Chapter 1, Problem 51P

To determine

Calculate the missing amount for the given statement.

Explanation of Solution

Calculate the missing amount for the given statement as follows:

Manufacturing R
Projected income statement
For one quarter
Particulars	Status Quo				Alternative		Difference
	Single product		Increase (decrease) percentage		Two products
Sales revenue	$50,000	(a)	25%	(b)	$62,500	(c)	$12,500
Costs:
Material	$15,000		22%		$18,300	(d)	$3,300	(e)
Labor	$8,000	(f)	30%	(g)	$10,400		$2,400
Rent	$2,000		10%	(h)	$2,200	(i)	$200	(j)
Depreciation	$5,000		15%		$5,750		$750
Utilities	$8,000	(k)	30%		$10,400		$2,400	(l)
Other	$3,000		25%	(m)	$3,750	(n)	$750
Total costs	$41,000				$50,800	(o)	$9,800	(p)
Operating profit	$9,000	(q)			$11,700		$2,700	(r)

Table (1)

Working notes:

(1) Calcualte the increase (decrease) percentage of rent (h).

Increase (decrease) percentage of rent is 10% (given).

(2) Calcualte the amount of rent for two products (i).

$\begin{array}{c}\text{Rent for two products = }\left[\begin{array}{l}\text{Rent for single product }\times \\ \left(100\%+\text{Increased percentage}\right)\end{array}\right]\\ =\$2,000\times 100\%+10\%\\ =\$2,000\times 110\%\\ =\$2,200\end{array}$

(3) Calcualte the amount of material for two products (d).

$\begin{array}{c}\text{Material for two products = }\left[\begin{array}{l}\text{Material for single product }\times \\ \left(100\%+\text{Increased percentage}\right)\end{array}\right]\\ =\$15,000\times 100\%+22\%\\ =\$15,000\times 122\%\\ =\$18,300\end{array}$

(4) Calcualte the amount of other cost for two products (n).

$\begin{array}{c}\text{Other costs for two products = }\left[\begin{array}{l}\text{Other costs for two products}-\\ \text{Other costs for single product}\end{array}\right]\\ =\$3,750-\$3,000\\ =\$750\end{array}$

(5) Calculate the increase (decrease) percentage of other costs (m).

$\begin{array}{c}\begin{array}{l}\text{Increase (decrease) }\\ \text{percentage of other costs}\end{array}\}=\frac{\text{Difference amount (4)}}{\text{Other cost for single product}}\times 100\\ =\frac{\$750}{\$3,000}\times 100\\ =25\%\end{array}$

(6) Calculate the total cost for two products (o).

$\begin{array}{c}\begin{array}{l}\text{Total costs for}\\ \text{two products}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Cost of materials+Cost of labor+Cost of rent+}\\ \text{Cost of depreciation+Cost of utilities+Other costs}\end{array}\right)\\ =\left(\begin{array}{l}\$18,300+\$10,400+\$2,200+\\ \$5,750+\$10,400+\$3,750\end{array}\right)\\ =\$50,800\end{array}$

(7) Calculate the sales revenue of two products (c).

$\begin{array}{c}\begin{array}{l}\text{Sales revenue }\\ \text{for two products }\end{array}\}\text{= }\left(\begin{array}{l}\text{Total costs for two products (6)+}\\ \text{Operating profits}\end{array}\right)\\ \text{=\$50,800+\$11,700}\\ \text{=\$62,500}\end{array}$

(8) Calcualte the sales revenue for single product (a).

$\begin{array}{c}\begin{array}{l}\text{Sales revenue }\\ \text{for single product }\end{array}\}\text{= }\left(\begin{array}{l}\text{Sales revenue for two products}-\\ \text{Difference amount}\end{array}\right)\\ =\$62,500-\$12,500\\ =\$50,000\end{array}$

(9) Calculate the increase (decrease) percentage of revenue (b).

$\begin{array}{c}\begin{array}{l}\text{Increase (decrease) }\\ \text{percentage of other costs}\end{array}\}=\frac{\text{Difference amount }}{\text{Other cost for single product (8)}}\times 100\\ =\frac{\$12,500}{\$50,000}\times 100\\ =25\%\end{array}$

(10) Calcualte the labor cost for single product (f).

$\begin{array}{c}\text{Labor cost for single product = }\left[\begin{array}{l}\text{Labor cost for two product}-\\ \text{Difference amount}\end{array}\right]\\ =\$10,400-\$2,400\\ =\$8,000\end{array}$

(11) Calcualte the the increase (decrease) percentage of utilities (g).

$\begin{array}{c}\begin{array}{l}\text{Increase (decrease) }\\ \text{percentage of utilites costs}\end{array}\}=1-\left[\frac{\text{Utilities cost for two products }}{\text{Utilties cost for single product }}\right]\times 100\\ =1-\left(\frac{\$10,400}{\$8,000}\right)\times 100\\ =30\%\end{array}$

(12) Calcualte the utilities cost for single product (k).

$\begin{array}{c}\begin{array}{l}\text{Utilities cost for }\\ \text{single product}\end{array}\}\text{ = }\frac{\text{Utilities cost for two product}}{\left[100\%+\text{Increased percentage}\right]}\\ =\frac{\$10,400}{\left(100\%+30\%\right)}\\ =\frac{\$10,400}{130\%}\\ =\$8,000\end{array}$

(13) Calcualte the difference amount of utilities cost (l).

$\begin{array}{c}\begin{array}{l}\text{Difference amount }\\ \text{of utilities cost}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Utilities cost for two products}-\\ \text{Utilities cost for single products}\end{array}\right)\\ =\$10,400-\$8,000\\ =\$2,400\end{array}$

(14) Calcualte the difference amount of total costs (p).

$\begin{array}{c}\begin{array}{l}\text{Difference amount }\\ \text{of total cost}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Total costs for two products}-\\ \text{Total costs for single products}\end{array}\right)\\ =\$50,800-\$41,000\\ =\$9,800\end{array}$

(15) Calculate the operating product for single product (q).

$\begin{array}{c}\begin{array}{l}\text{Operating profit for }\\ \text{single product }\end{array}\}\text{= }\left[\begin{array}{l}\text{Sales revenue for single product}-\\ \text{Total costs}\end{array}\right]\\ =\$50,000-\$41,000\\ =\$9,000\end{array}$

(16) Calculate the difference amount of operating profit (r).

$\begin{array}{c}\begin{array}{l}\text{Difference amount }\\ \text{of operating profit}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Operating profit for two products}-\\ \text{Opeating profi for single products}\end{array}\right)\\ =\$11,700-\$9,000\\ =\$2,700\end{array}$