Problem 6-15 Tamarisk Mining Company recently purchased a quartz mine that it in
ID: 2333793 • Letter: P
Question
Problem 6-15
Tamarisk Mining Company recently purchased a quartz mine that it intends to work for the next 10 years. According to state environmental laws, Tamarisk 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, Tamarisk 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 Tamarisk’s books.
There is no active market for retirement obligations such as these, but Tamarisk 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
Click here to view factor tables
What is the estimated fair value of Tamarisk’s asset retirement obligation? Tamarisk 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.)
Explanation / Answer
Solution:-
= 14,350 * 10%
= $1,435
= $22,450 * 30%
= $6,735
= 22,660 * 50%
= $11,330
= 27,050 * 10%
= $2,705
= ($1,435 + $6,735 + $11,330 + $2,705)
= $22,205
={ [$22,205 /( (1 + 5% )^13)] + [$22,205 /( (1 + 5% )^12) + [$22,205 /( (1 + 5% )^11) }
= {[22,205 / (1.05)^13] + [22,205 / (1.05)^12] + [ 22,205 / (1.05) ^ 11]}
= {[22,205 / 1.8856] + [22,205 / 1.7958 ] + [22,205 / 1.7103]
= {11,776.09 + 12,390.8 + 12,983.10}
= $37,124.15
$37,124
=$37,124
=[22,205 * (1 /(( 1+ 5%)^ 13))]+[22,205 * (1 / (( 1+ 5%) ^ 12)] +[(22,205 / (( 1 + 5%) ^ 11))]
=[22,205 * ( 1 / 1.8856)]+[22,205 * (1 / 1.7958)] + [22,205 * ( 1 / 1.7103)]
=[22,205 * 0.53032]+[22,205 * 0.55655] + [ 22,205 * 0.58469]
= 11,775.75 + 12,358.19 + 12,983.04
= $37,116.98
The Expected value of the restoration estimated cash out flow: Restoration Probability Cash outfl;ow * probability Estimated Assessments Cash outflow $14,350 10%= 14,350 * 10%
= $1,435
$22,450 30%= $22,450 * 30%
= $6,735
$22,660 50%= 22,660 * 50%
= $11,330
$27,050 10%= 27,050 * 10%
= $2,705
Expected value of the restoration eatimated annual outflows during the years= ($1,435 + $6,735 + $11,330 + $2,705)
= $22,205
The next step is to find the PV of the expected cash outflow during the years = [a / (1 + r) ^n]={ [$22,205 /( (1 + 5% )^13)] + [$22,205 /( (1 + 5% )^12) + [$22,205 /( (1 + 5% )^11) }
= {[22,205 / (1.05)^13] + [22,205 / (1.05)^12] + [ 22,205 / (1.05) ^ 11]}
= {[22,205 / 1.8856] + [22,205 / 1.7958 ] + [22,205 / 1.7103]
= {11,776.09 + 12,390.8 + 12,983.10}
= $37,124.15
$37,124
=$37,124
Alternatively, using factors tables,PV =[1 / ( 1 + r)^n]=[22,205 * (1 /(( 1+ 5%)^ 13))]+[22,205 * (1 / (( 1+ 5%) ^ 12)] +[(22,205 / (( 1 + 5%) ^ 11))]
=[22,205 * ( 1 / 1.8856)]+[22,205 * (1 / 1.7958)] + [22,205 * ( 1 / 1.7103)]
=[22,205 * 0.53032]+[22,205 * 0.55655] + [ 22,205 * 0.58469]
= 11,775.75 + 12,358.19 + 12,983.04
= $37,116.98
$37,117 Estimaated fair value of Skysong's assets retirement obligation $37,124