Question

(Depletion Computations—Minerals) At the beginning of 2017, Aristotle Company acquired a mine for \(970,000. Of this amount, \)100,000 was ascribed to the land value and the remaining portion to the minerals in the mine. Surveys conducted by geologists have indicated that approximately 12,000,000 units of ore appear to be in the mine. Aristotle incurred \(170,000 of development costs associated with this mine prior to any extraction of minerals. It also determined that the fair value of its obligation to prepare the land for an alternative use when all of the mineral has been removed was \)40,000. During 2017, 2,500,000 units of ore were extracted and 2,100,000 of these units were sold.

Instructions

Compute the following.

1. The total amount of depletion for 2017.
2. The amount that is charged as an expense for 2017 for the cost of the minerals sold during 2017.

Short answer

Answer

1. Depletion = $225,000
2. Expenses = $189,000

Step-by-step solution

Meaning of Depletion 

Theloss of natural resources as a result of access to them on a regular basis is called depletion.Hence, a company uses it when any kind of registered asset is involved, such as oil, coal, or gravel deposits.

(a) Calculating the amount of depletion for 2017

Calculating depletion per unit

$\begin{array}{rcl}\text{Depletion}\text{per}\text{unit}& =& \frac{\text{Cost}\text{mine}\text{acquired}-\text{Land}\text{value}+\text{Development}\text{cost}+\text{Fair}\text{value}\text{obligation}}{\text{Expected}\text{units}}\\ & =& \frac{\$970,000-\$100,000+\$170,000+\$40,000}{12,000,000}\\ & =& \frac{\$1,080,000}{12,000,000}\\ & =& \$0.09\end{array}$

Calculating the amount of depletion

$\begin{array}{rcl}\text{Depletion}& =& \text{Number}\text{of}\text{units}\text{extracted}\times \text{Depletion}\text{cost}\text{per}\text{unit}\\ & =& 2,500,000\times \$0.09\\ & =& \$225,000\end{array}$

(b) Calculating the amount that is charged as an expense for 2017 for the cost of the minerals sold during 2017

$\begin{array}{rcl}\text{Expenses}& =& \text{Number} \text{of}\text{units}\text{sold}\times \text{Depletion}\text{cost}\text{per}\text{unit}\\ & =& 2,100,000\times \$0.09\\ & =& \$189,000\end{array}$