Question

You own a coal mining company and are considering opening a new mine. The mine will cost $115.3 million to open. If this money is spent​ immediately, the mine will generate $21.1 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 $1.7 million per year in perpetuity. What does the IRR rule say about whether you should accept this​ opportunity? If the cost of capital is 7.6%​, what does the NPV rule​ say? Use the graph below to determine the​ IRR(s) in the problem. NPV of the Investment in the Coal Mine 5 10 15 20 -18 -8 2 12 22 32 Discount Rate (%) NPV ($ millions) The graph shows the NPV of the investment in the coal mine. The x-axis on the graph shows discount rate in percentage;

Answer 1

The IRR rule suggests that you should accept the opportunity if the internal rate of return (IRR) is greater than the cost of capital. In this case, the IRR can be inferred from the graph, and if it exceeds the cost of capital, the project is deemed acceptable. Meanwhile, the NPV rule advises accepting the opportunity if the net present value (NPV) is positive. If the cost of capital is 7.6%, the NPV can be determined from the graph at this rate to make an informed decision.

Step-by-step explanation:

The graph provides a visual representation of the NPV of the coal mine investment at various discount rates. To find the IRR, identify the discount rate where the NPV curve intersects the x-axis (discount rate) or where the NPV is zero. In this case, the IRR appears to be around 15%, suggesting that if the cost of capital is below 15%, the investment is viable.

For the NPV rule, calculate the NPV at the given cost of capital (7.6%). Locate the point on the graph corresponding to a 7.6% discount rate, and observe the associated NPV. If the NPV is positive, it indicates that the present value of future cash flows exceeds the initial investment, suggesting the project is financially favorable.

Considering the values from the graph, you can conclude whether the investment is financially sound based on both the IRR and NPV rules. The IRR exceeding the cost of capital and a positive NPV at the given discount rate would signify that the coal mine investment is economically justified.