Chapter 22, Problem 3PSA

To determine

Department Contribution statement:

Through the department contribution statement a company can decide whether any department should be eliminated or not. To take this decision, Company needs a departmental contribution statement. If department contribution statement figure is negative and income comes positive then company take decision to close that department.

To Identify: Departmental income statement.

Explanation of Solution

Particulars	Amount ($)	Amount ($)	Amount ($)	Amount ($)
	Clock	Mirror	Painting	Combined
Sales(A)	140,400	59,400	50,000	199,800
Cost of goods sold(A-C)	68,796	36,828	22,500	128,124
Gross profit$$\left(\text{C}=\text{A}\times \text{B}\right)$$	71,796	22,572	27,500	71,676
Gross profit margin(B)	51%	38%	55%	47.14%
Direct expense
Sales salaries	20,000	7,000	8,000	35,000
Advertisement expense	1,200	500	800	2,500
Store supplies used	972	432	500	1,904
Deprecation-Equipment	1,500	300	200	2,000
Total direct expense	23,672	8,232	9,500	41,404
Allocated expense
Rent expense	5,616	2,835	2,349	10,800
Utilities expense	2,080	1,050	870	4,000
Office expense	12,365.09	5,231.39	4,404	22,000
Total allocated expense	20,061	9,116	4,403.52	36,800
Total expense(D)	43,733	17,348	17,123	78,204
Net Income $\left(\text{E}=\text{C}-\text{D}\right)$	27,871	5,224	10,377	43,204

Working notes:

Given,
Clock department sale is 130,000.
Mirror department sale is 55,000.
Painting department sale is 50,000.
Increase in the sale is 8%.

Calculation of increase in sales of clock department,

$\begin{array}{c}\text{Total}\text{clock} \text{department}\text{sales}=\text{Clock} \text{department}\text{sale}\times \text{\%}\text{increasedin}\text{sales}\\ =\$130,000\times \frac{108}{100}\\ =\$140,400\end{array}$

Calculation of increase in sales of mirror department,

$\begin{array}{c}\text{Total}\text{mirror} \text{department}\text{sales}=\text{Mirror} \text{department}\text{sale}\times \text{\%}\text{increased}\text{in}\text{sales}\\ =\text{\$55,000}\times \frac{\text{108}}{100}\\ =\$59,400\end{array}$

Formula to calculate combined increased in sales,

$\begin{array}{c}\text{Total} \text{combined}\text{sales}= \text{Combined}\text{sale}\times \text{\%}\text{increased}\text{in}\text{sales}\\ =\text{\$185,000}\times \frac{\text{108}}{100}\\ =\$128,124\end{array}$

Given,
Clock department sale is 130,000.
Mirror department sale is 55,000.
Painting department sale is 50,000.
Gross profit margin of clock department is $66,300.
Gross profit margin of Mirror department is $20,900.
Gross profit margin of painting department is 55%.

Calculation of gross profit margin of clock department,

$\begin{array}{c}\text{Gross}\text{profit}\text{margin}=\frac{\text{Gross}\text{profit}}{\text{Sale}}\\ =\frac{\$66,300}{\$130,000}\\ =51\%\end{array}$

Calculation of gross profit margin of mirror department,

$\begin{array}{c}\text{Gross}\text{profit}\text{margin}=\frac{\text{Gross}\text{profit}}{\text{Sale}}\\ =\frac{\$20,900}{\$55,000}\\ =38\%\end{array}$

Calculation of gross profit margin of combined sale,

$\begin{array}{c}\text{Gross}\text{profit}\text{margin}=\frac{\text{Gross}\text{profit}}{\text{Sale}}\\ =\frac{\$87,200}{\$185,000}\\ =47.14\%\end{array}$

Given,
New sale of clock department is $140,400.
New sale of mirror department is $59,400.
New sale of painting department is $50,000.
New sale of painting department is $50,000.
New combined sale is $199,800.
Gross profit margin of clock department is 51%.
Gross profit margin of mirror department is 38%.
Gross profit margin of painting department is 55%.
Gross profit margin of combined sale is 47.14%.

