Strip Mining Inc. can develop a new mine at an initial cost of $14 million. The
ID: 2772235 • Letter: S
Question
Strip Mining Inc. can develop a new mine at an initial cost of $14 million. The mine will provide a cash flow of $42 million in 1 year. The land then must be reclaimed at a cost of $29 million in the second year.
What are the IRRs of this project? (Enter your answers in ascending order. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)
Should the firm develop the mine if the discount rate is 3%? 13%? 80%? 120%? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers in millions rounded to 3 decimal places.)
Strip Mining Inc. can develop a new mine at an initial cost of $14 million. The mine will provide a cash flow of $42 million in 1 year. The land then must be reclaimed at a cost of $29 million in the second year.
Explanation / Answer
Solution:
(a). IRR or Internal rate of return is the discount rate at which the initial investment in the project is equal to future cash flows from the project or we can say the rate at which the NPV of the project is equal to '0'
Since, the cash flows from the project are
-$14 m , +$42 m and -$29 m for years 0,1 and 2 respectively, the cash flows change sign twice , first from negative to positive and then from positive to negative.
Since the cash flows change sign twice, there will be two IRRs for the project.
Calculating, Let IRR be r
NPV = -14 + 42/(1+r) -29/(1+r)^2
As per the definition of IRR, NPV = 0,
Hence, 14 = 42/(1+r) -29/(1+r)^2,
Solving for IRR, r = 7.74% and 92.26%
(b). Now, we need to calculate NPV with all 4 discount rates to check whether the NPV is positive or negative. If the NPV comes out to be positive, we will develop the mine and if negative, we will not.
NPV = -14 + 42/(1+r) -29/(1+r)^2
Putting the value 3% in place of r in the above equation
NPV = -14 + 42/(1+3%) - 29/(1+3%)^2
= -0.55858
= -$0.56 m
Similarly , solve for other values of r and find out the NPV values
With 13%, NPV = $0.46
With 80%, NPV = $0.38
With 130%, NPV = -$0.90,
Now, NPV are negative when r = 3% and 130%, hence we will not develop the mine when r=3% and 130%
But when r=13% and 80%, we will develop the mine as the NPV are positive