Question

Waterway Mining Company recently purchased a quartz mine that it intends to work for the next 10 years. According to state environmental laws, Waterway 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, Waterway 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 Waterway’s books. There is no active market for retirement obligations such as these, but Waterway 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

$14,830 10%

21,750 30%

26,870 50%

28,040 10%

What is the estimated fair value of Waterway’s asset retirement obligation? Waterway determines that the appropriate discount rate for this estimation is 5%. Estimated fair value of Waterway’s asset retirement obligation

Answer 1

Annual expected restoration costs = 14830*10%+21750*30%+26870*50%+28040*10% =	$      24,247
Discounted value of retirement obligation at t10 = 24247*(1.05^3-1)/(0.05*1.05^3) =	$      66,031
PV (fair value) of the asset retirement obligation = 66031/1.05^10 =	$      40,537