Question

Convex Mechanical Supplies produces a product with the following costs as of July 1, 20X1:

Material	\(6
Labor	4
Overhead	2
	\)12

Beginning inventory at these costs on July 1 was 5,000 units. From July 1 to December 1, Convex produced 15,000 units. These units had a material cost of \(10 per unit. The costs for labor and overhead were the same. Convex uses FIFO inventory accounting.

Assuming that Convex sold 17,000 units during the last six months of

the year at \)20 each, what would gross profit be? What is the value of ending

inventory?

Short answer

The gross profit of the company is $88,000 and the value of ending inventory is $48,000.

Step-by-step solution

Beginning cost of inventory

$\begin{array}{rcl}\mathrm{Beginning}\mathrm{inventory}\mathrm{cost}& =& \mathrm{Beginning}\mathrm{units}\times \mathrm{Cost}\mathrm{of}\mathrm{production}\\ & =& 5,000\times \$12\\ & =& \$60,000\end{array}$

Cost of units produced

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{unist}\mathrm{produced}& =& \mathrm{Material}\mathrm{cost}+\mathrm{Labor}\mathrm{cost}+\mathrm{Overhead}\\ & =& \$10+\$4+\$2\\ & =& \$16\end{array}$

Cost of production

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{production}& =& \mathrm{Units}\mathrm{produced}\times \mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}\\ & =& 15,000\times \$16\\ & =& \$240,000\end{array}$

Cost of sales assuming FIFO inventory accounting method

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{sales}& =& \left(\mathrm{Beginning}\mathrm{units}\times \mathrm{Unit}\mathrm{price}\right)+\left(\mathrm{Balance}\mathrm{units}\times \mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}\right)\\ & =& \left(5,000\times \$12\right)+\left(\left(17,000-5,000\right)\times \$16\right)\\ & =& \$252,000\end{array}$

Gross profit

$\begin{array}{rcl}\mathrm{Gross}\mathrm{profit}& =& \mathrm{Sales}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \left(17,000\times \$20\right)-\$252,000\\ & =& \$88,000\end{array}$

Value of ending inventory

$\begin{array}{rcl}\mathrm{Ending}\mathrm{inventory}& =& \mathrm{Beginning}\mathrm{inventory}+\mathrm{Cost}\mathrm{of}\mathrm{production}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \$60,000+\$240,000-\$252,000\\ & =& \$48,000\end{array}$