If the appropriate interest rate is the value of this mining operation is closest to:

-$66,667

Explanation:

As this project is expected to yield returns forever, it is a perpetuity.

The Present Value is calculated as;

= Payment per year / (Yield - growth rate)

Mine will decline at 8% per year however so this will need to be accounted for;

= 15,000/ ( 10% - (-8%))

= $83,333.33

The Net Present Value is;

= Present value of cash inflows - Initial investment

= 83,333.33 - 150,000

= -$66,666.67

= -$66,667

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30