Strip Mining Inc. can develop a new mine at an initial cost of $12 million. The
ID: 2654629 • Letter: S
Question
Strip Mining Inc. can develop a new mine at an initial cost of $12 million. The mine will provide a cash flow of $40 million in 1 year. The land then must be reclaimed at a cost of $31 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 18%? 28%? 100%? 140%? (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 $12 million. The mine will provide a cash flow of $40 million in 1 year. The land then must be reclaimed at a cost of $31 million in the second year
Explanation / Answer
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.)
At IRR , NPV is equal to zero
0 = -12 + 40/(1+r) - 31/(1+r)^2
0 = -12*(1+r)^2 + 40*(1+r) - 31
31 = -12*(1+r^2 + 2r) + 40 + 40r
31 = -12 - 12r^2 - 24 r + 40 + 40 r
31 = 28 -12r^2 + 16 r
16r - 12r^2 = 31-28
4(4r-3r^2) = 3
-3r^2 + 4r - 0.75 = 0
r = (- 4 + (4^2 - 4*-3*-0.75)^(1/2))/(2*-3)
r = 22.57%
IRR = 22.57%
Should the firm develop the mine if the discount rate is 18%? 28%? 100%? 140%? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers in millions rounded to 3 decimal places.)
if the discount rate is 18%
NPV = -12 + 40/1.18 - 31/1.18^2
NPV = - $ 0.365
No its should not develop
if the discount rate is 28%
NPV = -12 + 40/1.28 - 31/1.28^2
NPV = $ 0.329
Yes its should develop
if the discount rate is 100%
NPV = -12 + 40/2 - 31/2^2
NPV = $ 0.25
Yes its should develop
if the discount rate is 140%
NPV = -12 + 40/2.4 - 31/2.4^2
NPV = - $ 0.715
No its should not develop