Question

You own a coal mining company and are considering opening a new mine. The mine will cost $117.1 million to open. If this money is spent​ immediately, the mine will generate

$19.9 million for the next 10 years. After​ that, the coal will run out and the site must be cleaned and maintained at environmental standards. The cleaning and maintenance are expected to cost $1.8 million per year in perpetuity. What does the IRR rule say about whether you should accept this​ opportunity? If the cost of capital is 7.5%​, what does the NPV rule​ say?

Answer 1

1.
IRR:
-117.1+19.9/x*(1-1/(1+x)^10)-1.8/(1+x)^10*1/x=0

=>IRR=x=2.45788%, 9.55153%

IRR gives multiple values hence no decision

2.
NPV=-117.1+19.9/7.5%*(1-1/(1+7.5%)^10)-1.8/(1+7.5%)^10*1/7.5%=7.85 million

Accept