You own a coal mining company and are considering opening a new mine. The mine itself will cost $$50$ million to open. If this money is spent immediately, the mine will generate $$20$ million for the next $5$ 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 $$2$ million per year in perpetuity. Which of the following statements are true? Select all that apply.

a$)$ The project$$s IRR cannot be calculated because NPV is never $0.$ b$)$ The project likely has more than two IRSS

c$)$ IRR of the project is negative

d$)$ At cost of capital $=5\%$ the NPV is positive

e$)$ At cost of capital $=10\%$ the NPV is positive

f$)$ At cost of capital $=20\%$ the NPV is negative

g$)$ The maximum NPV of the project is roughly $$75$ million

h$)$ Project NPV obtained as NPV $=-50+20/$r $*(1-1/(1+$r$)10)-2/($r$(1+$r$)10).$ Since there are $2$ sign changes

there could be $2$ IRRs $($it turns out there are indeed $2$ IRRs$).$ We get NPV$($r$=10\%)=65\mathrm{.}2$ and NPV$($r$=5\%)=79\mathrm{.}9.$