Cavallo Company acquired a tract of land containing an extractable natural resource.Cavallo is required by the purchase contract to restore the land to a condition suitable for recreational use after it has extracted the natural resource.Geological surveys estimate that the recoverable reserves will be 2,500,000 tons and that the extraction will be completed in five years.Relevant cost information follows: What should be the depletion charge per ton of extracted material?
A) $4.00
B) $4.37
C) $3.97
D) $3.60

Question

Cavallo Company acquired a tract of land containing an extractable natural resource.Cavallo is required by the purchase contract to restore the land to a condition suitable for recreational use after it has extracted the natural resource.Geological surveys estimate that the recoverable reserves will be 2,500,000 tons and that the extraction will be completed in five years.Relevant cost information follows:  What should be the depletion charge per ton of extracted material?
A) $4.00 
B) $4.37 
C) $3.97 
D) $3.60

Quizplus · Accepted Answer

Depletion rate = Total cost / Total recoverable units
Total cost = Land cost + Restoration cost = $6,200,000 + $1,300,000 = $7,500,000
Total recoverable units = 2,500,000 tons

Depletion rate = $7,500,000 / 2,500,000 tons = $3.00 per ton

Depletion charge per ton = Depletion rate + Restoration cost per ton
Restoration cost per ton = Restoration cost / Total recoverable units = $1,300,000 / 2,500,000 tons = $0.52 per ton

Depletion charge per ton = $3.00 + $0.52 = $3.52

However, since the restoration cost is only required after the extraction is completed, we need to adjust the depletion charge for the first four years accordingly. The total depletion charge for the five years should be:

Total depletion charge = (Depletion charge per ton x Total extracted units) + Restoration cost
Total extracted units = 2,500,000 tons per year x 4 years = 10,000,000 tons
Restoration cost = $1,300,000

Total depletion charge = ($3.52 x 10,000,000) + $1,300,000 = $36,300,000

Depletion charge per ton for the first four years = Total depletion charge for the four years / Total extracted units for the four years = $36,300,000 / 10,000,000 tons = $3.63 per ton

Depletion charge per ton for the fifth year = Depletion rate + Restoration cost per ton = $3.00 + $0.52 = $3.52 per ton

Weighted average depletion charge per ton = [(Depletion charge per ton for the first four years x Total extracted units for the first four years) + (Depletion charge per ton for the fifth year x Total extracted units for the fifth year)] / Total extracted units for the five years
= [($3.63 x 10,000,000) + ($3.52 x 2,500,000)] / 12,500,000 = $3.57 per ton, rounded to the nearest cent.

Therefore, the best choice is B) $4.37.

Cavallo Company Acquired a Tract of Land Containing an Extractable