Question

A gold mine is expected to bring $10,000 a year for the first 10 years, and...

  1. A gold mine is expected to bring $10,000 a year for the first 10 years, and $5,000 per year for the 2nd 10 years. Also it will require $30,000 outlay to properly close the mine at the end of 20 years. If you want 20% rate of return on this investment, how much money is the present value of the mine?
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Answer #1

PV of last 10 year CF at end of year 10

Project
Discount rate 0.2
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream 0 5000 5000 5000 5000 5000 5000 5000 5000 5000 -25000
Discounting factor 1 1.2 1.44 1.728 2.0736 2.48832 2.985984 3.583181 4.299817 5.15978 6.191736
Discounted cash flows project 0 4166.667 3472.222 2893.519 2411.2654 2009.388 1674.49 1395.408 1162.84 969.0335 -4037.64
NPV = Sum of discounted cash flows
NPV Project = 16117.19
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor

PV of project

Project
Discount rate 0.2
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream 0 10000 10000 10000 10000 10000 10000 10000 10000 10000 26117.19
Discounting factor 1 1.2 1.44 1.728 2.0736 2.48832 2.985984 3.583181 4.299817 5.15978 6.191736
Discounted cash flows project 0 8333.333 6944.444 5787.037 4822.5309 4018.776 3348.98 2790.816 2325.68 1938.067 4218.072
NPV = Sum of discounted cash flows
NPV Project = 44527.74
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
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