Calculation of gross profit of clock department,

$\begin{array}{c}\text{Gross}\text{profit}=\text{Gross}\text{profit}\text{margin}\times \text{Sale}\\ =\$140,400\times 51\%\\ =\$71,604\end{array}$

Calculation of gross profit of mirror department,

$\begin{array}{c}\text{Gross}\text{profit}=\text{Gross}\text{profit}\text{margin}\times \text{Sale}\\ =\$59,400\times 38\%\\ =\$22,572\end{array}$

Calculation of gross profit of painting department,

$\begin{array}{c}\text{Gross}\text{profit}=\text{Gross}\text{profit}\text{margin}\times \text{Sale}\\ =\$50,000\times 55\%\\ =\$27,500\end{array}$

Calculation of gross profit of combined sale,

$\begin{array}{c}\text{Gross}\text{profit}=\text{Gross}\text{profit}\text{margin}\times \text{Sale}\\ =\$199,800\times 47.14\%\\ =\$94,185.72\end{array}$

Given,
New sale of clock department is $140,400.
New sale of mirror department is $59,400.
New sale of painting department is $50,000.
Gross profit of clock department is $71,604.
Gross profit of mirror department is $22,572.
Gross profit of painting department is $27,500.
Gross profit of combined sale is $94,185.72.

Calculation of cost of goods sold of clock department,

$\begin{array}{c}\text{Cost}\text{of}\text{goods}\text{sold}=\text{Sale}-\text{Gross}\text{profit}\\ =\text{\$140,400}-\text{\$71,604}\\ \text{=\$68,796}\end{array}$

Calculation of cost of goods sold of mirror department,

$\begin{array}{c}\text{Cost}\text{of}\text{goods}\text{sold}=\text{Sale}-\text{Gross}\text{profit}\\ =\text{\$59,400}-\text{\$22,572}\\ =\text{\$36,828}\end{array}$

Calculation of cost of goods sold of painting department,

$\begin{array}{c}\text{Cost}\text{of}\text{goods}\text{sold}=\text{Sale}-\text{Gross}\text{profit}\\ =\text{\$50,000}-\text{\$27,500}\\ =\$22,500\end{array}$

Calculation of cost of goods sold of combined sale,

$\begin{array}{c}\text{Cost}\text{of}\text{goods}\text{sold}=\text{Sale}-\text{Gross}\text{profit}\\ =\text{\$199,800}-\text{\$94,185}\text{.72}\\ =\text{\$105,614}\text{.28}\end{array}$

Given,
Store supplies used by clock department are $900.
Store supplies used by mirror department are $400.
Store supplies used by painting department are $500.

Sales increased of the both department is 8%.

Calculation of store supplies of the clock department,

$\begin{array}{c}\text{Store}\text{suplies}\text{used}=\text{Store}\text{supplies}\times \text{\%}\text{increased}\text{in}\text{the}\text{sale}\\ =\text{\$900}\times \frac{\text{108}}{100}\\ =\$972\end{array}$

Calculation of store supplies of the mirror department,

$\begin{array}{c}\text{Store}\text{suplies}\text{used}=\text{Store}\text{supplies}\times \text{\%}\text{increased}\text{in}\text{the}\text{sale}\\ =\text{\$400}\times \frac{\text{108}}{100}\\ =\$432\end{array}$

Calculation of combined store supplies of the department,

$\begin{array}{c}\text{Combined}\text{supplies}=\left(\begin{array}{l}\text{Clock}\text{deparment}\text{used}\text{store}\text{supplies}\\ +\text{Mirror}\text{deparment}\text{used}\text{store}\text{supplies}\\ +\text{Painting}\text{deparment}\text{used}\text{store}\text{supplies}\end{array}\right)\\ =\$972+\$432+\$500\\ =\$1,904\end{array}$

Given,
Rent expense of the clock department is $7,020.
Rent expense of the mirror department is $3,780.
Painting department used the area of the clock department is one-fifth.
Painting department used the area of the mirror department is one-fourth.

Calculation of new rant expense of the clock department,

$\begin{array}{c}\text{New}\text{rent}\text{expense}=\text{Rent}\text{expense}\times \frac{4}{5}\text{used}\text{by}\text{the}\text{deparment}\\ =\text{\$7,020}\times \frac{4}{5}\\ =\$5,616\end{array}$

Calculation of the new rant expense of the mirror department,

$\begin{array}{c}\text{New}\text{rent}\text{expense}=\text{Rent}\text{expense}\times \frac{3}{4}\text{used}\text{by}\text{the}\text{deparment}\\ =\text{\$3,780}\times \frac{3}{4}\\ =\$2,835\end{array}$

