Question

A mining company plans to mine a gold deposit. It will have to invest $ 800 million at the end of year 0 and $ 150 million annually in operating costs. One year following the closure of the mine, the company will have to pay $ 40 million per year for 4 years to restore the site. Finally, the mining company will earn an average of $ 1,000 per tonne mined. Knowing that the life of the mine is 6 years, find neutral. Use an 8% rate of yeild. The answers are in millions of tonnes per year.

Answer 1

To have a neutral, his NPV should be zero given that the rate of yield is 8%. Suppose, he earns Revenue X each year.

We know that the NPV of Ct is Ct/(1+r)^t

So,

800=(X-150)/1.08+(X-150)/1.08^2+(X-150)/1.08^3+(X-150)/1.08^4+(X-150)/1.08^5+(X-150)/1.08^6-40/1.08^7-40/1.08^8-40/1.08^9-40/1.08^10  

800+40/1.08^7+40/1.08^8+40/1.08^9+40/1.08^10=(X-150)/1.08+(X-150)/1.08^2+(X-150)/1.08^3+(X-150)/1.08^4+(X-150)/1.08^5+(X-150)/1.08^6

883.488069399=(X-150)/1.08+(X-150)/1.08^2+(X-150)/1.08^3+(X-150)/1.08^4+(X-150)/1.08^5+(X-150)/1.08^6

341.11206=X-150

X=491.11206

The number of tonnes of mining will be 491.11206 million/1000 = 491112.06

So, it is 0.491112.06 million tons of mining each year.