Question

Sprint Shoes Inc. had a beginning inventory of 9,250 units on January 1, 20X1. Here were the costs associated with the inventory:

Material	\(15.00 per unit
Labor	8.00 per unit
Overhead	7.10 per unit

During 20X1, the firm produced 43,000 units with the following costs:

Material	\)17.50 per unit
Labor	8.80 per unit
Overhead	10.30 per unit

Sales for the year were 47,350 units at $44.60 each. Sprint Shoes uses LIFO accounting. What was the gross profit? What was the value of ending inventory?

Short answer

The gross profit of the company is $407,075 and the value of ending inventory is $147,490.

Step-by-step solution

Unit price of beginning inventory

$\begin{array}{rcl}\mathrm{Beginning}\mathrm{unit}\mathrm{price}& =& \mathrm{Material}\mathrm{cost}+\mathrm{Labor}\mathrm{cost}+\mathrm{Overheads}\\ & =& \$15+\$8+\$7.10\\ & =& \$30.10\end{array}$

Beginning cost of inventory

$\begin{array}{rcl}\mathrm{Beginning}\mathrm{inventory}\mathrm{cost}& =& \mathrm{Beginning}\mathrm{units}\times \mathrm{Unit}\mathrm{price}\\ & =& 9,250\times \$30.10\\ & =& \$278,425\end{array}$

Cost of units produced

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}& =& \mathrm{Material}\mathrm{cost}+\mathrm{Labor}\mathrm{cost}+\mathrm{Overhead}\\ & =& \$17.50+\$8.80+\$10.30\\ & =& \$36.60\end{array}$

Cost of production

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{production}& =& \mathrm{Units}\mathrm{produced}\times \mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}\\ & =& 43,000\times \$36.60\\ & =& \$1,573,800\end{array}$

Cost of sales assuming LIFO inventory accounting method

$\begin{array}{rcl}\mathrm{Cost}\mathrm{of}\mathrm{sales}& =& \left(\mathrm{Units}\mathrm{produced}\times \mathrm{Cost}\mathrm{of}\mathrm{units}\mathrm{produced}\right)+\left(\mathrm{Balance}\mathrm{units}\times \mathrm{Beginning}\mathrm{unit}\mathrm{cost}\right)\\ & =& \left(43,000\times \$36.60\right)+\left(\left(47,350-43,000\right)\times \$30.10\right)\\ & =& \$1,573,800+\$130,935\\ & =& \$1,704,735\end{array}$

Gross profit

$\begin{array}{rcl}\mathrm{Gross}\mathrm{profit}& =& \mathrm{Sales}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \left(47,350\times \$44.60\right)-\$1,704,735\\ & =& \$407,075\end{array}$

Value of ending inventory

$\begin{array}{rcl}\mathrm{Ending}\mathrm{inventory}& =& \mathrm{Beginning}\mathrm{inventory}+\mathrm{Cost}\mathrm{of}\mathrm{production}-\mathrm{Cost}\mathrm{of}\mathrm{sales}\\ & =& \$278,425+\$1,573,800-\$1,704,735\\ & =& \$147,490\end{array}$