Question

The Bradley Corporation produces a product with the following costs as of July 1, 20X1:

Material	\(4 per unit
Labor	4 per unit
Overhead	2 per unit

Beginning inventory at these costs on July 1 was 3,250 units. From July 1 to December 1, 20X1, Bradley produced 12,500 units. These units had a material cost of \)5, labor of \(4, and overhead of \)5 per unit. Bradley uses LIFO inventory accounting.

Assuming that Bradley sold 14,000 units during the last six months of

the year at $19 each, what is its gross profit? What is the value of ending

inventory?

Short answer

The gross profit of the company is $76,000 and the value of ending inventory is $35,000.

Step-by-step solution

Unit price of beginning inventory

$\begin{array}{rcl}\mathrm{Beginning}\mathrm{unit}\mathrm{price}& =& \mathrm{Material}\mathrm{cost}+\mathrm{Labor}\mathrm{cost}-\mathrm{Overhead}\\ & =& \$4+\$4+\$2\\ & =& \$10\end{array}$

Beginning cost of inventory

$\begin{array}{rcl}\mathrm{Beginning}\mathrm{inventory}\mathrm{cost}& =& \mathrm{Beginning}\mathrm{units}\times \mathrm{Unit}\mathrm{cost}\\ & =& 5,000\times \$10\\ & =& \$50,000\end{array}$

Cost of units produced

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}& =& \mathrm{Material}\mathrm{cost}+\mathrm{Labor}\mathrm{cost}+\mathrm{Overhead}\\ & =& \$5+\$4+\$5\\ & =& \$14\end{array}$

Cost of production

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{production}& =& \mathrm{Units}\mathrm{produced}\times \mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}\\ & =& 12,500\times \$14\\ & =& \$175,000\end{array}$

Cost of sales assuming LIFO inventory accounting method

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{sales}& =& \left(\mathrm{Produced}\mathrm{units}\times \mathrm{cost}\mathrm{of}\mathrm{production}\right)+\left(\mathrm{Balance}\mathrm{units}\times \mathrm{Beginning}\mathrm{unit}\mathrm{cost}\right)\\ & =& \left(12,500\times \$14\right)+\left(\left(14,000-12,500\right)\times \$10\right)\\ & =& \$175,000+\$15,000\\ & =& \$190,000\end{array}$

Gross profit

$\begin{array}{rcl}\mathrm{Gross}\mathrm{profit}& =& \mathrm{Sales}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \left(14,000\times \$19\right)-\$190,000\\ & =& \$76,000\end{array}$

Value of ending inventory

$\begin{array}{rcl}\mathrm{Ending}\mathrm{inventory}& =& \mathrm{Beginning}\mathrm{inventory}+\mathrm{Cost}\mathrm{of}\mathrm{production}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \$50,000+\$175,000-\$190,000\\ & =& \$35,000\end{array}$