Question

1. A gold mine is expected to bring $10,000 a year for the first 10 years, and $5,000 per year for the 2^nd 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?
   

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