Question

Vaughn Mining Company recently purchased a quartz mine that it intends to work for the next 10 years. According to state environmental laws, Vaughn must restore the mine site to its original natural prairie state after it ceases mining operations at the site. To properly account for the mine, Vaughn must estimate the fair value of this asset retirement obligation. This amount will be recorded as a liability and added to the value of the mine on Vaughn’s books.

There is no active market for retirement obligations such as these, but Vaughn has developed the following cash flow estimates based on its prior experience in mining-site restoration. It will take 3 years to restore the mine site when mining operations cease in 10 years. Each estimated cash outflow reflects an annual payment at the end of each year of the 3-year restoration period.

Restoration Estimated Cash Outflow Probability Assessment

$15,980 10%

23,070 30%

23,570 50%

32,470 10%

What is the estimated fair value of Vaughn’s asset retirement obligation? Vaughn determines that the appropriate discount rate for this estimation is 5%. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Estimated fair value of Vaughn’s asset retirement obligation $

Answer 1

Estimated fair value of Vaughn’s asset retirement obligation

Estimated fair value of Vaughn’s asset retirement obligation is the Present Value of the Expected cash outflow of the mining operation

Step – 1, Calculation of Expected Cash Outflow of the mining operation

Expected Cash outflow = Sum [Cash outflow x Probability]

= [$15,980 x 10%] + [$23,070 x 30%] + [$23,570 x 50%] + [$32,470 x 10%]

= $1,598 + 6,921 + 11,785 + 3,247

= $23,551

Step – 2, Estimated fair value of Vaughn’s asset retirement obligation

Estimated fair value of Vaughn’s asset retirement obligation = Present Value of Expected Cash Outflows

= $23,551 x [PVIF 5%, 10 Years]

= $23,551 / (1 + r) ⁿ

= $23,551 / (1 + 0.05) ¹⁰

= $23,551 / 1.62889

= $14,458 (Rounded to 0 decimal places)

“Hence, Estimated fair value of Vaughn’s asset retirement obligation = $14,458”