Chapter 17, Problem 34P

To determine

Allocate the service department costs of company R using the reciprocal-services method in combination with the dual-allocation approach.

Explanation of Solution

Reciprocal-services method: The term reciprocal service refers to the circumstances under which two or more service departments provide services to each other. Under this method, in order to reflect the reciprocal provision of services among all other service departments, a system of simultaneous equations is established. When once it is established, “all other service departments’ costs are allocated among the departments that use the various service departments’ output of services”. Moreover, this is the only cost allocation method that fully accounts for the reciprocal provision of services among departments.

Allocate the service department costs of company R using the reciprocal-services method in combination with the dual-allocation approach as follows:

Variable costs under short-run proportions:

Table (1)

Working note (1):

Assume that:

• The total variable cost of Human resources is denoted as H.
• The total variable cost of Administration and Accounting is denoted as A, and
• The total variable cost of patient records is denoted as R.

The equations are as follows:

$\left(\text{R}=24\text{,000}+\text{5\%H}\right)(1)$

$\left(\text{H}=\text{15,000}+\text{5\%A}\right)(2)$

$\left(\text{A}=47\text{,500}+2\text{0\%H}\right)(3)$

Now, Substitute equation (3) in equation (2).

$\begin{array}{c}\text{H}=\$\text{15,000}+\text{5\%A}\\ \text{H}=\$\text{15,000}+0.5\times \left(\$47,500+0.20\text{H}\right)\\ \text{H}=\$15,000+\$2,375+0.1\text{H}\\ 1\text{H}-0.1\text{H}=\$17,375\end{array}$

$\begin{array}{c}\text{0}\text{.99H}=\$17,375\\ \text{H}=\frac{\$17,375}{\text{0}\text{.99}}\\ \text{H}=\$17,551\end{array}$

Then, Substitute the computed value of H in equation (1) and (3):

Equation (1):

$\begin{array}{c}\text{R}=\$24\text{,000}+5\text{\%H}\\ =\$24,0\text{00}+\frac{5}{100}\times \$17,551\\ =\$24,000+\$878\\ \text{R}=\$24,878\end{array}$

Equation (3):

$\begin{array}{c}\text{A}=\$47\text{,500}+20\text{\%H}\\ =\$47,5\text{00}+\frac{20}{100}\times \$17,551\\ =\$47,5\text{00}+\$3,510\\ \text{A}=\$51,010\end{array}$

Fixed costs under long-run proportions:

Table (2)

Working note (2):

Assume that:

• The total variable cost of Human resources is denoted as H.
• The total variable cost of Administration and Accounting is denoted as A, and
• The total variable cost of patient records is denoted as R.

The equations are as follows:

$\left(\text{R}=76\text{,000}+10\text{\%H}\right)(4)$

$\left(\text{H}=4\text{5,000}+10\text{\%A}\right)(5)$

$\left(\text{A}=142\text{,500}+1\text{0\%H}\right)(6)$

Now, Substitute equation (6) in equation (5).

$\begin{array}{c}\text{H}=\$4\text{5,000}+10\text{\%A}\\ \text{H}=\$4\text{5,000}+0.10\times \left(\$142,500+0.10\text{H}\right)\\ \text{H}=\$45,000+\$14,250+0.01\text{H}\\ 1\text{H}-0.01\text{H}=\$59,250\end{array}$

     $\begin{array}{c}\text{0}\text{.99H}=\$59,250\\ \text{H}=\frac{\$59,250}{\text{0}\text{.99}}\\ \text{H}=\$59,848\end{array}$

Then, Substitute the computed value of H in equation (4) and (6):

Equation (4):

$\begin{array}{c}\text{R}=\$76\text{,000}+10\text{\%H}\\ =\$76,0\text{00}+\frac{10}{100}\times \$59,848\\ =\$76,000+\$5,985\\ \text{R}=\$81,985\end{array}$

Equation (6):

$\begin{array}{c}\text{A}=\$142\text{,500}+10\text{\%H}\\ =\$142,5\text{00}+\frac{10}{100}\times \$59,848\\ =\$142,5\text{00}+\$5,985\\ \text{A}=\$148,485\end{array}$

Total cost allocated:

Particulars	Orthopedics	Internal Medicine
Variable costs	$      29,705	$   56,796
Add: Fixed costs	$    111,582	$ 151,918
Total costs	$    141,286	$ 208,714
Grand total	$350,000

Table (3)