You own a coal mining company and are considering opening a new mine. The mine will cost $$$$117\mathrm{.}1$ million to open. If this money is spent$$ immediately, the mine will generate $$$$21\mathrm{.}9$ million for the next $10$ years. After$$ 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 $ $1\mathrm{.}8$ million per year in perpetuity. What does the IRR rule say about whether you should accept this$$ opportunity? If the cost of capital is $8\mathrm{.}1\%,$ what does the NPV rule$$ say?

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Part $1$

Use the graph below to determine the$$ IRR$($s$)$ in the problem.

NPV of the Investment

in the Coal Mine

$5$

$10$

$15$

$20$

$-15$

$-5$

$5$

$15$

$25$

$35$

Discount Rate $(\%)$

NPV $($$ millions$)$

The graph shows the NPV of the investment in the coal mine. The x$-$axis on the graph shows discount rate in percentage; the axis values range from $0$ to $20,$ at intervals of $5.$ The y$-$axis on the graph shows NPV in millions of dollars; the axis values range from minus $20$ to $29\mathrm{.}905+5,$ at intervals of $10.$ There is a steep curve that starts from the negative values of NPV$.$ The curve reaches its maximum point that is a positive NPV value. From this maximum point, the curve starts sloping downward indicating a decrease in NPV with the increase in discount rate.

What does the IRR rule say about whether you should accept this$$ opportunity?$($Select the best choice$$ below.$)$

A$.$

There are two IRR$$s$,$ so you cannot use the IRR as a criterion for accepting the opportunity.

Your answer is correct.B$.$

Accept the opportunity because the IRR is greater than the cost of capital.

C$.$

Reject the opportunity because the IRR is lower than the $8\mathrm{.}1\%$ cost of capital.

D$.$

The IRR is $12\mathrm{.}43\%,$ so accept the opportunity.

Part $2$

The NPV using the cost of capital of $8\mathrm{.}1\%$ is $$$

$$

enter your response here million.$($Round to three decimal$$ places.$)$