Calculation of new rant expense of the painting department,

$\begin{array}{c}\text{Rent}\text{expense}=\left[\begin{array}{c}\left(\frac{\text{Rent}\text{expense}\text{of}\text{clock}\text{deparment}}{\text{5}}\right)\\ +\left(\frac{\text{Rent}\text{expense}\text{of}\text{mirror}\text{deparment}}{\text{4}}\right)\end{array}\right]\\ =\frac{\$7,020}{5}+\frac{\$3,780}{4}\\ =\$1,404+\$945\\ =\$2,349\end{array}$

Calculation of combines rent expense,

$\begin{array}{c}\text{Combined}\text{expense}=\left(\begin{array}{l}\text{Rent}\text{expense}\text{of}\text{clock}\text{deparment}\\ +\text{Rent}\text{expense}\text{of}\text{mirror}\text{deparment}\\ +\text{Rent}\text{expense}\text{of}\text{painting}\text{deparment}\end{array}\right)\\ =\$5,616+\$2,835+\$2,349\\ =\$10,800\end{array}$

Given,
Utilities expense of the clock department is $2,600.
Utilities expense of the mirror department is $1,400.
Painting department used the area of the clock department is one-fifth.
Painting department used the area of the mirror department is one-fourth.

Calculation of new utilities expense of the clock department,

$\begin{array}{c}\text{New}\text{Utilities}\text{expense}=\text{Utilities}\text{expense}\times \frac{4}{5}\text{used}\text{by}\text{the}\text{deparment}\\ =\text{\$2,600}\times \frac{4}{5}\\ =\$2,080\end{array}$

Calculation of new utilities expense of the mirror department,

$\begin{array}{c}\text{New}\text{Utilities}\text{expense}=\text{Utilities}\text{expense}\times \frac{3}{4}\text{used}\text{by}\text{the}\text{deparment}\\ =\text{\$1,400}\times \frac{3}{4}\\ =\$1,050\end{array}$

Calculation of new utilities expense of the painting department,

$\begin{array}{c}\text{Utilities}\text{expense}=\left[\begin{array}{c}\left(\frac{\text{Utilities}\text{expense}\text{of}\text{clock}\text{deparment}}{\text{5}}\right)\\ +\left(\frac{\text{Utilities}\text{expense}\text{of}\text{mirror}\text{deparment}}{\text{4}}\right)\end{array}\right]\\ =\frac{\$2,600}{5}+\frac{\$3,780}{4}\\ =\$520+\$945\\ =\$1,465\end{array}$

Calculation of office expense of the clock department,

$\begin{array}{c}\text{New}\text{Office}\text{expense}=\frac{\text{Sales}}{\text{Combined}\text{sale}}\times \text{Combined}\text{expense}\\ \text{=}\frac{\text{\$140,400}}{\$249,800}\times \$22,000\\ =\$12,365\end{array}$

Calculation of office expense of the mirror department,

$\begin{array}{c}\text{New}\text{Office}\text{expense}=\frac{\text{Sales}}{\text{Combined}\text{sale}}\times \text{Combined}\text{expense}\\ \text{=}\frac{\text{\$59,400}}{\$249,800}\times \$22,000\\ =\$5,231.39\end{array}$

Calculation of office expense of the painting department,

$\begin{array}{c}\text{Office}\text{expense}=\left(\begin{array}{l}\text{Total}\text{office}\text{expense}-\text{Clock}\text{department}\text{expense}\\ -\text{Mirror}\text{department}\text{expense}\end{array}\right)\\ =\text{\$22,000}-\text{\$12,365}\text{.09}-\text{\$5,231}\text{.39}\\ =\text{\$4,404}\end{array}$

Given,
Total expense of the clock department is $43,733.
Total expense of the mirror department is $17,348.
Total expense of the painting department is $17,123.
Gross profit of clock department is $71,604.
Gross profit of mirror department is $22,572.
Gross profit of painting department is $27,500.

Calculation of net income of the clock department,

$\begin{array}{c}\text{Net}\text{income}=\text{Gross}\text{profit}-\text{Total}\text{expense}\\ =\$71,604-\$43,733\\ =\$27,871\end{array}$

Calculation of net income of the mirror department,

$\begin{array}{c}\text{Net}\text{income}=\text{Gross}\text{profit}-\text{Total}\text{expense}\\ =\text{\$36,828}-\text{\$17,348}\\ =\$5,224\end{array}$

Calculation of net income of the painting department,

$\begin{array}{c}\text{Net}\text{income}=\text{Gross}\text{profit}-\text{Total}\text{expense}\\ =\text{\$22,500}-\text{\$17,123}\\ =\$10,377\end{array}$