Chapter 6, Problem 33P

a.

To determine

Ascertain the amount of depletion expense that would be recognized on 2018 income statement for each of the two reserves.

Explanation of Solution

Depletion:

Depletion is a concept which is same as depreciation. It is the allocation of cost of natural resources to expense over resource’s the useful time in a systematic and normal manner.

Silver mine – Depletion:

2018:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{silver}\text{ore}\text{mined}\end{array})\text{=Tons}\text{of}\text{silver}\text{ore}\text{mined}\text{×}\text{Rate}\text{per}\text{ton}\\ \text{=14,000tons × \$15 (W}\text{.N}\text{. 1)}\\ \text{=}\text{\$210,000}\end{array}$

Timber – Depletion:

2018:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{timber}\end{array})\text{=Number}\text{of}\text{board feet}\text{cut}\left(\text{lumber}\right)\text{×}\text{Rate}\text{per}\text{feet}\\ \text{=500,000 boards×\$1}\text{.60 (W}\text{.N}\text{. 2)}\\ \text{=}\text{\$800,000}\end{array}$

Working note 1:

Calculate the rate of silver ore per ton:

$\begin{array}{c}\text{Rate}\text{of}\text{silver}\text{ore}\text{per}\text{ton}\text{=}\frac{\text{Purchase}\text{price}\text{of}\text{silver}\text{ore}}{\text{Estimated}\text{yield}\text{of}\text{silver}\text{ore}}\\ \text{=}\frac{\text{\$1,500,000}}{\text{100,000}\text{tons}}\\ \text{=\$15per}\text{ton}\end{array}$

Working note 2:

Calculate the rate per board feet of timber:

$\begin{array}{c}\text{Rate}\text{per}\text{feet}\text{=}\frac{\text{Purchase}\text{price}\text{of}\text{land}-\text{Appraisal}\text{of}\text{land}}{\text{Estimated}\text{yield}\text{of}\text{timber}}\\ \text{=}\frac{\text{\$1,700,000}-\text{\$100,000}}{\text{1,000,000feet}}\\ \text{=}\frac{\text{\$1,600,000}}{\text{1,000,000 feet}}\\ \text{=}\text{\$1}\text{.60 per}\text{board}\text{feet}\end{array}$

b.

To determine

Ascertain the amount of depletion expense that would be recognized on 2019 income statement for each of the two reserves.

Explanation of Solution

Ascertain the amount of depletion expense that would be recognized on 2019 income statement for each of the two reserves as follows:

Silver mine – Depletion:

2019:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{silver}\text{ore}\text{mined}\end{array})\text{=Tons}\text{of}\text{silver}\text{ore}\text{extracted}\text{×}\text{Rate}\text{per}\text{ton}\\ \text{=20,000tons×\$15 (W}\text{.N}\text{. 1)}\\ \text{=}\text{\$300,000}\end{array}$

Timber – Depletion:

2019:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{timber}\end{array})\text{=Number}\text{of}\text{board feet}\text{cut}\left(\text{lumber}\right)\text{×}\text{Rate}\text{per}\text{feet}\\ \text{=300,000 boards×\$1}\text{.60 (W}\text{. N}\text{. 2)}\\ \text{=}\text{\$480,000}\end{array}$

Gold Mine - Depletion:

2019:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{gold}\text{ore}\end{array})\text{=Tons}\text{of}\text{gold}\text{ore}\text{extracted}\text{×}\text{Rate}\text{per}\text{ton }\\ \text{=}\text{4,000}\text{tons × \$54 (W}\text{.}\text{}\text{N}\text{.3)}\\ \text{=}\text{\$216,000}\end{array}$

Oil reserves - Depletion:

2019:

