Chapter 20, Problem 20.7P

(1)

To determine

Depreciation:  Depreciation refers to decrease in value of the asset over a period due to use, wear and tear or obsolescence. In other words it is a method of reallocating the cost of the asset over its useful life.

Depletion: Depletion is the reduction in the value of natural resource which belongs to the company.

To compute:  The depletion and depreciation of the mine, mining equipments and facilities of Company M for 2016 and 2017.

Explanation of Solution

Calculate the cost of the mineral mine

Cost of the mineral mine is purchase price plus development expenses. Use the following formula:

$\text{Cost of minaral mine = Purchase price + Development costs}$

$\begin{array}{c}\text{Cost of minaral mine = Purchase price + development costs}\\ \text{=\$1,600,000}\text{+}\text{\$600,000}\\ =\$2,200,000\end{array}$

Therefore, cost of the mine is $2,200,000.

1. a. Calculate depletion on mine for the years 2016 and 2017.

To compute a unit depletion rate, deduct the residual value of the asset from the asset value and divide it by the total number of units that expect to recover. The formula for the unit depletion rate is:

$\begin{array}{l}\text{Depletion per unit = }\frac{\text{Cost of the asset }-\text{ Residual value}}{\text{Number of units expected to recover}}\\ \end{array}$

In 2016, Company M estimated that 400,000 tons of ore would be extracted and residual value would be $100,000. In the year 2017, the estimate of total tons of ore in the mine was revised from 400,000 tons to 487,000 tons. In 2016, 50,000 tons and during 2017, 80,000 tons of ore were extracted.

Depletion of mineral mine for 2016:

$\begin{array}{c}\text{Depletion per ton = }\frac{\$2,200,000-\$100,000}{400,000\text{tons}}\\ =\$5.25\text{per ton}\\ \text{For}\text{the}\text{year 2016,}\text{Depletion = \$5}\text{.25 × 50,000 tons }\\ \text{= \$262,500}\end{array}$

Depletion of mineral mine for 2017:

$\begin{array}{c}\text{Revised Depletion per ton = }\frac{\left(\$2,200,000-\$262,000\right)-\$100,000}{\left(487,500-50,000\right)\text{tons}}\\ =\$4.2\text{per}\text{ton}\\ \text{For}\text{the}\text{year 2017,}\text{Depletion = \$4}\text{.2 × 80,000 tons }\\ \text{= \$336,000}\end{array}$

1. b. Compute depreciation on mining equipments for the years 2016 and 2017:

In the given case, Company M uses the units of production method to determine the depreciation on mining facilities and equipments. A unit of production method determines the depreciation based on the actual production or usage of the asset. Mining equipment costing $80,000 was purchased and installed at the site and estimates that it can be sold at auction for $4,000 after the mining project is completed.

Use the below formula to determine the amount of depreciation per ton. 

$\begin{array}{l}\text{Depreciation per ton = }\frac{\text{Cost of the asset }-\text{ Residual value}}{\text{Number of tons of minaral ore to be extracted}}\\ \end{array}$

Depreciation on mining equipments for 2016:

$\begin{array}{c}\text{Depreciation per ton = }\frac{\$80,000-\$4,000}{400,000\text{tons}}\\ =\$0.19\text{per ton}\\ \text{For}\text{the}\text{year 2016,}\text{Depreciation = \$0}\text{.19 × 50,000 tons }\\ \text{= \$9,500}\end{array}$

Depreciation on mining equipments for 2017:

$\begin{array}{c}\text{Revised Depreciation per ton = }\frac{\left(\$80,000-\$9,500\right)-\$4,000}{\left(487,500-50,000\right)\text{tons}}\\ =\$1.52\text{per}\text{ton}\\ \text{For}\text{the}\text{year 2017,}\text{Depreciation = \$1}\text{.52 × 80,000 tons }\\ \text{= \$12,160}\end{array}$

1. c. Compute depreciation on mining facilities for the years 2016 and 2017:

Company M built various structures and small storage buildings on the site at a cost of $150,000 having useful life of 10 years. No residual value is estimated.

Depreciation on mining facilities for 2016:

$\begin{array}{c}\text{Depreciation per ton = }\frac{\$150,000-\$0}{400,000\text{tons}}\\ =\$0.375\text{per ton}\\ \text{For}\text{the}\text{year 2016,}\text{Depreciation = \$0}\text{.375 × 50,000 tons }\\ \text{= \$18,750}\end{array}$

Depreciation on mining facilities for 2017:

$\begin{array}{c}\text{Revised Depreciation per ton = }\frac{\$150,000-\$18,750}{\left(487,500-50,000\right)\text{tons}}\\ =\$0.30\text{per}\text{ton}\\ \text{For}\text{the}\text{year 2017,}\text{Depreciation = \$0}\text{.30 × 80,000 tons }\\ \text{= \$24,000}\end{array}$

Hence, Depletion of mineral mine for the year 2016, is $262,000, for the year 2017, revised depletion is $336,000. Depreciation on mining equipment for the year 2016, is $9,500, for the year 2017 revised depreciation is $12,160. Depreciation on the mining facilities for the year 2016, is $18,750, for the year 2017 revised depreciation is $24,000.

(2)

To determine

To compute:  The book values of the mineral mine, facilities (structures) and equipments as of December 31, 2017.

Explanation of Solution

Compute the book value of the mineral mine.

 Computation of the book value of the mineral mine is as follows:

Particulars	Amount in $	Amount in $
Cost of the mineral mine		2,200,000
Less: Accumulated depletion:
For the year 2016	262,500
For the year 2017	336,000	(598,500)
Book value of the mineral mine		1,601,500

Table (1)

Hence, book value of the mineral mine is $1,601,500 as of December 31, 2017.

Compute the book value of the mining facilities (structures):

Computation of the book value of the mining facilities (structures) is as follows

Particulars	Amount in $	Amount in $
Cost of the mining facilities		150,000
Less: Accumulated depreciation:
For the year 2018	18,750
For the year 2019	24,000	42,750
Book value of the mining facilities		107,250

Table (2)

Hence, book value of the mining facilities (structures) is $107 250, as of December 31, 2017.

Compute the book value of the mining equipments:

Computation of the book value of the mining equipments is as follows

Particulars	Amount in $	Amount in $
Cost of the mining equipments		80,000
Less: Accumulated depreciation:
For the year 2016	9,500
For the year 2017	12,160	21,660
Book value of the mining equipment		58,340

Table (3)

Hence, book value of the mining equipments is $58,340, as of December 31, 2017.

Accumulated depreciation is deducted from the cost of the asset because of reduction in the value of the asset due to usage and extracting the mineral ore.