Question

You own a coal mining company and are considering opening a new mine. The mine itself will cost $ 116.8 million to open. If this money is spent​ immediately, the mine will generate $ 20.5 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 $ 1.6 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?

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

A. The IRR is r equals 10.71 %​, so accept the opportunity.

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

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

D. Reject the opportunity because the IRR is lower than the 7.6 % cost of capital.

b.The NPV using the cost of capital of 7.6 % is ​$ nothing million. ​(Round to three decimal​ places.)

c.The plot of the NPV as a function of the discount rate is n shaped. It intersects the x​-axis at r equals 1.94 % and r equals 10.71 % What does the NPV rule​ say? ​ (Select the best choice​ below.)

A. If the opportunity cost of capital is between r equals 1.94 % and r equals 10.71 %​, the investment should be undertaken.

B. Reject the project because the NPV is negative.

C. If the opportunity cost of capital is greater than r equals 10.71 %​, the investment should be undertaken.

D. If the opportunity cost of capital is less than r equals 1.94 %​, the investment should be undertaken.

Answer 1

Value of Cleaning and maintainance cost till maturity in the 10th year = amount / interest rate

= 1600000/.076

= 2105263 = 2.1035 million

The IRR formula is as follows:

Accordingly IRR = 11.65% So accordingly we will substitute the values in the above equation and in the 10th year(ie in CF 10) we will take $20.5million and deduct 2.105million from it and substitute in the equation

accrdingly IRR= 11.65%

NPV = cash inflow/ (1+i)ⁿ - initial investment

i = 7.6%

So accordingly we will substitute the values in the above equation and in the cash flow for 10th year(ie in CF 10) we will take $20.5million and deduct 2.105million from it and substitute in the equation

hence the NPV comes to 22.261 million

a) since we see IRR(11.65%) is greater that cost of capital (7.6%) hence we must accepts the opportunity.

hence the correct option is A

b) the NPV comes to 22.261 million

c) Accordingly using the formula of NPV when i = 1.94% we get NPV = 66.185 million and when i = 10.71 we get NPV = 4.650 million

hence If the opportunity cost of capital is greater than r equals 10.71 %​, the investment should be undertaken.

Hence the correct option is C