Chapter 11, Problem 11.13P

Depreciation and depletion; change in useful life; asset retirement obligation; Chapters 10 and 11

• LO11–2, LO11–3, LO11–5

On May 1, 2018, Hecala Mining entered into an agreement with the state of New Mexico to obtain the rights to operate a mineral mine in New Mexico for $10 million. Additional costs and purchases included the following:

Development costs in preparing the mine	$3,200,000
Mining equipment	140,000
Construction of various structures on site	68,000

After the minerals are removed from the mine, the equipment will be sold for an estimated residual value of $10,000. The structures will be torn down.

Geologists estimate that 800,000 tons of ore can be extracted from the mine. After the ore is removed the land will revert back to the state of New Mexico.

The contract with the state requires Hecala to restore the land to its original condition after mining operations are completed in approximately four years. Management has provided the following possible outflows for the restoration costs:

Cash Outflow	Probability
$600,000	30%
700,000	30%
800,000	40%

Hecala’s credit-adjusted risk-free interest rate is 8%. During 2018, Hecala extracted 120,000 tons of ore from the mine.

The company’s fiscal year ends on December 31.

Required:

1. Determine the amount at which Hecala will record the mine.

2. Calculate the depletion of the mine and the depreciation of the mining facilities and equipment for 2018, assuming that Hecala uses the units-of-production method for both depreciation and depletion. Round depletion and depreciation rates to four decimals.

3. How much accretion expense will the company record in its income statement for the 2018 fiscal year?

4. Are depletion of the mine and depreciation of the mining facilities and equipment reported as separate expenses in the income statement? Discuss the accounting treatment of these items in the income statement and balance sheet.

5. During 2019, Hecala changed its estimate of the total amount of ore originally in the mine from 800,000 to 1,000,000 tons. Briefly describe the accounting treatment the company will employ to account for the change and calculate the depletion of the mine and depreciation of the mining facilities and equipment for 2019 assuming Hecala extracted 150,000 tons of ore in 2019.

To determine

Depreciation:

Depreciation refers to the reduction in the monetary value of a fixed asset due to its wear and tear or obsolescence. It is a method of distributing the cost of the fixed assets over its estimated useful life. The following is the formula to calculate the depreciation.

$\text{Depreciation cost = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

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.

Unit-of-activity Method:

Under this method of depreciation, the depreciation expense is calculated on the basis of units produced in a year. This method is suitable when a company has fluctuating productive rate. The formula to calculate the depreciation expense under this method is as follows:

$\text{Depreciation per unit = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated units of useful life}}$

To Determine: The amount at which H Mining will record the mine.

Explanation of Solution

Determine the amount at which H Mining will record the mine.

Particulars	Amount ($)
Mining site	1,000,000
Development costs	320,000
Restoration costs	521,871
Total	13,721,871

Table (1)

Working note:

Determine the present value of the restoration costs.

Cash flows		Probability		Total
$600,000	$\times$	30%	=	180,000
$00,000	$\times$	30%	=	210,000
$800,000	$\times$	40%	=	320,000
Total				710,000

Table (2)

Determine the present value of the total restoration cost.

$\begin{array}{c}\text{Present value of \$710,000 = \$710,000 x }\text{.73503}\\ \text{= \$521,871}\end{array}$

Note: PV factor (Present value of $1: n = 4, i = 8%) is taken from the table value (Table 2 in Appendix from textbook).

To determine

To Calculate: The depletion and depreciation on the mine and mining facilities and equipment for 2018 using units-of-production method.

Explanation of Solution

Calculate depletion expense on the mine for 2018.

$\begin{array}{c}\text{Depletion Expense}=\left(\begin{array}{l}\text{Depletion Cost per Unit }\\ \times \text{ Number of units Extracted and Sold}\end{array}\right)\\ =\$17.1523\times 120,000\text{tons}\\ \text{=\$2,058,276}\end{array}$

Working Note:

Calculate depletion per ton.

$\begin{array}{c}\text{Depletion Cost per ton }=\frac{\text{Cost of the asset }}{\text{Estimated Number of Units}}\\ =\frac{\$13,721,871}{800,000\text{tons}}\\ =\$17.1523\text{per ton}\end{array}$

Hence, the depletion of the mine for the year 2018 is $2,058,276.

Determine the depreciation expense for machinery for the year 2018.

$\begin{array}{c}\text{Depreciation Expense}=\text{Depreciation per unit}\times \text{Usage}\\ \text{= \$0}\text{.1625}\times \text{\$120,000 tons}\\ \text{= \$19,500}\end{array}$

Working Note:

Determine the depreciation per ton for machinery using units-of-production method.

$\begin{array}{c}\text{Depreciation per ton}=\frac{\text{Cost}-\text{Residual value}}{\text{Estmated units of usefule life}}\\ =\frac{\$140,000-\$10,000}{8,000,000\text{tons}}\\ =\$0.1625\text{per ton}\end{array}$

Hence, the depreciation expense on the machinery (equipment) for the year 2018 is $19,500.

Determine the depreciation per unit for structures using units-of-production method.

Determine the depreciation expense for structure for the year 2018.

$\begin{array}{c}\text{Depreciation Expense}=\text{Depreciation per unit}\times \text{Usage}\\ \text{= \$0}\text{.85}\times \text{\$120,000 tons}\\ \text{= \$10,200}\end{array}$

Working Note:

$\begin{array}{c}\text{Depreciation per ton}=\frac{\text{Cost}}{\text{Estmated units of usefule life}}\\ =\frac{\$68,000}{800,000\text{tons}}\\ =\$0.85\text{per ton}\end{array}$

Hence, the depreciation expense on structures (mining facilities) for the year 2018 is $10,200.

