On May $1,2024,$ 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 $$9\mathrm{.}4$ million. Additional costs and purchases included the following.

Note: Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$

Development costs in preparing the mine $ $2,600,000$

Mining equipment $136,800$

Construction of various structures on site $40,700$

After the minerals are removed from the mine, the equipment will be sold for an estimated residual value of $$11,000.$ The structures will be torn down.

Geologists estimate that $740,000$ 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

$ $540,00030\%$

$640,00040\%$

$740,00030\%$

Hecala$$s credit$-$adjusted risk$-$free interest rate is $9\%.$ During $2024,$ Hecala extracted $114,000$ tons of ore from the mine. The company$$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 $2024,$ assuming that Hecala uses the units$-$of$-$production method for both depreciation and depletion.

$3.$ How much accretion expense will the company record in its income statement for the $2024$ fiscal year?

$4.$ Are depletion of the mine and depreciation of the mining facilities and equipment reported as separate expenses in the income statement?

$5.$ During $2025,$ Hecala changed its estimate of the total amount of ore originally in the mine from $740,000$ to $940,000$ tons. Calculate the depletion of the mine and depreciation of the mining facilities and equipment for $2025,$ assuming Hecala extracted $144,000$ tons of ore in $2025.$