$\begin{array}{c}\begin{array}{l}\text{Depletion}\text{Expense}\\ \text{of}\text{oil}\text{reserves}\end{array})\text{=Barrels of oil reserves}\text{extracted}\text{×}\text{Rate}\text{per}\text{barrel}\\ \text{=}\text{50,000}\text{barrels}\text{×}\text{\$5 (W}\text{.N 4)}\\ \text{=}\text{\$250,000}\end{array}$

Working note 3:

Calculate the rate of gold mine per ton:

$\begin{array}{c}\text{Rate}\text{of}\text{gold}\text{mine}\text{per}\text{ton}\text{=}\frac{\text{Purchase}\text{price}\text{of}\text{gold}\text{mine}}{\text{Estimated}\text{yield}\text{of}\text{gold}\text{mine}}\\ \text{=}\frac{\text{\$2,700,000}}{\text{50,000}\text{tons}}\\ \text{=\$54per}\text{ton}\end{array}$

Working note 4:

Calculate the rate of oil per barrel:

$\begin{array}{c}\text{Rate}\text{of}\text{oil}\text{per}\text{barrel}\text{=}\frac{\text{Purchase}\text{price}\text{of}\text{oil}\text{reserves}}{\text{Number}\text{of}\text{oil}\text{barrels}\text{extracted}}\\ \text{=}\frac{\text{\$1,300,000}}{\text{260,000}\text{barrels}}\\ \text{=\$5per}\text{barrel}\end{array}$

c.

To determine

Prepare the portion of the balance sheet that reports natural resources.

Explanation of Solution

Prepare the portion of the balance sheet that reports natural resources as follows:

Company P
Partial Balance Sheet
For the year ended December 31, 2019
Natural Resources	Amount ($)
Silver Min (W.N 5)	990,000
Timber (W.N 6)	320,000
Gold Mine (W.N 7)	2,484,000
Oil Reserves (W.N 8)	1,050,000
Total Natural Resources	4,844,000
Land	100,000
Total	4,944,000

  Table (1)

Working notes 5:

Calculate the Book value of silver mine:

$\begin{array}{c}\text{Book}\text{value}\text{of}\text{Silver}\text{mine}\text{=}\left(\begin{array}{l}\text{Purchase}\text{price}\text{of}\text{siler}\text{mine}-\\ \text{Depletion}\text{expense}\text{of}\text{2018}-\\ \text{Depletion}\text{expense}\text{of}\text{2019}\end{array}\right)\\ \text{=\$1,500,000}-\text{\$210,000}-\text{\$300,000}\\ \text{=\$990,000}\end{array}$

Working notes 6:

Calculate the Book value of Timber:

$\begin{array}{c}\text{Book}\text{value}\text{of}\text{Timber}\text{=}\left(\begin{array}{l}\text{Purchase}\text{price}\text{of}\text{timber}-\\ \text{Depletion}\text{expense}\text{of}\text{2018}-\\ \text{Depletion}\text{expense}\text{of}\text{2019}\end{array}\right)\\ \text{=\$1,600,000}-\text{\$800,000}-\text{\$480,000}\\ \text{=\$320,000}\end{array}$

Working notes 7:

Calculate the Book value of Gold mine:

$\begin{array}{c}\text{Book}\text{value}\text{of}\text{gold}\text{mine}\text{=}\left(\begin{array}{l}\text{Purchase}\text{price}\text{of}\text{gold}\text{mine}-\\ -\text{Depletion}\text{expense}\text{of}\text{2019}\end{array}\right)\\ \text{=\$2,700,000}-\text{\$216,000}\\ \text{=\$2,484,000}\end{array}$

Working notes 8:

Calculate the book value of Oil Reserves:

$\begin{array}{c}\text{Book}\text{value}\text{of}\text{oil}\text{reserves}\text{=}\left(\begin{array}{l}\text{Purchase}\text{price}\text{of}\text{oil}\text{reserves}-\\ -\text{Depletion}\text{expense}\text{of}\text{2017}\end{array}\right)\\ \text{=\$1,300,000-\$250,000}\\ \text{=\$1,050,000}\end{array}$