To determine

The amount of accretion expense the company will record in its income statement for the 2018 fiscal year.

Explanation of Solution

Determine the accretion expenses recorded in the income statement for the 2018 fiscal year (May 1, 2018 to December 31, 2018).

$\begin{array}{c}\text{Accretion }\text{expense = }\left(\begin{array}{l}\text{Restoration cost }\\ \times \text{ Credit adjsuted risk free interest rate}\\ \times \frac{\text{Number of months }}{12}\end{array}\right)\\ =\$521,871\times 0.08\times \frac{8}{12}\\ =\$27,833\end{array}$

Conclusion

Hence, the accretion expense for the year 2018 is $27,833.

To determine

To Discuss: Whether the depletion of the mine and the depreciation of the mining facilities and equipment are reported as separate expense in the income statement, and their accounting treatment in the income statement and balance sheet.

Explanation of Solution

Yes, the depletion of the mine and the depreciation of the mining facilities and equipment are reported as separate expense in the income statement.

Accounting Treatment for Depreciation and Depletion

• The depreciation is treated as the part of the manufacturing equipment cost, and will be included in the cost of the inventory. Likewise, depletion determined is also a part of the product cost, and this cost will also be included in the inventory.
• When the mineral is sold, the depletion and depreciation cost will be included in the cost of goods sold on the income statement.

To determine

To Discuss: The accounting treatment the company will employ to account for the change.

Explanation of Solution

The accounting treatment the company will employ to account for the change in estimate of the total amount of ore is that it prospectively depreciate the remaining depreciable base (book value of the asset on the date of change less any residual value) of the asset over its remaining useful life of the asset.

Calculate the depletion of the mine for the year 2019. 

$\begin{array}{c}\text{2019}\text{depletion = Depletion rate }\times \text{Tons extracted }\\ \text{= \$13}\text{.2541}\times 150,000\text{tons}\\ \text{=\$1,988,115}\end{array}$

Working Notes:

Determine the remaining depletable cost.

$\begin{array}{c}\text{Remaining}\text{depletable}\text{cost}\text{=}\text{Original cost – 2018 depletion }\\ \text{= \$13,721,871 – \$2,058,276}\\ \text{=\$11,663,595}\end{array}$

Determine the revised estimate of tons remaining.

$\begin{array}{c}\text{Revised estimate of tons remaining = New estimate – Extracted }\\ \text{= 1,000,000 tons – 120,000 tons}\\ \text{=880,000 tons}\end{array}$

Determine the depletion rate.

$\begin{array}{c}\text{Depletion rate = }\frac{\text{Remaining depletable cost }}{\text{Revised estimate of tons remaining }}\\ =\frac{\$111,663,595}{880,000\text{tons}}\\ =\$13.2541\text{per ton}\end{array}$

Thus, the depletion for the year 2019 is $1,988,115.

Calculate the depreciation for equipment for the year 2019.

$\begin{array}{c}\text{2019}\text{depreciation = Depreciation rate}\times \text{Tons extracted }\\ \text{= \$0}\text{.1256 per ton}\times 150,000\text{tons}\\ \text{=\$18,840}\end{array}$

Working Notes:

Determine the remaining depreciable cost.

$\begin{array}{c}\text{Remaining}\text{depreciable cost}\text{=}\left(\begin{array}{l}\text{Original cost }\\ \text{ – 2018 depreciation }\\ \text{– Residual value}\end{array}\right)\\ \text{= \$140,000 – \$19,500 – \$10,000}\\ \text{=\$120,500}\end{array}$

Determine the revised estimate of tons remaining.

$\begin{array}{c}\text{Revised estimate of tons remaining = New estimate – Extracted }\\ \text{= 1,000,000 tons – 120,000 tons}\\ \text{=880,000 tons}\end{array}$

Determine the depreciation rate.

$\begin{array}{c}\text{Depletion rate = }\frac{\text{Remaining depreciable cost }}{\text{Revised estimate of tons remaining }}\\ =\frac{\$110,500}{880,000\text{tons}}\\ =\$0.1256\text{tons}\end{array}$

Thus, the depreciation for the year 2019 is $18,840.

Calculate the depreciation of structures for the year 2019.

Determine depreciation for the year 2019.

$\begin{array}{c}\text{2019}\text{depreciation = Depreciation rate }\times \text{Tons extracted }\\ \text{= \$0}\text{.0657 per ton}\times 150,000\text{tons}\\ \text{=\$9,855}\end{array}$

Working Note:

Determine the remaining depreciable cost.

$\begin{array}{c}\text{Remaining}\text{depreciable cost}\text{=}\left(\begin{array}{l}\text{Original cost }\\ \text{ – 2016 depreciation }\end{array}\right)\\ \text{= \$68,000 – \$10,200 }\\ \text{=\$57,800}\end{array}$

Determine the revised estimate of tons remaining.

$\begin{array}{c}\text{Revised estimate of tons remaining = New estimate – Extracted }\\ \text{= 1,000,000 tons – 120,000 tons}\\ \text{=880,000 tons}\end{array}$

Determine the depreciation rate.

$\begin{array}{c}\text{Depletion rate = }\frac{\text{Remaining depreciable cost }}{\text{Revised estimate of tons remaining }}\\ =\frac{\$57,800}{880,000\text{tons}}\\ =\$0.0657\text{tons}\end{array}$

Thus, the depreciation for the year 2019 is $9,855.