Question

Culver Mining Company recently purchased a quartz mine that it intends to work for the next 10 years. According to state environmental laws, Culver 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, Culver 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 Culver's books. There is no active market for retirement obligations such as these, but Culver has developed the following cash flów 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 $15,780 23,430 22,610 31,150 Assessment 10% 30% 50% 10% Click here to view factor tables What is the estimated fair value of Culver's asset retirement obligation? Culver determines that the appropriate discount rate for this estimation is 5%. (Round factor values to 5 decimal places, eg. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Estimated fair value of Culver's asset retirement obligation 62708 Click if you would like to Show Work for this question: Q

Answer 1

Firstly, let us calculate the Restoration Estimated Cash outflow in $ every year by multiplying (Restoration Estimated Cash outflow in $) by the (Probability Assessment)

Restoration Estimated Cash outflow in $	Probability Assessment	Restoration Estimated Cash outflow in $ * Probability Assessment
15780	0.1	1578
23430	0.3	7029
22610	0.5	11305
31150	0.1	3115
		23027

Therefore, Culver Mining Company will require an expenditure of $ 23027 every year for 3 years after the completion of 10 years.

Year	Cash Outflow $
11	23027
12	23027
13	23027

The Present Value of the above three Cash Outflows at the end of 10th Year can be calculated by using the formula in the Excel as

=PV(0.05,3,23027)

Where,
RATE 0.05
NPER 3
PMT 23027

The Present value of the same at the end of 10th Year comes to $ 62708.23

Therefore, if the company wants to make a provision of the above Expenditure today then it has a time period of 10 years to built a corpus of $ 62708.23 and assuming the rate of interest as 5% per annum, the Present value of $ 62708.23 today can be calculated by using the following formula on the Excel:

=PV(0.05,10,,G7)

Where,

RATE 0.05
NPER 10
FV 62708.23

The Present value of the same today comes to $ 38497.41.

Finally, we can say that if the company invests $ 38497.41 today at an interest rate of 5% per annum, then at the end of 10 years the it will be able to built a corpus of $ 62708.23 which will be sufficient for the Annual payment of $ 23027 at the end of 11th Year, 12th Year and 13th Year.