing system, the job of R markets was overcosted by an amount of $125, and the job of M job was undercosted by $970. Using the simplified costing system, the job of M Products required 60% partner hours (30/50), and hence it was undercosted, whereas the job of R Markets required only 25% (5/20) partner hours, and hence, it was slightly overcosted.