Question

You own a coal mining company and are considering opening a new mine. The mine itself will cost $ 118.1 million to open. If this money is spent​ immediately, the mine will generate $ 21.3 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 8.3 %​, what does the NPV rule​ say?

Answer 1

First of all we shall calculate the IRR of the project by using the below formula:

Lower Rate + [ Lower Rate NPV / ( Lower Rate NPV - Higher Rate NPV ) ] x ( Higher Rate - Lower Rate )

Now lets calculate the projects NPV at a rate of say 10%

= ( $ 118.1 million) + $ 21.3 million / 1.10¹ + $ 21.3 million / 1.10² + $ 21.3 million / 1.10³ + $ 21.3 million / 1.10⁴ + $ 21.3 million / 1.10⁵ + $ 21.3 million / 1.10⁶ + $ 21.3 million / 1.10⁷ + $ 21.3 million / 1.10⁸ + $ 21.3 million / 1.10⁹ + $ 21.3 million / 1.10¹⁰ - 1 / 1.10¹⁰ ( $ 1.7 million / 0.10 )

= $ 6.23 Million Approximately

Now lets calculate the projects NPV at a rate of say 11.5%

= ( $ 118.1 million) + $ 21.3 million / 1.115¹ + $ 21.3 million / 1.115² + $ 21.3 million / 1.115³ + $ 21.3 million / 1.115⁴ + $ 21.3 million / 1.115⁵ + $ 21.3 million / 1.115⁶ + $ 21.3 million / 1.115⁷ + $ 21.3 million / 1.115⁸ + $ 21.3 million / 1.115⁹ + $ 21.3 million / 1.115¹⁰ - 1 / 1.115¹⁰ ( $ 1.7 million / 0.115 )

= $ - 0.22 Million Approximately

Since IRR is the rate at which the projects NPV is zero, hence the IRR must be in between these two rates.

Now feeding these values in the above mentioned formula we shall get IRR as below:

10% + [ $ 6.23 million / ( $ 6.23 million - ( $ 0.22 million ) ] x ( 11.5 - 10 )

= 11.45% Approximately

Since IRR is greater than the cost of capital hence the project should be accepted.

NPV computation at cost of capital of 8.3%

= ( $ 118.1 million) + $ 21.3 million / 1.083¹ + $ 21.3 million / 1.083² + $ 21.3 million / 1.083³ + $ 21.3 million / 1.083⁴ + $ 21.3 million / 1.083⁵ + $ 21.3 million / 1.083⁶ + $ 21.3 million / 1.083⁷ + $ 21.3 million / 1.083⁸ + $ 21.3 million / 1.083⁹ + $ 21.3 million / 1.083¹⁰ - 1 / 1.083¹⁰ ( $ 1.7 million / 0.083 )

= $ 13.68 million Approximately

Since the NPV of the project is positive, hence the project should be accepted

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